Modeling of Human Aging Using a Systems Approach

Modeling of Human Aging using a Systems Approach

A Thesis

Submitted to the Faculty

Drexel University

Glenn R. Booker

in partial fulfillment of the

requirements for the degree

Doctor of Philosophy

October 2011

Acknowledgments

Thanks to:  My advisor, Dr. Andres Kriete  Members of Dr. Kriete’s research team o Dr. Ulrich Rodeck, William Beggs, Nirupama Yalamanchili, Kelli Mayo, Drew Clearfield, David Boorman, Mariam Albahrani, Ryan Danowski , and Visish Srinivasan  The team of Dr. Albert-László Barabási (Northeastern University) for data sharing  Dr. William Bosl (Harvard Medical School) for Bionet And thanks to my dissertation committee:  Dr. Fred Allen (Biomed)  Dr. Uri Hershberg (Biomed)  Dr. Longjian Liu (Public Health)  Dr. Daniel Marenda (Bioscience)  Dr. Ahmet Sacan (Biomed)

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TABLE OF CONTENTS

LIST OF TABLES ...... x

LIST OF FIGURES ...... xiii

ABSTRACT ...... xvii

INTRODUCTION ...... 1

Systems Approach to Aging ...... 3

What is Aging? ...... 6

Aging Theories ...... 8

Energy consumption theories of aging ...... 10

Evolutionary theories of aging ...... 11

Programmed theories of aging ...... 12

Damage accumulation theories of aging ...... 14

Network theories of aging ...... 16

Gaps in existing theories of aging ...... 16

Scope ...... 16

Scope Exclusions ...... 17

Research Hypotheses ...... 18

Novel Elements ...... 18

REVIEW OF COMPUTATIONAL APPROACHES ...... 20

Model Species and Tissues ...... 20

Differential Equations ...... 22

Bayesian and Boolean Logic ...... 24

Fuzzy Logic ...... 27

Reliability Modeling ...... 30

Multi‐scale Modeling ...... 31

METHODS ...... 34

Experimental Data ...... 34

Scope of Samples ...... 34

Cell Lines and Culture Procedures ...... 35

Methodology ...... 35

Microarray Analysis ...... 35

NF‐κB DNA Binding Activity Assay ...... 36

Other Data ...... 36

Data Summary ...... 37

CELL MODELING ...... 38

The Vicious Cycle Model ...... 38

Physiological mechanisms in the Vicious Cycle Model ...... 38

Mitochondrial respiration ...... 38

Generation of ROS and Oxidized Proteins ...... 41

Bionet Vicious Cycle model ...... 41

Vicious Cycle versus Retrograde Response model ...... 42

Discussion of the Bionet Vicious Cycle Model ...... 43

Documentation of Bionet Application ...... 44

Conclusion from the Vicious Cycle Model ...... 46

The Adaptive Response Model ...... 47

Physiological mechanisms in the Adaptive Response model ...... 47

Retrograde response ...... 47

Inflammation ...... 47

Superoxide dismutases (SOD) ...... 49

Calcium pathways ...... 49

Feedback via mTOR ...... 50

UPR and EOR ...... 50

Bionet Adaptive Response model ...... 51

Sensitivity Analysis ...... 52

Introduction and Criteria ...... 52

Baseline results ...... 53

Input parameters ...... 53

Analysis ...... 53

Discussion of Adaptive Response models ...... 57

Transcription factors and gene expression candidates ...... 58

Conclusion from the Adaptive Response Model ...... 59

POPULATION STUDIES ...... 60

Physiology of aging ...... 60

The Gompertz Model ...... 60

ABC studies ...... 61

Aging and Disease ...... 61

Diseasome ...... 62

Linear decline ...... 65

Stochastic component studies ...... 69

The Weitz & Fraser model ...... 69

Implementation of Weitz & Fraser viability equation ...... 71

Analysis of Weitz & Fraser viability equation ...... 72

Gene Expression Variability ...... 74

Changes in Stochastic Component ...... 77

Changes in life expectancy ...... 79

Longitudinal Study of Mortality Rates ...... 81

Conclusion of Longitudinal Study ...... 86

Serial Linear Decline ...... 87

Conservation of energy argument ...... 87

Effect on somatic viability ...... 90

Conclusion for serial linear decline ...... 95

Mortality rates versus age ...... 95

United States ...... 96

Analysis of mortality data from WHO ...... 99

Discussion of Residual Data ...... 107

Compare WHO and Census Mortality Data ...... 113

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Residuals for serial linear decline model ...... 114

Conclusion for mortality data studies ...... 116

GENERIC NETWORK MODELS ...... 117

Network Model Mechanisms ...... 117

Network Model Descriptions ...... 121

Network Model Results ...... 122

Baseline Bowtie network model ...... 122

Inhibited Bowtie network model ...... 123

Regular network model ...... 124

Sensitivity Studies using the Baseline Bowtie model ...... 125

Number of cases per run ...... 125

Effect of Linear Decline Rate ...... 126

No linear decline, vary sigma ...... 128

Repeatability Study ...... 130

Discussion of Network Models ...... 132

Conclusion from the network models ...... 133

CONCLUSIONS AND OUTLOOK ...... 135

Conclusions ...... 135

Outlook ...... 142

Publications ...... 143

REFERENCES ...... 144

Appendix A. Aging Terminology ...... 164

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Appendix B. Scope Exclusions ...... 167

Gender ...... 167

Race ...... 167

Genetic traits ...... 167

Environmental causes ...... 168

Diet ...... 169

Heavy metals ...... 169

Exercise ...... 170

Psychological and sociological effects ...... 170

Appendix C. Bionet models ...... 172

Appendix C‐1. Bionet Vicious Cycle (VC) model ...... 172

Appendix C‐2. Bionet Retrograde Response (RR) model ...... 174

Appendix C‐3. Bionet Adaptive Response Model ...... 186

Appendix D. Bionet Source Code Analysis ...... 194

Introduction ...... 194

General Bionet Design Characteristics ...... 194

Overall Code Structure ...... 195

Class Diagram ...... 196

Class Constructors ...... 198

Detailed Source Code Description ...... 199

Appendix E. Detailed Procedure for Transcription Factor Analysis ...... 210

Appendix F. Diseasome data structure ...... 216

Appendix G. Mortality data ...... 222

Appendix G‐1. Mortality rates by age for the USA in 2000 ...... 222

Appendix G‐2. Sources for WHO mortality rates ...... 224

Appendix G‐3. Categories of causes of death in NVS data ...... 224

Appendix H. Matlab source code ...... 232

Appendix H‐1. Weitz & Fraser Viability Model ...... 232

Appendix H‐2. Network Model Matlab Code ...... 237

Appendix I. Projects, Organizations, Markup Languages & Ontologies ...... 253

VITA ...... 256

LIST OF TABLES

1. Overview of major concepts ...... 1

2. Possible levels of scale in a systems approach ...... 5

3. Biological model species ...... 21

4. Baseline reactions and reaction rates ...... 54

4. Baseline reactions and reaction rates (continued) ...... 55

5. Detailed calculations for reaction rate sensitivity study ...... 55

5. Detailed calculations for reaction rate sensitivity study (continued) ...... 56

6. Aging biomarker candidates based on transcription factor analysis ...... 59

7. Rates of linear decline per (Shock & Yiengst, 1955) ...... 66

8. Summary of Percent Loss due to Aging per decade for various organ systems or characteristics ...... 68

9. Regression parameters by gender ...... 70

10. Linear regression results for Spanish people in 1990, 2000, and 2008...... 81

11. Life expectancy at birth for Spain (e0, years) ...... 85

12. Rates of linear decline in cardiopulmonary systems ...... 88

13. Best fit cases for N=3 and N=4 serial linear decline...... 92

14. Regression coefficients for serial linear decline models and real world data ...... 93

15. Linear regression of log(mortality rate) versus age ...... 101

16. Linear regression parameters in Switzerland, Sweden, and Spain ...... 105

17. Linear regression summary for all cases ...... 108

18. Linear increase in stochastic component 'sigma' with age ...... 122

19. Mean resilience measure for six identical runs (age 70, sigma 4, baseline bowtie model) ...... 131

C‐1. Initial Values and Ranges for each Node ...... 180

C‐2. Bionet Default Centroids for Reaction Input and Output Levels...... 181

C‐3. Bionet Reactant Types ...... 181

C‐4. Model Reactions ...... 182

D‐1. Bionet Class Constructors ...... 198

D‐2. Bionet.java method summary ...... 199

D‐2. Bionet.java method summary (continued) ...... 200

D‐3. Bionet.java method descriptions ...... 200

D‐3. Bionet.java method descriptions (continued) ...... 201

D‐4. EvolveBionet.java method summary ...... 202

D‐5. FitnessCalculator.java method summary ...... 203

D‐6. Main.java method summary ...... 203

D‐7. Node.java method summary ...... 204

D‐8. PlotTimeSeries.java method summary ...... 205

D‐9. RandomSequence.java method summary ...... 206

D‐10. Reaction.java method summary ...... 207

D‐10. Reaction.java method summary (continued)...... 208

D‐11. RuleTable.java method summary ...... 209

E‐1. Candidate aging biomarker genes ...... 213

E‐2. Number of Binding Sites for various pathways ...... 214

E‐2. Number of Binding Sites for various pathways (continued) ...... 215

F‐1. Table S1 ‐ Curated Morbid Map file with disease ID and class assignment (2929 entries) ...... 216

F‐2. Table S2 ‐ Network characteristics of diseases (1284 entries) ...... 218

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F‐3. Table S3 ‐ Network characteristics of disease genes. (1777 entries) ...... 219

F‐4. Table S4 ‐ List of human protein‐protein interactons. (22,052 entries) ...... 220

F‐5. Table ‘bipartite’ – map diseases to genes (2673 entries) ...... 220

F‐6. Table ‘disease’ – map diseases to other diseases (3054 entries) ...... 221

F‐7. Table ‘gene’ – map genes to other genes (14,982 entries) ...... 221

G‐1. USA mortality rates in 2000 ...... 222

G‐1. USA mortality rates in 2000 (continued)...... 224

I‐1. Relevant references for systems modeling of aging ...... 253

I‐1. Relevant references for systems modeling of aging (continued) ...... 255

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LIST OF FIGURES

1. Balancing top‐down and bottom‐up analyses in a systems approach...... 4

2. Blind men around an elephant (text added) (Osho, 2010) ...... 9

3. Vicious cycle of mitochondrial DNA damage ...... 15

4. Bayesian probabilistic graphical model (Friedman, 2004) ...... 25

5. Boolean model of apoptosis, from (Thieffry, et al., 2009) ...... 26

6. The Bathtub Curve (Wilkins, 2002) ...... 30

7. Cartoon of a mitochondrion (Lesnefsky & Hoppel, 2006) ...... 39

8. Mitochondrial respiration process (Lesnefsky & Hoppel, 2006) ...... 40

9. Bionet Vicious Cycle model (Booker, 2008) ...... 43

10. Bionet VC model output ...... 44

11. Bionet Class Diagram ...... 46

12. Inflammation and aging ...... 48

13. Final Bionet Adaptive Response Model (A Kriete, Bosl, & Booker, 2010) ...... 52

14. Bionet Adaptive Response model output (A Kriete, et al., 2010) ...... 57

15. Diseasome data structure mapping ...... 63

16. MS Access query for mapping diseasome to gene expression data ...... 64

17. Measurements of decline with age (Strehler, 1959) ...... 67

18. Range of Mortality Rate Residuals for each Age ...... 71

19. Demonstrating that N=50,000 lives and N=1 million lives have very similar histograms for the Weitz & Fraser simulation...... 72

20. Weitz & Fraser equation with 80x linear increase in slope (eps), and 5x linear decline in stochastic component (sigma)...... 73

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21. Weitz & Fraser model with sigma increasing in a step function from 0.1 to 1.5 times that between ages 40 and 70...... 74

22. Log(mortality rate) versus age for various Weitz & Fraser models, compared to the aging death rate extracted from the USA vital statistics...... 79

23. Life expectancy in the USA since 1900 ...... 80

24. log(mortality rate) versus age for variable and fixed birth life expectancy (e0) ...... 80

25. Mortality rates for Spanish males in 1990, 2000, and 2008...... 82

26. Mortality rates for Spanish females in 1990, 2000, and 2008...... 82

27. Residuals for Spanish males for 1990, 2000, and 2008 ...... 84

28. Residuals for Spanish females for 1990, 2000, and 2008 ...... 84

29. Residual linear regression Constant versus Slope for 1990, 2000, and 2008...... 86

30. Simple compartment model for conservation of energy analysis ...... 88

31. Oxygen output to the body versus age ...... 89

32. Viability versus Age for various values of 'n' Viability = (1 ‐ s*age)^n with s = 6.5% per decade ...... 91

33. Log(mortality rate) versus Age for various N values of serial linear decline ...... 91

34. Log‐linear plot comparing the best serial linear cases to real world data...... 94

35. Log‐log plot comparing the best serial linear cases to real world data ...... 94

36. Deaths rates for males in the USA in 1900 and 1996...... 96

37. Death rate by age in the USA for 2000 (Appendix G‐1) ...... 97

38. Death rate versus age for the USA, 2000 ...... 98

39. Residual between regression and actual death rates, USA 2000 ...... 99

40. Log of mortality rates versus age for males from selected countries, 2008 WHO data ...... 100

41. Log of mortality rates versus age for females from selected countries, 2008 WHO data ...... 100

42. Linear regression for females in Japan ...... 102

43. Residuals for males for ages 30‐100 ...... 103

44. Residuals for females for ages 30‐100 ...... 103

45. Mortality rates for males in Switzerland, Sweden, and Spain ...... 104

46. Mortality rates for females in Switzerland, Sweden, and Spain ...... 105

47. Residuals for males in Switzerland, Sweden, and Spain ...... 106

48. Residuals for females in Switzerland, Sweden, and Spain ...... 107

49. Mortality rate residuals for males in six countries ...... 109

50. Mortality rate residuals for females in six countries ...... 109

51. Mortality rate residuals for males and females in six countries ...... 110

52. Mean mortality rate residual versus age ...... 111

53. Mean mortality rate residual and estimated curve fit...... 113

54. Year 2000 mortality rate residuals for males and females, comparing Census and WHO data ...... 114

55. Residuals for serial linear decline models (N=3 and N=4), the Gompertz curve, NHS data for mortality due to aging, and WHO mortality curves for deaths due to all causes ...... 115

56. The Baseline Bowtie network model ...... 118

57 The Inhibited Bowtie network model ...... 119

58 The Regular network model...... 120

59. Mean resilience for each tier of the bowtie model (time units vs age) ...... 123

60. Mean resilience measure for Inhibited Bowtie model ...... 124

61. Mean resilience measure for the regular network model, as a function of age and tier ...... 125

62. Comparison of mean resilience measure between 100 and 1000 cases each (e.g. 30/100 is age 30, with 100 cases per run) ...... 126

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63. Mean resilience of baseline bowtie model, halving the rate of linear decline at various ages 30/10 means age 30, decline=0.010; 90/05 means age 90, decline=0.005 ...... 127

64. Percent changes in mean resilience for Tier 5 and for all Tiers, as a function of age ...... 128

65. Mean resilience measure for no linear decline, and varying sigma from 2 to 6 ..... 129

66. Overall mean resilience measure versus age, comparing the baseline (with linear decline) to the same sigma values without linear decline...... 130

67. Mean resilience measure for six identical runs, by tier of the baseline bowtie network model at age 70 ...... 131

68. Mean resilience measure of all three network models as a function of age ...... 132

69. Concept map of this dissertation ...... 141

A‐1. Viability curves from different model organisms have a similar, characteristic shape...... 165

C‐1. Bionet AR model (Booker, 2008) ...... 175

C‐2. Retrograde Response Bionet model outputs ...... 176

C‐3. Bionet AR Model results ...... 177

C‐4. Complex Bionet RR Model (Booker, et al., 2008) ...... 178

D‐1. Bionet Class Diagram ...... 197

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ABSTRACT Modeling of Human Aging using a Systems Approach Glenn R. Booker Andres Kriete, Ph.D.

The healthy aging process involves a range of biological pathways which were investigated based on data from adult human fibroblasts of various ages. Two hybrid computational models integrating organelle phenotypes with molecular mechanisms

were developed using a fuzzy logic, rule‐based approach. One was a vicious cycle model which represents uncontrolled damage accumulation in a positive feedback loop, leading to a rapid cellular degradation. The second model was an adaptive response model which showed that the stress sensors NF‐kB and mTOR provide negative

feedback loops causing a linear decline with age, observed in many cellular and physiological parameters.

Simulations of mortality data led to discovery that a serial linear model of viability decline with a variable stochastic component would result in mortality rates to match recent data from industrialized countries. Further exploration using general

computational models of biochemical networks showed the impact of the rate of linear decline, initial stochastic changes in reaction rates, and network topology on resilience and stability. The conclusion is that linear decline with age is observed and modeled at the cellular through organ system levels however mortality rates are compounded by

several factors at the somatic level, leading to the serial linear decline model which combines linear decline with power law frailty models.

INTRODUCTION “Aging seems to be the only available way to live a long life.” — Daniel Francois Esprit Auber (Troen, 2003) Aging is a complex problem because it involves many biological systems, and affects all of them in a variety of ways. This dissertation focuses on using data from human samples to infer the pathways activated with age, and then explore if the trends observed at the cellular level connect to mortality rates at the population level.

Table 1 outlines the major biological concepts and data sources used in this work, the types of modeling and analyses employed, and the resulting tools and products produced.

1. Overview of major concepts Biological concepts and Modeling approaches Tools and products data sources and analyses developed  Assays and gene  Positive and negative  Cellular pathway models expression data feedback loops  Weitz & Fraser viability  Linear decline with  Fuzzy logic models simulation age  Monte Carlo  Mortality rate modeling  Stochastic influences simulations (power law and Gompertz)  Mortality rate data  Regression analyses  Mortality rate residuals  Biological network modeling

The key biological foundations herein start with assays and gene expression data from quiescent human fibroblasts, connect that to trends in linear decline with age observed

2 from the cellular level through entire organ systems. Stochastic influences and mortality rate data provide additional perspectives on larger physical scale behavior.

The gene expression data suggest the presence of positive and negative biological feedback loops which are explored through the development of fuzzy logic models to identify the specific feedback loops activated through healthy aging. This led to Monte

Carlo simulations and regression analyses to understand the connection between linear decline and mortality rate data in the presence of stochastic variability from person to person. The novel outputs from this work included cellular pathway models using fuzzy

logic and demonstrating the feedback loops, and a Weitz & Fraser viability simulation incorporating linear decline and stochastic influences to predict mortality rates using power law and Gompertz rates of decline. Mortality rate residuals explored oscillations about the mortality rate regression versus time, and supported the presence of two mortality rate plateaus. Biological network modeling provided additional perspective on

non‐linear behavior observed at the somatic and populations levels of scale, influenced by the typical topology of biological networks.

This section will define what a 'systems approach' is, what is meant by 'aging,' review major aging theories and how this approach is different from them, define the scope of

this research and its research hypotheses, and finally outline the rest of this dissertation.

Systems Approach to Aging

The title of this work focuses on using a 'Systems Approach,' so it is important to define that concept.

Complex problems tend to be approached by reducing the scope of their complexity, and solving or analyzing the simpler problem. In the context of aging, this has led to many theories of aging, discussed later, which tend to focus on one key cause or culprit.

While this is successful in producing detailed analysis within that scope, the bigger picture remains elusive because aging has no such single cause. Therefore it makes sense to approach aging in a more holistic manner, integrating perspectives from many types of analysis into a unified model (L. A. Gavrilov & Gavrilova, 2003; Jameson, 2004;

Sinclair, 2005; Strange, 2005).

The systems approach (Barzilai, Ye, MacCarthy, Bergman, & Atzmon, 2007) is balancing the top‐down approach (Figure 1) from the demographic and somatic perspective, with

the bottom‐up perspective, looking from the gene expression and cellular level of data.

This integration across many physical scales connects this systems approach to the

Physiome project, which is discussed under Multi‐scale modeling.

There are also hybrid approaches to modeling which use multiple but more closely

related layers (e.g. gene and protein, or molecular and phenotype). An example of the former is the analysis of protein‐protein interactions (Walter, Jean, Vincent, Russ, &

Jérême, 2009), which take into account not only the sequence of genes but also the ways in which post‐translational modifications may occur, and how that affects the

4 overall protein which results. Network models using this approach can help identify modules which are influential in aging, however this doesn't address their connection to larger levels of physical scale (Z. Zhang et al., 2007). An example of the latter form of hybrid approach is seen in (Guarente & Kenyon, 2000), where molecular and phenotypic changes in yeast are correlated.

1. Balancing top-down and bottom-up analyses in a systems approach. Images represent the population level (background), then from the upper left diagonal ‐ individuals, skin tissue, fibroblasts, organelles within one cell, and NF‐kB

The levels of physical scale in a systems approach to modeling biological systems are summarized in Table 2. The sequence of structures above the family level is open to

5 many interpretations (Reference, 2009). For example, "race, like ethnicity in general, is a cultural category rather than a biological reality" (Kottak, 2010).

2. Possible levels of scale in a systems approach Mostly from (Hunter, 2004; Hunter & Nielsen, 2005) Structure Function Culture Race? Ethnicity? Society? Community? Civilization? Family Social unit Person Body Organ systems – 11 or 12 systems; Circulatory, respiratory, musculo‐ Varies skeletal, integument, digestive, central nervous system, endocrine, lymphatic, male & female reproductive, and special sense organs. Organ – 50 organs; liver, heart, skin, brain, stomach, etc. Varies Tissue – four major types; muscle, nerve, connective, and epithelial Movement, communication, structure, protection Cell – 200‐300 cell types, in 17 categories; blood, bone, cardiac, Varies cartilage, CNS, epidermal, gastrointestinal, immune, neural, liver, pancreatic, respiratory, sensory system, skeletal muscle, generic, and male & female reproductive cells. Organelle – 9 common organelles (cell membrane, mitochondria, Varies nucleus, endoplasmic reticulum, Golgi apparatus, centrioles, ribosomes, lysosomes and peroxisomes), plus specialized types (e.g. muscle’s sarcoplasmic reticulum). Proteins (100,000), lipids, carbohydrates + DNA = cell components Nine families of proteins: gene regulation proteins, structural proteins, receptor proteins, signaling proteins, transport proteins, motor proteins, enzymatic proteins, storage proteins and defensive proteins. Translation, protein folding, post‐translation modification Transcription, gene regulation, post‐transcription modification Genes – 19,000 to 35,000 of them. DNA – 3.2 billion base pairs More for females?

The use of a systems approach is complementary to the concept of systems biology

(Brazma, Krestyaninova, & Sarkans, 2006; Cowley, 2004; Hood, 2003; Jaqaman &

Danuser, 2006; Klipp, Herwig, Kowald, Wierling, & Lehrach, 2005; Rapin et al., 2006; van

Beek, 2004) which is a computational systems approach.

"Systems biology is the study of an organism, viewed as an integrated and interacting network of genes, proteins and biochemical reactions which give rise to life." (ISB, 2010)

Systems biology diverges from the traditional reductionist approach to science.

(Strange, 2005) Science was founded on breaking problems into smaller and smaller problems, until an individual problem could be solved and understood, much like common approaches for engineering problems. In other words, science is "rooted in the assumption that complex problems are solvable by dividing them into smaller, simpler, and thus more tractable units" (Ahn, Tewari, Poon, & Phillips, 2006). Therefore systems biology gives us a way to model a systems approach. As we discuss in the next section, aging is a global, multilevel phenomenon, from genes to populations, which warrants more comprehensive, hybrid approaches with the ultimate goal of predicting the aging process and possibly lifespan.

What is Aging?

Aging is described by (T. Kirkwood, 1996) as "the passage of chronological time is eventually associated with a generalized impairment of physiological functions, a decreased ability to respond to a wide range of stresses, an increased risk of age‐ associated disease, and an increased likelihood of death."

Troen (Troen, 2003) gives the characteristics of aging for mammals as:

1. Increased mortality with age after maturation.

2. Changes in biochemical composition in tissues with age.

3. Progressive decrease in physiological capacity with age.

4. Reduced ability to respond adaptively to environmental stimuli with age.

5. Increased susceptibility and vulnerability to disease.

Similarly (E. J. Masoro, 1995) defines aging as "deteriorative changes with time during postmaturational life that underlie an increasing vulnerability to challenges, thereby decreasing the ability of the organism to survive."

Aging is not universal in nature. Bacteria do not age, for example. Some suggest that somatic differentiation is enough for a species to age. (E. J. Masoro, 1995) For example the nematode C. elegans (Kimball, 2010) only has 959 cells, but they are clearly differentiated and it certainly ages.

Successful aging is also defined as the process of "aging without chronic disease and/or decreased lifespan due to fatal disease." (Y. Zhang & Herman, 2002) However the best

measure for successful aging is still quite open to discussion. (Bowling & Iliffe, 2006)

Other terminology associated with aging and longevity are defined in Appendix A.

"The idea is to die young as late as possible." ‐ Ashley Montagu (BrainyQuote, 2011)

Aging Theories

In order to understand the Systems Approach as it applies to human aging, it is important to be familiar with the predominant theories of aging.

The process of aging has been known as long as people have existed, so it’s not surprising that theories to explain our limited life span have ranged from precisely mechanistic (such as the telomere theory introduced under programmed theories) to the divine. (Moses, 1611; Weinert & Timiras, 2003) There are literally hundreds of theories of aging. (Medvedev, 1990)

Physical and mental aging can be disconnected, as evidenced by conditions such as

progeria (PRF, 2010). Progeria (e.g. Hutchinson‐Gilford Progeria Syndrome) causes

rapidly accelerated physical aging, yet doesn’t affect the mental development of the affected children.

Aging theories are like the blind men gathered around an elephant (Figure 2) in the fable of Sufi Jalaluddin Rumi (Osho, 2010). Each has a clear but incomplete concept of the

creature, because they only examine part of it. Likewise, many aging theories are partly true, but they fail to explain the whole process. This has led to many combinations of theories.

Inflammation

Mind ROS Genetics AGING Environment

2. Blind men around an elephant (text added) (Osho, 2010)

There isn’t even agreement on how to organize theories of aging. For example, (E. J.

Masoro, 1995) divides them into two major categories, namely genetic programs and homeostatic failure.

Aging theories are grouped here into the following categories.

 Energy consumption theories, such as rate of living and caloric restriction theories  Evolutionary theories are generally related to the need for procreation, such as the disposable soma theory and pleiotropy  Programmed theories, which includes telomere, longevity gene, and programmed senescence theories  Damage accumulation theories, such as free radical and DNA mutation theories  Network theories of aging, which tend to integrate two or more of the previous types of theories.

New theories of aging are being proposed frequently, and often involve combinations of existing theories, such as the Gene Slicing Theory of Aging (Burzynski, 2005) and the

EORS Theory of Aging (Brewer, 2010).

Energy consumption theories of aging

Energy consumption theories of aging include the rate of living theory and caloric restriction theories. Their common basis is that less energy utilization results in greater longevity.

One of the oldest formal theories of aging was the rate of living theory. It was based on the observation that long‐lived animals (e.g. turtles) exert less energy per unit mass than short‐lived animals (e.g. hamsters). The rate of living theory was first defined by

Rubner in 1908 and expanded by Pearl based on analysis of dozens of species from insects to animals. (E. J. Masoro, 1995) However birds and primates are among the species that violate the rate of living theory by living longer than would be predicted

(Finkel & Holbrook, 2000).

The rate of living theory is often summarized by a graph of life span potential (LSP) versus specific metabolic rate (SMR). (E. J. Masoro, 1995)

Caloric restriction theories don’t explain the aging process per se, but instead rely on the

observation that a substantial reduction in caloric intake for many animals can significantly extend their life expectancy (for a review, see (Heilbronn & Ravussin,

2003)). This theory was validated circa 1935 by McCay et al, backing up preliminary work as far back as 1917 by Osborne et al (E. Masoro, 2005). Many species have been noted to follow this theory, including rats, mice, yeast, fish, hamsters, and dogs.

Evolutionary theories of aging

The evolutionary theories of aging assess the aging process as an outcome of evolutionary need, because evolution‐critical processes focus on the need to reproduce and get the next generation off to a successful start. Beyond those objectives, somatic support and maintenance capabilities are superfluous. The disposable soma theory and antagonistic pleiotropy fall into this category.

The disposable soma theory of aging was first proposed in 1979 by Kirkwood (T.

Kirkwood & Kowald, 1997). It is "based on optimal allocation of metabolic resources between somatic maintenance and reproduction" (T. B. L. Kirkwood & Austad, 2000).

Normal biological processes to repair DNA damage and oxidant damage require energy.

Once reproduction is no longer possible, there is logically and evolutionarily no reason to waste energy on somatic maintenance after the offspring are raised.

Antagonistic pleiotropy is closely related to the disposable soma theory, but more focused on the genetic level (T. Kirkwood, 2005; Promislow, 2004; Stearns, 2010; Troen,

2003). It is the observation that a single gene can participate in multiple unrelated processes. Kirkwood in (T. B. L. Kirkwood, 1996) categorized genetic processes related to senescence three ways (a) "genes that regulate intrinsic processes of somatic maintenance and repair" which are related to the disposable soma theory of aging, (b)

"genes which confer advantages in the early stages of life but prove deleterious later will, nevertheless, be favoured through selection if the late harmful effects are outweighed by the early benefits" (antagonistic pleiotropy), and (c) "mutations that have purely deleterious effects but have their actions at such late ages that the power

of natural selection to remove them is too weak." This last category (c) is part of the damage accumulation theories of aging.

Programmed theories of aging

The programmed theories of aging include telomere, longevity gene, gene knockouts, and programmed senescence theories.

When discussing the causes of aging, many people recall hearing about the shortening of telomeres1, so that theory is included here for completeness. Telomere attrition is the process in vertebrates whereby the ends of genes become shorter each time that gene is replicated. (Blasco, 2005; Epel et al., 2004) When the telomeres get too short the gene can no longer be copied, and replicative senescence has been reached. (Flores,

Cayuela, & Blasco, 2005; Keefe et al., 2005; Lechel et al., 2005; Marcotte & Wang, 2002;

Satyanarayana & Rudolph, 2004; Shay & Wright, 2001) Hence telomeres serve as a

“mitotic clock” (Aviv, 2002). Shay and Wright summarized their role nicely: " Telomeres are repetitive DNA sequences at the ends of linear chromosomes. Telomerase, a cellular reverse transcriptase, helps stabilize telomere length in human stem, reproductive and cancer cells by adding TTAGGG repeats onto the telomeres. Each time a telomerase‐ negative cell divides some telomeric sequences are lost. When telomeres are short, cells enter an irreversible growth arrest state called replicative senescence." (Shay & Wright,

2001)

1 Informal observation by the author, when people inquired about the subject of this dissertation.

Telomere length is inversely proportional to age, and is a highly heritable trait, hence it has connections to aging. Telomere length is also affected by the levels of Reactive

Oxygen Species (ROS) present, so this theory of aging interacts with the damage accumulation theories. Telomere shortening also slows the growth of tumors

(Wiemann et al., 2005; Wright & Shay, 2001), so it has both beneficial and harmful effects in that situation. For purposes here, however, telomere shortening is not related to successful or healthy aging.

Since many diseases are directly connected to genetic abnormalities, it makes sense to

look for genetic traits which favor longevity. Researchers typically use statistical methods such as multiple regression or factor analysis to look for genes which are common in very old healthy individuals, where biological age is determined by a series of physiological tests and measurements (Karasik, Demissie, Cupples, & Kiel, 2005). Due

to a lack of agreement on methodologies, and differences from one sample to the next, there has been no agreement to date on genetic traits associated with aging. Similarly,

(Capri, 2006) looked for genetic biomarkers in Italian centenarians, and concluded "the genetics of human longevity appears to be quite peculiar in a context where antagonistic pleiotropy can play a major role and genes can have a different biological role at different ages." Studies of identical twins show that genetic components of aging can constitute between 20 and 35% of the overall aging process. (T. B. L. Kirkwood,

1996; Lewis, 2004)

Other attempts to find genes associated with aging are inspired by "some of the most compelling evidence in support of a genetic basis for cellular senescence ... introduction

of particular chromosomes into immortalized cell lines causes them to acquire a senescent phenotype." (E. J. Masoro, 1995) Chromosomes 1 and 4 are the most promising sites for human aging genes.

Recent attention to this area (Sebastiani et al., 2010) found 150 SNPs which are present in about 70% of centenarians. However they recognized that other factors were also very significant, such as nutrition, income, etc.

Gene knockouts identify the effect of removing specific genes on the longevity of animal models. These approaches are discussed in Appendix B under Genetic traits.

Programmed senescence occurs at the cellular level via apoptosis, so it is plausible to

look for a similar mechanism at the somatic level. None has been found in animals, however.

One could argue that Genesis 6:3 is a divine programmed senescence, "And the LORD said, My spirit shall not always strive with man, for that he also is flesh: yet his days shall

be an hundred and twenty years." (Moses, 1611)

Damage accumulation theories of aging

The damage accumulation theories of aging include the free radical and DNA mutation theories. Often the source of damage is a stochastic process, in direct contrast to the programmed theories which are more deterministic. From (Hayflick, 2000) "Ageing is a stochastic process that occurs after reproductive maturation and results from the diminishing energy available to maintain molecular fidelity."

The free radical theory of aging focuses on damage from ROS as the key cause of aging.

Free radicals and reactive oxidative species (ROS) damage cell components (Ashok & Ali,

1999 ; de Magalhaes & Church, 2006; Fleury, Mignotte, & Vayssière, 2002). While some studies have shown increases in cellular ROS with age, others do not. As a result,

"available evidence does not eliminate or positively implicate free radical damage as a component of aging processes." (E. J. Masoro, 1995)

The DNA mutation theory of aging or mitochondrial theory of aging (Beckman & Ames,

1998; Dufour & Larsson, 2004; Jacobs et al., 2005; Krishnan, Greaves, Reeve, & Turnbull,

2007; Kujoth, 2006; M. T. Lin, Simon, Beal, Kim, & Ahn, 2002; Loeb, 2005; Sato, Nakada,

& Hayashi, 2006; Trifunovic, 2005; Wohlgemuth et al., 2005) is closely related to the free radical theory, because ROS is a common cause of damage to DNA machinery, resulting in aging (Figure 3). This theory "proposes that the accumulation of mutations in the mitochondrial genome may be responsible in part for the mitochondrial phenomenology of aging." (Beckman & Ames, 1998) More specifically, damage to the electron transfer chain (ETC) produces leakage of ROS, which damages the ETC further, causing the vicious cycle. The ETC is discussed later under Mitochondrial Respiration.

3. Vicious cycle of mitochondrial DNA damage (Alexeyev, Ledoux, & Wilson, 2004 )

Other causes of mitochondrial damage can include solar energy or terrestrial radiation, which were addressed in the Scope section under Environmental causes.

Network theories of aging

Network theories of aging are the result of recognizing the interconnection among these theories, so network theories integrate different aging theories. (T. Kirkwood & Kowald,

1997) An example is the MARS model, which combines models of mitochondrial ROS production, aberrant proteins, free radicals, and scavengers (Kowald, 1996; Kowald &

Kirkwood, 1994).

Biological pathways form networks, based on gene expressions which produce the species involved. (Andrec, Kholodenko, Levy, & Sontag, 2005; Barabási & Oltvai, 2004;

Csete & Doyle, 2002 ; El‐Samad, Prajna, Papachristodoulou, Doyle, & Khammash, 2006 )

Gaps in existing theories of aging

While hundreds of theories of aging exist, they do not adequately relate cellular level activities with the effects of those activities on overall somatic linear decline, or the negative feedback loops which support healthy aging in spite of deterioration of cellular mechanisms. Furthermore, computational systems approaches seem to lag behind applications in other fields, given the biological complexity so some reduction in complexity is needed as outlined in the next section.

Scope

It is critical to bound the problem of interest, therefore we define the scope of the work discussed herein, and identify areas of scope which were considered but are

deliberately omitted because they turned out to be intractable both with our

experimental and methodological realms. Future work could address those areas omitted.

This work focuses on human (Homo Sapiens) aging. The objective is to understand the interaction between damage accumulation and regulation of biological pathways activated as a result of normal healthy aging. The goal is to promote healthy or

'successful' aging, not the more common objective of lifespan extension (Blagosklonny,

2006; Hayflick, 2000; Seeman, 2001; Y. Zhang & Herman, 2002). While many definitions of successful aging exist (Bowling & Iliffe, 2006), the one used herein is focusing on biologic integrity and medical health. "Successful aging is multidimensional,

encompassing the avoidance of disease and disability, the maintenance of high physical and cognitive function, and sustained engagement in social and productive activities"

(Rowe & Kahn, 1997).

The laboratory gene expression data used herein is limited in scope to come from quiescent fibroblasts from Caucasian males aged 20 to 92, and therefore the cell models are limited to that foundation.

The computational cell models developed are at the cellular level, however the results obtained are also investigated for their presence on population‐level data and trends.

Scope Exclusions

Since aging affects many biological processes, scope limitations are needed even within a systems approach. Specifically, this work does not attempt to identify effects due to

factors of gender, race, genetic traits of aging, environmental causes, diet, heavy metals, exercise, or psychological condition. Each of these factors is discussed in Appendix B.

Research Hypotheses

The research hypotheses to be examined are:

 Conceptual models can be combined with systems theory and experimental data to derive at a computational hybrid cell model of aging. Data considered here stems from different studies including a gene expression study of human fibroblasts from donors of different age, allowing us to identify key pathways and mechanisms during healthy aging.  Linear decline in gross physiological parameters with age, caused by a linear decline of cellular parameters, leads to exponential increase in population level mortality rate. We seek to express this linearity in decline by a descriptive, more mechanistic mathematical model as compared to ad‐hoc mathematical descriptions.  Generic biological network models can identify the influence of network characteristics and topology of linear decline and stochastic influences on predicted death rates, as measured by the resilience of the network. Novel Elements

In order to achieve these goals, this work includes the following major novel elements:

 First use of fuzzy logic modeling for aging, and development of the Vicious Cycle, Retrograde Response, and Adaptive Response models, combining molecular interactions, regulatory mechanisms, oxidative damage and organelle phenotypes in a hybrid fashion (as compared to a protein network model).  Development of detailed documentation for the rule‐based computational environment (Bionet)  Development of the residual concept for mortality rate analysis

 Identification of long term cyclical variation in mortality rate about the Gompertz curve  Development of a numerical model for the Weitz & Fraser viability equation  Development of generic network models, adapting models developed in CellDesigner to determine their steady state resilience as a function of age.  First indication of a mortality rate plateau around age 60.

The rest of this thesis will 1) discuss computational biology approaches and develop cell models of aging based on data from fibroblasts to determine if affected pathways can be identified. 2) Analyze linear decline in a population‐level model to determine if an

exponential increase in mortality rate occurs. 3) Develop generic network models to

explore the effects of linear decline, stochastic components, and topology on the resilience of the network.

REVIEW OF COMPUTATIONAL APPROACHES The development of computational models of aging often relies on a wide range of techniques, many of which were considered for use here or were actually used. This section provides an overview of common model species and approaches.

In order to analyze biological systems computationally, model species and tissues are often used to understand simpler and shorter‐lived systems than humans.

Many computational approaches have been used for analysis of biological systems, including differential equations, fuzzy logic, Bayesian logic, Boolean logic, reliability modeling, and multi‐scale modeling. By reviewing the different methods, their strengths and weakness, we were able to identify the most suitable computational platform to develop a hybrid, whole cell model of aging.

Model Species and Tissues

In order to test the effectiveness of biological models, experiments are often done on model species because 1) the lifespan of humans precludes lab testing, and 2) ethical

issues preclude some kinds of testing which can be safely done on other species.

A key complicating factor in computational models is the use experimentally of various model species, as summarized in Table 3, which makes comparisons across species challenging (Guarente & Kenyon, 2000). Such comparisons are typically made by

looking for genetic homologs and analogous pathways. (Dang et al., 2008; de Magalhaes

& Toussaint, 2004; Guarente & Kenyon, 2000; Kawahara, Adler, Chang, & Segal, 2008;

Shmookler Reis & Ebert, 1996; Sykiotis & Bohmann, 2010) Some species such as D.

melanogaster are widely used because they are easy to manipulate genetically, such as

producing knockouts of specific genes. (Barbash, 2010)

Computational models may also be focused on specific organs or tissue types, such as:

 Cardiac models (J. B. Bassingthwaighte, 2005; Kerckhoffs, Healy, Usyk, & Mcculloch, 2006; Rudy, 2000; Stalidis, Maglaveras, Efstratiadis, Dimitriadis, & Pappas, 2002)  Mammary gland models (Hinck, Lewis, & Egan, 2006)  Bone models (Defranoux, Stokes, Young, & Kahn, 2005)  Vascular transport models (Beard, 2001; Lagana et al., 2005; Popel, Pries, & Slaaf, 1999; Porta, Baselli, & Cerutti, 2006)  Brain (Finkelstein et al., 2004 ; Suffczynski, Wendling, Bellanger, & Da Silva, 2006)

3. Biological model species Common Name Latin Name (example) Advantages Amoeba Dictyostelium discoideum Single cell eukaryote Bacterium Escherichia coli Single cell prokaryote Fly, Fruit Drosophilia melanogaster Short lived insect Human Homo sapiens sapiens Most realistic model for people! Mouse, lab Mus musculus Short lived mammal Nematode Caenorhabditis elegans No genetic variation, short lived Rat, Norway Rattus norvegicus Short lived mammal Yeast, Baker’s Saccharomyces cerevisiae Single cell eukaryote

Differential Equations

A common computational approach is to analyze biological pathways as a set of differential equations over time. One example is the modeling of signaling pathways, such as the EGF‐MAPK pathway (Schoeberl, Eichler‐Jonsson, Gilles, & Muller, 2002),

The MARS model (Kowald & Kirkwood, 1996) is another example of this approach, where reactions are modeled between individual species, and the solution of the quantities of those species over time is solved using a tool such as Matlab (Schmidt,

2005; Ullah, Schmidt, Cho, & Wolkenhauer, 2006). This approach can be quite successful, however it is often challenging to find complete and accurate data on species' initial concentrations and reaction rates. Often data from animal models or in vitro tests must be used in the absence of complete knowledge of the system.

Modeling of cellular behavior can be done in great detail quantitatively (Moore & Noble,

2004; Wallace, 2005; Werner, 2005), however doing so at larger physical scales requires obtaining extensive species quantity and reaction rate data. Gaps in such data may be filled using extrapolation from other model species or other techniques.

For analysis of mechanisms altered through aging, modeling using differential equations was implemented in Matlab version R2009b. For analytical clarity each reaction or interaction was modeled using a set of first order differential equations. The time rate of change of the quantity of each n nodes is given by the vector equation:

D(X)/dt = A * X where X is an nth order vector, and A is an n x n matrix of coefficients, which may be functions of time or contain nonlinear terms

To get arrow directionality, the following rules were used to convert the Bionet models

to Matlab:

 A reaction with a product (pro) has the arrow pointing to that product, e.g.

MRSP_ATP, regardless of whether the other reactant is an inhibitor (inh) or

activator (act).

 A reaction with a substrate (sub) has the arrow pointing away from that node,

e.g. MRSP_ACT, regardless of whether the other reactant is an inhibitor or

activator.

To determine the set of ODEs for modeling in Matlab, based on (Haefner, 2005) the rules are:

 For arrows pointing to the node, the reaction rates are multiplied by the value of

the source node, e.g. d(Energy_tot)/dt = +(Energy_totals) * ATPconsume

 For arrows pointing away from the node, the reaction rate could be multiplied by

negative the source or destination node's value times the reaction rate. For

consistency, we'll assume the source node's value, to balance the equation with

the first assumption; and see later if this assumption needs to be changed. This

is consistent with most of equations 4.27 and 4.28 in (Haefner, 2005), but is

inconsistent with how terms such as +/‐ uG and +/‐ rD are handled there. It's

possible to need to examine each reaction individually to determine which way it

needs to be handled.

Bayesian and Boolean Logic

Bayesian and Boolean logic are introduced here to form the foundation for understanding fuzzy logic modeling. Bayesian approaches are widely used for computational biology. (de Jong, 2002; Friedman, 2004; Ishwaran, Rao, & Kogalur,

2006; Yang, Bakshi, Rathman, & Blower, 2002) Boolean logic is the basis for computers,

so that is well suited to computational approaches as well. The Bayesian approach uses

probability theory developed by Bayes (Bayes, 1763), generalized by Laplace (Stigler,

1986) and tweaked by von Neumann (von Neumann & Morgenstern, 1944) and others.

The Bayesian approach is based on developing a probabilistic graphical model of the

system of interest. (Draper, 2004; Friedman, 2004; Sachs, 2005) The nodes represent species, and the lines connecting the nodes represent reactions in which the species become other nodes. But unlike a deterministic model, in which the reactions always take place according to the relevant conservation laws, in this model probabilities are assigned to whether each reaction will take place, as shown in Figure 4. The probabilities can depend on the quantities of each species, which are typically integer values but not necessarily binary (e.g. 0, 1, 2).

Once initialized, a Bayesian network derives the probabilities through a method called network inference. This process changes one arc at a time, and sees if the 'score' improves, which means the model more closely represents the experimental data.

The motivation for using a Bayesian network is that it can be used to reconstruct a regulatory network "where the expression level of each gene depends on the activity

levels of its regulators " (Friedman, 2004). Hence "Bayesian networks can represent complex stochastic nonlinear relationships among multiple interacting molecules, and their probabilistic nature can accommodate noise that is inherent to biologically derived data." (Sachs, 2005)

4. Bayesian probabilistic graphical model (Friedman, 2004) Shows how the Gene Clusters (GC) and Array Clusters (AC) contribute to the gene expression amounts (X). Part C is the Bayesian probability table which is being used to predict the mean () and standard deviation () of a Gaussian distribution of gene expression levels for some Spot

Boolean modeling (Albert, 2004; Chaves, Albert, & Sontag, 2005; Pandey et al., 2010;

Thieffry et al., 2009) is based on binary on/off values for each node, corresponding to

that gene expression being turned on or off, or that species being present or not.

Decisions about which reactions take place follow logic rule tables which can change over discrete time steps. The inputs for a Boolean model are therefore relatively simple, so "Boolean or logical networks are well suited to reproduce the qualitative behavior of

extensive networks even with a limited amount of experimental data." (Thieffry, et al.,

2009) This simplicity allows very complex reactions to be modeled, such as the 86‐node model of apoptosis in Figure 5.

5. Boolean model of apoptosis, from (Thieffry, et al., 2009)

A Boolean model can also have sources and sinks to help drive model behavior; in Figure

5 the green squares are sources from a housekeeping function.

Because of the simple on/off nature of each node, only qualitative inferences about system behavior can be obtained. "The Boolean formalism is especially useful for qualitative representation of signaling and regulatory networks where activation and inhibition are the essential processes" (R. Thomas, 1998)

This research does not use Boolean modeling, however understanding it does provide a clearer context for understanding Fuzzy Logic modeling, which was used via the Bionet tool.

Fuzzy Logic

Fuzzy logic has a clearly defined starting point, with a seminal paper by Lotfi A. Zadeh in

1965. (Moraga, 2005) While its practical applications started with control theory, it has found application in agricultural and biological systems (Center & Verma, 1998; Franco‐

Lara & Weuster‐Botz, 2007). Most of the biological applications have focused on analysis of pathways and gene expression levels (Du, Gong, Wurtele, & Dickerson, 2005;

Linden & Bhaya, 2007; B. A. Sokhansanj & Fitch, 2001; Bahrad A. Sokhansanj, Fitch,

Quong, & Quong, 2004; Woolf & Wang, 2000). Fuzzy analysis allows larger scale hybrid models to be created from qualitative gene expression data (Nicholls, 2004 ), so it is a key part of this systems approach to aging.

Like Bayesian and Boolean modeling, the system is represented by a directed graph network, with nodes representing species and arcs represent reactions changing one

node into another. However in fuzzy logic, the quantity of each node is represented semi‐quantitatively by percentages of several defined states. Here for example six states are used for each node, representing quantities from about 'zero' to 'very high.'

Each of those states can have different rules for its impact on the rate of the reactions leading away from that state. In this way, basic reaction roles like inhibition and activation can be modeled, but also more complex concepts can be included.

The goals of the fuzzy modeling portion of this research are to:

 Expand and refine the fuzzy models of cellular behavior to include relevant cellular processes, such as metabolic fluxes, organelle phenotypes such as the ability to produce ATP, biosynthesis rates in the Endoplasmic Reticulum, molecular stress responses and inflammation relevant for the aging process.  Refine modeling parameters (e.g. initial conditions, concentrations, organelle descriptors) based on experimental assays and published sources. The primary advantage of fuzzy logic over Boolean logic is that the former can generate semi‐quantitative results instead of only qualitative results. The fuzzy logic tool used for modeling biological networks is called Bionet.

The Bionet application uses nodes to identify key variables of interest in the system, and defines reactions (processes), which involve one or more nodes. “Nodes can represent any quantity for which rules of change can be defined.” (Bosl, 2007) The range of values for each node is typically scaled to a range from zero to unity. Reactions are defined by a reaction rate value, the nodes involved in the reaction, and the role each node plays in the reaction.

There are four types of roles, as follows, with definitions excerpted from (Bosl, 2007):

 “As the concentration of substrate increases, the reaction rate increases proportionately.  A product is produced in a reaction. It does not affect the reaction rate, except that when the product concentration reaches its highest allowable amount the reaction rate goes to zero.  Activators have the same default rules as a substrate: as the concentration increases, the reaction rate contribution increases. Activators and inhibitors have a stoichiometry of 0, indicating that the reaction does not change their concentration.  An inhibitor causes a reaction rate to slow as its concentration increases. When absent, an inhibitor has no effect on a reaction rate, which is then wholly determined by the concentrations of substrates and activators. As the amount of inhibitor increases, the reaction rate slows.” In order for Bionet to model reactions, the inputs are taken in normal quantified terms, which are then fuzzified. That process converts them into fuzzy values, based on

percentages of set values. For nodes with a range from zero to one, the default is to use

six sets linguistically zero, very low, low, medium, high and very high; corresponding to linear mean fractions of 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0 respectively. Logarithmic mean fractions can be used as well, and the centroid of each mean fraction can also be customized.

Additional details on fuzzy logic modeling parameters are given in Appendix C‐1.

Once the inputs have been fuzzified, the reactions are calculated for each time step until the simulation is complete. The reactions are analyzed based on functional hybrid Petri nets (Girault & Valk, 2003) then de‐fuzzified to report them in normal quantified real number terms.

Reliability Modeling

A novel analytical approach to aging is to view the body as a system of components which may fail in various modes, then analyze aging as a problem in reliability engineering (L. Gavrilov, 2001; LA Gavrilov & Gavrilova, 2004). While this approach has been pursued about a decade, it has been identified only by some as an area for growth

(E. J. Masoro, 1995).

The reliability modeling concept of the bathtub curve for failure rates is used later for modeling the stochastic component in the viability equation of Weitz & Fraser (Weitz &

Fraser, 2001). The bathtub curve (Figure 6) shows that failure rates for many things

(light bulbs, people, cars, etc.) follows three phases ‐ an initial high rate of failure, then a low plateau of low failure rates, ending with high failure rates (Wilkins, 2002).

6. The Bathtub Curve (Wilkins, 2002)

The argument is that redundant biological systems are claimed to follow an exponential curve for mortality rate, whereas redundant mechanical systems follow power law curves, such as variations on the Weibull formulas. The difference between them arises from the fact that the exponential curve results from a high initial failure rate.

The work of Gavrilov and Gavrilova insists that exponential curves correspond to human mortality data better than power law models. "An attempt to explain the exponential deterioration of biosystems in terms of reliability theory led to a paradoxical conjecture that biological systems start their adult life with a high load of initial damage" (L. A.

Gavrilov & Gavrilova, 2003). However the analysis here starts at age 30 for humans, when "a high load of initial damage" is outside the scope of the model, therefore that could explain why our conclusions differ from theirs.

Multi‐scale Modeling

A ‘systems approach’ integrates cellular level gene expression data with larger scale biological pathways, organism‐level diseases and population‐scale demographic data.

This multiscale perspective is analogous to efforts such as the Physiome project. (J.

Bassingthwaighte, Chizeck, & Les, 2006; Hunter & Nielsen, 2005) The Physiome project aims to integrate modeling from the sub‐cellular level up to the system or somatic level

(Crampin, 2004).

The first major success in multiscale modeling is in cardiac modeling (J. B.

Bassingthwaighte, 2005). Attempts have been started to model structural elements

(Feig, Karanicolas, & Brooks Iii, 2004), and another major research direction is the integration of information from various –omics data sets (Joyce & Palsson, 2006).

There are many challenges in integrating data across multiple levels of modeling.

 Spatial scales range from nanometer distance (e.g. diameter of an ion channel) to the meter‐scale size of an adult human, for a factor of 10^9.  Temporal scales range from microsecond events (Brownian motion) to billions of seconds in a human lifespan, for a factor of 10^15. o As a result, computation of a solution is often a computationally stiff problem, and may require several levels of complexity of models (less complex when that’s accurate enough, more complex when required)  Making the transition between stochastic (state transition, Monte Carlo) and continuum models  Making transitions among 3‐D, 2‐D, and 1‐D models  Structure and function are heavily intertwined in biology, and structure is heavily dependent upon biochemical processes  Connecting the genome, proteome, morphome (organism structure, and includes aging effects), and physiome (J. Bassingthwaighte, 2000)  Knowing applicability and limits of models across various conditions, species, etc. o This isn’t just for humans! Since some data comes from other model organisms, we need to be able to translate models across species. o What happens when the valid scope of a model is exceeded? In order to answer that we must know the limitations and assumptions behind each model. Geoffrey West has done extensive study of the scaling laws across all living species, from

bacteria to blue whales, including lifespan, heart rate, energy consumption, lifespan and many other parameters. (A. Kriete, Sokhansanj, Coppock, & West, 2006; West &

Bergman, 2009; West & Brown, 2005; West et al., 2003) This supports multiscale modeling efforts by identifying similarities across species. In summary, individual models typically capture some aspects or property of the complexity of aging, but they may not be deeply connected mechanistically. Finding common properties that would allow connecting and converging some models, motivated the discussion of the linearity theme of this thesis.

METHODS This section summarizes assays and gene expression work published in part in (Andres

Kriete et al., 2008) and data derived from other teams working with human fibroblasts, including (Greco, 2003). It is summarized here because the data generated was the basis for the computational pathway models developed herein. It plays a critical role in this research because it shows that nuclear factor kappa B (NF‐kB) is a key stress sensor for aging, and activates multiple feedback loops to help mitigate the effects of aging. The involvement of NF‐kB to the chronic inflammatory phenotype in aging has been

discussed (Adler et al., 2007; Hanninen, Salminen, Helenius, & Lehtinen, 1996), but we

here interpret NF‐kB as a specific feedback mechanism which contributes to the overall linear decline of the cell.

Experimental Data

Genome‐wide gene expression studies from quiescent human fibroblasts in a cross‐ sectional study of varying age subjects (age 17 to 94), and identified genes which are significantly (>2.5 or <1/2.5 fold) up‐ or down‐regulated. (Yalamanchili et al., 2006) The use of quiescent cells is particularly significant because other studies looking for gene expression with age use active cells (Bahar, 2006 ; Fraser, 2005; Park & Prolla, 2005).

Growth factor starvation for 24 hours, representing the state of the majority of cells in‐ vivo helps to isolate pathways associated with aging.

Scope of Samples

This summary of the scope of samples and analysis methodology below are quoted almost verbatim from (Andres Kriete, et al., 2008), and are shown in italics.

Cell Lines and Culture Procedures

Human fibroblast cultures, established from skin samples derived from young and old donors, were obtained from the NIA Aging Cell Repository (Coriell Institute for Medical Research, Camden, NJ). All cell lines originated from 2 mm punch biopsies taken from the medial aspect of the upper arm. The donors were members of the Baltimore Longitudinal Study of Aging (BLSA) (Shock, 1984). The cell lines investigated had normal karyotypes. Coriell catalog numbers of these cell lines for the group of young donors were AG10803 (22 yrs), AG0454B (29 yrs), AG PI00924/PI00923B (29‐II yrs), AG13153 (30 yrs) and AG04438 (33 yrs) and for the group of middle‐age and old donors AG04456 (49 yrs), AG04659 (65 yrs), AG13369 (68‐I yrs), AG14251 (68‐II yrs), AG11243 (74 yrs), AG09156 (81 yrs), AG13349 (86 yrs), AG13129 (89 yrs) and AG04064 (92 yrs). AG04456 (49 yrs) and AG14251 (68 yrs) were from the same donor. Cells were grown in medium consisting of EMEM (Mediatech, Herndon, VA) supplemented with 2 mM L‐glutamine and 15% FBS without antibiotics at 37 C and 5% CO2 according to Coriell’s standard procedures. To avoid influence of replicative senescence, cell lines selected for our cultures had undergone no more than half of the maximum population doublings at which previously determined senescence would occur. Twenty four hours prior to RNA collection cells were placed in growth factor‐free medium (MEM supplemented with 0.2% Bovine Serum Albumin / BSA). The protocol to prepare cells for microarray gene expression analysis was as follows: (Day 1) Cells were plated at 9,000 ‐ 12,000 cells per cm2 in regular growth medium; (Day 2) Cell culture medium was changed to growth‐factor‐free medium (EMEM with 0.2% BSA and 1% L‐glutamine); (Day 3) Cells were washed with ice cold phosphate‐buffered saline (PBS). Qiagen lysis buffer (RLT) was used to prepare cell lysates which were stored at ‐80 °C. Cell cycle distribution was determined by PI staining followed by FACS analysis. Percentage of cells in S‐ phase before starvation was generally >10% and after mitogen starvation <1%. Methodology

Microarray Analysis

RNA was isolated from the cell lysate using Qiagen RNeasy mini kit according to the manufacturer’s instructions. Gene expression analysis was performed using the Codelink human bioarray containing single‐stranded 30‐mer oligonucleotide probes (Applied Microarrays, Tempe, AZ) and chips were run in duplicate. Details of this platform are available on the vendor’s homepage. Characteristics of the Codelink platform have been evaluated by us (Young et al., 2003), and as part of the microarray quality control (MAQC) assessment (Canales et al., 2006). Sample preparation and hybridization followed procedures described in (Young, et al.,

2003). Slides were scanned at 5 μm resolution with a ScanArray 4000xl (Perkin Elmer, Waltham, MA) and analyzed with the CodeLink Analysis Software, providing an integrated optical density (IOD) value for each hybridization spot, which is a measurement of an integrated background intensity value subtracted from the total pixel intensities within the area of the spot. The data was uploaded onto the Gene Expression Omnibus2. Expressions of characterized genes related to immunity and inflammation were identified, replicate readouts were averaged, outliers detected and differential expressions determined. A variance filter trimmed the resulting list (p<0.15). We used a correlative approach to search for similarities between the NF‐κB profile and expression of genes related to inflammation. In modification of previously used rank correlation for template matching of phenotypical markers (Boyce et al., 2005; A. Kriete et al., 2003), we used Pearson correlation as a measure of similarity, because the NF‐κB values of the samples from young donors were close and within error margins, which can lead to low correlation values if ranked wrongly. Finally, the data was clustered by a dendrogram, using single linkage analysis and a Canberra distance metric (J‐ Express, Molmine AS, Norway). NF‐κB DNA Binding Activity Assay

We analyzed the DNA binding activity of NF‐κB p65/RelA, a major component of the heterodimeric p50/RelA complex, with a chemiluminescent DNA binding assay in nuclear fractions. Cells were plated at subconfluency in regular growth medium. Twenty‐four hours later, normal growth medium was replaced with growth factor‐free base medium for another 24 hours. On the day of sample collection, the cells (1.5 to 2 x106/sample) were washed once with PBS and trypsinized. They were centrifuged at 200‐300 × g for 10 minutes and cell pellets were collected. The nuclear cell fractions were prepared using NE‐PER® Nuclear and Cytoplasmic Extraction Reagents (Pierce Biotechnology, Product No. 78833, Rockford, IL) according to the manufacturer’s instructions. Ten µg of the nuclear cell fractions were used from each cell‐line and their NF‐κB p65 DNA binding activity was determined using the EZ‐Detect NF‐κB p65 Transcription Factor Kit (Pierce Biotechnology, Product No. 89859, Rockford, IL) according to the manufacturer’s protocol. Two biological replicates of each sample were prepared and the signal of four readouts with a Veritas Microplate Luminometer was averaged. Other Data

Other supporting experimental data, primary from studies of human fibroblasts considered included the decline in mitochondrial respiration (Greco et al., 2003), the

2 http://www.ncbi.nlm.nih.gov/geo/

increase in oxidized proteins and reduction of ATP levels (Miyoshi, Oubrahim, Chock, &

Stadtman, 2006), as well as the decreased activity of mTOR with age (Mulligan,

Gonzalez, Kumar, Davis, & Saupe, 2005; Wang et al., 2002). Additional relationships were taken from investigations with other mammalian cell types, such as hierarchy of

ATP‐consuming processes (Buttgereit & Brand, 1995), alterations of the ATP/ADP ratio

(Marcinek, Schenkman, Ciesielski, Lee, & Conley, 2005), and increase of glycolysis with age (D'Aurelio et al., 2001; Luptak et al., 2007).

Data Summary

Of the 16,220 genes analyzed, 504 were significantly up‐regulated, and 224 were down‐

regulated. In conjunction with proteomic assays, markers of damage and organelle activity, the The data suggests:

 Calcium homeostasis changes with age  ROS did not increase with age  Oxidative damage increased with age  Glycolysis activity increases with age  ATP and biosynthesis decrease with age  Inflammation and apoptosis‐inhibiting genes increased with age These laboratory results inspired the development of computational molecular models of cellular aging. The first computational model to be developed was the vicious cycle model, to replicate the free radical theory of aging and other damage accumulation theories of aging.

CELL MODELING The Vicious Cycle Model

This section presents the Vicious Cycle model, as developed in the Bionet fuzzy logic framework and again in a Matlab‐based ODE environment. The Vicious Cycle model is a conceptual model suggested by (Bandy & Davison, 1990). Some variation on the Vicious

Cycle model is ubiquitous in aging literature because it represents the outcome of damage accumulation theories. Here it is the first step to merge mechanistic, molecular processes with an element from systems theory (earlier called Cybernetics, (Wiener,

1961)), namely a positive feedback loop.

Physiological mechanisms in the Vicious Cycle Model

The Vicious Cycle Model of aging relies on two major processes. Cells convert ADP into

ATP through phosphorylation in the process of mitochondrial respiration. A key byproduct of this process is the generation of reactive oxygen species (ROS). The second major process is the impaired ability to degrade and remove incorrect proteins from cells, resulting in accumulation of proteins which interferes with normal cell functioning.

Mitochondrial respiration

Most biological processes in organisms ranging from single cell organisms to blue whales depend on availability of adenosine triphosphate (ATP) to fuel them. (Woodruff, West,

& Brown, 2002) In return, they remove a phosphate group, turning each molecule of

ATP into adenosine diphosphate (ADP). This is recharged back into ATP via

mitochondrial respiration. (Lesnefsky & Hoppel, 2006) Typically each cell has on the

order of dozens to hundreds of mitochondria to perform this function, without which everyone would be dead in a matter of minutes.

Mitochondrial respiration takes place between the convoluted matrix surface inside the mitochondria and the intermembrane space which surrounds it. (Figure 7) Respiration is powered by the electron transport chain (ETC) which involves four complexes (I to IV in

Figure 8). (Lesnefsky & Hoppel, 2006) The ETC generates an inner membrane proton gradient. The actual process of phosphorylation to create ATP from ADP takes place in complex V using this proton gradient. These processes are powered by the presence of glucose and oxygen.

7. Cartoon of a mitochondrion (Lesnefsky & Hoppel, 2006)

8. Mitochondrial respiration process (Lesnefsky & Hoppel, 2006) Complexes I to IV are the electron transport chain; complex V (far right) performs phosphorylation to create ATP from ADP.

Complexes I and III are of particular interest, because they are the main source of reactive oxygen species (ROS) generation as a byproduct during mitochondrial respiration.

Damage to mitochondrial respiration triggers retrograde response pathways which are not yet fully understood. (Jazwinski & Miceli, 2005) This is part of a larger scope of

research to determine the control mechanisms for energy regulation. (C. Mathieu &

Peter, 2010)

Mitochondrial respiration is controlled by many pathways, including mTOR. (Arlow et al., 2007; Ramanathan & Schreiber, 2009) Inhibition of mitochondrial respiration in C. elegans extends lifespan in a process similar to the retrograde response. (Cary,

Lunceford, Clarke, Cristina, & Kenyon, 2009) In the absence of enough oxygen present, cells will reduce mitochondrial respiration and switch to glycolysis to generate ATP.

Glycolysis is a separate process for generating ATP independently of normal mitochondrial respiration. Glycolysis is regulated by IL‐3. (A. L. Mathieu et al., 2002)

Glycolysis has the advantage of being able to operate without oxygen, but it is far less efficient at producing ATP (about 1/11th or 1/12th as efficient).

Generation of ROS and Oxidized Proteins

Many cellular characteristics change with age; “age‐related increases in oxidatively

modified proteins, DNA, and lipids” have been observed. (E. J. Masoro, 1995) Impaired protein degradation and removal machinery may account for an increase in protein content. There are three pathways for normal protein degradation in mammalian cells ‐ cytosolic, autophagic, and heterophagic pathways. (E. J. Masoro, 1995)

A key difference between the gene expression analysis earlier and the accumulation of proteins with age is that "the appearance of abnormal proteins in senescent animals is not due to errors in gene expression but arises posttranslationally by a variety of mechanisms." (E. J. Masoro, 1995)

Bionet Vicious Cycle model

The model used for preliminary analysis is the Bionet tool (Bosl, 2007; Doi, Fujita,

Matsuno, Nagasaki, & Miyano, 2004). Developed by Dr. William Bosl of Harvard Medical

School, Bionet is a Java‐based application, that uses fuzzy logic to model cellular pathways.

Fuzzy logic is well suited to modeling of biological pathways, as summarized by (Bosl,

2007). "Fuzzy logic is a computational method for formulating and transferring human

expert knowledge to computational models. It provides a flexible tool for modeling the relationship between input and output information and is distinguished by its robustness with respect to noise and variations in system parameters. This characteristic seems to mirror the robustness of biological systems and their remarkable ability to achieve precise functional control from imprecise components "

Nodes typically represent the quantity of a species, scaled from 0 to 1 in six fuzzy ranges

(near zero, plus very low to very high).

Vicious Cycle versus Retrograde Response model

The Free Radical and DNA damage theories of aging both indicate that damage to the cell occurs and accumulates throughout life. That damage, whether from ROS or other disturbances, leads to an exponential decay in the body due to deterioration of the mitochondria. The first conceptual Bionet VC model is shown in Figure 9.

The vicious cycle model shown in Figure 9 represents basic cellular functions. ATP is used in bio‐synthesis, which recycles the resulting ADP (not shown) via the Krebs cycle, powered by the Electron Transport Chain (ETC). Normal functioning of the ETC produces ROS, and yet the increase of ROS reduces the effectiveness of the ETC. The presence of ROS activates the creation of SOD (anti‐oxidants such as superoxide dismutase), and the purpose of SOD is to reduce the amount of ROS.

The results of this model are discussed in the next section.

9. Bionet Vicious Cycle model (Booker, 2008)

Discussion of the Bionet Vicious Cycle Model

The results of the Bionet VC model is shown in Figure 10. The vicious cycle model shows a strong increase in ROS, corresponding to a sharp decline in the cell's ability to perform bio‐synthesis, while ATP levels remain nearly constant. The time scale of these simulations are on a non‐dimensional scale, representing the period of a human life.

ROS

ATP

biosynth

10. Bionet VC model output

The vicious cycle model is therefore consistent with biological observations that

uncontrolled increases in ROS lead to a sharp decline in biosynthesis. This decline would in reality be truncated by apoptosis of the cell when excessive ROS levels are reached

(Alberto, Pilar, José, & Gustavo, 2006).

Documentation of Bionet Application

In order to understand Bionet more fully, documentation of its source code was developed. The full documentation is in Appendix D, including the algorithms used for each class and method. A summary is presented here.

Bionet is written in Java, and has seven classes shown in the class diagram in Figure 11.

 Bionet.java is the primary class for executing one simulation. Multiple simulations can be performed in one run using the genetic matching algorithm, which was not used for this project.  EvolveBionet.java’s purpose is to perform the genetic matching algorithm. It is being extracted from Bionet.java.  FitnessCalculator.java returns the fitness parameter from an array  Main.java creates a family of bionets, each of which is a separate simulation.  Node.java defines the nodes used to model a given species, and fuzzify the input conditions for that node.  PlotTimeSeries.java uses JFrame to plot results of the Bionet simulation.  RandomSequence.java generates a random walk through a Vector variable.  Reaction.java determines how reactions among nodes are handled.  RuleTable.java defines the rules for handling fuzzy logic reactions. The Main routine executes first, as is required in Java. Each simulation instantiates a

Bionet object, which runs the simulation for one set of model inputs. This includes following Rule Tables to evaluate each Reaction between Nodes within that Bionet. The overall Fitness level of the simulation is calculated, where the actual results for species' quantities over time are compared to expected values.

An option not exercised in the Bionet application allows multiple Bionet simulations to

be executed, using genetic matching algorithms to randomly change the Bionet model characteristics. The genetic algorithms follow approaches such as described in

(Affenzeller, Wagner, Winkler, & Beham, 2009). As a result of the fitness assessment of each simulation, an improved model may be determined. This option was not used

because the exact basis for the fitness assessment could not be determined.

11. Bionet Class Diagram Only non‐primitive attributes are shown. Getter and setter methods are omitted.

Finally, the PlotTimeSeries class invokes the JFrame plotting utilities to present line plots of selected species' quantities over time, as shown elsewhere in this document.

Conclusion from the Vicious Cycle Model

The Bionet Vicious Cycle Model affirms that a cell with a positive feedback loop to generate ROS will keep doing so until cellular death occurs. This model is consistent with damage accumulation theories of aging, but not with experimental data.

The Adaptive Response Model

Physiological mechanisms in the Adaptive Response model

With respect to the mismatch of experimental data with the VC model, we hypothesize that adaptive mechanisms play a role in aging diverting the behavior of the model from the accelerated decline. This section describes the mechanisms which were considered for inclusion in what we call the Adaptive Response model. Several mechanisms were

discussed contributing to the cellular behavior.

Retrograde response

The retrograde response (RR) is when a cell slows using oxidative phosphorylation

(oxphos) to produce energy (ATP), and instead uses much less efficient glycolysis to produce ATP. The RR has been observed in yeast and other simple organisms (C. elegans), and a similar mechanisms has been suggested in humans or other mammals.

(Ronald A. Butow & Avadhani, 2004; Cary, et al., 2009; Srinivasan, Kriete, Sacan, &

Jazwinski, 2010) , potentially involving NF‐kB.

Inflammation

Aging often produces a chronic low level of inflammation, which it has in common with a wide range of diseases, as shown in Figure 12. For examples, connections to inflammation and aging have been made for the following conditions:

 Dementia (Bruunsgaard, 2006; Peila & Launer, 2006; Ravaglia et al., 2007)  Cancer (Ahmad et al., 2009; Caruso, 2004)  Cardiovascular disease (Bruunsgaard, 2006; Candore, 2006)  Diabetes (Figaro et al., 2006; Ramasamy, 2005)

 Caloric Restriction (R. Kalani, Judge, Carter, Pahor, & Leeuwenburg, 2006 ; Ugochukwu & Figgers, 2007) Because of the connection between the interleukins (IL‐x) and inflammation response

(Boxman, 1996 ; Pedersen, Bruunsgaard, & Pedersen, 2001), they have often been the subject of aging related studies (Fried et al., 2006; Hirose et al., 2004 ; Maraldi et al.,

2006 ).

Kidney Cardiovascular Cystatin C Arthritis Genes Muscle polymorphism Cancer

ABC Body Neurological Inflammation Study dementia Chronic, low grade

Zinc and Diabetes Magnesium levels Caloric restriction Cytokines Longevity/ IL-1 to IL-6, mortality; connect TNF-alpha to robustness? ROS SOD1, SOD2

12. Inflammation and aging

Since NF‐kB is a major regulator of inflammation and is constitutively active in samples from older donors, (Blumenberg, Gazel, & Banno, 2005; Mayo & Kriete, 2009), the

Adaptive Response model presented herein is consistent with this pervasive connection between aging and inflammation‐related diseases.

Superoxide dismutases (SOD)

"Superoxide dismutases (SOD) are a class of enzymes that catalyze the dismutation of

superoxide into oxygen and hydrogen peroxide."3 Various forms of SOD are based on

the elements CuZn, Mn, Fe, or Ni. While important for removal of ROS, it appears that

SOD activity does not change with age. No significant differences in CuZn or Mn SOD in skin fibroblasts was found from age 4 to 98 yrs (E. J. Masoro, 1995). In muscle tissue,

levels of CuZn SOD and Mn SOD varied with age from one specific muscle type to the next (Hollander, Bejma, Ookawara, Ohno, & Ji, 2000). Increased levels of Mn SOD is one of the reasons for increased life expectancy for females (Borrás et al., 2005). Of note, the regulation of SODs has been discussed in terms of a compensatory mechanisms.

Inhibition of the mitochondrial ETC as a function of superoxide production has been suggested by Gardner et al. (Gardner, Moradas-Ferreira, & Salvador, 2006; Gardner,

Salvador, & Moradas-Ferreira, 2002). Recently, this concept was revisited to explain the absence of lifespan reduction in SOD scavenger knockouts in C-elegans (Gruber et al.,

2011).

Calcium pathways

The "calcium ion is a potent modulator of cell proliferation for fibroblasts" (E. J. Masoro,

1995) and is involved in many intracellular signaling pathways (Rizzuto, Duchen, &

Pozzan, 2004; Rolfe & Brown, 1997 ), hence many studies have focused on it as a key element of the aging process (Brookes, 2004; Peterson, Ratan, Shelanski, & Goldman,

3 http://www.lifevantage.com/protandim‐glossary.aspx

1986; Puzianowska‐Kuznicka & Kuznicki, 2009; Ray et al., 2000; Toescu, Verkhratsky, &

Landfield, 2004; Wu et al., 2007). Intracellular calcium levels control activation of NF‐kB

(Glazner, 2001), so it is of possible relevance to the models developed here.

In our data, Calcium levels were slightly changed with age in early data, however later expansion of that analysis showed no significant role of Calcium in the pathways activated by aging in human fibroblasts.

Feedback via mTOR

The most recent experimental data have suggested a connection that may relate the

oxidative stress sensor NF‐kB with the low energy (ATP) sensor mTOR (mammalian

Target Of Rapamycin). The kinase mTOR is negatively regulated by energy availability

(ATP), with a role in mitochondrial respiration, protein synthesis and autophagy. In addition to its role in mitochondrial signaling in aging (Schieke & Finkel, 2006) and its contribution to metabolic remodelling, mTOR is also extensively studied in connection with cancer (Arlow, et al., 2007; Duncan et al., 2008; Wilkinson et al., 2009).

UPR and EOR

Some of the gene expression results hinted at involvement of the endoplasmic reticulum (ER) in the aging process. The Unfolded Protein Response (UPR) (Ben‐Zvi,

Miller, & Morimoto, 2009; Lai, Teodoro, & Volchuk, 2007; J. H. Lin et al., 2007) and

Endoplasmic reticulum Overload Response (EOR) (Kowald, 2000; Soti & Csermely, 2007)

are two major effects that might be seen when the process of creating proteins becomes defective. The defects typically result after initial protein formation, when it’s

being folded into its final form. The UPR "is aimed initially at compensating for damage but can eventually trigger cell death if ER dysfunction is severe or prolonged." (Xu, 2005)

EOR is a potential mechanism for NF‐kB activation, but data is lacking that this mechanism plays a significant role in the context of aging. Nevertheless, UPR and EOR are related to the 'garbage accumulation' family of aging theories (Stroikin, Dalen,

Brunk, & Terman, 2005). Failures to manage misfolded proteins result in the accumulation of garbage in the cell, which leads to further damage and eventually cell death. The heat shock response (cytoplasmic stress response) is closely related to the

UPR (Fedoroff, 2006). The investigation into UPR, EOR, and heat shock response was motivated by the role of autophagy in aging, which removes misfolded proteins, however no direct connection to UPR, EOR, and heat shock response with increasing age

was established.

Bionet Adaptive Response model

Results from our studies favored support to a retrograde response mechanisms

(Appendix C‐2). This led to the Adaptive Response model, which was implemented in

Bionet (see Appendix C‐3). The Adaptive Response model is summarized in Figure 13.

The positive feedback loop between mitochondria and ROS is familiar from the Vicious

Cycle model, and oxidative damage is ongoing, but in this AR model it is mitigated by negative feedback loops through NF‐kB and mTOR to down‐regulate mitochondrial respiration, ROS, and biosynthesis.

13. Final Bionet Adaptive Response Model (A Kriete, Bosl, & Booker, 2010)

This model was the baseline case used for sensitivity studies in the PLoS paper (A Kriete, et al., 2010), which are summarized in the next section.

Sensitivity Analysis

Introduction and Criteria

The purpose of the sensitivity study is to examine the effect of changing one input reaction rate at a time, and see what effect it has on the projected lifespan of the organism. This study uses depletion of ATPconsume as a marker for lifespan, since that variable corresponds to the amount of protein synthesis taking place. As a practical

matter, the first time step with ATPconsume < 0.1 is used for the lifespan, since it generally never reaches zero, and sometimes oscillates before getting close to zero.

The initial set of runs will increase each reaction rate individually by 5% to see what effect that has on lifespan. Based on those results we'll determine if 1) a change of 1%

is needed, and if 2) the effect of lowering reaction rates also needs to be examined.

Baseline results

The baseline Bionet model data file is listed in Appendix C‐3. It produces the results shown in Figure 14. This analysis is based on using the 11/2/2006 version of Bionet, running under Windows 7 Home Premium. The first value of ATPconsume < 0.1 is reached at t=34.05 in the baseline case. This establishes the baseline 'lifespan' value.

Input parameters

The reactions, their baseline rates, and percent change in lifespan are summarized in

Table 4.

Analysis

The output files from each run (e.g. Plus01.txt.out) were imported into Microsoft Excel

2007. The first time step with ATPconsume below 0.1 was recorded as the end of the

'lifespan' of the organism. The baseline value was at time step 34.05. Time resolution was in intervals of 0.01.

Complete sensitivity study results are given in Table 5. Two reactions

(MRSP_deactivation and Biosynth_consumed) produced a sharp decrease in lifespan when their reaction rate was increased by 5%. Two more reactions (MRSP_ADP and

ATP_used) produced a strong decrease in lifespan, and two reactions (MTOR_ROS and

ROS_produced) produced a slight increase in lifespan. Four reactions (MRSP_activation,

MRSP_ATP, Biosynth_act, and Biosynth_ADP) produced oscillations in ATPconsume, so that it never went below 0.1.

4. Baseline reactions and reaction rates See Analysis section for discussion of the 'N/A' results Reaction name Baseline rate % change lifespan ADP_Glycolysis 0.1 ‐1.09 ATP_used 1.0 ‐27.78 Autophagy_MTOR 0.5 ‐0.15 Autophagy_OXPROT 0.15 1.35 Biosynth_act 1.0 N/A Biosynth_ADP 1.0 N/A Biosynth_consumed 1.0 ‐40.32 Biosynth_mTOR_inh 0.1 ‐0.38 Biosynth_mTOR_inh 0.1 ‐0.26 Biosynth_NFKB_inflamm 0.05 2.61 Biosynth_OXPROT_inh 0.01 ‐0.29 Energy_totals 0.015 0.23 Glycolysis_ATP 0.1 1.70 MRSP_activation 0.8 N/A MRSP_ADP 1.0 ‐29.72 MRSP_ATP 1.0 N/A MRSP_change 0.15 ‐0.88 MRSP_change 0.15 0.12 MRSP_deactivation 0.8 ‐42.35 MRSP_inhibition 0.15 ‐3.38

Reaction name Baseline rate % change lifespan MTOR_ATP 0.10 ‐5.17 MTOR_ROS 0.095 12.31 NADPHOXD_produced 0.1 0.03 NFKB_decay 0.4 ‐0.18 NFKB_Stress_OXPROT 0.2 0.18 NFKB_Stress_ROS 0.2 ‐0.23 OXPROT_Bio 0.1 ‐1.20 OXPROT_ROS 0.1 0.15 ProteinSynth 0.08 ‐0.26 ROS_decay 0.4 ‐8.37 ROS_produced 0.25 12.92 ROS_produced 0.50 3.79 ROS_scavenge 0.2 ‐1.26 4. Baseline reactions and reaction rates (continued)

5. Detailed calculations for reaction rate sensitivity study % change lifespan = 100*(Lifespan‐34.05)/34.05 Reaction name Baseline 1.05* Lifespan % change Comments rate rate lifespan OXPROT_ROS 0.1 0.105 34.1 0.15 OXPROT_Bio 0.1 0.105 33.64 -1.20 ROS_decay 0.4 0.42 31.2 -8.37 ROS_scavenge 0.2 0.21 33.62 -1.26 Glycolysis_ATP 0.1 0.105 34.63 1.70 ADP_Glycolysis 0.1 0.105 33.68 -1.09 MRSP_activation 0.8 0.84 N/A N/A never 'died'; lowest value of ATPconsume was about .60 MRSP_change 0.15 0.1575 33.75 -0.88 MRSP_change 0.15 0.1575 34.09 0.12 MRSP_inhibition 0.15 0.1575 32.9 -3.38 MRSP_ATP 1 1.05 N/A N/A never 'died'; lowest value of ATPconsume was about .26

Reaction name Baseline 1.05* Lifespan % change Comments rate rate lifespan MRSP_ADP 1 1.05 23.93 -29.72 ROS_produced 0.25 0.2625 38.45 12.92 ROS_produced 0.5 0.525 35.34 3.79 NADPHOXD_produced 0.1 0.105 34.06 0.03 MRSP_deactivation 0.8 0.84 19.63 -42.35 NFKB_decay 0.4 0.42 33.99 -0.18 NFKB_Stress_ROS 0.2 0.21 33.97 -0.23 NFKB_Stress_OXPROT 0.2 0.21 34.11 0.18 MTOR_ATP 0.1 0.105 32.29 -5.17 MTOR_ROS 0.095 0.9975 38.24 12.31 Autophagy_OXPROT 0.15 0.1575 34.51 1.35 Autophagy_MTOR 0.5 0.525 34 -0.15 Biosynth_act 1 1.05 N/A N/A never 'died'; lowest value of ATPconsume was about .53 ProteinSynth 0.08 0.084 33.96 -0.26 Biosynth_OXPROT_inh 0.01 0.0105 33.95 -0.29 Biosynth_mTOR_inh 0.1 0.105 33.92 -0.38 Biosynth_mTOR_inh 0.1 0.105 33.96 -0.26 Biosynth_NFKB_inflamm 0.05 0.0525 34.94 2.61 ATP_used 1 0.105 24.59 -27.78 Biosynth_ADP 1 0.105 N/A N/A never 'died'; lowest value of ATPconsume was about .28 Energy_totals 0.015 0.01575 34.13 0.23 Biosynth_consumed 1 1.05 20.32 -40.32 5. Detailed calculations for reaction rate sensitivity study (continued)

Discussion of Adaptive Response models

Sample output from the Adaptive Response model is shown in Figure 14. The increase in oxidized proteins activates NF‐kB. Low levels of ATP consumption decrease mTOR and mitochondrial respiration, but increase autophagy and glycolysis.

14. Bionet Adaptive Response model output (A Kriete, et al., 2010)

The Adaptive Response model also shows more linear decline in energy than the vicious cycle model, which is consistent with the overall linear decline theme noted earlier.

Transcription factors and gene expression candidates

Given the gene expression data from the Methods section, a transcription factor analysis was conducted to determine if there were major pathways activated in organelles other than the mitochondria. The primary focus of the analysis has been to look for pathways which are activated based on changes in gene expression. Another approach is to look for candidate genes which have a large number of tetracycline‐ responsive element (TRE) promoters involving the pathway of interest, and possibly identify a candidate biomarker for aging. This approach is based on work such as the summary by (Johnson, 2006) where biomarkers have been identified to track "proteins

that change expression or in some way correlate with chronological age."

Given a list of 384 genes with 182 identifiable TREs (developed by others in the research team), the procedure in Appendix E was followed to determine which genes are statistically relevant to insulin, mitochondrial, or lysosomal pathways. The procedure

first identified candidate genes, then did linear regression analysis against NF‐kB

expression levels to keep only genes which correlate to NF‐kB.

The gene candidates are summarized in Table 6. Two genes are based on association with lysosomal pathway, none were associated with insulin pathways, and the rest are

associated with mitochondrial pathways.

This analysis confirms that the effects of aging are primarily seen in mitochondria, with lysosomal processes also affected. This is consistent with the pathways identified in the

Adaptive Response model focusing on mitochondrial respiration and autophagy.

6. Aging biomarker candidates based on transcription factor analysis Accession No. Name Associated with NM_000032 ALAS2 Mito NM_001688 ATP5F1 Mito NM_004162 RAB5A Lyso NM_005391 PDK3 Mito NM_006477 RASL10A Lyso NM_015700 HIRIP5 Mito NM_017609 C10orf92 Mito NM_032549 IMMP2L Mito NM_032857 LACTB Mito

Conclusion from the Adaptive Response Model

The Adaptive Response model shows that the addition of negative feedback loops to the

Vicious Cycle model produces a decrease in mitochondrial respiration, and an increase autophagy and glycolysis, all consistent with gene expression data from human fibroblasts. Furthermore, the model demonstrates that linear decline in ATP consumption and a limited increase in ROS are predicted, which are also consistent with

gene expression data and the former with linear decline observed in hundreds of physiological parameters and organ systems.

POPULATION STUDIES "No one wants to die. Even people who want to go to heaven don't want to die to get there. And yet death is the destination we all share. No one has ever escaped it. And that is as it should be, because death is very likely the single best invention of life. It is life's change agent. It clears out the old to make way for the new." Steve Jobs, 2005

While most of the discussion so far is at the cellular level, it is important to consider the impact of aging on the body as a whole, as measured at the population level. The objective of this section is to make connections between the observations made at the cellular level with demographic‐scale data. This section will discuss the physiology of aging and key efforts to model it such as the Gompertz curve and linear decline, then discuss mortality rate behavior and investigate a new parameter called the residual.

The concept of linear decline will be taken to a viability model, which matches mortality

data better than the Gompertz curve when the concept of serial linear decline is introduced.

Physiology of aging

The physiology of aging humans has been studied extensively at the somatic level.

Work such as the Gompertz model, the "Health, Aging and Body Composition Study"

(ABC study) and measurement of linear decline in gross physiological parameters have documented the effects of aging at the tissue level and up.

The Gompertz Model

Study of the death rate with age shows a log‐linear behavior with age, in humans from roughly age 25 to age 85. This behavior was first described mathematically by the

Gompertz curve. (Guess & WITTEN, 1988; Weitz & Fraser, 2001; Witten, 1986)

Equations for the Gompertz curve have been developed for various species, and generally differ for males and females.

The mortality rate is given by m(t) = A*exp(Gt). Let MRDT = ln(2)/G = Mortality Rate

Doubling Time, and IMR = Initial Mortality Rate at puberty = A. For humans IMR=0.0002 and MRDT = 8 yrs, and t is the age in years. (E. J. Masoro, 1995) This gives us m(t) =

0.0002 exp(t*ln(2)/8) = 0.0002 exp(0.0866434 t) where ‘t’ is the age in years.

ABC studies

The ABC studies (Fried, et al., 2006; Maraldi, et al., 2006 ) examine the effects of aging on specific aspects of the body, such as kidney function, cardiac events, alcohol consumption, and many others. These studies typically examine hundreds of test subjects and follow them for long periods (years) to determine if certain physical or physiological characteristics impact the long term health of the subjects. For example,

(Maraldi, et al., 2006 ) concluded that "Light to moderate alcohol consumption was associated with significantly lower rates of cardiac events and longer survival, independent of its antiinflammatory effect."

Aging and Disease

Some diseases have a higher incidence with increasing age, so they have been statistically grouped into age‐dependent and age‐related diseases. Based on death rates from disease being similar to the age‐specific death rate, we can identify which diseases are age‐dependent. (Pletcher & Geyer, 1999) They are acute myocardial infarction,

ischemic heart disease, cerebrovascular disease, type II diabetes, osteoporosis,

Alzheimer's disease, and Parkinson's disease. Weaker connections to age‐specific death rate are considered age‐related diseases, namely multiple sclerosis, ALS, gout, peptic ulcer, and most cancers except prostate cancer (E. J. Masoro, 1995).

Diseasome

This investigation examined whether there is a coincidence between genes changing expression with age and known genetic mutations involved in disease. We therefore used data from the human disease network, or diseasome, which was assembled to identify genes which, when mutated, have been identified with causing specific diseases. (Goh et al., 2007) For example, Acromegaly has been associated with

mutations in the genes GNAS (Entrez ID 2778) and SSTR5 (6755).

The preliminary list of genes up‐ or down‐regulated with age were cross‐referenced with the diseasome using the data structure shown in Figure 15 and described in more detail in Appendix F. The gene expression data identified genes by their accession numbers

(NM_xxxxx). In contrast, the diseasome uses Entrez ID numbers to identify genes.

[disease] [S4] protein-protein Disease Gene PK disease_ID PK Entrez_ID name [S2] name class symbol degree size class-degree [S3] degree size no_of_classes

[bipartite] [bipartite] [S1]

Chromosome bipartite

PK OMIM_ID PK newkey

Chromosome disease_ID Entrez_ID

15. Diseasome data structure mapping This is an entity relationship diagram, where the labels on each relation are the data tables from (Goh, 2007; Goh, et al., 2007) used to map those relations.

The DAVID tool was used to translate between these identifiers. Used the Database for

Annotation, Visualization and Integrated Discovery (DAVID) tool4 to translate gene

expression data from NM identifiers (e.g. REFSEQ‐MRNA) to Entrez IDs

(ENTREZ_GENE_ID). DAVID was also used to translate gene symbols (NFKB1, NFKB2 and

RELA) to their NM and Entrez identifiers for humans.

Figure 16 shows the data structure used in Microsoft Access 2003 to extract data. The

disease ID, Entrez ID, and Accession numbers were used for primary keys across these data tables.

4 http://david.abcc.ncifcrf.gov/conversion.jsp

16. MS Access query for mapping diseasome to gene expression data

This analysis identified 119 diseases, based on 81 genes. Of these 81 genes, 22 genes were down‐regulated, and 59 up. Nine of these 119 diseases are strongly associated with increased age including:

 Cardiomyopathy  Dilated_cardiomyopathy_with_woolly_hair_and_keratoderma  Diabetes_mellitus  Cancers o Colon_cancer o Leukemia o Gastric_cancer o Non‐Hodgkin_lymphoma o Sarcoma,_synovial

o Pituitary_tumor,_invasive

Notice that these conditions are all included in the age‐related or age‐dependent diseases according to (E. J. Masoro, 1995). This illustrates why it is so hard to isolate healthy aging processes from diseases associated with aging ‐ they affect the same pathways in many cases. Our experimental approach uses cells in quiescence to silence pathways that are part of normal cell metabolism, making it easier to find pathways associated with aging.

Linear decline

The decline of a wide range of physiological parameters with age has been measured, and found to be a linear decline in most cases. Shock’s work in the 1950’s and 1960’s is best known for this (E. J. Masoro, 1995; Shock, 1957, 1967).

Shock (Shock & Yiengst, 1955) focused on respiratory measurements in males, and found that:

 There was no change with age in respiratory rate, ventilation volume, tidal volume, or pulse rate.  There was a rise in %O2 expired air and a decrease in %CO2 (Table 7) The data given by Shock were converted into the percent change in that parameter per

decade, relative to the estimated value at age 30 since the Strehler data later starts at age 30. The Slope, Constant, and R^2 are from linear regressions in Microsoft Excel.

7. Rates of linear decline per (Shock & Yiengst, 1955) CO2 BMR heat elimination O2 uptake production cc/min cc/min cal/sq m/hr %O2 %CO2 Constant 216.69 266.65 41.02 17.294 3.129 Slope ‐0.890 ‐1.089 ‐0.121 0.013 ‐0.011 R^2 0.966 0.962 0.966 0.991 0.964 % change per decade relative to age 30 ‐4.69 ‐4.65 ‐3.23 +0.75 ‐4.09

In (Shock, 1967) he tries to show that the 'rate of aging' is connected to the slope of the

Gompertz curve. In his Figure 4B he is inconsistent in citing his own work ‐ it's unclear if the top curve is from 1850 or 1900. His Figure 5 shows a linear regression for cardiac

output versus age, but the equation for the curve isn't given. At age 20 I estimate the regression line to be at 6.7 l/min; at age 80 I estimate 3.5 l/min. This gives a slope of

(3.5‐6.7)/(80‐20) = ‐0.0533 l/min*yr. The estimated value at age 30 is 6.7 ‐ 10*0.0533 =

6.2 l/min. Hence as a percent change per decade relative to age 30, cardiac output decreases by ‐0.0533/6.2*10*100 = 8.6%/decade.

Shock (1967) also cites the famous Strehler chart (Figure 17) showing the percent loss of various capacities relative to age 30.

17. Measurements of decline with age (Strehler, 1959)

Of these quantities, we have already assessed BMR, which we predicted would have a

value at age 90 of 100 ‐ (90‐30)/10*3.23 = 80.6% which is quite good agreement.

The renal measures are somewhat variable relative to each other ‐ to assess renal output use the GFR, which would be about 60% at age 85. This leads to a percent decrease per decade of (1‐.6)*100/(85‐30)/10 = 7.3% per decade.

Finally the (Sehl & Yates, 2001) report cites linear loss rates from 445 variables as an average of 0.65% per year, hence 6.5% per decade. Broken down by the thirteen systems examined, we can add their data to the Shock and Strehler data to produce a summary of percent change in physiological behavior per decade (Table 8).

8. Summary of Percent Loss due to Aging per decade for various organ systems or characteristics Quantity or System Percent loss per decade Source %O2 expired -0.8 (Shock, 1955) Respiratory rate 0 (Shock, 1955) Ventilation volume 0 (Shock, 1955) Tidal volume 0 (Shock, 1955) Pulse rate 0 (Shock, 1955) BMR heat production 3.2 (Shock, 1955) CNS 3.4 (Sehl, 2001) Musculoskeletal 3.6 (Sehl, 2001) Circulatory-hematopoietic 4.0 (Sehl, 2001) Renal 4.1 (Sehl, 2001) %CO2 expired 4.1 (Shock, 1955) CO2 elimination 4.7 (Shock, 1955) O2 uptake 4.7 (Shock, 1955) Integumentary 5.2 (Sehl, 2001) Chromosomal structure and function 5.4 (Sehl, 2001) Gastrointestinal 6.0 (Sehl, 2001) Endocrine (non-reproductive) 6.3 (Sehl, 2001) Average of 445 variables 6.5 (Sehl, 2001) GFR (renal) 7.3 (Strehler, 1959) Respiratory 8.4 (Sehl, 2001) Cardiac output 8.6 (Shock, 1967) Thermoregulatory 9.5 (Sehl, 2001) Immunological 11.0 (Sehl, 2001) Autonomic immune 11.9 (Sehl, 2001) Endocrine (reproductive) 12.8 (Sehl, 2001)

Some studies have also tried to account for circadian variation in parameters, such as

(Zumoff et al., 1982), who examined male hormones. They concluded that "The plasma total testosterone concentration showed a slow continuous decline with age, decreasing

about 35% between 21 and 85 yr of age" but "The concentration of [gonadotropin] FSH showed a continuous linear increase with age; the level at age 85 was about 2.5 times the level at age 21." This example highlights that the concept of 'linear decline' with age doesn't necessarily mean everything literally decreases with age ‐ some parameters can increase linearly.

Stochastic component studies

Given the foundation of linear decline from both empirical measurements and simulation results from the Adaptive Response model, can we develop a mortality rate model that is consistent with typical real world data?

The Weitz & Fraser model

Each mortality rate curve has some variability between genders and from one country to another. Can we connect this to the stochastic component in equation 1 of (Weitz &

Fraser, 2001)? Their equation for the viability v at time t+1 was

v(t+1) = v(t) ‐  + *chi(t) (Equation 1, (Weitz & Fraser, 2001))

where  is a constant drift, analogous to the rate of linear decline

 is the standard deviation of stochastic fluctuations, and

chi(t) is an uncorrelated Gaussian random variable with zero mean and unit

standard deviation.

The constant drift term  corresponds here to the slope of the linear regression in log(mortality rate) versus age. Can equation (6) and some stochastic measure of our data be used to find some analogy to (or refinement of) the *chi(t) term?

In order to assess the magnitude of the stochastic term, examine several possible measures to pick the most meaningful one.

The standard errors of the mortality rate linear regressions show about 5‐6% of the average value, as shown in Table 9. Females show a steeper slope and lower Constant term, which is consistent with their lower mortality rate and longer life expectancy.

9. Regression parameters by gender For linear regression of log(mortality rate) = Slope*age + Constant for six countries MALES average st dev stdev/average Slope 0.0410 0.0025 0.062 Constant ‐4.40 0.22 ‐0.049 R^2 0.998

FEMALES average st dev stdev/average Slope 0.0440 0.0025 0.057 Constant ‐4.82 0.22 ‐0.045 R^2 0.994

In contrast the range of residuals for each age shows an average value of 0.12 +/‐ 0.04, as shown in Figure 18. While the range of residuals also appears periodic, it doesn't have any correlation to the mean value of the residuals (R^2 = 0.033). Since the mean

residuals pass through zero, the range divided by the mean isn't a meaningful metric either.

Range of Residuals 0.2000 0.1800 0.1600 0.1400 0.1200 0.1000 0.0800 0.0600 0.0400 0.0200 0.0000 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

18. Range of Mortality Rate Residuals for each Age Mean range is 0.12 +/‐ 0.04

Hence the best measure of the magnitude of stochastic behavior appears to be the ratio of standard deviation/mean, which gives us a magnitude of about 5‐6%.

Implementation of Weitz & Fraser viability equation

The next step is to construct a random walk following the equation of Weitz & Fraser

(Weitz & Fraser, 2001). Based on the viability equation, define parameters in a Matlab model (Appendix H‐1).

viable = viable ‐ eps + sigma*(rand()‐0.5) Equation (2)

In this model, define the viability for one life starting at 1.0, and trace viability in 0.1 year time increments until death occurs when viable <= 0.0. Repeat for many lives, and plot a histogram of deaths in five‐year intervals, to mimic the WHO data.

The standard number of lives per simulation was set at 50,000 after it was determined that the histogram was essentially identical to that for 1,000,000 lives (Figure 19.)

Count for 50,000 lives Count for 1 million lives 10000 200000 9000 180000 8000 160000 7000 140000 6000 120000 5000 100000 4000 80000 3000 60000 2000 40000 1000 20000 0 0 5 152535455565758595105115125 5 152535455565758595105115125

19. Demonstrating that N=50,000 lives and N=1 million lives have very similar histograms for the Weitz & Fraser simulation.

Analysis of Weitz & Fraser viability equation

A wide range of variations on the Weitz & Fraser equation was tried in order to improve agreement with actual mortality rate data, which is linear on a log‐linear scale

(log(mortality rate) vs age).

The first linear mortality curve came from a case where eps and sigma both behave linearly. The slope of linear decline, eps, increased linearly from 0.00005 to 80 times that value at age 100, while the magnitude of the stochastic component (sigma) started at 0.10 and linearly descended to 0.20 of that value. The result is shown in Figure 20.

While this gives a linear mortality rate curve in the region of interest (circa age 30 to

100), it doesn't correspond to any known relevant physiological data.

20. Weitz & Fraser equation with 80x linear increase in slope (eps), and 5x linear decline in stochastic component (sigma).

The concept of linear decline with age is a central theme of decades of observation

(Shock, 1957) as noted previously, so based on that the value of slope was fixed (eps = constant). A wide range of variations on the behavior of sigma were tried.

Based on the work of (Lu & Pan, 2004), an increase in sigma between ages 40 and 70 was tried, resulting in the Figure 21. Lu & Pan noted that variability of gene expression was increased between those ages. Here the value of 'decline' means the factor of sigma between ages 40 and 70 is 1.5, and the factor is 1.0 otherwise. This step function increase in sigma produces a clear step function spike in mortality rate, verifying a key

observation from the Weitz & Fraser model ‐ an increase in sigma (stochastic component) increases the mortality rate.

21. Weitz & Fraser model with sigma increasing in a step function from 0.1 to 1.5 times that between ages 40 and 70. Notice the corresponding step increase in mortality rate.

Gene Expression Variability

To help determine if changes in the stochastic component were justified based on changes in gene expression variability with age, a brief study was done.

Bahar (Bahar, 2006 ) looked for signs of stochastic gene expression with age in mouse hearts as a result of somatic DNA damage. He found gene expression "heterogeneity was significantly elevated at old age." Housekeeping and heart‐specific genes were more variable in expression with age, however the COX mitochondrial genes and some proteases were not.

Golden (Golden, 2004) studied individual gene expression of wild type and daf‐2 mutant C. elegans. Hints at (Herndon, 2002) being a source for stochastic aspects of nematode aging. "A generalized linear model (GLM) detected no global trend in the data towards increased variance in gene expression with age. ... To identify any genes for which the variance in expression values differed across time points, we applied a

Bartlett test to the data. Only one gene was identified in each genotype: for N2 this gene was T12A2.3 (a translation initiation factor), whose variance in gene expression peaks at 14 days." Gene expression measurements were taken at ages 4, 9, 14, and 19 days. Given the life expectancy of the species, this would hint at agreement with increased gene expression in midlife for humans.

Herndon (Herndon, 2002) examined the mobility and aging characteristics of C. elegans, such as the development of sarcopenia. While not commenting on variability from one specimen to the next, they noted that "Our observations raise the possibility that many genes expressed at the end of the reproductive period might continue to be expressed long into the lifespan" and "biosynthesis might be poorly regulated during post‐ reproductive life so that a ‘left‐on’ profile of gene expression could endure. Consistent with this, no major changes in C. elegans proteins resolved on two‐dimensional gels occur over time."

Lu (Lu & Pan, 2004) was the basis for our saying that gene expression increases variability between ages 40 and 70, then decreases. The study was for human brain samples. Their plots of percent intact DNA versus age support the notion of a plateau in ability up to about age 60. "The young adult and extreme aged human populations are

relatively homogeneous in their gene expression patterns in prefrontal cortex. However, the middle age population between 40 and 70 years of age exhibits much greater heterogeneity."

Petropoulos (Petropoulos, 2001) looked for changes in gene expression in mice which could lead to accumulation of oxidized proteins with age, with homology to human and

bovine aging. They focused on PMSR expression in the kidney, liver, and brain of mice

at ages 9, 18, 24, and 26 months. Their quantified Western blots show no consistent trend in uncertainty for protein levels with age, relative to the 9 month values.

Raj (Raj & van Oudenaarden, 2008) looked at the effects of stochastic gene expression on cellular functions. For example, "When the transcription rate is high, variability in protein levels is low (A), but when the transcription rate is lowered and the translation rate is raised, gene expression is far noisier (B), even at the same mean, as shown in

Ozbudak et al. (2002)." They address negative and positive feedback loops explicitly.

They cite (Bahar, 2006 ) and (Newlands, 1998, not cited).

Roth (Roth, 2002) looked for the "Influence of age, sex, and strength training on human muscle gene expression" however it only identifies genes differentially expressed between 'young' and 'old' groups and does not quantify the uncertainty in that expression. They do note however that "high interindividual variability is common in skeletal muscle array experiments, which can obscure general patterns of expression"

Zahn (Zahn et al., 2005) presents AGEMAP, a "Gene Expression Database for Aging in

Mice." Their goal is to "compare gene expression profiles for aging between different tissues in order to identify common aging biomarkers." They maintain "there is little in

common between aging expression profiles across different human tissues. However, a small amount of overlap was found involving six genetic pathways that showed similar age regulation among the kidney, skeletal muscle, and brain" Their data for 16 organs is at http://cmgm.stanford.edu/~kimlab/aging_mouse/. The article is at http://www.plosgenetics.org/article/info%3Adoi%2F10.1371%2Fjournal.pgen.0030201

This could be used to assess variability across the 5 male and 5 female samples. For example the Muscle data set gives "Expression data are log2 transformed and normalized by using a Z‐transformation, as explained mathematically in Cheadle et al.

(2003)" which is citing (Cheadle, Vawter, Freed, & Becker, 2003).

The conclusion from this gene expression variability study was that, depending on the animal model and organ selected, a wide range of rules for changes in gene expression variability with age could be justified.

Changes in Stochastic Component

Can changes in the stochastic component affect the mortality curve?

Based on the previous section, comparing several variations on the Matlab model of

Fraser and Weitz & Fraser's viability equation. For this sensitivity study, ignore the runs with increasing slope (eps) and consider only fixed eps. Use the baseline value of eps=0.0015 throughout. Therefore the only parameter under investigation is the magnitude and time change of sigma, the stochastic component.

 Sigma = 0 is a trivial case, since the model becomes deterministic  Sigma = constant

 Sigma declines exponentially according to an equation of the form EXP(‐const*age)  Sigma declines linearly, until reaching a minimum value at age 100, and stays constant after that.  Sigma declines according to the exponential decline, then rises exponentially late in life (the bathtub curve). A constant is added to the bathtub curve to prevent trivially small sigma in midlife.  Then compare these mortality rate curves to the aging death rate extracted from the USA Vital Statistics (4/9/11), per Appendix G‐3. The result in Figure 22 shows that the effect sigma has on the curve is minimal. Only the

fixed sigma curve is noticeably different at low ages, and none of them are very close to the actual aging death rate.

From these models of the stochastic component, we can conclude:

 A high sigma value (magnitude of the stochastic component) produces a wide dispersion of the death rates.  A low sigma value produces a deterministic death rate. Figure 22 shows that, contrary to expectations, a linear decline in viability with age does not produce a mortality rate curve similar to real world data, regardless of the variations in the stochastic component.

22. Log(mortality rate) versus age for various Weitz & Fraser models, compared to the aging death rate extracted from the USA vital statistics.

Changes in life expectancy

An underlying assumption for the previous analysis was that the life expectancy was constant for all generations of people. However life expectancy in the USA and other industrialized countries has risen substantially in the last century, as shown in Figure 23.

Taking this into account, each 5‐year cohort of lives were tracked using fixed eps and sigma values, to see what effect the overall mortality rate in 2005 would be. For example, the cohort born in 1930‐1934 has a life expectancy of 59.2 years, which corresponds to an eps value of 0.1 years/e0 = 0.001689. That cohort's number of deaths in 2005‐2009 were predicted, and used to find the mortality rate contribution for those deaths. The net result from this approach is shown in Figure 24.

Life Expectancy (yrs) (USA, all races & sexes) 80

40 1900 1920 1940 1960 1980 2000

23. Life expectancy in the USA since 1900 Based on National Vital Statistics Reports such as NVSR Volume 58, Number 19 (final data for 2007, Table 8) Notice that 1950 is an inflection point, with much faster gains in life expectancy before that.

0.5 0 ‐0.5 ‐1 ‐1.5 ‐2 variable e0 ‐2.5 e0=fixed ‐3 ‐3.5 ‐4 ‐4.5 0 20 40 60 80 100 120

24. log(mortality rate) versus age for variable and fixed birth life expectancy (e0)

Figure 24 shows that the variable life expectancy produces a sharp increase in mortality rate for people born before 1950 (hence age 55+ in 2005), but does not help make the mortality rate curve more linear, as is desired.

Longitudinal Study of Mortality Rates How do we know that the patterns observed aren't just due to major environmental factors, such as war, epidemic, etc.? Examine one country across three sets of measurements to look for drift of the mortality curve with time.

 Pick Spain as the country of interest, since it displays well behaved trends with clear peaks, and see if the peaks move laterally from one data set to the next.  Data sets from WHO are available for 1990, 2000, and 2008, so do residual analysis for those dates. The log(mortality rate) data is plotted in Figures 25 and 26. Notice there seems to be some downward movement of the curves, indicating improved mortality rates especially for children and young adults, but no lateral translation.

Linear regressions were run for ages 30 to 100, and the results are shown in Table 10.

10. Linear regression results for Spanish people in 1990, 2000, and 2008. Case m‐1990 f‐1990 m‐2000 f‐2000 m‐2008 f‐2008

R^2 0.9951 0.9912 0.9977 0.9888 0.9988 0.9895

Slope 0.03777 0.04453 0.03789 0.04456 0.04054 0.04554

Constant ‐4.027 ‐4.736 ‐4.105 ‐4.819 ‐4.345 ‐4.954

0.0 ‐0.5 ‐1.0 ‐1.5

‐2.0 m‐1990 ‐2.5 m‐2000 ‐3.0 m‐2008 ‐3.5 ‐4.0 ‐4.5 0 20406080100

25. Mortality rates for Spanish males in 1990, 2000, and 2008.

0.0 ‐0.5 ‐1.0 ‐1.5

‐2.0 f‐1990 ‐2.5 f‐2000 ‐3.0 f‐2008 ‐3.5 ‐4.0 ‐4.5 0 20406080100

26. Mortality rates for Spanish females in 1990, 2000, and 2008.

The residuals were calculated, and are shown in Figures 27 and 28. If the data was drifting to the right because of environmental factors, one might expect parallel curves, with 1990 data on the left and 2008 data on the right. If life expectancy is improving overall, then earlier data (1990) should have a higher residual in middle ages, and lower mortality rate in advanced age (i.e. more people die young).

These residual analysis results seem mixed with respect to the influence of environmental factors.

 In Figure 27, the men's residual minimums seem to drift in proportion to the date of the data, e.g. they occur at ages 45, 55, and 65. However the peak late in life only drifts about five years, from age 85 to 90. o The men's residuals do not show a clear pattern for the magnitude of the minimum or maximum.  In Figure 28 between ages 65 and 85, the curves are clearly drifting to the right with time, but with far less magnitude than the time difference between data sets (the drift is about five years, but the data covers an 18‐year time span). The data for ages below 60 do not appear to have a clear drift trend. o The women's residuals show a clear decreasing trend for the minimum, and a slight increase in the maximum late in life.

0.20

0.15

0.10 m‐1990 0.05 m‐2000 m‐2008 0.00 30 40 50 60 70 80 90 100 ‐0.05

‐0.10

27. Residuals for Spanish males for 1990, 2000, and 2008

0.25 0.20 0.15 0.10

0.05 f‐1990 0.00 f‐2000 ‐0.05 30 40 50 60 70 80 90 100 f‐2008 ‐0.10 ‐0.15 ‐0.20 ‐0.25

28. Residuals for Spanish females for 1990, 2000, and 2008

The life expectancy at birth (e0) for the time periods of interest are given in Table 11.

This confirms the earlier supposition that life expectancy is increasing for males and

females.

11. Life expectancy at birth for Spain (e0, years) 1990 2000 2008

Males 73.3 75.8 77.7

Females 80.4 82.7 84.3

Finally, examine the relationship between the regression slopes and Y‐intercepts

(constants) for these cases. They are plotted as Constant versus Slope in Figure 29 for males and females. The Constant is monotonically decreasing for each data set, so the top point is 1990 and the bottom point is 2008.

In Figure 29 there doesn't appear to be a clear trend in the regression parameters, other than the slope is increasing with time, and the Y‐intercept Constant is decreasing. This trend is consistent with the increased life expectancy (as the slope of log(mortality rate) versus age increases, the mortality rate at low ages decreases), but provides no other insight.

‐4 ‐4.1 ‐4.2 ‐4.3 ‐4.4 ‐4.5 m‐Const ‐4.6 f‐Const ‐4.7 ‐4.8 ‐4.9 ‐5 0.035 0.04 0.045 0.05

29. Residual linear regression Constant versus Slope for 1990, 2000, and 2008.

Conclusion of Longitudinal Study

In conclusion of this part of the analysis, there seems to be no clear sign of environmental factors biasing the residual analysis. Most of the trends observed in residual versus age can be explained by the increase in life expectancy over time for an industrialized country.

Serial Linear Decline

Given that linear decline in viability with age does not produce agreement with known mortality rates, we looked for other possible hypotheses. One can use an energy turnover argument to provide the first basis for the concept defined here as "serial linear decline”, which is later extended by a multicomponent network model.

Conservation of energy argument

What if we base the measurement of 'viability' on the energy available to the body, namely through oxygen delivered by the cardiopulmonary system? The basis for this concept is that every system in the body depends on the Krebs cycle to create ATP, and therefore the amount of work the body can do (a possible measure of its viability) is

directly proportional to the rate oxygen delivered to its cells. The form for this analysis is a simple conservation of energy analysis.

Assume we start with a 30‐year‐old white male subject, who has 100% of normal cardiac output and 100% of normal lung gas exchange efficiency. The impact of aging on this subject in this model, based on the linear decline results given earlier, could be shown in

Figure 30 and Table 12.

We'll assume to account for cardiac output only once, for the ventricles, although it's possible that atrial output is also reduced. The key output from this model is the volume of fully oxygenated blood output from the heart, since that corresponds to the amount of energy available to the body.

30. Simple compartment model for conservation of energy analysis

12. Rates of linear decline in cardiopulmonary systems Pathway Rate of linear decline (%/decade) Comments 1. Pulmonary arteries None Needed for conservation of mass in the model. 2. Pulmonary veins O2 uptake, 4.7% 3. Veins None Needed for conservation of mass in the model. 4. Arteries Cardiac output, 8.6% Key output

The net result (called 'O2 output') in Figure 31 is not quite linear, and also shows a stronger slope of decline than either of the inputs.

100 90 80 70 Lung output 60 Cardiac output 50 y = 0.004x2 ‐ 1.5725x + 143.54 O2 output 40 R² = 1 Linear (O2 output) 30 20 y = ‐1.0471x + 128.58 Poly. (O2 output) R² = 0.9941 10 0 30 40 50 60 70 80 90 100

31. Oxygen output to the body versus age

Notice that the linear regression for O2 output is a good fit, but the quadratic regression is exact (R^2=1). This shows that the cumulative effect of multiple linear declines in the body can result in a net effect that is NOT linear! The mathematical basis for this is straightforward. The linear decline in cardiac output is being multiplied by the reduction in lung efficiency because there is less blood available, and that blood has a lower percentage of oxygen than normal. In percentages, this result is based on the following:

O2 output = Cardiac output * O2 uptake = (100‐4.7*(age‐30)/10)(1‐.0086*(age‐30)/10) = (100‐0.47(age‐30))(100‐0.86(age‐30) = (114.1‐0.47*age)(125.8‐0.86*age) O2 output = 14,353.78 ‐ 157.252*age + 0.4042*age^2

In the spreadsheet for Figure 31, one variable was in percentages and one not, which is

why this is different from the regression formula shown by a factor of 100.

Effect on somatic viability

Given this possibility of some number of organ systems linearly declining, AND feeding their linear decline into the next system, what effect does this produce on viability at the somatic level? Since the non‐zero rates of linear decline are within a factor of two from the mean value of 6.5% per decade, we can use this as the typical rate of linear decline for some number of systems 'n'. The net effect on viability with age for various values of 'n' is given in Figure 32.

The Weitz & Fraser model discussed earlier uses the rate of decline of viability, so take

the derivative of the viability equation in Figure 32 with respect to age, and then take its

inverse to get the slope of decline for the Weitz & Fraser model.

 Slope of decline = eps*n*(1 ‐ const*age)^(1 ‐ n) where 'const' is the rate of decline per year, 'n' is the number of serial declines in the system, and eps is now a scaling factor Preliminary analysis (Figure 33) showed that n=3 and n=4 both gave excellent linearity for the mortality rate curve.

1.00 0.90 0.80 0.70 N=1 0.60 N=2 0.50 N=3 0.40 N=4 0.30 0.20 N=5 0.10 0.00 0 20406080100

32. Viability versus Age for various values of 'n' Viability = (1 - s*age)^n with s = 6.5% per decade

0.0

‐0.5

‐1.0 n=1 MR ‐1.5 n=2 MR ‐2.0 n=3 MR ‐2.5 n=4 MR n=5 MR ‐3.0 n=7 MR ‐3.5

‐4.0 30 40 50 60 70 80 90 100

33. Log(mortality rate) versus Age for various N values of serial linear decline Rate of linear decline 6.5%/decade. On this basis, dismiss the N=1, 2, 5, and 7 cases.

Using a fixed sigma value of 0.05, the cases for serial linear decline with N=3 and N=4 were optimized (Table 13) to give the best linear mortality rate with age, and most

closely match the slope of a log‐log plot (log(mortality rate) versus log(age)) to real world data which suggests that a log‐log mortality rate versus age slope of about 4.0 to

4.2 matches a wide range of mammals.

13. Best fit cases for N=3 and N=4 serial linear decline. Eps = 0.00012 and sigma = 0.05 for both Case N=3 N=4

Rate of linear decline 6.0%/decade 4.5%/decade

meanlife = 99.1991 meanlife = 87.6586

minlife = 22.7000 minlife = 19.3000

maxlife = 140.3000 maxlife = 138.3000

liferange = 117.6000 liferange = 119

The mean lifespan is slightly higher for the N=3 case, but both are very linear from age

30‐90. The N=3 case gives a slightly more realistic histogram.

Table 14 compares the linear regression coefficients for the N=3 and N=4 serial linear decline models to real world data from the 2007 National Vital Statistics reports

(counting only deaths due to aging, see Appendix G‐3 for details), and WHO data for males in the USA from 2008 (all causes of death).

14. Regression coefficients for serial linear decline models and real world data Based on linear regressions from ages 30‐90. N=3 N=4 NVS aging only WHO 2008m slope for log‐linear 0.031 0.031 0.033 0.033 R^2 log‐linear 0.961 0.949 0.990 0.999

slope for log‐log 4.028 4.115 4.113 4.232 R^2 log‐log 0.996 0.992 0.976 0.973

Figures 34 and 35 give the log‐linear and log‐log plots comparing the data in Table 14 with NVS and WHO data. The raw magnitudes of the data are slightly off, but the linearity and behavior are otherwise in excellent agreement.

0.0

‐0.5

‐1.0 N=3 ‐1.5 N=4 NVS aging only ‐2.0 WHO 2008m ‐2.5

‐3.0 30 40 50 60 70 80 90

34. Log-linear plot comparing the best serial linear cases to real world data. log(mortality rate) versus age

0.0

‐0.5

‐1.0 N=3 ‐1.5 N=4 NVS aging only ‐2.0 WHO 2008m ‐2.5

‐3.0 1.5 1.6 1.7 1.8 1.9 2.0

35. Log-log plot comparing the best serial linear cases to real world data log(mortality rate) versus log(age)

Conclusion for serial linear decline

Overall both the N=3 and N=4 serial linear regressions provide excellent agreement with linearity and slope to real world mortality rate data. This produces an interesting possibility that both modes are occurring in the body, and therefore we can't tell which is a better fit for observed mortality data. This shows that the serial linear

decline model is a viable way to connect the linear decline observed and measured since

the 1950's in organ systems with the Weitz & Fraser model of viability and concepts of feedback loops modeled at the cellular level, and show that they can map to mortality

data at the population level.

Mortality rates versus age

The death rate curve differs by gender, and changes over time and location, and generally resembles a bathtub curve, as discussed earlier under Reliability modeling.

Figure 36 shows the death rates for males in the United States in the years 1900 and

1996.

36. Deaths rates for males in the USA in 1900 and 1996.

United States

US Census data was obtained for death rates by single year age. (Census, 2004) The death rate is defined5 for a given age as the number of deaths per 1000 people.

As shown in Figure 37, the death rate reaches a minimum around age 10 or 11, and doesn’t settle into a log10‐linear pattern until about age 30. From age 30 on, an exponential increase in death rate was seen. However slight perturbations about the

5 Based on http://www.biology‐online.org/dictionary/Mortality_rate

97 exponential trend were seen, as shown in Figure 38. These perturbations formed the basis for subsequent investigation.

Expected Death Rate per 1000 people

2.00

1.50

1.00

0.50 Log(total) Log(male) 0.00 Log(female)

Log(death rate) Log(death -0.50

-1.00

-1.50 0 102030405060708090 Age (yrs)

37. Death rate by age in the USA for 2000 (Appendix G-1)

Regression of male and female death rates, ages 30-99

3.00 male y = 0.0368x - 1.0667 2.50 2 R = 0.9975 2.00 logmale 1.50 logfemale 1.00 Linear (logfemale) Linear (logmale) 0.50 Log10(death rate) Log10(death

0.00

-0.50 female 30 50 70 90 y = 0.0403x - 1.4812 R2 = 0.9977 Age, yrs

38. Death rate versus age for the USA, 2000 Notice that the data points oscillate above and below the linear regression lines.

To investigate these perturbations, the residual between the log‐linear regression and the actual death rate was calculated, as shown in Figure 39. The residual is defined as:

Residual = actual death rate – estimated death rate

Figure 39 shows a surprisingly cyclical behavior, with a period on the order of 60 years.

It ends with a strong downturn in death rate, which agrees with observations of a plateau in death rate at ages 90+ (Vaupel et al., 1998; Weitz & Fraser, 2001). This also agrees with the Gompertz limitation of being valid up to age 85. The question is, what

happens above age 85 to produce this change in behavior away from Gompertz? That remains an area for further investigation.

To determine if this cyclical residual is a fluke, death rate data for other industrialized countries were obtained from the World Health Organization (WHO).

Residuals of log(death rate) by age

0.10

0.05

Rmale 0.00 Rfemale estimated -0.05 Residual = actual - -0.10 30 40 50 60 70 80 90 100 Age

39. Residual between regression and actual death rates, USA 2000

Analysis of mortality data from WHO

The WHO life tables for 2008 are the primary source for this analysis (Appendix G‐2).

The age‐specific death rate nMx is the mortality rate used. Mortality rate data for the

USA, Germany, and Japan were extracted from the life tables, and the base 10 log taken to get the data in Figures 40 and 41. Genders are plotted on separate Figures to emphasize regional differences. Figures 40 and 41 show some differences between countries, but overall a log‐linear increase in mortality rate from about age 30 up.

100

40. Log of mortality rates versus age for males from selected countries, 2008 WHO data

41. Log of mortality rates versus age for females from selected countries, 2008 WHO data

Running linear regressions from age 30 to 100 using SPSS version 18, we obtain the

parameters in Table 15. Visually, all of the data have periodic movement about the

101 regression line, though some more strongly than others. The most pronounced case is shown in Figure 42, for females in Japan. In general, females had more variation about the regression line than males. All of the t parameters are far above the 1.96 minimum value for 95% level of confidence, and p < .001 (p < 1E‐13 is the weakest significance, for females in Japan).

15. Linear regression of log(mortality rate) versus age log(mortality rate) = Slope*Age + Constant Slope and constant are given by (value +/‐ std err) Case R2 Slope Constant Weakest |T| > M ‐ USA .998 .03660 +/‐ .00050 ‐4.031 +/‐ .034 73 F ‐ USA .997 .03950 +/‐ .00056 ‐4.392 +/‐ .039 70 M ‐ Japan .998 .04068 +/‐ .00044 ‐4.417 +/‐ .030 91 F ‐ Japan .987 .04263 +/‐ .00135 ‐4.819 +/‐ .093 31 M ‐ Germany .999 .04100 +/‐ .00036 ‐4.380 +/‐ .025 114 F ‐ Germany .996 .04517 +/‐ .00075 ‐4.862 +/‐ .052 60

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42. Linear regression for females in Japan

Calculate the residuals which are defined as the difference between the observed data and the linear regressions for each case.

 Residual = Actual value ‐ linear regression estimate = actual ‐ (slope*age + const)

The residuals for males and females are shown in Figures 43 and 44. From them we can

make some observations:

 All of the data shows a strong dip in mortality rate around age 65‐70

 Germany has the most pronounced mortality rate plateau for both sexes, and

USA the least.

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43. Residuals for males for ages 30-100 Residual = (Actual mortality rate) ‐ (linear regression estimate)

44. Residuals for females for ages 30-100

 Males have more variability in mortality rate with age compared to the linear

model from Gompertz

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 The magnitudes of the residuals differ by a factor of two ‐ the females' residual

data has twice the range of the males'

Repeat the analysis for three other countries, keeping Northern European ancestry, and avoiding as much influence from WWII and other outside events. Pick Sweden,

Switzerland, and Spain. The log of mortality rates are given for males and females in

Figures 45 and 46. Spain appears to have a higher mortality rate for males, otherwise the curves for males and females appear very similar.

45. Mortality rates for males in Switzerland, Sweden, and Spain

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46. Mortality rates for females in Switzerland, Sweden, and Spain

Again doing regression analysis for ages 30‐100 and extract the coefficients, this time using the Excel functions RSQ, SLOPE, and INTERCEPT. These functions were verified to

produce the same results given by SPSS. The coefficients are given in Table 16.

16. Linear regression parameters in Switzerland, Sweden, and Spain Case m‐Switz f‐Switz m‐Swe f‐Swe m‐Spain f‐Spain R2 0.9986 0.9947 0.9981 0.9983 0.9988 0.9895 Slope 0.04312 0.04563 0.04380 0.04565 0.04054 0.04554 Constant ‐4.603 ‐4.969 ‐4.627 ‐4.917 ‐4.345 ‐4.954

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The residuals for males and females are shown in Figures 47 and 48. The trend is very clear from about age 65 up, with less pronounced variation from the Gompertz curve for males at lower ages.

47. Residuals for males in Switzerland, Sweden, and Spain

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48. Residuals for females in Switzerland, Sweden, and Spain

Discussion of Residual Data

Mortality data were obtained for six countries from WHO life tables for 2008 for males and females. The countries are the USA, Japan, Germany, Switzerland, Sweden, and

Spain. All of these countries report 100% completeness for this level of mortality rate data. The log of each mortality rate was taken, and linear regression was done on log(mortality rate) versus age for ages 30 to 100 (Table 17). The regressions had an average slope of 0.0425 +/‐ 0.0029 standard deviation, Y‐intercept constant of

‐4.6 +/‐ 0.3, and an R2 value of 0.996 +/‐ 0.004.

 log(Mortality rate) = Slope*Age + Constant

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17. Linear regression summary for all cases m‐USA f‐USA m‐Japan f‐Japan m‐Germany f‐Germany Slope 0.03660 0.03950 0.04068 0.04263 0.04100 0.04517 Constant ‐4.031 ‐4.392 ‐4.417 ‐4.819 ‐4.380 ‐4.862 R2 0.9976 0.9974 0.9985 0.9871 0.9990 0.9964

m‐Switz f‐Switz m‐Swe f‐Swe m‐Spain f‐Spain Slope 0.04312 0.04563 0.04380 0.04565 0.04054 0.04554 Constant ‐4.603 ‐4.969 ‐4.627 ‐4.917 ‐4.345 ‐4.954 R2 0.9986 0.9947 0.9981 0.9983 0.9988 0.9895

The residual was calculated as the difference between the actual mortality rate, and that predicted by the linear regression. Residuals are plotted by gender in Figures 49 and 50.

 Residual = Actual value ‐ linear regression estimate = actual ‐ (slope*age + const) Some observations about Figures 49 and 50.

 Notice that the magnitude of the Y axis is very different between males and females. Males have a total range of residuals of about 0.17, whereas females have a residual range of about 0.35.  Males show a clear residual trend from about age 50 up, whereas females show a clear trend throughout the entire age range (30‐100).  All cases have negative residual for ages 65 and 70, and positive residuals for ages 85 and 90.  The mortality rate plateau is very clear for most cases, with a few notable exceptions (males and females in the USA, and females in Japan).

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0.12 0.10 0.08 Rm‐USA 0.06 Rm‐Japan 0.04 Rm‐Germany 0.02 Rm‐Switz 0.00 Rm‐Swe ‐0.02 30 50 70 90 Rm‐Spain ‐0.04 ‐0.06 ‐0.08

49. Mortality rate residuals for males in six countries

0.20

0.15

0.10 Rf‐USA 0.05 Rf‐Japan 0.00 Rf‐Germany 30 50 70 90 ‐0.05 Rf‐Switz Rf‐Swe ‐0.10 Rf‐Spain ‐0.15

‐0.20

‐0.25

50. Mortality rate residuals for females in six countries

All of the residual data is shown in Figure 51. The trends seem clear from about age 50 up, only the amplitude of the curve varies from country to country.

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0.20 Rm‐USA 0.15 Rf‐USA 0.10 Rm‐Japan 0.05 Rf‐Japan 0.00 Rm‐Germany 30 50 70 90 ‐0.05 Rf‐Germany Rm‐Switz ‐0.10 Rf‐Switz ‐0.15 Rm‐Swe ‐0.20 Rf‐Swe ‐0.25

51. Mortality rate residuals for males and females in six countries Data symbols omitted for clarity.

Based on Figure 51, find the mean mortality rate residual curve and use that as the midline for modeling this behavior as a modification of the Weitz & Fraser equation.

Figure 52 shows the mean mortality rate residuals, averaged for males and females over six industrialized countries. From age 50‐100 this is displaying sinusoidal behavior.

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Mean Mort Rate Residual 0.080 0.060 0.040 0.020 0.000 ‐0.020 30 40 50 60 70 80 90 100 ‐0.040 ‐0.060 ‐0.080 ‐0.100

52. Mean mortality rate residual versus age

Based on Figure 52, if we assume a sinusoidal form and assume the max and min values are at ages 65 and 90, the equation is:

Resid = A*sin(B*age+C) + D

Where A, B, C and D need to be determined from the data. Assume the min and max values are at ages 65 and 90 to find B and C.

 At age=65, sin(B*age+C)=‐1 hence B*65+C = 3pi/2 (1)  At age=90, sin(B*age+C)=+1 hence B*90+C= 5pi/2 (2) Rewrite (1)

 C = 1.5pi ‐ 65B (3) Substitute (3) into (2) to get

 90B + (1.5pi ‐65B) = 5pi/2 = 2.5pi

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 25B = 2.5pi ‐ 1.5pi = pi  B = pi/25 Put this into (3) to get

 C = 1.5pi ‐ 65B = 1.5pi ‐ 65(pi/25) = (1.5 ‐ 65/25)pi = ‐1.1pi Hence the equation appears to be of the form

 Resid = A*sin(age*pi/25 ‐ 1.1pi) + D Which is valid for Age from 50 to 100. Now use the magnitude of the max and min to get A and D.

 At Age=65, Resid = ‐0.085 so ‐0.085 = ‐A + D (4)  At Age=90, Resid = 0.049 so 0.049 = +A + D (5) Add equations (4) and (5) to get

 2D = ‐0.036  D = ‐0.018 From (4) we get A = D + 0.085 = 0.067

So a rough curve fit to Figure 52 for ages 50 to 100 is

Resid = 0.067*sin(age*pi/25 ‐ 1.1pi) ‐ 0.018 (6)

This is plotted in Figure 53, which shows remarkably good agreement with the data, and

provides a mathematical fit for the mortality rate plateau after age 90.

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0.080

0.060

0.040

0.020 Mean Mort Rate 0.000 Residual 0 20406080100120 ‐0.020 Equation (6)

‐0.040

‐0.060

‐0.080

‐0.100

53. Mean mortality rate residual and estimated curve fit. Equation (6) is Resid = 0.067*sin(age*pi/25 ‐ 1.1pi) ‐ 0.018

Compare WHO and Census Mortality Data

This is a brief sensitivity study to determine if there is a significant difference between mortality data in one year increments of age, versus that given in five year increments.

The US Census provided data in one year intervals, whereas the data reported to WHO was in five‐year increments. The value of residuals were calculated for both sources for

males and females in the USA as of the year 2000 (Figure 54). While the higher resolution of the Census data is apparent, they both show the same trends for the residuals. As a result we conclude that the low resolution of WHO data is not a significant impediment to making meaningful trend analyses.

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0.08

0.06

0.04

0.02 m‐Census 0.00 f‐Census ‐0.02 m‐WHO f‐WHO ‐0.04

‐0.06

‐0.08 30 40 50 60 70 80 90 100

54. Year 2000 mortality rate residuals for males and females, comparing Census and WHO data

Residuals for serial linear decline model

Given this concept of residuals to compare mortality models and data to log‐linear regressions, evaluate how the serial linear decline models compare to the Gompertz curve and actual mortality data. Figure 55 compares residuals for the best two versions of the serial linear decline model (N=3 and N=4 for the power) with the mortality curve

predicted by the exponential Gompertz model. The serial linear decline models both have the opposite second derivative from the Gompertz model.

However the Figure also shows residuals for WHO data (for all causes of death) and NVS data cited earlier, which isolates causes of death due to healthy aging. The WHO data

shows similar behavior as the Gompertz curve, but on a much smaller magnitude scale.

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Of particular interest is the NVS data, which follows the serial linear decline model closely until age 50, then drops off more quickly.

While not conclusive, it may be significant that the behavior of mortality rate residuals due to healthy aging does not follow the same shape as mortality rate residuals due to

all causes of death.

0.3

0.2

0.1 N=3 0 N=4 Gompertz ‐0.1 NVS aging only ‐0.2 WHO 2008m

‐0.3

‐0.4 30 40 50 60 70 80 90

55. Residuals for serial linear decline models (N=3 and N=4), the Gompertz curve, NHS data for mortality due to aging, and WHO mortality curves for deaths due to all causes

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Conclusion for mortality data studies

The mean mortality rate for six industrialized countries exhibits deviations from an exponential increase in mortality rate (here defined as 'residuals') which appear to be sinusoidal from age 50 to 100 and approximately follow equation (6). This sinusoidal behavior could be a contributing factor to the mortality rate plateau observed above age 90, and suggests a second mortality rate plateau around age 60.

This analysis points to a possible fundamental difference between behavior of residuals associated with healthy aging, and those associated with all causes of mortality. The serial linear decline model more closely resembles residuals from healthy aging than the

Gompertz curve.

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GENERIC NETWORK MODELS The Weitz & Fraser models were based on using linear decline with a stochastic component. To get from that to the serial linear decline model, a conservation of energy argument was used. It is desirable, however, to find a better explanation of the connection between cellular level linear decline and power law behavior at the population level mortality rate. The goal is to find a mechanistic explanation of the power law behavior seen in serial linear decline. What if that linear decline framework were applied to a cellular level model of generic species, to see if it can predict the

change in resilience of a typical biochemical network as it ages?

Network Model Mechanisms

Generic models (C. Mathieu & Peter, 2010) are a valuable tool to "translate the generic mechanism into a set of coupled nonlinear ordinary differential equations" (Csikasznagy,

Battogtokh, Chen, Novak, & Tyson, 2006).

To apply them here three models were developed, first in CellDesigner (Funahashi,

Morohashi, & Kitano, 2003; Kitano, 2003), then exported into Matlab and modified extensively (Appendix H‐2). The three models are:

 A baseline bowtie network model (Figure 56), representing a typical biochemical pathway which depends on a critical component in the middle of the pathway such as NF‐kB. The purpose of this structure is to mimic scale‐free networks which are common in biology (Csete & Doyle, 2002 ; Jeong, Tombor, Albert, Oltvai, & Barabasi, 2000). "The topology of genetic and metabolic networks is organized according to a scale‐free distribution, in which hubs with large numbers of links are present." (Ferrarini, Bertelli, Feala, McCulloch, & Paternostro, 2005)

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 An inhibited bowtie network model (Figure 57), identical to the first model except a feedback loop was added to represent a downstream species providing gene expression changes which are passed upstream. This is by analogy to the feedback loops seen earlier affecting biosynthesis and other cell functions.  A regular network model (Figure 58), which lacks the critical component feature but is otherwise similar to the other models in terms of total number of species, number of input and output species, etc. The purpose of this model is to provide comparison for the importance of network topology on resilience.

Tier 1

Tier 2

Tier 3

Tier 4

Tier 5

56. The Baseline Bowtie network model

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All three network models are open systems ‐ energy flows in through input species

(nodes s1 through s6), flows through the model, and leaves via output species (nodes s14 through s19). As a result, the models will all reach homeostasis eventually, as the quantities of each species settles into some balance point depending on the relative reaction rates. This is designed to simulate initially perturbing the system by setting artificial species quantities of all 1.0, then seeing how long it takes for the system to return to homeostasis.

57 The Inhibited Bowtie network model

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Since all species usually reach some homeostatic value eventually, the key measure for this model's response to perturbation is defined as the resilience measure, which is the time at which the quantity of each species changes less than some small amount from the previous time step. The resilience measure is averaged not only over the 100 simulations per run, but also over each group of species defined as Tiers in each network model.

Since reaction rates slow linearly with age, we expected the resilience measure to go up with age, since it should take longer for the network to reach homeostasis.

58 The Regular network model

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Network Model Descriptions

Key assumptions and definitions in the creation of these models were:

 All species start at a quantity of 1.0 units.  Reaction rates may decline linearly with age, starting at age 30  The initial rate for each reaction may change from its nominal value by a factor of sigma*(a random number from 0 to 1). Typical sigma values from 2 to 6 mean that each reaction rate may range from zero to 2 to 6 times its nominal value.  To average out the stochastic effects, a Monte Carlo (Chatterjee, 2005; Marino, Ray, Kirschner, & Hogue, 2008) approach was used, with 100 runs of each simulation executed, and the results averaged.  Simulations of 4000 time units were executed, with intervals of 1.0 time units between numeric integration time steps.  Numeric integration was used to allow reaction rates to change with time, specifically the ode45 solver in Matlab.  The following parameters are set in the file 'netmodel.m'. o To allow for species which reach steady state very slowly, set the time

limit for each case (endtime) to 4000 units regardless of age. Use a time

increment (deltatime) of 1.0 time units.

o Keep the resilience parameter fixed at deltamin = 0.0000001 (1E‐07). This is the small amount described previously as "the quantity of each species changes less than some small amount from the previous time step."

o Use linear decline parameter (linear) of 0.010. For contrast, a linear decline rate of 0.005 will be used to assess its impact on selected ages.

 The command line syntax is netmodel(ncases,sigma,age)

o Use 100 cases per run (ncases) as the default, but try 1000 cases a few times for comparison.

o Examine ages from 30 to 110 in 10 year increments (age).

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o Let the stochastic component (sigma) increase linearly with age (Table 18).

18. Linear increase in stochastic component 'sigma' with age Age Sigma 30 2.0 40 2.5 50 3.0 60 3.5 70 4.0 80 4.5 90 5.0 100 5.5 110 6.0

Each execution of a run (made up of 100 cases, 4000 time units each) took about 3 minutes using Matlab R2009b on an Intel Xeon E5506 processor running Windows 7

Home Premium with 6 GB of RAM.

Network Model Results

Baseline Bowtie network model

If we look at the mean resilience measure versus age, it might help to view the average resilience of each tier of the network model, defined as follows:

 Tier 1 is nodes s1 to s6 (i.e. the top row of the model)  Tier 2 is nodes s7 to s9  Tier 3 is node s10  Tier 4 is nodes s11 to s13

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 Tier 5 is nodes s14 to s19 (i.e. the bottom row of the model)

The mean resilience for the baseline case is shown in Figure 59. Tier 5 doesn't show any strong trends, but tiers 3 and 4 are increasing with age.

59. Mean resilience for each tier of the bowtie model (time units vs age)

Inhibited Bowtie network model

The inhibited bowtie network gave the following mean resilience measure as a function of age and tier in the model (Figure 60). Notice that tiers 3 and 4 rise sharply in resilience measure with age, corresponding to a slower response to a perturbation.

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60. Mean resilience measure for Inhibited Bowtie model

Regular network model

The inner tiers 2‐4 are different for the regular model, here we have

 Tier 1 is s1 through s6  Tier 2 is s8 and s9  Tier 3 is s7, s10, and s13  Tier 4 is s11 and s12  Tier 5 is s14 through s19

The result for the regular network model is shown in Figure 61. The increase in resilience measure at high ages is weaker, and the relative resilience of each tier stays consistent with age.

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61. Mean resilience measure for the regular network model, as a function of age and tier

Sensitivity Studies using the Baseline Bowtie model

Number of cases per run

The number of cases per run is 100 in the baseline. See if using 1000 cases produces significantly different results, for ages 30 and 90 (Figure 62).

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62. Comparison of mean resilience measure between 100 and 1000 cases each (e.g. 30/100 is age 30, with 100 cases per run)

This shows that there is some variation, up to about 100 time units, but on the overall time scale the difference is not large.

Effect of Linear Decline Rate

All the previous runs in this analysis used linear=0.010 for the rate of linear decline with age. Now halve that rate and see what effect it has on the resilience parameter.

Measure resilience of the baseline bowtie network model from ages 30 to 110 in 20 year increments, using the baseline 100 cases per run.

So how did the reduction in the rate of linear decline affect the resilience of the bowtie network model? Figure 63 shows its effect on mean resilience for each tier.

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63. Mean resilience of baseline bowtie model, halving the rate of linear decline at various ages 30/10 means age 30, decline=0.010; 90/05 means age 90, decline=0.005

Comparing each pair of clusters, it appears that the mean resilience of Tier 5 at each age appears to be declining when the rate of linear decline is reduced. Examining this further, the mean resilience of Tier 5 and the overall mean resilience of each age are shown in Figure 64.

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64. Percent changes in mean resilience for Tier 5 and for all Tiers, as a function of age When the rate of linear decline was halved from 0.010 to 0.005

Figure 64 shows that halving the rate of linear decline has significant and nonlinear effects on resilience of the system.

No linear decline, vary sigma

Changes in linear decline were examined for various values of the stochastic parameter sigma; so examine in more detail the effect of changing sigma with no linear decline effect. Using the baseline bowtie model, eliminate linear decline by choosing age=30, and vary sigma from 2 to 6. For a given sigma value, the initial rate for each reaction will

be randomly selected between 0% and sigma*100% of the nominal value, so larger values of sigma tend to produce higher reaction rates on average. The result is shown in

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Figure 65. As sigma increases, the mean reaction rate increases, and therefore the resilience measure decreases because the network reaches homeostasis sooner.

65. Mean resilience measure for no linear decline, and varying sigma from 2 to 6 by Tier of the baseline bowtie network model

If we compare this study to the equivalent baseline case when linear decline is being used (linear=0.010) we get Figure 66. Linear decline increases the resilience measure, which means the system is slower to reach homeostasis. That makes sense: slower reaction rates make the system respond slower, increasing the resilience measure.

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1200

1000

800

600 Baseline No linear decline 400

200

0 30 40 50 60 70 80 90 100 110

66. Overall mean resilience measure versus age, comparing the baseline (with linear decline) to the same sigma values without linear decline.

Repeatability Study

There is some variation in output from one run to the next, as the 1000‐case study hinted. To better quantify this, take a typical case (age 70 for the baseline bowtie model), run it six times and evaluate descriptive statistics for the resilience measure

(Table 19). Other than larger variability seen in Tier 1, a standard deviation of about 50 time units or less seems to be typical.

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19. Mean resilience measure for six identical runs (age 70, sigma 4, baseline bowtie model) Mean Std dev Min Max Tier 1 683 158 467 865 Tier 2 617 47 573 696 Tier 3 632 32 588 678 Tier 4 781 46 725 856 Tier 5 1079 27 1048 1120 Overall mean resilience 803 51 727 863

The six cases are shown in Figure 67 to show variability for identical inputs.

67. Mean resilience measure for six identical runs, by tier of the baseline bowtie network model at age 70

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Discussion of Network Models

Comparing mean resilience measure of all three network models over all species as a function of age, we have Figure 68.

68. Mean resilience measure of all three network models as a function of age

The parallel motion of the baseline and inhibited bowtie models is surprising, however it appears that the addition of a feedback loop slows reaching homeostasis.

The regular model shows a different trend in resilience with age, mostly contrary to the movement of the bowtie models, however the magnitude of changes is marginally large

enough to be significant.

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Conclusion from the network models

The baseline bowtie model shows that the resilience of middle tiers of the network (the core of the network, if you will) get weaker with age. The inhibited bowtie model showed consistently higher resilience measure than the baseline bowtie model, giving the surprising result that the addition of a feedback loop slowed the response time of the network. Furthermore, the regular network model gave largely the same resilience with age, with a slight increase for large ages (100+).

The sensitivity studies showed that:

 Halving the rate of linear decline with age gave significant and non‐linear effect on the resilience of the system.  Increasing the stochastic component for a fixed value of linear decline produced decreased mean resilience measure, since the larger stochastic component produces higher mean reaction rates, producing faster system homeostasis.  Similarly, eliminating linear decline of reaction rates with age reduced the mean resilience measure, because of higher mean reaction rates.  Checking for consistency from one run to the next showed that differences in mean resilience measures on the order of 50 to 100 time units are not significant. In summary, we have identified linear decline with age, increasing variance with age and

the network topology beyond a concatenated serial component “energy model “as

parameters which may shape mortality rates. The baseline bow‐tie network, the

inhibitory network and the regular network all show a trend indicating resilience to have

a minimum at middle ages. We hypothesize that this behavior may be at the root of

134 fluctuations seen in residuals as shown in Figures 29 and 100. These are second order contributions that offer an opportunity for future investigations.

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CONCLUSIONS AND OUTLOOK

The conclusions from this research are presented, followed by the outlook for future work in this area, and publications associated with it.

Conclusions

The hypotheses examined in this thesis were to integrate key data of organelle function, pathways, and their activity during normal (healthy or “successful”) aging, with the help

of experimentally available data, into a conceptual, hybrid whole cell model, to simulate the aging process, and to further connect those trends seen on the cellular level to mortality rate and viability models at the demographic level.

To establish the foundation for this research, this thesis reviewed the major theories of

aging (Alexeyev, et al., 2004 ; Weinert & Timiras, 2003), divided into categories of energy consumption, evolutionary, programmed, damage accumulation (Lesnefsky &

Hoppel, 2006), and network theories of aging (Jameson, 2004; T. Kirkwood & Kowald,

1997). These theories and models capture some aspects or property of the complexity

of aging, and in an attempt to find a common property that would allow connecting and converging some models across scales, from cell to the population level, motivated the discussion of the linearity theme of this thesis, Existing theories of aging were found to be lacking in recognition of the linear decline associated with aging, and did not appreciably account for the presence of negative feedback loops that mediate the impact of ongoing damage at the cellular level. To narrow the scope exclusions for the assembly of cellular models were meticulously defined. Subsequently, common

136 approaches for computational biology were discussed, specifically differential equations, fuzzy logic, Bayesian logic, Boolean logic (Albert, 2004), reliability modeling

(L. A. Gavrilov & Gavilova, 2004 ), and multi‐scale modeling (Crampin, Smith, & Hunter,

2004 ; Moore & Noble, 2004). Fuzzy logic modeling was outlined as the most promising approach to assemble a whole cell model and, if compared to Boolean logic, provided more continuous and semi‐quantitative results.

The physiological mechanisms of aging were defined, including the generation of reactive oxygen species as part of normal mitochondrial respiration (Lesnefsky &

Hoppel, 2006), the role of mTOR in autophagy (Liu et al., 2009), the retrograde response

(R. A. Butow & Avadhani, 2004 ), inflammation (Ahmad, et al., 2009), anti‐oxidants such as SOD, and other mechanisms. The use of a systems approach for modeling aging was justified based on the interactions among organelles and pathways, both at the cellular level and across different somatic physical scales.

Specific computational models were developed for the Vicious Cycle and Adaptive

Response models (Alberto, et al., 2006; A Kriete, et al., 2010) to demonstrate that experimental data can support clear sets of positive and negative feedback loops that reflect the cells' ability to compensate for damage and failed cellular mechanisms with increasing age (Booker, Bosl, & Kriete, 2009; Booker, Yalamanchili, & Kriete, 2008;

Clearfield, Booker, & Kriete, 2010). While fuzzy logic modeling has been used for biological systems before (Center & Verma, 1998; Du, et al., 2005; Franco‐Lara &

Weuster‐Botz, 2007; Bahrad A. Sokhansanj, et al., 2004), this was the first application of fuzzy logic modeling to aging. Extensive documentation of the Bionet (Bosl, 2007) fuzzy

137 logic application's Java source code was developed to help improve our ability to use it effectively. This helped identify the methodology and algorithms used for the cellular models, contributing to better understanding of this open source software application.

The use of the Fuzzy Logic approach helped make it feasible to include both specific species such as ADP and ATP in the models, but also represent markers, more complex entities and phenotypical states of organelles such as biosynthesis and oxidative phosphorylation. The vicious cycle model demonstrated that uncontrolled increases in

ROS lead to a sharp decline in biosynthesis, and would most likely would result in

cellular apoptosis. By extending the VC to an adaptive response (AR) model shows that

NF‐kB plays a critical role in cellular survival via negative feedback loops that down‐ regulate mitochondrial respiration, ROS, and biosynthesis (A Kriete, et al., 2010). The work of (Adler, et al., 2007) demonstrates a way to validate the role of NF‐kB in aging, through experimental NF‐kB inhibition. Furthermore, there is experimental evidence for the activity Mtor and its effect on lifespan, using pharmacological inhibition [cite see our

PLOS paper], also consistent with the AR model.

A sensitivity study of the AR model identified key reactions, which highlight the importance of those three aspects of the model. Key observations from the AR model are that an increase in oxidized proteins activates NF‐kB; while low levels of ATP consumption decrease mTOR and mitochondrial respiration, but increase autophagy and glycolysis. The Vicious Cycle model was well established in the literature, however the Adaptive Response model suggests a new perspective in our understanding of aging mechanisms, and represents a major insight into cellular survival mechanisms to

138 prevent the buildup of ROS with age. Analysis of gene expressions identified nine candidate biomarkers for aging, involving mitochondrial or lysosomal processes also represented in the AR model.

Cross‐referencing gene expression with the human disease network (Goh, et al., 2007) resulted in identification of nine diseases, all of which are age‐related or age‐dependent

diseases. This helps explain why the pathways associated with healthy aging have been so elusive ‐ the same pathways are also involved in aging‐related diseases, so it wasn't until this work looked at gene expression from quiescent fibroblasts that those pathways could be identified. Gene expression studies have been done extensively in

the context of aging (Fraser, 2005; Miller et al., 2002; Shmookler Reis & Ebert, 1996), however the data used here are derived from quiescent cells.

The trends in cell model predictions were used to establish connections to somatic‐level linear decline. The Gompertz mortality model (Guess & WITTEN, 1988; Rose, Rauser,

Mueller, & Benford, 2006) and linear decline with age (Sehl & Yates, 2001; Shock, 1984) were used to establish the context for understanding death rates for males and females in six industrialized countries. In all cases, a periodic trend was observed around a log‐

linear regression of death rates from age 30 to 100. The 'residual' was defined as the difference between the actual mortality rate and the linear regression prediction. This mortality rate residual is a novel measure. From age 50 to 100 the residual demonstrated a clear mean period of about 50 years. This shows not only the well‐ known mortality rate plateau around age 90 (Vaupel, et al., 1998; Weitz & Fraser, 2001),

139 but indicates a second plateau at age 60. This second mortality rate plateau has not been identified before.

The mortality rate data was connected to linear decline via the Weitz & Fraser viability equation (Weitz & Fraser, 2001), which modeled a linear decline in individual viability with time in addition to a stochastic component. A Matlab model of viability was developed to simulate 50,000 random lives and calculate the resulting mortality rate curve. This viability model is novel. Even though linear decline has been noted at levels of scale from cellular to organ systems (as noted above), a constant linear rate of

decline in the Weitz & Fraser model did not produce realistic mortality rate curves.

Studies of the variability of gene expression with age were conducted to see if the stochastic component could alter the mortality rate curve appreciably, but no clear trends in variability with age were reported (Bahar, 2006 ; Chowers, 2003; Zahn, et al.,

2005), and a variety of stochastic component variability profiles all had minimal effect on the shape of the mortality rate curve. A longitudinal study for one country showed that there was no clear influence of environmental factors on the mortality rate

residuals, beyond the well known general trend of increasing life expectancy in industrialized countries (Kinsella & Gist, 1998; T. B. L. Kirkwood, 1996 ; K. Thomas,

2010).

In order to explain real world mortality rate data (CDC, 2007), a novel approach was added to the Weitz & Fraser model. The "serial linear decline" model was based on the

observation that multiple organ systems, all of which are each undergoing linear decline, feed their outputs into each other, producing an overall rate of decline which is

140 closer to power law models (L. A. Gavrilov & Gavrilova, 2003) or a polynomial‐based rate of somatic decline. This model blends linear decline and power law models in a novel way, and shows that this approach gives more realistic results than traditional

Gompertzian mortality models (cited above).

Finally, the last piece of this thesis looked at generic open network models of biological species interacting. Two models used bow‐tie structures, which are emulating typical scale‐free networks seen in biology (Ferrarini, et al., 2005; Jeong, et al., 2000). In contrast the third model used a more homogeneous structure with the same number of

species represented. We developed Monte Carlo simulations of these models, using

stochastic variation in the reaction rates. To measure the effect of aging, linear decline in reaction rates and linear increase in stochastic effects were used. The responsiveness of the model was measured using a novel 'resilience' parameter, analogous to the time constant of a control system (Chen, Novak, & Tyson, 2003; Novosel’tsev, 2006). These network models illustrated the effect of network topology on resilience, and showed that resilience behaves in a nonlinear manner at the system level.

This work builds on prior modeling approaches such as the MARS cellular model (Kowald

& Kirkwood, 1996) and the Weitz & Fraser viability model to integrate the concepts of linear decline with age, stochastic effects from gene expression variability, and open network systems analysis models.

A concept map of this thesis is shown in Figure 69. The presence of linear decline was well known at levels from cellular to organ systems. Here we showed that the fuzzy logic model of adaptive response was consistent with linear decline, was in agreement

141 with laboratory data, and pointed to negative feedback loops to protect cells during aging. Power laws were well known in reliability theory and aging. Here we combined the concepts of linear decline with power laws and a conservation of energy argument to produce serial linear decline, which demonstrated very good mortality rate linearity.

69. Concept map of this dissertation

Network models provided further support for the idea of serial linear elements in a bowtie network combining to produce outputs which are nonlinear. Finally analysis of mortality rate data against purely exponential Gompertz decline produced the

142 observation of residuals which exhibit periodic behavior, and predict a new mortality rate plateau around age 60. These residuals also hint that the aging mortality rate might be a better guide than the overall mortality rate for all causes.

Outlook

There are three major categories of future work in this area: Analysis of metabolic

decline in different tissue types or animal models could be performed, then compare and contrast them with the results obtained here. Corresponding computational models can be developed and refined as more data becomes available. Fuzzy logic modeling has more potential for helping to identify candidate pathways. To do so,

activation of the genetic matching algorithm in Bionet, and tailoring of the fitness

calculation to aging are good next steps.

The mortality rate plateau around age 60 warrants further investigation. It was known that the Gompertz curve wasn't valid above about age 85, but this second plateau could be a significant finding.

The network models are prime areas for further investigation of feedback loops and their effect on the resilience of biological networks. The extent to which serial linearly declining components produce nonlinear outputs could yield additional insights into the mortality rate plateaus and the mortality rate residuals. The residual concept in mortality rates can be investigated in other species, across longer time periods in humans, and in non‐industrialized countries. The categories of causes of death in the

143

NVS data can be refined, and this will help clarify how well the mortality rate due to healthy aging corresponds to the serial linear decline model.

Publications

Publications associated with this work include:

 Clearfield, D, Booker, G, and Kriete, A. (Dec 2010) A Top‐Down Whole Cell Modeling Approach of Aging. Poster presented at the Systems Biology of Human Aging (SBHA) conference, Philadelphia, PA.  Kriete A, Bosl WJ, and Booker G. (2010). Rule‐Based Cell Systems Model of Aging using Feedback Loop Motifs Mediated by Stress Responses. PLoS Comput Biol 6(6): e1000820. doi:10.1371/journal.pcbi.1000820.  Booker, G, Bosl, W, and Kriete, A. (Aug 2009) Fuzzy Logic Modeling of Stress Responses in Cell Aging. Poster and paper presented at the Foundations of Systems Biology in Engineering (FOSBE) conference, Englewood, CO.  Booker, G, Yalamanchili, N, and Kriete, A. (Nov 2008) Fuzzy Logic Model of Cellular Stress in Response to Atypical Activation of NF‐kB. Poster presented at Greater Philadelphia Bioinformatics Alliance (GPBA) Retreat, and at the Sprit of Entrepreneurship in Life Saving Solutions showcase, both in Philadelphia, PA.  A paper based on serial linear decline and the network models is in preparation.

144

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Appendix A. Aging Terminology

Key terms and concepts related to aging and mortality are defined here to ensure a common foundation upon which to discuss them. Additional resources are listed in

Appendix I.

Lifespan is the amount of time before death for an individual. Since single data points are of little interest, the median or average lifespan for a population is a measure of longevity (T. B. L. Kirkwood, 1996).

The maximum lifespan or maximum lifespan potential (MLSP) or Life span potential (LSP) attracts a lot of publicity, and is believed to be constant for a species (Troen, 2003). The

MLSP is the longest a member of a species is typically expected to live. For that reason,

MLSP “is not a definitive but an empirically recorded value, there is considerable variation in the reported longevities of mammals.” (Ku, BRUNK, & SOHAL, 1993) For examples, the MLSP for a mouse is 3.5 years; hamster, 4 years; rat, 4.5 years; guinea pig,

7.5 years; rabbit, 18 years; pig, 27 years; and cow, 30 years. Humans have an MLSP of about 120 years.

Life expectancy is the average amount of time before death occurs for some population, relative to some starting age. Life expectancy at birth is commonly used as the basis for comparison among nations; in developed nations it has gone "from about 49 years in

1900 to about 76 years in 1979" (Hayflick, 2000) and continues to rise slowly (B. L. K.

Thomas, 2008).

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Longevity describes the distribution of lifespans for some population.

Mortality rate is the rate of death occurring for some population. For example, the mortality rate can be measured for male Caucasian humans in the Unites States in some year. The mortality rate as a function of age is the death rate. The complement of the death rate is the viability curve, as shown in Figure A‐1 for various species, which gives the percent of the population still alive at some age.

Survival curves give the percent of survivors versus age, which is the same as the

viability curve. In contrast, death or mortality rate curves give the probability of death

occurring within a given age. (E. J. Masoro, 1995)

A-1. Viability curves from different model organisms have a similar, characteristic shape. Representative mortality data are shown for Homo sapiens, Mus musculus, and Caenorhabditis elegans. Two different types of aging, replicative and postdiauxic survival, are shown for S. cerevisiae. (Kaeberlein, 2001)

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Senescence is often used synonymously with 'aging' to describe something of advanced age, or the process of healthy aging.

Replicative senescence is the end of an organism's ability to reproduce. In cells it is when mitosis is no longer possible. In human females it typically refers to menopause.

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Appendix B. Scope Exclusions

This Appendix discusses factors which may influence aging, but are not specifically addressed in this research. They are included here for future work.

Gender

Gender has a well documented effect on life expectancy. Life expectancy for females is always higher than for males unless outside events intervene (war, famine, pandemic, etc.). While some of this difference is due to gender‐specific risk factors (Kinsella & Gist,

1998; Verbrugge, 1989), there is work that suggests estrogen slows aging by increasing expression of antioxidants (Borrás, et al., 2005).

Race

Race does not seem to be studied per se as a factor in the aging process. Given the level of racial intermixing in most modern societies, it would be difficult to isolate a group of test subjects racially, unless they were very geographically isolated as well. In those cases the subjects would be isolated genetically as well. Body composition studies

(Fried, et al., 2006; Maraldi, et al., 2006 ) identify differences in the aging phenotype by

race, however they do not examine causation of those differences.

Genetic traits

Genetic traits are often sought as the Holy Grail of aging. If there were only some gene we could 'fix' that would make us live forever...however these is no such gene.

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Genetic studies are often based on gene knockouts from animal models (Bartke et al.,

2001; Hekimi & Guarente, 2003; Jackson, Galecki, Burke, & Miller, 2002; Miller, et al.,

2002) to determine the pathways affected by each gene. This approach is of limited value when critical pathways are affected such as mitochondrial respiration or NF‐kB, and/or dozens of biological processes. Gene knockouts in worms and insects have produced increases in lifespan on the order of 20‐70% by affecting pathways for processing insulin, reducing oxidative stress, and others. (Bartke, 2005) Others look for evolutionary insight into the aging process. (Toussaint & de Magalhaes, 2002)

Nevertheless, attempts to find genes associated with aging continue (Capri, 2006;

Kenyon, 2010; Lewis, 2004; Nemoto, 2006; Sebastiani, et al., 2010). Sebastiani found

150 single‐nucleotide polymorphisms (SNPs) which appeared in 77% of centenarians studied.

In an attempt to isolate genetic traits of aging, identical twins have been studied for

longevity. (Bartke, et al., 2001; Karasik, et al., 2005) The heritability of survival ranges from 20‐50%, depending on the study examined. Therefore while genetics helps promote healthy long life, it isn't the root cause. This has led to examination of various cellular pathways that could be a more direct connection to successful aging.

Environmental causes

The environment causes a wide range of influences on aging. The most direct include the effect of infectious and inflammatory diseases, which encourage many diseases of old age. (Crimmins & Finch, 2006) Pollution also can affect older adults, through a

169 pathway of "external pollution sources → human exposures → internal dose → early biologic effect → adverse health eﬀects." (Geller & Zenick, 2005)

Environmental factors also include lifestyle choices, which have been examined in terms of the resulting genetic damage. (Ramsey et al., 1995)

Other environmental approaches include examination of the effects of UV light on skin aging ‐ not surprisingly from a cosmetic science journal. (Pillai, Oresajo, & Hayward,

2005 )

Diet

Diet is well known to be a significant factor in aging. Beyond the caloric restriction approach discussed later, other more specific dietary changes have been investigated.

Magnesium deficiency in rats, for example, has been shown to affect blood pressure, inflammation, and oxidant stress defenses. (Blache et al., 2006) There is also some work on the effect of 'natural' health products, and their effect on immune function and chronic diseases. (Haddad, Azar, Groom, & Boivin, 2005)

Similarly, the contents of one's diet has also been investigated, not just the calorie count. A lower‐carbohydrate "Paleolithic diet" was shown to provide health benefits compared to a high‐carb diet. (Jönsson et al., 2006)

Heavy metals

Heavy metals such as zinc (Bertoni‐Freddari et al., 2006; Frazzini, Rockabrand,

Mocchegiani, & Sensi, 2006; Mocchegiani et al., 2006; Vasto et al., 2006) and manganese (Borrás, et al., 2005) have been investigated for their connection to aging.

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Zinc is primarily examined as a dietary supplement, whereas manganese is connected to its antioxidant role in the enzyme Mn‐SOD (manganese superoxide dismutase).

Exercise

Exercise and aging studies typically focus on the effects of exercise on immune response

(e.g. the interleukin cytokines) (Arai, Duarte, & Natale, 2006; Hamada, Vannier, Sacheck,

Witsell, & Roubenoff, 2005; R Kalani, Judge, Carter, Pahor, & Leeuwenburg, 2006), oxidative stress (Bar‐Shai, Carmeli, Ljubuncic, & Reznick, 2008; Sacheck et al., 2006), or overall health (Warburton, 2006). Since our work is based on gene expression of cells sitting quietly in a dish, these works are outside the scope of our investigation.

Psychological and sociological effects

Psychological and sociological effects on aging and longevity are omitted from this study. This category includes religious beliefs, psychological stress, and neurological diseases.

Religious or spiritual beliefs are also commonly attributed to increased longevity. One survey in 2006 showed that 23% of the centenarians interviewed attributed their longevity to their faith. (Reuters, 2006) More recently the degree of 'faith' has been shown to increase with age, though its causal effect has not been proven. (Buettner,

2010)

A few people believe we die simply because we expect to. They call it the "death urge."

Therefore if we change that assumption we can live to be hundreds or thousands of years old. For example, "The belief that death is inevitable and beyond our control kills more people than all other causes of death combined. In fact, it kills approximately 2 %

171 of the entire population on the planet every year." (Orr, 2008) Such viewpoints are clearly well outside of accepted science.

Psychological stress can have a well documented impact on biological systems such as the immune response (Epel, et al., 2004; Segerstrom & Miller, 2004), so it is likely that

psychological factors are also important in aging.

While some aging‐related neurological diseases such as Alzheimer's Disease (Das &

Golde, 2006; Huang, Fowler, Xu, Zhang, & Gibson, 2005; Li et al., 2004; M. T. Lin, et al.,

2002; Nilsson et al., 1990; Pedersen, et al., 2001; Pei & Hugon, 2008; Peterson, et al.,

1986; B. L. K. Thomas, 2006; Yates, 2002) and Parkinson's Disease (Heiman, Valjent,

Santini, Fisone, & Greengard, 2009; Michel, 2006) have substantial overlap with the areas investigated here, we are not specifically trying to address them.

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Appendix C. Bionet models

This Appendix presents the Bionet data files used for the vicious cycle, retrograde response, and adaptive reponse models.

Appendix C‐1. Bionet Vicious Cycle (VC) model

For node definitions and summary of input parameters, see Appendix C‐2.

The VC input file has been abbreviated to remove extraneous reactions and nodes. This is the VC080522.net data file.

# Bionet model of Aging # Case VC - the vicious cycle # Glenn Booker 5/22/2008 # With reaction changes dated 5/4/08 from AK # and ATP quantity separated from ATP Demand # compared to RR model, remove nodes PTEN, Akt, IkBa, IkBb, NFkB, Ca, and Nucleus # ATP more inhibited nFuzzyStates 6 starttime 0.0 endtime 5.0 ntimesteps 10000

PopulationSize 1 nGenerations 1 mutationRate 0.05

Exp

# define variables to be plotted Plot ROS Plot ATP Plot ATPdemand #Plot NFkB #Plot Ca Plot ETC Plot biosynth

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# Define nodes, assuming default range of [0,1] for most, using the initial values shown # avoid initial conditions of max value, since reactions shut off (per lesson of 5/16/08) #Node Akt 0.5 # give ATP quantity a range from 0 to 100, and initial value of 1.0 Node ATP 1.0 0.0 100.0 Node ATPdemand 0.8 # biosynth covers biosynthesis processes, which burn ATP Node biosynth 0.8 #Node Ca 0.2 Node ETC 0.8 #Node IkBa 0.5 #Node IkBb 0.5 #Node NFkB 0.5 #Node Nucleus 0.5 Node Oxphos 0.8 #Node PTEN 0.5 Node ROS 0.2 Node SOD 0.5

# define reactions, using default modeling rules for each type of reactant #1 Reaction ATPdemand_Oxphos 1.0 pro Oxphos act ATPdemand #2 Reaction Oxphos_ETC 1.0 sub Oxphos pro ETC #3 ATP production is proportional to the strength of the mitochondria # weakened by slowing the reaction 5/21/08 Reaction ETC_ATP 0.1 pro ATP act ETC 0 1 2 3 4 5 #5 ROS production is inversely proportional to the strength of the mitochondria # strengthen ROS production 5/21/08 Reaction ETC_ROS 10.0 inh ETC 5 4 3 2 1 0 pro ROS #7 Reaction ROS_SOD 1.0 act ROS pro SOD #8

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Reaction SOD_ROS 1.0 pro ROS inh SOD #16 Reaction ROS_ETC 1.0 pro ETC inh ROS #18 shut off this reaction 5/22/08 to keep biosynth constant #Reaction ATP_biosynth 10.0 # pro biosynth # sub ATP #19 Reaction biosynth_ATPdemand 0.5 pro ATPdemand sub biosynth # # end of input file

Appendix C‐2. Bionet Retrograde Response (RR) model

If a retrograde response (Ronald A. Butow & Avadhani, 2004) is being activated in the cell, it should slow oxphos (oxidative phosphorylation) and increase glycolysis, in order to prevent ROS damage from accumulating, i.e. it’s a pro‐survival mechanism. The increased activity of the transcription factor NF‐kB with age is believed to be the major regulating mechanism for many intracellular processes.

The first Bionet retrograde response model is shown in Figure C‐1. The detailed inputs for it are listed later in this Appendix.

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Mitochondrial Electron Krebs Cycle Transport (Oxphos) ATP Chain (ETC) m

PTEN ROS SOD Ca2+ Calcineurin UPS

Akt IkB IkB

NF- B

Nucleus

No Down- Legend: Up- change regulated regulated

C-1. Bionet AR model (Booker, 2008)

The retrograde response model produced the results shown in Figure C‐2. Note that the

ROS level is bounded instead of continuing to the maximum level of 1.0, as it did in the

VC model. This gives semi‐quantitative agreement with gene expression data, which show ROS levels controlled with increasing age.

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NF-kB

ROS

ATP

biosynth

C-2. Retrograde Response Bionet model outputs

The Bionet Retrograde Response model produced the results shown in Figure C‐3. This shows that ROS levels increase much more sharply for the vicious cycle model, and the retrograde response model down‐regulates oxidative phosphorylation. Both of these results are consistent with reported physiological behavior.

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Behavior of Vicious Cycle (VC) and Retrograde Response (RR) Models

ATP/ OXPHOS (VC) Apoptosis X ATP/OXPHOS (RR)

NF-kB /Ca(RR)

ETC (RR) ROS(VC)

ETC (VC) RELATIVE CONCENTRATION

ROS(RR)

TIME C-3. Bionet AR Model results

More complex RR models were developed, such as one shown in Figure C‐4, however their complexity made it impractical to tune their reaction rates with experimental data.

As a result, the Bionet platform was set aside, in order to compare the fuzzy models with ones based on ODEs.

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C-4. Complex Bionet RR Model (Booker, et al., 2008)

RR Model Node Definitions The fourteen nodes are defined as follows:

 Akt

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 ATP – the level of ATP in the mitochondrion  ATPdemand – the demand for ATP creation  Biosynth – the cellular processes which burn ATP to meet various needs, e.g. respiration, movement, etc.  Ca – the calcium2+ level, and correspondingly the level of Calcineurin in the cytosol. This really represents two reactions, but both have been observed to be upregulated, so for the moment we’ll model them as one reaction.  ETC – the electron transport chain, which is mainly represented by the mitochondrial membrane potential. Mitochondrial damage is represented by reduction of the membrane potential.  IkBa – IkB and IkB make NF‐kB inert, and hence incapable of causing changes in gene expression.  IkBb  NFkB  Nucleus – the cell’s nucleus, in which changes in gene expression are made  Oxphos – the Krebs cycle for oxidative phosphorylation  PTEN  ROS  SOD – the level of SOD includes the scavengers, which inhibit or reduce the ROS level. In defining a node in Bionet, the default magnitude range for each node is [0,1], and the initial value is zero. For each simulation Case, we need to define the initial value or quantity for each node, as shown in Table C‐1. Assume the magnitude range for each node will remain the same across all simulations.

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C‐1. Initial Values and Ranges for each Node Node Range Initial Value Source Akt [0,1] 0.5 ATP [0,100] 1.0 Greco ATPdemand [0,1] 0.8 Biosynth [0,1] 0.5 Ca [0,1] 0.2 [Butow] ETC [0,1] 0.8 Greco IkBa [0,1] 0.5 IkBb [0,1] 0.5 NFkB [0,1] 0.5 Nucleus [0,1] 0.5 Oxphos [0,1] 0.8 Greco PTEN [0,1] 0.5 ROS [0,1] 0.2 Greco SOD [0,1] 0.5

The default range of six fuzzy values for the inputs and outputs for each reaction is from

0 to 1, with the centroid of each fuzzy value defined in increments of 0.2, hence the centroids are given in Table C‐2.

Reaction Definitions To model this we need fifteen reactions, which will be labeled by the reactant and product or inhibited quantity. The four types of reactants defined by default in Bionet are summarized in Table C‐3. An enzyme type (enz) also exists, but was not defined in

(Bosl, 2007).

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C‐2. Bionet Default Centroids for Reaction Input and Output Levels Input or output value Name Centroid is at 0 Zero 0 1 Very low 0.2 2 Low 0.4 3 Medium 0.6 4 High 0.8 5 Very high 1.0

C‐3. Bionet Reactant Types Reactant Type Default Comments (keyword) Stoichiometry Substrate (sub) ‐1 Is assumed to be used up in the reaction. Product (pro) +1 Is produced by the reaction. Activator (act) 0 Acts as a catalyst for the reaction, but does not change value. Inhibitor (inh) 0 Slows or prevents reaction, but does not change value.

For each reaction, we need to define the rate constant, and the role of all reactants, as shown in Table C‐4. Assume the default stoichiometry, fuzzy values, and centroids from

Tables C‐2 and C‐3 will be used. The default rate constant for a reaction is one.

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C‐4. Model Reactions Rate constants in micromolar per second. Reaction Name Rate Substrate Product Activator Inhibitor Source Const. 1. ATP_Oxphos* 1.0 Oxphos ATP 2. Oxphos_ETC 1.0 Oxphos ATP ETC 3. (removed) 4. Oxphos_PTEN 1.0 Oxphos PTEN 5. ETC_ROS 1.0 ROS ETC 6. ETC_Ca** 1.0 Ca ETC 7. ROS_SOD 1.0 SOD ROS 8. SOD_ROS 1.0 ROS SOD 9. PTEN_Akt 1.0 PTEN Akt 10. ROS_IkBa 1.0 IkBa ROS 11. Ca_IkBb 0.5*** IkBb Ca 12. IkBa_NFkB 0.5 NF‐kB IkBa Werner 13. IkBb_NFkB 0.5 NF‐kB IkBb Werner 14. NFkB_Nucleus 0.09 Nucleus NF‐kB Werner 15. Nucleus_ATP 1.0 ATP Nucleus 16. ROS_ETC 1.0 ETC ROS *** Rate is halved due to two reactions, Ca‐Calcineurin‐IkBb.

Reaction #16 was added to reflect increased ROS damages the membrane potential. ETC measures the level of damage in the mitochondria. Healthy mitochondria (ETC=1) produce lots of ATP and little ROS. Conversely, unhealthy mitochondria (ETC=0) produce little ATP and lots of ROS.

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Results Cases were run for 5 seconds of simulation, with 10,000 time steps. Execution time was a couple of seconds per case. The results are shown in the body of the thesis.

Model Details Here is the RR080522.net data file, as of 5/22/08. This is the last version described above.

# Bionet model of Aging # Case RR - the retrograde response # Glenn Booker 5/22/2008 # With reaction changes dated 5/4/08 from AK # and ATP quantity separated from ATP Demand # inhibit ATP more, and burn ROS faster nFuzzyStates 6 starttime 0.0 endtime 5.0 ntimesteps 10000

PopulationSize 1 nGenerations 1 mutationRate 0.05

Exp

# define variables to be plotted Plot ROS Plot ATP Plot ATPdemand Plot NFkB Plot biosynth Plot ETC

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# Define nodes, assuming default range of [0,1] for most, using the initial values shown # avoid initial conditions of max value, since reactions shut off (per lesson of 5/16/08) Node Akt 0.5 # give ATP quantity a range from 0 to 100, and initial value of 1.0 Node ATP 1.0 0.0 100.0 Node ATPdemand 0.8 # biosynth covers biosynthesis processes, which burn ATP Node biosynth 0.8 Node Ca 0.2 Node ETC 0.8 Node IkBa 0.5 Node IkBb 0.5 Node NFkB 0.5 Node Nucleus 0.5 Node Oxphos 0.8 Node PTEN 0.5 Node ROS 0.2 Node SOD 0.5

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#4 Reaction Oxphos_PTEN 1.0 sub Oxphos pro PTEN #5 ROS production is inversely proportional to the strength of the mitochondria Reaction ETC_ROS 10.0 inh ETC 5 4 3 2 1 0 pro ROS #6 Reaction ETC_Ca 1.0 inh ETC pro Ca #7 Reaction ROS_SOD 1.0 act ROS pro SOD #8 Reaction SOD_ROS 1.0 pro ROS inh SOD #9 Reaction PTEN_Akt 1.0 pro Akt sub PTEN #10 Reaction ROS_IkBa 1.0 pro IkBa inh ROS #11 Reaction Ca_IkBb 0.5 pro IkBb inh Ca #12 rate data for reactions 12-14 are from Werner, Science 2005 Reaction IkBa_NFkB 0.5 pro NFkB inh IkBa

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#13 Reaction IkBb_NFkB 0.5 pro NFkB inh IkBb #14 Reaction NFkB_Nucleus 0.09 pro Nucleus act NFkB #15 comment this reaction out for the VC model Reaction Nucleus_ATPdemand 1.0 pro ATPdemand inh Nucleus #16 Reaction ROS_ETC 1.0 pro ETC inh ROS #17 ATP decay removed in favor of adding biosynth process #Reaction ATP_decay 1.0 # sub ATP #18 Reaction ATP_biosynth 0.01 pro biosynth sub ATP #19 changed biosynth from sub to act on 5/22/08 Reaction biosynth_ATPdemand 2.0 pro ATPdemand # sub biosynth act biosynth # # end of input file

Appendix C‐3. Bionet Adaptive Response Model

Based on the earlier models of the Vicious Cycle (VC) and Retrograde Response (RR), Dr.

Kriete developed a detailed model of the Adaptive Response feedback loops. This was the baseline used for sensitivity studies on the effects of changing reaction rates.

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# Bionet Model # # Adaptive Response NF-kB & mTor # # Dec 28, 2009 # nFuzzyStates 6 starttime 0.0 endtime 50.0 ntimesteps 5000

PopulationSize 1 nGenerations 1 mutationRate 0.05

Exp

# Define variables to be plotted # Plot ROS # Level of free radicals Plot OXPROT # Level of oxidized proteins Plot MRSP # Mitochondrial respiration Plot ATP # ATP levels Plot Energy_tot # Total Energy turnover Plot ADP # ADP levels Plot ATPconsume # Protein Synthesis Plot ProtBiosynth # Biosynthesis activity

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Plot NFKB # NFkB levels Plot MTOR #Plot of mTor activity # # # Define nodes, start with initial condition # ATP and Biosynthesis high, ROS and NF-kB set low Node ATP 0.70 Node ADP 0.70 Node ATPconsume 0.80 Node ProtBiosynth 0.8 Node Energy_tot 0.0 Node MRSP 0.80 Node NFKB 0.07 Node MTOR 0.4 Node ROS 0.1 Node OXPROT 0.0 # # Processes # # # 01 Free radical levels # # ROS causes increase in oxidized proteins # production independent of previous protein concentration # but saturates at highest level of 6 states (5 5 5 5 5 0) at rate 0.02 # activated by ROS concentration (default = 0 1 2 3 4 5) # was 0.1 Reaction OXPROT_ROS 0.1 pro OXPROT 5 5 5 5 5 0 act ROS # Oxidation dependent on protein turnover Reaction OXPROT_Bio 0.1 pro OXPROT 5 5 5 5 5 0 inh ProtBiosynth # Lower protein output related to Biosynthesis

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# increases portion of oxidized proteins # Reaction ROS_decay 0.4 sub ROS 1 2 3 4 5 5 # NFKB activates scavengers Reaction ROS_scavenge 0.2 sub ROS 1 2 3 4 5 5 act NFKB # # # 02 Mitochondrial activity # # Damage by ROS inhibits mitochondrial respiration # # # Buildup of mitochondrial respiration # (mito membrane potential) dependent on ATP levels # # Addtl. ATP generated by glycolysis Reaction Glycolysis_ATP 0.1 pro ATP 5 5 5 5 5 0 act MTOR 5 3 0 0 0 0 # ADP consumed by Glycolysis Reaction ADP_Glycolysis 0.1 sub ADP 0 5 5 5 5 5 act MTOR 5 3 0 0 0 0 # # Remaining ADP builds membrane potential Reaction MRSP_activation 0.8 pro MRSP 5 5 5 5 5 5 act ADP # # 2nd feedback loop # # Downregulation of mitochondrial respiration by stress response # Reaction MRSP_change 0.15

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sub MRSP 5 5 5 5 5 5 act MTOR 2 1 0 0 0 0 Reaction MRSP_change 0.15 pro MRSP 5 5 5 5 5 5 act MTOR 0 0 0 1 2 3 # was 0.25 Reaction MRSP_inhibition 0.15 sub MRSP 5 5 5 5 5 5 act OXPROT Reaction MRSP_ATP 1.0 pro ATP 5 5 5 5 5 0 act MRSP Reaction MRSP_ADP 1.0 sub ADP 5 5 5 5 5 5 act MRSP # ROS related to mitochondrial activity and damage >>> was 0.2 Reaction ROS_produced 0.25 pro ROS 5 5 5 5 5 0 act MRSP Reaction ROS_produced 0.50 pro ROS 5 5 5 5 5 0 act OXPROT # ROS produced by NADPH oxidase system # through autocrine loop Reaction NADPHOXD_produced 0.1 pro ROS 5 5 5 5 5 0 act NFKB Reaction MRSP_deactivation 0.8 sub MRSP 5 5 5 5 5 5 act ATP # # # NF-kB degradation Reaction NFKB_decay 0.4 sub NFKB 0 1 2 3 4 5 # # Activation of Stress Response

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# through ROS levels and oxidized proteins (1:1) # Reaction NFKB_Stress_ROS 0.2 pro NFKB 5 5 5 5 5 0 act ROS Reaction NFKB_Stress_OXPROT 0.2 pro NFKB 5 5 5 5 5 0 act OXPROT # was 0.105 Reaction MTOR_ATP 0.10 sub MTOR 0 1 5 5 5 5 inh ATP # critical parameter ! Reaction MTOR_ROS 0.095 pro MTOR 5 5 5 1 1 0 act ROS # # Autophagy # Reaction Autophagy_OXPROT 0.15 sub OXPROT 1 2 3 4 5 5 act ATP # Reaction Autophagy_MTOR 0.5 sub OXPROT 1 2 3 4 5 act MTOR 5 4 0 0 0 0 # # 03 ER Reactions # # ATP consumption inhibited by oxidized proteins, damage to ER # # Production of ADP Reaction Biosynth_act 1.0 pro ATPconsume 5 5 5 5 5 0 act ATP # Effective Protein Synthesis Reaction ProteinSynth 0.08

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sub ProtBiosynth 5 5 5 5 5 5 inh ATPconsume # # Oxidative damage to ribosomes # Reaction Biosynth_OXPROT_inh 0.01 sub ATPconsume 5 5 5 5 5 5 act OXPROT # # Modulation of ATP consumption regulated by mTor # Reaction Biosynth_mTOR_inh 0.1 sub ATPconsume 5 5 5 5 5 5 act MTOR 5 3 0 0 0 0 Reaction Biosynth_mTOR_inh 0.1 pro ATPconsume 5 5 5 5 5 5 act MTOR 0 0 0 3 5 0 # # Biosynthesis required for upregulated inflammatory proteins # Reaction Biosynth_NFKB_inflamm 0.05 pro ATPconsume 5 5 5 5 5 5 act NFKB Reaction ATP_used 1.0 sub ATP 5 5 5 5 5 5 act ATPconsume Reaction Biosynth_ADP 1.0 pro ADP 5 5 5 5 5 0 act ATPconsume # # total accumulated energy turnover # Reaction Energy_totals 0.015 pro Energy_tot 5 5 5 5 5 5 act ATPconsume # Reaction Biosynth_consumed 1.0

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sub ATPconsume 5 5 5 5 5 5 act ADP # # end of input file

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Appendix D. Bionet Source Code Analysis

Introduction

This is an analysis of the Java source code for version 2.0 of the Bionet program, last modified on December 22, 2008, and developed under the Sun Netbeans 6 development environment. The objective of this analysis is to understand the existing

code, before improvements can be made to it, as discussed with Dr. Bosl on February 3,

2009.

The Bionet program was developed by William Bosl to perform fuzzy logic modeling of biological systems – typically via interacting pathways at the cellular level.

General Public License (GPL) version 2 or later.

General Bionet Design Characteristics

Bionet follows a typical engineering software design pattern – read data from an input file, do calculations, and show the output. More specific to its Java implementation, the following design traits are noted about Bionet.

 There is only one case where inheritance is used, namely PlotTimeSeries is a subclass of JFrame.  There are no interface methods.  There are no abstract classes.  There are no final variables (constants).  The Bionet source code is all part of one package ‘bionet’, hence a package diagram would be the same as the class diagram.

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Overall Code Structure

Code Classes Bionet consists of nine Java files, whose scope and purpose will be discussed in detail.

 Bionet.java  EvolveBionet.java  FitnessCalculator.java  Main.java  Node.java  PlotTimeSeries.java  RandomSequence.java  Reaction.java  RuleTable.java

Native and Imported Code Sources The following built‐in Java libraries are used by various modules within Bionet:

Window event handlers  import java.awt.event.WindowAdapter  import java.awt.event.WindowEvent Input and Output

 import java.io.BufferedReader  import java.io.FileInputStream  import java.io.FileNotFoundException  import java.io.FileOutputStream  import java.io.InputStreamReader  import java.io.IOException  import java.io.PrintStream

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Utilities

 import java.util.ArrayList  import java.util.logging.Level  import java.util.logging.Logger  import java.util.Random  import java.util.Vector GUI libraries

 import javax.swing.JFrame In addition, libraries are used from executable jar files jcommon-1.0.0

(http://www.jfree.org/jcommon/) and jfreechart-1.0.1

(http://www.jfree.org/jfreechart/).

 import org.jfree.chart.ChartFactory  import org.jfree.chart.ChartPanel  import org.jfree.chart.JFreeChart  import org.jfree.chart.plot.PlotOrientation  import org.jfree.data.general.DefaultPieDataset  import org.jfree.data.xy.XYDataset  import org.jfree.data.xy.XYSeries  import org.jfree.data.xy.XYSeriesCollection

Class Diagram

The basic class diagram for Bionet is shown in Figure D‐1. Some of the complexity in the

Bionet class is going to be offloaded to EvolveBionet, but that move hasn’t been

completed yet.

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D-1. Bionet Class Diagram The get and set methods are omitted, unless those are the only methods for a class. Attributes are omitted for brevity, except non‐primitive attributes. The method Bionet.readNetworkFile is the only private method; the rest are all public.

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Class Constructors

Bionet has class constructors, as summarized in Table D‐1. The main purpose of this table is to show the parameters needed for each class. Note that Node and Reaction classes use polymorphism to make the parameter lists optional.

D‐1. Bionet Class Constructors Visibility Type Class Name Parameters public Bionet (Bionet parent, String infilename, int level, String experimentFilename) public EvolveBionet () public FitnessCalculator (int iparams[], double dparams[]) public Node () public Node (int listN, boolean discrete, String na, double v, int nSets, double[] sPts, String u, int nt) public class PlotTimeSeries extends JFrame public class RandomSequence public Reaction () public Reaction (int listN, String inName, Node N) RuleTable (String rulefilename) throws FileNotFoundException, IOException

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Detailed Source Code Description

Bionet.java The Bionet class is the largest single class, with approximately 2748 physical lines of code including its methods. It defines the public class Bionet, which has the methods described in Table D‐2, sorted by Method Name. Class declarations (e.g. public class bionet) are omitted. The Methods are then described in Table D‐3.

D‐2. Bionet.java method summary Visibility Type Method Name Parameters Returns public void Bionet2Genome () public void copyGene () public void createFuzzyRules () public void createNewActiveSite () public void createNewReaction () public void genomeToBionet () public double getFitness (FitnessCalculator fc) fc.getFitnessValue() public int[] getGenome () genome public double getMutationRate () mutationRate public String getNextDataLine (BufferedReader B, String line) public int getNNodes () nNodes public String[] getNodeNames () nodeNames public int getNodeNumberFromName (String name, boolean printMessage) public int getNTimeSteps () nTimeSteps public Random getRandomSequence () new Random()

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Visibility Type Method Name Parameters Returns public int getSaveInterval () saveInterval public double[] getTime () public double[] getTimeCourseForNode (String name) public Vector getVNodes () vNodes public void initializeValues () private void readNetworkFile (String infilename) private void readNetworkFile (Vector AllLines) private void readNetworkFile_v2 (Vector AllLines) public void run () public void setAllTimeParameters (double begin, double end, int n) public void setKnockoutExperiments (String fn) public void setWholeGenome () public void timeStep () public void writeSimpleNetworkFile (String outfilename) D‐2. Bionet.java method summary (continued)

D‐3. Bionet.java method descriptions Method Name Description Bionet Class desription for the entire module Bionet2Genome Converts bionet array of reactions to a genome matching input copyGene Part of the mutation process for genetic matching algorithm createFuzzyRules Create rule cases for each reaction rate – output is a lookup table. createNewActiveSite Related to createNewReaction method. createNewReaction A mutation approach which keeps the same node, but applies a new reaction type. genomeToBionet Converts genome matching back to bionet format getFitness

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Method Name Description getGenome getMutationRate getNextDataLine getNNodes getNodeNames getNodeNumberFromName getNTimeSteps getRandomSequence getSaveInterval getTime getTimeCourseForNode Allocates a lot of RAM to do scoring of nodes. Better to write to a file, then do scoring from that. getVNodes initializeValues readNetworkFile (String infilename) readNetworkFile (Vector Huge routine which reads the network description data file. AllLines) Should put in a separate module, and add a module to read scoring rules. readNetworkFile_v2 run Runs the Main routine setAllTimeParameters setKnockoutExperiments Defines rules for genetic matching algorithm setWholeGenome Prepares for genetic matching algorithm timeStep writeSimpleNetworkFile D‐3. Bionet.java method descriptions (continued)

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The Bionet class looks for the rule file, which should be in the same directory as the source code, and be called "rulebase.txt”.

The EvolveBionet class should be extracted from Bionet.

EvolveBionet.java EvolveBionet is a smaller module, about 314 physical lines of code, whose purpose is to perform the genetic matching algorithm. As shown in Table D‐4, this module consists of

a class declaration, and the entire contents of the module is one method, “evolve”.

D‐4. EvolveBionet.java method summary Visibility Type Method Name Parameters Returns public void evolve()

The evolve method algorithm consists of the following major steps:

 Calculates fitness of each node using bionet.fitness  Calls bionet.bionet2genome, and  Silences nodes which are knocked out  Mutates them based on the getmutationrate, and genomemutation, but doesn’t mutate the best member  Does crossover using randgen and getgenome,  Computes using bionet.genometobionet and initializevalues  Runs the experiment bionet.run  Scores the nodes, and uses a bubble sort to find the best matches  Shows and plots the best members  Repeat the whole process for as many generations as specified in the data file

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FitnessCalculator.java The FitnessCalculator module exists only to return (get) the fitness array for the input parameter dparams, as shown in Table D‐5.

D‐5. FitnessCalculator.java method summary Visibility Type Method Name Parameters Returns public double getFitnessValue (fit)

Main.java This module creates the family of bionets, each member of whom is an experiment

(simulation). It is one of the larger modules, about 400 lines of code, and as shown in

Table D‐6, consists of a single method, ‘main’.

D‐6. Main.java method summary Visibility Type Method Name Parameters Returns public static void main (String[] argv)

The input String ‘argv’ is the file location for the bionet simulation parameters.

Each bionet is created using the methods bionet.genomeToBionet.

The mutation, crossover, fitness calculation, and sorting which appear in EvolveBionet also appear here. It isn’t immediately clear which set of code is actually being used.

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Node.java The class node.java is about 300 physical lines of code, and its purpose is to define the nodes used within a given parameter, and fuzzify inputs.

The centroid locations can be set using linear, exponential, or log scales (corresponding to ‘scale’ = 0, 1, or 2). The default is to have only three fuzzy sets (nFuzzySets = 3), with the expected range from zero to unity.

The fuzzify function determines the fraction of nearest fuzzy values (fvalue) which correspond to a given number, e.g. like the example of 0.42 corresponding to 24% low and 76% medium (I made those up).

The methods in Node.java are summarized in Table D‐7.

D‐7. Node.java method summary Visibility Type Method Name Parameters Returns public boolean isDiscrete() discreteFlag public void setValue (double v) public void setDiscrete (boolean flag) public void updateTseries (int t) public void fuzzify() public void fuzzify(double newCentroid[])

PlotTimeSeries.java This is a short routine, about 114 physical lines, used in conjunction with JFrame (import javax.swing.JFrame) to plot the results of the bionet simulation. As noted in the comments, the parameters input are:

* Plot the data in dataArray in an xy multiline graph

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* @param dataNames array of strings naming the datasets

* @param dataArray the data

* @param generation

* @param score

The default plot size is 800x500 pixels, apparently. The few methods in this class are summarized in Table D‐8. The class declaration is noted simply because it invokes

JFrame. The only method is Plot.

The last method, ‘main’, is apparently a test pie chart using JFreeChart (chart =

ChartFactory.createPieChart). It is omitted from the class diagram in Figure B‐1.

D‐8. PlotTimeSeries.java method summary Visibility Type Method Parameters Returns Name public void Plot (int ntseries, String[] dataNames, double[][] dataArray, int generation, double score) public static main (String[] args) void

RandomSequence.java This is a very short routine (72 physical lines) used to generate a random walk (variable name ‘seq’) through the Vector ‘orderedArray’, using the procedure of Srivastava and

Gomez (exact source unknown). The method ensures that all indices will be generated once and only once, in the sole method getRandomSequence.

The method in RandomSequence.java is shown in Table D‐9.

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D‐9. RandomSequence.java method summary Visibility Type Method Name Parameters Returns public int[] getRandomSequence (int N)

Reaction.java This sizable class (464 physical lines) has a herd of methods described in Table D‐10.

This class uses the Node class.

Method defaultReactionRules defines code numbers (type) for each role in a reaction:

 Node type within the reaction:  1: substrate (consumable source)  2: source (non‐consumed substrate)  3: product  4: inhibitor  5: activator  6: event (what’s this??)  14: generic enzyme In getNoise, it appears that the noise is a Gaussian distribution about some noise_mean

+/‐ noise_sd which were set by setNoise. It appears that ‘noise_trauma’ can be added to the noise, which is another Gaussian distribution about trauma_amp +/‐ trauma_sd; trauma also appears to have a duration component, all set by setTrauma.

In setReactionType, the following code values are allowed for reaction types (rtype):

 0 ==> min rule for combining reactants  1 ==> max rule for combining reactants  2 ==> sum rule for combining reactants

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 3 ==> harmonic mean rule for combining reactants  4 ==> arithmetic mean rule for combining reactants  5==> reaction is an arithmetic operation on operands

D‐10. Reaction.java method summary Visibility Type Method Name Parameters Returns public double getNoise (double t) (noise+noise_trauma) public double getProbability() public int getReactionType() (rtype) public double getRatePrior() (ratePrior) public double getReactantPrior (int r) reactantPrior.elementAt(r). doubleValue() public void setNoise (boolean fl,double mu,double sd) public void setRatePrior (double p) public void setTrauma (double freq,double duration, double amp, double sd) public void setValue (double v) public void setrateLevelCoeff (int fr) public void setrateLevelCoeff (int fr, int nFS, double low, double high) public void setRateCoeff (double rc) public void setReactionType (int rt) public void setActiveTimeIntervals (double tIntervals[])

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Visibility Type Method Name Parameters Returns public boolean activeTimeIntervalCheck (double t) public void addNode (int n,int t,int r[],int emask,int istoich,int s[],double cent[],double K_Michaelis) public void addNode (int n,int t,int r[],int emask,int istoich,int s[],double cent[],double K_Michaelis, double prior) public int[] defaultReactionRules (int i,int type) (new_rule) D‐10. Reaction.java method summary (continued)

RuleTable.java This object contains the list of fuzzy logic rules, a String name for each rule, and the number of fuzzy states in each rule. The default values for the number of fuzzy states is

6, and the number of rules is 13 (nFuzzyStates=6; nRules=13).

Default values for reaction rate arrays are a logarithmic scale from 0.001 to 10.0 with nine values (low = 0.001; high = 10.0; nRates = 9; loglinear = "log";)

The data file is read one line at a time, looking for keywords NFUZZYSTATES,

RATERANGE, or RULE to define each line’s contents. The routine is case insensitive.

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In method getNextDataLine, lines which are white space or comments (starts with #) are ignored.

The methods in RuleTable.java are shown in Table D‐11.

D‐11. RuleTable.java method summary Visibility Type Method Name Parameters Returns Public int getNFuzzyStates() nFuzzyStates Public int[] getRule (int r) rules[r] Public double[] getRateList() rateList Public int[] getRule (String name) Public String getNextDataLine (BufferedReader B, String line)

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Appendix E. Detailed Procedure for Transcription Factor Analysis

This analysis is to examine the gene expression data in three ways, hopefully to identify a candidate biomarker for aging. The approach is to look for three pathways affected by aging, and see if they have any genes in common. The pathways of interest are:

 Part One: Mitochondrial functions  Part Two: Lysosomal functions  Part Three: Insulin pathways In all three Parts the process followed is the same. First we identify candidate genes which have a large number of TREs involving the pathway of interest, then use linear

regression on the log2‐transformed gene expression levels to see which genes are significantly connected to NF‐kB gene expression.

Identify candidate genes

1. Start with the gene expression data in GE+TF‐Curated‐Sept30‐2009.xls under the CL‐TREs worksheet. 2. Search the description column G for the keyword(s) of interest. 3. Create a new worksheet, e.g. 'mito' for mitochondrial genes. 4. Copy the column headings from the CL‐TREs worksheet to the mito worksheet 5. Copy the rows (genes) which match the search terms. 6. Once all genes have been copied to the mito worksheet, in a row below them add the values in columns corresponding to the TREs (here, columns I through GH). 7. Copy the mito worksheet to a new worksheet, for example 'mito refined'. Delete columns C through H, so you have the Name and Accession number for each gene, followed by all the TREs.

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8. Determine a critical minimum number of TREs that are significant ‐ typically 2 to 4, depending on the number of candidate genes. 9. In the mito refined worksheet, delete all the columns whose sums are less than the critical value. 10. The result in the mito refined worksheet is the set of all genes which have involvement in the pathway of interest, and have at least the critical number of TREs involved. Do regression analysis to refine the list of candidate genes

1. Given the list of candidate genes from above, create a new worksheet, e.g. inhibited. 2. Copy the accession numbers of the candidate genes to the inhibited worksheet. 3. Go to the CL‐Expressions worksheet, and copy the rows with matching accession numbers to the new worksheet. 4. Go to the Phenotype worksheet, and copy the gene expression data for NF‐kB. Make sure all expression data is log2‐transformed values. Use the Excel formula '=LOG(A5,2)' to transform the data, where A5 is cell containing the raw gene expression value. 5. The goal is to do linear regression analysis on the log2‐transformed gene expressions, with NF‐kB expression data as the X axis, and each gene's expression data as the Y axis. 6. Find the R^2 value of each linear regression with an Excel formula of the form =RSQ(E9:R9,E$8:R$8) Where E9:R9 is the range of Y axis expression levels, and E$8:R$8 is the range of X axis expression levels. 7. Fill that formula down for all candidate genes. 8. Similarly, use a formula of the form =SLOPE(E9:R9,E$8:R$8)

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to find the slope of the linear regression, and fill down that formula for all candidate genes. 9. Look up the critical R value for df = N‐2. Here, N is the number of age data points, 14, so df = 12. Look up the critical R value for df=12, which is 0.532, making the critical R^2 value equal to 0.283. The critical R^2 value is for the proper degrees of freedom6 (df = n‐2). 10. Throw out all candidate genes which have linear regression R^2 less than the critical R^2 value. Sort the remaining candidate genes in order of accession number, so their short names can be easily found. 11. Calculate the percent change in gene expression for the remaining candidate genes when NF‐kB is inhibited, using: % change = 100*(2^(92‐Bay11) ‐ 2^92)/2^92 where '92' is the gene expression from the normal 92‐year‐old sample, and 'Bay11' is the same sample with NF‐kB inhibited with Bay‐11. Repeat the above process for each Part of this analysis.

Then compare the outputs from all three Parts and see if there are any biomarkers or shared pathways. Also search for commonality among the TREs from the candidate genes.

Effect of NF‐kB inhibition on mitochondrial genes of interest Here are the changes in log2‐transformed gene expression levels when NF‐kB is

inhibited (92‐bay11) versus normal quiescent cells (92). Ironically, the strongest candidate from regression analysis (ATP5F1) shows the weakest magnitude change in

expression during inhibition, and HIRIP5 has the strongest percent change.

6 http://www.gifted.uconn.edu/siegle/research/Correlation/corrchrt.htm

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The percent change when NF‐kB is inhibited ("% change") is calculated from raw gene expression levels

% change = 100*(2^(92‐Bay11) ‐ 2^92)/2^92

The genes of interest are summarized in Table E‐1, including whether they were associated with Mitochondrial or Lysosomal pathways. The R2 value and slope of the

linear regression against NF‐kB expression is given, along with the percent change in expression when NF‐kB is inhibited using Bay‐11.

E‐1. Candidate aging biomarker genes Linear Accession Associated % change with Name R squared regression No. with NF‐kB inhibited slope NM_000032 ALAS2 Mito 0.306 3.025 ‐83.55 NM_001688 ATP5F1 Mito 0.603 ‐5.835 141.38 NM_004162 RAB5A Lyso 0.548 1.705 7.74 NM_005391 PDK3 Mito 0.501 1.344 73.48 NM_006477 RASL10A Lyso 0.620 4.910 ‐96.14 NM_015700 HIRIP5 Mito 0.296 ‐3.156 ‐74.92 NM_017609 C10orf92 Mito 0.487 2.501 141.21 NM_032549 IMMP2L Mito 0.421 2.245 ‐62.17 NM_032857 LACTB Mito No data

Table 31 includes results from all three parts of this analysis ‐ mitochondrial, lysosomal, and insulin‐related genes. There were no statistically significant insulin‐related genes.

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TRE Summary Mitochondrial TREs have at least four binding sites, Lysosomal TREs at least three, and

Insulin‐related TREs have at least two. They are summarized in Table E‐2. The three

TREs which have multiple binding sites for all three types of pathways are right justified.

The Kid3 TRE is omnipresent, so it has no value as a biomarker.

E‐2. Number of Binding Sites for various pathways TRE Mito. binding Lyso. binding Insulin binding sites sites sites BCL6/V$BCL6_Q3 6 3 BRCA1:USF2/V$BRCA_01 6 3 CdxA/V$CDXA_02 7 4 4 CHOP:C/EBPalpha/V$CHOP_01 5 4 c‐Myc:Max/V$MYCMAX_03 9 3 CP2/LBP‐1c/LSF/V$CP2_02 3 DBP/V$DBP_Q6 5 3 ETF/V$ETF_Q6 4 FAC1/V$FAC1_01 4 GATA‐X/V$GATA_C 5 Hand1:E47/V$HAND1E47_01 6 HMG IY/V$HMGIY_Q6 4 3 HNF3alpha/V$HNF3ALPHA_Q6 3 HNF3beta/V$HNF3B_01 6 IPF1/V$IPF1_Q4 8 4 Kid3/V$KID3_01 80 29 9 LEF1, TCF1/V$LEF1TCF1_Q4 4 MAZ/V$MAZ_Q6 3 MYB/V$MYB_Q3 4

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TRE Mito. binding Lyso. binding Insulin binding sites sites sites Nkx2‐5/V$NKX25_Q5 7 7 3 OG‐2/V$OG2_01 7 3 2 Pax‐8/V$PAX8_01 5 PLZF/V$PLZF_02 4 PPARalpha:RXRalpha/V$PPARA_02 2 RFX/V$RFX_Q6 6 4 Sp1/V$SP1_Q2_01 4 Spz1/V$SPZ1_01 4 TBP/V$TBP_Q6 2 TBX5/V$TBX5_01 4 Tel‐2/V$TEL2_Q6 5 TTF‐1 (Nkx2‐1)/V$TTF1_Q6 5 2 v‐Myb/V$VMYB_02 6 YY1/V$YY1_Q6 3 ZF5/V$ZF5_B 6 E‐2. Number of Binding Sites for various pathways (continued)

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Appendix F. Diseasome data structure

This is a summary of the raw data structure from seven files at http://www.nd.edu/~alb/Publication06/145‐HumanDisease_PNAS‐14My07‐Proc/Suppl/ on 12/15/07 from K‐I Goh, corresponding here to Tables F‐1 through F‐7. They were used to reverse engineer the data structure needed to map the connection between genes differently regulated with age, and diseases associated with higher incidence with age.

F‐1. Table S1 ‐ Curated Morbid Map file with disease ID and class assignment (2929 entries) This maps a unique disorder name to the genes associated with causing it. Field Data Notes, or Values type Disease ID int Non‐unique identifier for each disorder Disorder text Unique name of disorder name Gene symbols text CSV list of genes associated with that disorder OMIM ID int Chromosome identifier for affected genes Chromosome text Range of chromosome portions affected Class text List of 22 specific values for affected systems, e.g. bone, cancer, cardiovascular, etc. Multiple and unclassified are also options.

Acronyms

Bipartite table = data connecting the HDN to the DGN, per Goh’s paper in PNAS.

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DGN = Disease Gene Network, shows which genes are connected to each other

HDN = Human Disease Network, shows which diseases are connected to each

other

MM = Morbid Map, part of the OMIM, appears here as table S1.

NCBI = National Center for Biotechnology Information, www.ncbi.nlm.nih.gov

OMIM = Online Mendelian Inheritance in Man database,

http://www.ncbi.nlm.nih.gov/sites/entrez?db=OMIM

PPI = protein‐protein interaction

Entrez ID is from NCBI Entrez Gene database, http://www.ncbi.nlm.nih.gov/sites/entrez?db=gene.

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F‐2. Table S2 ‐ Network characteristics of diseases (1284 entries) This simplifies S1 so each Disease ID is given a single name. Field Data Notes, or Values type Disease ID int Unique identifier for each disorder. NOT the same field in S1, this one is unique, so each disorder is grouped to a common name. Name text Unique name of disorder’s common name. Same as Disorder name in S1. Disorder class text List of specific values for affected systems. Same as Class in S1. Size (s) Int Number of associated genes per disorder. This is the number of entries in the “Genes implicated” field. Range is 1 to 41. The sum of the Size entries is 2673, the number of entries in the ‘bipartite’ table below. Hence the many to many disorder:gene relationship is in bipartite. Degree (k) Int Number of network graph degrees (how many diseases this Disease ID is connected to) in the HDN. Range is 0 to 50. Class‐degree (k) Int Number of distinct disorder classes this Disease ID connects to. Range is 0 to 11. Genes implicated (Entrez text CSV list of genes affected. Gene name and Entrez ID are ID) [comma‐deliminated] given, e.g. “MTP (4547), APOB (338)”

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F‐3. Table S3 ‐ Network characteristics of disease genes. (1777 entries) Map from each unique gene to its Implicated diseases. Field Data Notes, or Values type Entrez ID int Same as Entrez ID cited in S2. Maps to one gene symbol. Symbol text Name of gene, e.g. ACADS, Is a unique field in this table. Disorder class text List of specific values for affected systems. Class of disease gene is assigned if all the implicated diseases are of same class, otherwise, it is assigned "Grey." Size (s) Int Number of ‘Implicated diseases’ per associated gene. Range is 1 to 11. Sum of entries is again 2673, pointing to the bipartite table. Degree (k) Int Number of network graph degrees in the HDN. Range is 0 to 70. Sum of these values is 14,982, the number of entries in the table ‘gene’. Number of classes int Number of disorder classes associated with this gene. associated Range is 0 to 5. Values >1 have a new disorder class, “Grey”. Implicated diseases text CSV list of diseases and their ID numbers; the Disease ID (Disease ID) [comma‐ corresponds to same field in S1. deliminated]

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F‐4. Table S4 ‐ List of human protein‐protein interactons. (22,052 entries) Lists many:many connection between proteins, by Entrez ID of genes which produce them. Field Data type Notes, or Values Entrez ID 1 Int Same as Entrez ID cited in S3. not unique Symbol 1 text Name of gene, same as Symbol in S3 Entrez ID 2 Int Same as Entrez ID cited in S3. not unique Symbol 2 text Name of gene, same as Symbol in S3 Data Source (R: Rual et al; S: Text 1 char Just what the field header says. Stelzl et al; L: Literature curation)

F‐5. Table ‘bipartite’ – map diseases to genes (2673 entries) This maps disease ID to one or more Entrez ID Field Data type Notes, or Values #Disease_id Int Same as Disease ID in S1 non unique Entrez_id Int Same as Entrez ID in S3 non unique

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F‐6. Table ‘disease’ – map diseases to other diseases (3054 entries) The range of disease IDs corresponds to diseases with Degree>0 in S2. Field Data type Notes, or Values #Disease_id1 Int Same as Disease ID in S1 non unique. Range of values is 9 to 9308. Disease_id2 Int Same as Disease ID in S1 non unique. Range of values is 9 to 9308. Weight Int Unknown; value is 1‐5

F‐7. Table ‘gene’ – map genes to other genes (14,982 entries) Field Data type Notes, or Values #Entrez_id1 Int Same as Entrez ID in S3 non unique Entrez_id2 Int Same as Entrez ID in S3 non unique Weight Int Unknown; value is 1‐4

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Appendix G. Mortality data

This Appendix provides sample raw data for mortality rates, identifies sources for WHO mortality rates, and lists the categories of causes of death from National Vital Statistics data.

Appendix G‐1. Mortality rates by age for the USA in 2000

Mortality rates are the number of deaths per 1000 people of that age that year. Table

G‐1 gives the mortality rates in the USA for the year 2000.

G‐1. USA mortality rates in 2000 Death Death rate Death Death rate Age rate male female Age rate male female 0 7.95 6.53 14 0.35 0.22 1 0.56 0.46 15 0.49 0.28 2 0.38 0.31 16 0.73 0.37 3 0.29 0.20 17 0.94 0.40 4 0.22 0.19 18 1.17 0.47 5 0.21 0.16 19 1.33 0.45 6 0.19 0.14 20 1.35 0.46 7 0.17 0.15 21 1.43 0.49 8 0.16 0.13 22 1.37 0.47 9 0.16 0.13 23 1.35 0.47 10 0.18 0.12 24 1.35 0.46 11 0.21 0.15 25 1.27 0.49 12 0.22 0.14 26 1.27 0.50 13 0.26 0.17 27 1.31 0.54

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Death Death rate Death Death rate Age rate male female Age rate male female 28 1.29 0.55 58 10.61 6.56 29 1.34 0.58 59 11.78 7.29 30 1.28 0.59 60 12.68 7.90 31 1.40 0.67 61 13.68 8.92 32 1.45 0.74 62 15.26 9.72 33 1.57 0.81 63 16.79 10.52 34 1.70 0.86 64 18.52 11.64 35 1.74 0.92 65 19.62 12.56 36 1.90 1.01 66 21.52 13.98 37 2.05 1.15 67 23.82 15.19 38 2.25 1.23 68 25.80 16.58 39 2.36 1.36 69 27.78 17.66 40 2.57 1.45 70 30.53 19.41 41 2.80 1.61 71 33.60 21.25 42 3.00 1.69 72 37.09 23.39 43 3.34 1.91 73 40.17 25.53 44 3.59 1.99 74 43.58 28.03 45 3.81 2.16 75 47.54 31.22 46 4.20 2.28 76 51.76 33.97 47 4.54 2.51 77 57.24 37.39 48 4.95 2.69 78 62.07 41.36 49 5.29 2.93 79 68.99 45.47 50 5.50 3.16 80 75.49 51.15 51 5.92 3.41 81 81.19 55.53 52 6.37 3.74 82 92.77 63.46 53 6.92 4.21 83 100.74 70.22 54 7.22 4.47 84 111.55 78.42 55 8.32 4.99 85 123.62 87.90 56 8.96 5.52 86 137.53 98.49 57 9.86 6.06 87 149.60 109.85

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Death Death rate Death Death rate Age rate male female Age rate male female 88 163.53 122.59 95 289.77 256.07 89 180.33 135.99 96 319.04 277.38 90 195.40 154.29 97 330.81 301.41 91 216.07 172.74 98 346.27 326.20 92 235.49 194.72 99 329.80 331.83 93 257.65 210.45 100 286.83 382.12 94 272.64 232.22 G‐1. USA mortality rates in 2000 (continued)

Appendix G‐2. Sources for WHO mortality rates

WHO mortality rate data were obtained from the following sources:

http://www.who.int/whosis/mort/download/en/index.html

http://www.who.int/healthinfo/morttables/en/

http://www.who.int/healthinfo/statistics/mortality_life_tables/en/ (primary)

Appendix G‐3. Categories of causes of death in NVS data

Data on the number of deaths by age and cause were grouped into four categories:

 Category 1 = Age‐dependent deaths: o Acute myocardial infarction o Ischemic heart disease, Cerebrovascular disease o Type II diabetes o Osteoporosis o Alzheimer's disease, Parkinson's disease  Category 2 = Age‐related deaths o Multiple sclerosis o ALS, Gout, Peptic ulcer

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o Most cancers (malignant neoplasms) except prostate cancer  Category 3 = Other non‐age‐related causes o Accidents, suicide, homicide, HIV, pregnancy, congenital defects  Category 4 = Deaths due to aging o Including infections, heart disease, hypertension, and atherosclerosis The specific causes of death in each category are as follows.

Category 1: Age‐dependent deaths Diabetes mellitus

Parkinson's disease

Alzheimer's disease

Acute myocardial infarction

Other acute ischemic heart diseases

Atherosclerotic cardiovascular disease, so described

All other forms of chronic ischemic heart disease

Cerebrovascular diseases

Category 2: Age‐related deaths Malignant neoplasms of lip, oral cavity and pharynx

Malignant neoplasm of esophagus

Malignant neoplasm of stomach

Malignant neoplasms of colon, rectum and anus

Malignant neoplasms of liver and intrahepatic bile ducts

Malignant neoplasm of pancreas

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Malignant neoplasm of larynx

Malignant neoplasms of trachea, bronchus and lung

Malignant melanoma of skin

Malignant neoplasm of breast

Malignant neoplasm of cervix uteri

Malignant neoplasms of corpus uteri and uterus, part unspecified

Malignant neoplasm of ovary

Malignant neoplasms of kidney and renal pelvis

Malignant neoplasm of bladder

Malignant neoplasms of meninges, brain and other parts of central nervous system

Hodgkins disease

Non‐Hodgkins lymphoma

Leukemia

Multiple myeloma and immunoproliferative neoplasms

Other and unspecified malignant neoplasms of lymphoid, hematopoietic and related

tissue

All other and unspecified malignant neoplasms

In situ neoplasms, benign neoplasms and neoplasms of uncertain or unknown behavior

Anemias

Peptic ulcer

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Category 3: Other non‐age‐related causes Motor vehicle accidents

Other land transport accidents

Water, air and space, and other and unspecified transport accidents and their sequelae

Falls

Accidental discharge of firearms

Accidental drowning and submersion

Accidental exposure to smoke, fire and flames

Accidental poisoning and exposure to noxious substances

Other and unspecified nontransport accidents and their sequelae

Intentional self‐harm (suicide) by discharge of firearms

Intentional self‐harm (suicide) by other and unspecified means and their sequelae

Assault (homicide) by discharge of firearms

Assault (homicide) by other and unspecified means and their sequelae

Legal intervention

Discharge of firearms, undetermined intent

Other and unspecified events of undetermined intent and their sequelae

Operations of war and their sequelae

Complications of medical and surgical care

Pregnancy with abortive outcome

Other complications of pregnancy, childbirth and the puerperium

Human immunodeficiency virus (HIV) disease

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Malaria

Whooping cough

Certain conditions originating in the perinatal period

Congenital malformations, deformations and chromosomal abnormalities

Scarlet fever and erysipelas

Category 4: Deaths due to aging Salmonella infections

Shigellosis and amebiasis

Certain other intestinal infections

Respiratory tuberculosis

Other tuberculosis

Meningococcal infection

Septicemia

Syphilis

Acute poliomyelitis

Arthropod‐borne viral encephalitis

Measles

Viral hepatitis

Other and unspecified infectious and parasitic diseases and their sequelae

Malignant neoplasm of prostate

Malnutrition

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Other nutritional deficiencies

Meningitis

Acute rheumatic fever and chronic rheumatic heart diseases

Hypertensive heart disease

Hypertensive heart and renal disease

Acute and subacute endocarditis

Diseases of pericardium and acute myocarditis

Heart failure

All other forms of heart disease

Essential (primary) hypertension and hypertensive renal disease

Atherosclerosis

Aortic aneurysm and dissection

Other diseases of arteries, arterioles and capillaries

Other disorders of circulatory system

Influenza

Pneumonia

Acute bronchitis and bronchiolitis

Unspecified acute lower respiratory infection

Bronchitis, chronic and unspecified

Emphysema

Asthma

Other chronic lower respiratory diseases

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Pneumoconioses and chemical effects

Pneumonitis due to solids and liquids

Other diseases of respiratory system

Diseases of appendix

Hernia

Alcoholic liver disease

Other chronic liver disease and cirrhosis

Cholelithiasis and other disorders of gallbladder

Acute and rapidly progressive nephritic and nephrotic syndrome

Chronic glomerulonephritis, nephritis and nephropathy, not specified as acute or

chronic, and renal scerosis, unspecified

Renal failure

Other disorders of kidney

Infections of kidney

Hyperplasia of prostate

Inflammatory diseases of female pelvic organs

Symptoms, signs and abnormal clinical and laboratory findings, not elsewhere

classified

All other diseases (Residual)

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The last two causes of death are catch‐all categories. They are included with deaths due to healthy aging, though they contribute a large number of deaths at young ages where the exact cause of death was not determined.

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Appendix H. Matlab source code

Appendix H‐1. Weitz & Fraser Viability Model

This is the model of Weitz & Fraser's viability equation. Function drift is the main program. Function lifespan traces each life through a random walk. Depending on the function selected for changes in slope (eps) or stochastic component magnitude (sigma), it might call the functions expdecline, rampout, or lindecline.

function drift(eps, sigma, decline) % drift model of viability % based on Fraser and Weitz & Fraser 2007 % Glenn Booker April 9, 2011 % % define the slope of decline (eps) %eps = 0.0015; % define the magnitude of the random error (sigma) %sigma = 0.020; % 'decline' is the linear decline parameter for stochastic magnitude % the number of lifespans nlives = 50000; % define array to keep lifespans of each run lifearray = zeros(nlives,1); % define array of histogram values in 5-year increments bucketsize = 5; % max number of bucketsize-year buckets is histomax histomax = 50; % histodata needs five columns; no relation to bucketsize histodata = zeros(histomax,5); for j=1:histomax % low value of age for each bucketsize-year span % e.g. 35 means 35-39.999

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histodata(j,1) = j*bucketsize; end % for i=1:nlives % find lifespan for this person lifearray(i,1)=tracelife(eps, sigma, decline); bucketfix = fix(lifearray(i,1)/bucketsize); % handle exceptions if lifespan > histomax*5 or < 5 yrs if bucketfix > histomax bucketfix = histomax; elseif bucketfix < 1 bucketfix = 1; end histodata(bucketfix,2) = histodata(bucketfix,2) + 1; end % deliberately show these summary values on screen meanlife = mean(lifearray) minlife = min(lifearray) maxlife = max(lifearray) liferange = maxlife-minlife % calculate cumulative number of deaths histodata(1,3) = 0.; for i=2:histomax histodata(i,3) = histodata(i-1,3)+histodata(i,2); end % convert cumulative deaths to cumulative number left alive histodata(:,3) = nlives - histodata(:,3); % calculate mortality rate histodata(1,4) = histodata(1,2)/nlives; for i=2:histomax histodata(i,4) = histodata(i,2)/histodata(i-1,3); end for i=1:histomax if histodata(i,4) > 0.0000001 histodata(i,5) = log10(histodata(i,4)); end end

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% now plot log(Mortality rate) vs age for a fixed range of ages lowage = 5/bucketsize; highage = 115/bucketsize; figure(1),subplot(2,1,1); plot(histodata(lowage:highage,1),histodata(lowage:highage,5)); xlabel('Age'); ylabel('log10(Mortality Rate)'); title(['Mortality rate curve for eps ',num2str(eps),', sigma ',num2str(sigma),' and decline ',num2str(decline)]); % % plot the histogram, number of deaths versus age % subplot(2,1,2); bar(histodata(lowage:highage,1),histodata(lowage:highage,2)); xlabel('Age'); ylabel('Number of deaths per time period'); title(['Histogram for eps ',num2str(eps),', sigma ',num2str(sigma),' and decline ',num2str(decline)]); % define and export lifearray for SPSS histogram analysis % use plain text file so > 64k rows can be used %DS2 = dataset(lifearray); %export(DS2,'File','lifearray.xls', 'Delimiter','tab'); % define and export histogram for SPSS plotting DS3 = dataset(histodata); export(DS3,'XLSFile','histodata.xls'); end % end of function drift % function lifespan=tracelife(eps, sigma, decline) % trace viability of human until death % Glenn Booker March 15, 2011 % assume viability starts at 1.0, and death occurs when it is <= 0.0 offset = 0.50; viable = 1.0; timemax = 500.; deltat = 0.1;

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% maxdecline is the previous 'decline' function for fold-change in slope maxdecline = 1.; for time=deltat:deltat:timemax % add linear decline function 2/17/11, amended 3/15/11 %declinefactor = linfunction(time,maxdecline); % omit using stepsig 4/9/11 %stepvalue = stepsig(time,decline); %rampfcn = rampfunction(time, decline); % exp decline in sigma added 5/7/11 %declinefactor = expfunction(time); % ramp function from 5/3/11 %rampfcn = rampfunction(time, decline); %viable = viable - eps + rampfcn*sigma*(rand()-offset); % constant sigma from 5/12/11 %viable = viable - eps + sigma*(rand()-offset); % linear decline in sigma adapted from 4/9/11 %stepvalue = linfunction(time, decline); %viable = viable - eps + stepvalue*sigma*(rand()-offset); % bathtub curve calculations 5/12/11; decline is not used k = 0.005; beta = 0.3; alpha1 = 0.1; nvalue = 1.1; const = 0.025; bathtub = k*beta*time^(beta-1.)*exp(alpha1*time) + exp(- 1.*const*time^nvalue); viable = viable - eps + bathtub*sigma*(rand()-offset); if viable <= 0.0 break end end lifespan = time; end % end of function tracelife % function expdecline=expfunction(time)

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% new function for exponential decline in sigma for all time 0 to infinity % the 'decline' parameter isn't being used. const = 0.025; nvalue = 1.0; expdecline = exp(-1.0*const*(time^nvalue)); end % end of function expfunction % function rampout=rampfunction(time, decline) % solve for linear decline factor % Glenn Booker May 3, 2011 % lindecline is linear from 1.0 to decline (miny) during time 0 to midage % then linear increase from y=decline to y=endy from age midage to 100 % then constant at y=endy for age>100 % miny = decline; endy = 0.5; midage = 60.; value = endy; if (time < midage) value = (miny-1.)*time/midage + 1.; elseif (time > midage) && (time < 100.) slope = (endy-miny)/(100.-midage); bvalue = miny - slope*midage; value = slope*time + bvalue; end rampout = value; end % end of rampfunction % function lindecline=linfunction(time, xdecline) % solve for linear decline factor % Glenn Booker January 17, 2011 % lindecline is linear from 1.0 to xdecline during time 0 to 100 % its value is fixed at xdecline after that

237 value = xdecline; if(time<100) value = (xdecline-1)*time/100 + 1.0; end lindecline = value; end % end of function linfunction %

Appendix H‐2. Network Model Matlab Code

Here is the raw Matlab code, derived from taking the CellDesigner model of the baseline bowtie network model, and using the Systems Biology Workbench's SBML Translator to convert it to Matlab form. The first piece of code is the raw results from translating the

Baseline Bowtie network model.

Baseline Bowtie Network Model (raw CellDesigner code) function xdot = ScaledNetwork(time,x) % synopsis: % xdot = ScaledNetwork (time, x) % x0 = ScaledNetwork % % ScaledNetwork can be used with odeN functions as follows: % % x0 = ScaledNetwork; % [t,x] = ode23s(@ScaledNetwork, [0 100], ScaledNetwork); % plot (t,x); % % where 100 is the end time % % When ScaledNetwork is used without any arguments it returns a vector of % the initial concentrations of the 25 floating species. % Otherwise ScaledNetwork should be called with two arguments: % time and x. time is the current time. x is the vector of the

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% concentrations of the 25 floating species. % When these parameters are supplied ScaledNetwork returns a vector of % the rates of change of the concentrations of the 25 floating species. % % the following table shows the mapping between the vector % index of a floating species and the species name. % % NOTE for compartmental models % matlab translator generates code that when simulated in matlab, % produces results which have the units of species amounts. Users % should divide the results for each species with the volume of the % compartment it resides in, in order to obtain concentrations. % % Indx Name % x(1) s1 % x(2) s2 % x(3) s3 % x(4) s4 % x(5) s5 % x(6) s6 % x(7) s7 % x(8) s8 % x(9) s9 % x(10) s10 % x(11) s11 % x(12) s12 % x(13) s13 % x(14) s14 % x(15) s15 % x(16) s16 % x(17) s17 % x(18) s18 % x(19) s19 % x(20) s28 % x(21) s29 % x(22) s30

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% x(23) s32 % x(24) s33 % x(25) s31 xdot = zeros(25, 1);

% List of Compartments vol__default = 1; %default

% Boundary Conditions g_p1 = 1; % s22 = i1 [Amount] g_p2 = 1; % s23 = i2 [Amount] g_p3 = 1; % s24 = i3 [Amount] g_p4 = 1; % s25 = i4 [Amount] g_p5 = 1; % s26 = i5 [Amount] g_p6 = 1; % s27 = i6 [Amount]

% Local Parameters par_r1_p1 = 0.005; % [re2, k5] par_r1_p2 = 0.01; % [re2, k1] par_r2_p1 = 0.01; % [re3, k4] par_r3_p1 = 0.005; % [re4, k5] par_r3_p2 = 0.01; % [re4, k1] par_r4_p1 = 0.005; % [re5, k6] par_r4_p2 = 0.01; % [re5, k1] par_r5_p1 = 1; % [re6, k1] par_r5_p2 = 0.01; % [re6, k2] par_r5_p3 = 0.005; % [re6, k3] par_r5_p4 = 0.01; % [re6, k4] par_r6_p1 = 1; % [re7, k1] par_r6_p2 = 0.01; % [re7, k2] par_r6_p3 = 0.005; % [re7, k3] par_r6_p4 = 0.01; % [re7, k4] par_r7_p1 = 0.02; % [re8, k2] par_r8_p1 = 0.02; % [re9, k3] par_r9_p1 = 0.02; % [re10, k2] par_r10_p1 = 0.02; % [re11, k5]

240 par_r11_p1 = 0.02; % [re12, k3] par_r12_p1 = 0.02; % [re13, k1] par_r13_p1 = 1; % [re14, k1] par_r13_p2 = 0.01; % [re14, k2] par_r13_p3 = 0.01; % [re14, k3] par_r14_p1 = 1; % [re15, k1] par_r14_p2 = 0.01; % [re15, k2] par_r14_p3 = 0.01; % [re15, k3] par_r15_p1 = 0.01; % [re17, k4] par_r16_p1 = 0.01; % [re18, k4] par_r17_p1 = 0.01; % [re19, k1] par_r18_p1 = 0.01; % [re20, k1] par_r19_p1 = 1; % [re22, k1] par_r20_p1 = 1; % [re23, k1] par_r21_p1 = 1; % [re24, k1] par_r22_p1 = 1; % [re25, k1] par_r23_p1 = 1; % [re26, k1] par_r24_p1 = 1; % [re27, k1] par_r25_p1 = 0.1; % [re28, k3] par_r25_p2 = 0.01; % [re28, k1] par_r25_p3 = 1; % [re28, k2] par_r25_p4 = 0.01; % [re28, k4] par_r26_p1 = 0.1; % [re29, k4] par_r26_p2 = 0.01; % [re29, k1] par_r27_p1 = 0.005; % [re30, k2] par_r27_p2 = 0.1; % [re30, k1] par_r27_p3 = 0.01; % [re30, k3] par_r28_p1 = 0.005; % [re31, k2] par_r28_p2 = 0.1; % [re31, k1] par_r28_p3 = 0.01; % [re31, k3] par_r29_p1 = 0.01; % [re32, k2] par_r30_p1 = 0.1; % [re33, k2] par_r30_p2 = 0.01; % [re33, k1] if (nargin == 0)

% set initial conditions

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xdot(1) = 1; % s1 = s1 [Amount] xdot(2) = 1; % s2 = s2 [Amount] xdot(3) = 1; % s3 = s3 [Amount] xdot(4) = 1; % s4 = s4 [Amount] xdot(5) = 1; % s5 = s5 [Amount] xdot(6) = 1; % s6 = s6 [Amount] xdot(7) = 1; % s7 = s7 [Amount] xdot(8) = 1; % s8 = s8 [Amount] xdot(9) = 1; % s9 = s9 [Amount] xdot(10) = 1; % s10 = s10 [Amount] xdot(11) = 1; % s11 = s11 [Amount] xdot(12) = 1; % s12 = s12 [Amount] xdot(13) = 1; % s13 = s13 [Amount] xdot(14) = 1; % s14 = s14 [Amount] xdot(15) = 1; % s15 = s15 [Amount] xdot(16) = 1; % s16 = s16 [Amount] xdot(17) = 1; % s17 = s17 [Amount] xdot(18) = 1; % s18 = s18 [Amount] xdot(19) = 1; % s19 = s19 [Amount] xdot(20) = 1; % s28 = o1 [Amount] xdot(21) = 1; % s29 = o2 [Amount] xdot(22) = 1; % s30 = o3 [Amount] xdot(23) = 1; % s32 = o5 [Amount] xdot(24) = 1; % s33 = o6 [Amount] xdot(25) = 1; % s31 = o4 [Amount] else

% calculate rates of change R0 = (x(1))*par_r1_p2; R1 = (x(2))*par_r2_p1; R2 = (x(3))*par_r3_p2; R3 = (x(4))*par_r4_p2; R4 = (x(5))*par_r5_p4; R5 = (x(6))*par_r6_p4; R6 = (x(7))*par_r7_p1; R7 = (x(8))*par_r8_p1;

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R8 = (x(9))*par_r9_p1; R9 = (x(10))*par_r10_p1; R10 = (x(10))*par_r11_p1; R11 = (x(10))*par_r12_p1; R12 = (x(11))*par_r13_p3; R13 = (x(11))*par_r14_p3; R14 = (x(12))*par_r15_p1; R15 = (x(12))*par_r16_p1; R16 = (x(13))*par_r17_p1; R17 = (x(13))*par_r18_p1; R18 = ((g_p1)-(x(1)))*par_r19_p1; R19 = ((g_p2)-(x(2)))*par_r20_p1; R20 = ((g_p3)-(x(3)))*par_r21_p1; R21 = ((g_p4)-(x(4)))*par_r22_p1; R22 = ((g_p5)-(x(5)))*par_r23_p1; R23 = ((g_p6)-(x(6)))*par_r24_p1; R24 = (x(14))*par_r25_p4; R25 = (x(15))*par_r26_p2; R26 = (x(16))*par_r27_p3; R27 = (x(17))*par_r28_p3; R28 = (x(18))*par_r29_p1; R29 = (x(19))*par_r30_p2;

xdot = [ - R0 + R18 - R1 + R19 - R2 + R20 - R3 + R21 - R4 + R22 - R5 + R23 + R0 + R1 - R6 + R2 + R3 - R7 + R4 + R5 - R8 + R6 + R7 + R8 - R9 - R10 - R11 + R9 - R12 - R13 + R10 - R14 - R15 + R11 - R16 - R17

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+ R12 - R24 + R13 - R25 + R14 - R26 + R15 - R27 + R16 - R28 + R17 - R29 + R24 + R25 + R26 + R28 + R29 + R27 ]; end;

The next two pieces of code are the model developed from the raw SBML Translator output. There are two functions, netmodel and ScaledNetwork. The former is called from the command line in Matlab.

Matlab code for Baseline Bowtie model ‐ netmodel.m function netmodel(ncases,sigma,age) % network model of pathway decline % based on ScaledNetwork-noinh6.xml, received 9/19/11 % Glenn Booker September 27, 2011 % adapted 9/21/11 to use numeric integration of time-varying coefficients % based on a Matlab VC model developed in June 2010 global A rates % global variable rates keeps the reaction rate for all 33 reactions rates = zeros(33,1); % % set rate of linear decline with age, magnitude of stochastic changes % in reaction rates, and age of simulation, respectively linear=0.010; %sigma=5.0;

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%age=90.; % % set time limits for the simulation starttime = 0.0; deltatime = 1.0; endtime = 4000.0; % % set fixed time intervals t = starttime:deltatime:endtime; % % set initial conditions xdot for s1 to s19 and outputs o1 to o6 % xdot0 = zeros(25, 1); xdot0(1) = 1.; % s1 = s1 [Amount] xdot0(2) = 1.; % s2 = s2 [Amount] xdot0(3) = 1.; % s3 = s3 [Amount] xdot0(4) = 1.; % s4 = s4 [Amount] xdot0(5) = 1.; % s5 = s5 [Amount] xdot0(6) = 1.; % s6 = s6 [Amount] xdot0(7) = 1.; % s7 = s7 [Amount] xdot0(8) = 1.; % s8 = s8 [Amount] xdot0(9) = 1.; % s9 = s9 [Amount] xdot0(10) = 1.; % s10 = s10 [Amount] xdot0(11) = 1.; % s11 = s11 [Amount] xdot0(12) = 1.; % s12 = s12 [Amount] xdot0(13) = 1.; % s13 = s13 [Amount] xdot0(14) = 1.; % s14 = s14 [Amount] xdot0(15) = 1.; % s15 = s15 [Amount] xdot0(16) = 1.; % s16 = s16 [Amount] xdot0(17) = 1.; % s17 = s17 [Amount] xdot0(18) = 1.; % s18 = s18 [Amount] xdot0(19) = 1.; % s19 = s19 [Amount] xdot0(20) = 1.; % s28 = o1 [Amount] xdot0(21) = 1.; % s29 = o2 [Amount] xdot0(22) = 1.; % s30 = o3 [Amount] xdot0(23) = 1.; % s32 = o5 [Amount] xdot0(24) = 1.; % s33 = o6 [Amount]

245 xdot0(25) = 1.; % s31 = o4 [Amount] % % the following table shows the mapping between the vector % index of a floating species and the species name. % % Indx Name % x(1) s1 % x(2) s2 % x(3) s3 % x(4) s4 % x(5) s5 % x(6) s6 % x(7) s7 % x(8) s8 % x(9) s9 % x(10) s10 % x(11) s11 % x(12) s12 % x(13) s13 % x(14) s14 % x(15) s15 % x(16) s16 % x(17) s17 % x(18) s18 % x(19) s19 % x(20) s28 % x(21) s29 % x(22) s30 % x(23) s32 % x(24) s33 % x(25) s31 % % List of Compartments %vol__default = 1; %default but not used % % define number of runs at each age %ncases=100; % set at the command line

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% % initialize counter for how many cases failed (exceeded homeostatic range) failcount = zeros(ncases, 1); resil = zeros(ncases,19); deltamin = 0.0000001; % define the lower and upper limits of species concentration at endtime % to constitute non-homeostatic behavior failminimum = 0.1; failmaximum = 10.0; % % solve species quantities x over time t for each of the ncases simulations % for runnn=1:ncases % define the linear decline and random variation factor for each % reaction, e.g. rates(9) is used for reaction re9 % set unused or unaltered reaction factors to unity rates(1)=1.; rates(2)=(1-linear*(age-30.))*sigma*(rand()); rates(3)=(1-linear*(age-30.))*sigma*rand(); rates(4)=(1-linear*(age-30.))*sigma*rand(); rates(5)=(1-linear*(age-30.))*sigma*rand(); rates(6)=(1-linear*(age-30.))*sigma*rand(); rates(7)=(1-linear*(age-30.))*sigma*rand(); rates(8)=(1-linear*(age-30.))*sigma*rand(); rates(9)=(1-linear*(age-30.))*sigma*rand(); rates(10)=(1-linear*(age-30.))*sigma*rand(); rates(11)=(1-linear*(age-30.))*sigma*rand(); rates(12)=(1-linear*(age-30.))*sigma*rand(); rates(13)=(1-linear*(age-30.))*sigma*rand(); rates(14)=(1-linear*(age-30.))*sigma*rand(); rates(15)=(1-linear*(age-30.))*sigma*rand(); rates(16)=1.; rates(17)=(1-linear*(age-30.))*sigma*rand(); rates(18)=(1-linear*(age-30.))*sigma*rand(); rates(19)=(1-linear*(age-30.))*sigma*rand();

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rates(20)=(1-linear*(age-30.))*sigma*rand(); rates(21)=1.; rates(22)=1.; rates(23)=1.; rates(24)=1.; rates(25)=1.; rates(26)=1.; rates(27)=1.; rates(28)=(1-linear*(age-30.))*sigma*rand(); rates(29)=(1-linear*(age-30.))*sigma*rand(); rates(30)=(1-linear*(age-30.))*sigma*rand(); rates(31)=(1-linear*(age-30.))*sigma*rand(); rates(32)=(1-linear*(age-30.))*sigma*rand(); rates(33)=(1-linear*(age-30.))*sigma*rand(); % fname = 'ScaledNetwork'; [t,x] = ode45(fname, t, xdot0); %[t,x] = ode23s(@ScaledNetwork, [0, endtime], xdot0); %[t,x] = ode15s(@ScaledNetwork, [0, endtime], xdot0); % count the number of species which end with x<0.02 as failed cases tlength = length(t); failcounter=0; for varloop=1:19 if x(tlength,varloop)failmaximum failcounter=failcounter+1; end end failcount(runnn)=failcounter; % assess the measure of resilience, added 9/26/11 for varloop=1:19 for rownumber=1:tlength-1 difference=abs(x(rownumber,varloop)- x(rownumber+1,varloop)); if difference

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resil(runnn,varloop)=t(rownumber+1); break end end end end if ncases < 11 resil end meanresil=mean(resil)' stddevresil=std(resil)' meancount=mean(failcount) stddevcount=std(failcount) %failcount % plot the last case plot (t,x(:,1:19)); % % export last case to Excel % DS3 = dataset(t,x); export(DS3,'XLSFile','network.xls'); % % export resilience data to Excel % DS4 = dataset(resil); export(DS4,'XLSFile','resilience.xls'); % end of netmodel

Matlab code for Baseline Bowtie model ‐ ScaledNetwork.m function xdot = ScaledNetwork(time,x) % adjust inputs for a given time step by some rate of linear decline and a % stochastic factor global A rates % Local Parameters reaction rate constants % redefine the random component for each reaction

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% par_r1_p1 = 0.005*rates(2); % [re2, k5] par_r1_p2 = 0.01*rates(2); % [re2, k1] par_r2_p1 = 0.01*rates(3); % [re3, k4] par_r3_p1 = 0.005*rates(4); % [re4, k5] par_r3_p2 = 0.01*rates(4); % [re4, k1] par_r4_p1 = 0.005*rates(5); % [re5, k6] par_r4_p2 = 0.01*rates(5); % [re5, k1] par_r5_p1 = 1.*rates(6); % [re6, k1] par_r5_p2 = 0.01*rates(6); % [re6, k2] par_r5_p3 = 0.005*rates(6); % [re6, k3] par_r5_p4 = 0.01*rates(6); % [re6, k4] par_r6_p1 = 1.*rates(7); % [re7, k1] par_r6_p2 = 0.01*rates(7); % [re7, k2] par_r6_p3 = 0.005*rates(7); % [re7, k3] par_r6_p4 = 0.01*rates(7); % [re7, k4] par_r7_p1 = 0.02*rates(8); % [re8, k2] par_r8_p1 = 0.02*rates(9); % [re9, k3] par_r9_p1 = 0.02*rates(10); % [re10, k2] par_r10_p1 = 0.02*rates(11); % [re11, k5] par_r11_p1 = 0.02*rates(12); % [re12, k3] par_r12_p1 = 0.02*rates(13); % [re13, k1] par_r13_p1 = 1.*rates(14); % [re14, k1] par_r13_p2 = 0.01*rates(14); % [re14, k2] par_r13_p3 = 0.01*rates(14); % [re14, k3] par_r14_p1 = 1.*rates(15); % [re15, k1] par_r14_p2 = 0.01*rates(15); % [re15, k2] par_r14_p3 = 0.01*rates(15); % [re15, k3] par_r15_p1 = 0.01*rates(17); % [re17, k4] par_r16_p1 = 0.01*rates(18); % [re18, k4] par_r17_p1 = 0.01*rates(19); % [re19, k1] par_r18_p1 = 0.01*rates(20); % [re20, k1] % don't decline input reaction rates par_r19_p1 = 1.; % [re22, k1] par_r20_p1 = 1.; % [re23, k1] par_r21_p1 = 1.; % [re24, k1] par_r22_p1 = 1.; % [re25, k1]

250 par_r23_p1 = 1.; % [re26, k1] par_r24_p1 = 1.; % [re27, k1] par_r25_p1 = 0.1*rates(28); % [re28, k3] par_r25_p2 = 0.01*rates(28); % [re28, k1] par_r25_p3 = 1.*rates(28); % [re28, k2] par_r25_p4 = 0.01*rates(28); % [re28, k4] par_r26_p1 = 0.1*rates(29); % [re29, k4] par_r26_p2 = 0.01*rates(29); % [re29, k1] par_r27_p1 = 0.005*rates(30); % [re30, k2] par_r27_p2 = 0.1*rates(30); % [re30, k1] par_r27_p3 = 0.01*rates(30); % [re30, k3] par_r28_p1 = 0.005*rates(31); % [re31, k2] par_r28_p2 = 0.1*rates(31); % [re31, k1] par_r28_p3 = 0.01*rates(31); % [re31, k3] par_r29_p1 = 0.01*rates(32); % [re32, k2] par_r30_p1 = 0.1*rates(33); % [re33, k2] par_r30_p2 = 0.01*rates(33); % [re33, k1] % % Boundary Conditions for inputs s22 to s27 g_p1 = 1; % s22 = i1 [Amount] g_p2 = 1; % s23 = i2 [Amount] g_p3 = 1; % s24 = i3 [Amount] g_p4 = 1; % s25 = i4 [Amount] g_p5 = 1; % s26 = i5 [Amount] g_p6 = 1; % s27 = i6 [Amount] % % calculate rates of change R0 = (x(1))*par_r1_p2; R1 = (x(2))*par_r2_p1; R2 = (x(3))*par_r3_p2; R3 = (x(4))*par_r4_p2; R4 = (x(5))*par_r5_p4; R5 = (x(6))*par_r6_p4; R6 = (x(7))*par_r7_p1; R7 = (x(8))*par_r8_p1; R8 = (x(9))*par_r9_p1; R9 = (x(10))*par_r10_p1;

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R10 = (x(10))*par_r11_p1; R11 = (x(10))*par_r12_p1; R12 = (x(11))*par_r13_p3; R13 = (x(11))*par_r14_p3; R14 = (x(12))*par_r15_p1; R15 = (x(12))*par_r16_p1; R16 = (x(13))*par_r17_p1; R17 = (x(13))*par_r18_p1; R18 = ((g_p1)-(x(1)))*par_r19_p1; R19 = ((g_p2)-(x(2)))*par_r20_p1; R20 = ((g_p3)-(x(3)))*par_r21_p1; R21 = ((g_p4)-(x(4)))*par_r22_p1; R22 = ((g_p5)-(x(5)))*par_r23_p1; R23 = ((g_p6)-(x(6)))*par_r24_p1; R24 = (x(14))*par_r25_p4; R25 = (x(15))*par_r26_p2; R26 = (x(16))*par_r27_p3; R27 = (x(17))*par_r28_p3; R28 = (x(18))*par_r29_p1; R29 = (x(19))*par_r30_p2; % d(x)/dt = A*(x) A = [-R0+R18 -R1+R19 -R2+R20 -R3+R21 -R4+R22 -R5+R23 +R0+R1-R6 +R2+R3-R7 +R4+R5-R8 +R6+R7+R8-R9-R10-R11 +R9-R12-R13 +R10-R14-R15 +R11-R16-R17 +R12-R24 +R13-R25 +R14-R26

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+R15-R27 +R16-R28 +R17-R29 +R24 +R25 +R26 +R28 +R29 +R27]; % xdot = A.*x; % end of xdot

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Appendix I. Projects, Organizations, Markup Languages & Ontologies

Table I‐1 identifies Projects, Organizations, Markup Languages & Ontologies relevant to systems modeling of aging.

I‐1. Relevant references for systems modeling of aging Name Description AnatML Anatomy muscular/skeletal markup language, supposedly developed in NZ (links dead as of 8/17/06). Has link at Physiome page, but is still dead as of 9/21/06. APS The American Physiological Society, the United States branch of the IUPS BASIS Biology of ageing e‐science integration and simulation system, formed in 2002. BMES Biomedical Engineering Society CellDesigner SBML‐based software for diagramming biological networks. CellML The purpose of CellML is to store and exchange computer‐based mathematical models. Has an API. CISBAN Centre for Integrated Systems Biology of Ageing and Nutrition (UK) DAVID DAVID Bioinformatic Resources EASE Expression Analysis Systematic Explorer, shows DAVID data. FieldML Part of physiome project, FieldML is an XML‐based language for describing time‐varying and spatially‐varying fields. GAN Gene Aging Nexus (GAN) is a data mining platform for the biogerontological‐ geriatric research community. Hosted at USC. Gene “…provides a controlled vocabulary to describe gene and gene product Ontology attributes in any organism” Consortium GEO Gene Expression Omnibus, run by NIH

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Name Description GO Gene Ontology, www.geneontology.org GOBO Global Open Biological Ontologies, now Open Biomedical Ontologies. Human During 1990‐2003, it mapped the human genome from 5 individuals. Genome IEEE‐EMBS IEEE Engineering in Medicine and Biology Society IUPS International Union of Physiological Sciences, sponsor of Physiome project. KEGG KEGG pathways database KGML ML for KEGG Lung Atlas PI at U of Iowa is Joseph Reinhardt. B Li published on this in 2003 – see Project (Crampin, 2004a) MAF Multimodal Application Framework, http://sirio.cineca.it/B3C/MAF/ MAGE‐ML MAGE‐ML aims to provide a standard for the representation of microarray expression data. MathML MathML is a low‐level specification for describing mathematics as a basis for machine to machine communication. From W3C. Metagraph “The MetaGraph Framework is designed to solve problems encountered when managing multiple hypotheses of changing biological information associated with experimental data.” Last updated 2003? OME Open Microscopy Environment, www.openmicroscopy.org OWL Ontology web language, www.w3.org/2004/OWL/ PathwayML? Physiome The Physiome Project is a worldwide public domain effort to provide a computational framework for understanding human and other eukaryotic physiology. See also http://www.physiome.org.nz/. PhysioML XML for physiological modeling ProteinML Cited by Hunter – no other source? PubMed PubMed Central – major source for bio papers SBML The Systems Biology Markup Language (SBML) is a computer‐readable format for representing models of biochemical reaction networks.

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Name Description SBW Systems Biology Workbench (e.g. from Keck Graduate Institute) SimBios http://simbios.stanford.edu/index.html technology infrastructure for physiome project SysML SysML is a domain‐specific modeling language for systems engineering applications. Probably not relevant to this project; see SBML instead. TissueML Replaced by FieldML, per www.bioeng.auckland.ac.nz/projects/software/planning.php (June 2003) UML Unified Modeling Language, created by the Object Management Group. UMLS ‘The purpose of NLM's Unified Medical Language System (UMLS) is to facilitate the development of computer systems that behave as if they "understand" the meaning of the language of biomedicine and health.’ Visible Human An NIH project started in 1998. Project XML Extensible Markup Language, a derivative of SGML (Standard Generalized Markup Language), defined by the World Wide Web Consortium (W3C). I‐1. Relevant references for systems modeling of aging (continued)

See also http://www.physiome.org/Links/index.html for more MLs, and

http://www.sofg.org/resources/general.html for other ontologies.

This thesis was completed using Microsoft Office 2007 running on Microsoft Windows 7, with citation management by EndNote version X4. It was formatted in accordance with the Drexel University Thesis Manual dated 6/1/2009.

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VITA

Dr. Glenn R. Booker is an Associate Teaching Professor for Drexel University’s College of

Information Science and Technology, and started teaching for Drexel in 1998. He has over 18 years of industry experience as a government contractor or civilian employee, working in aerospace and information system design, development, and maintenance.

He earned a Master of Science degree in Mechanical Engineering from the University of

California at Berkeley (1990). He earned a Bachelor’s degree in Aerospace Engineering &

Mechanics from the University of Minnesota at Minneapolis, with a Minor in German (1985).

 Clearfield, D, Booker, G, and Kriete, A. (Dec 2010) A Top‐Down Whole Cell Modeling

Approach of Aging. Poster presented at the Systems Biology of Human Aging (SBHA)

conference, Philadelphia, PA.

 Kriete A, Bosl WJ, and Booker G. (2010). Rule‐Based Cell Systems Model of Aging using

Feedback Loop Motifs Mediated by Stress Responses. PLoS Comput Biol 6(6): e1000820.

doi:10.1371/journal.pcbi.1000820.

 Booker, G, Bosl, W, and Kriete, A. (Aug 2009) Fuzzy Logic Modeling of Stress Responses

in Cell Aging. Poster and paper presented at the Foundations of Systems Biology in

Engineering (FOSBE) conference, Englewood, CO.

 Booker, G, Yalamanchili, N, and Kriete, A. (Nov 2008) Fuzzy Logic Model of Cellular

Stress in Response to Atypical Activation of NF‐kB. Poster presented at Greater

Philadelphia Bioinformatics Alliance (GPBA) Retreat, and at the Sprit of

Entrepreneurship in Life Saving Solutions showcase, both in Philadelphia, PA.