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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. POWER LAWS AND DYNAMICS IN MACROSCOPIC & MICROSCOPIC
SYSTEMS: PHARMACEUTICAL PERSPECTIVES
DISSERTATION
Presented in Partial Fulfillm ent o f the Requirements for
the Degree Doctor o f Philosophy in the
Graduate School o f The Ohio State University
By
Teh-Min Hu, M.S.
*****
The Ohio State University 2002
Dissertation Committee:
Dr. W illiam L. Hayton, Adviser Approved by
D r. Kenneth K . Chan
Dr. Susan R. Maflery A dviser Dr. Mark A . Morse College o f Pharmacy
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ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor. Ml 48106-1346
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT
Power-Iaw relationships (y = ax1*) are ubiquitous and extensively studied. The first
part o f my dissertation investigated theoretical and empirical power-law relationships that
are drug-related. Statistical analysis and Monte Carlo simulation were used to
characterize uncertainty in the allometric exponent (b) o f drag clearance. W hile the
individual b values o f 91 drugs generally fe ll w ithin a broad range between 0.2 and 1.2,
the b value from the aggregated clearance values (adjusted to a common a value) was
0.74, with a 99% C l o f 0.71 to 0.76. However, the b value for the predominantly renally
excreted drugs tended towards 0.67. The simulation results suggested that the wide range
o f b values observed for individual drugs could have resulted from random variability in
clearance values determined in the lim ited number o f species used for each drug.
Chapter 3 characterized a novel power-law relationship. Using drug interaction
information reported in 1981,1991 and 1999, a drug-drug interaction network was
described in which the interacting drugs were treated as nodes and were connected with
undirected links that represented interactions. The connectivity o f the resulting network
followed a power-law distribution. The scaling exponent was close to -1 3 and
independent o f the network size. A dynamic model was proposed to account for the
observed scale-free structure o f the network.
i i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapters 4 and 5 experimentally and theoretically explored complex interactions
among pathophysioIogicaQy relevant molecules. Chapter 4 investigated dynamic
interactions among the enzyme superoxide dismutase (SOD), the free radicals nitric oxide
(NO) and superoxide (O O , and the antioxidant glutathione (GSH) in an in v itro model
system. The results showed that SOD's effects on nitrosation were biphasic and dynamic
in nature; i.e., while low concentrations o f SOD were pro-nitrosative, high SOD
concentrations inhibited nitrosation. However, even the in itia lly inhibitory, high SOD
concentrations (> 500 U/ml) became pro-nitrosative over time. SOD predominantly
exhibited the pro-nitrosative effect when GSH was present. Theoretical results in chapter
5 suggested that GSH may modulate the nitrosation reaction in a switch-like manner, and
that concurrently high NO and O f generation may result in nonlinear dynamics o f the
nitrogen oxide species.
i i i i i i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. To My Parents & T o th e M em ory o f M y G randm a
hr
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENTS
I thank my adviser, Dr. W illiam Hayton, fo r inspiration, intellectual support,
encouragement and enthusiasm, which made this dissertation possible. His modest,
rigorous and open-minded attitude toward scientific study has had a great influence on
me. I am sincerely grateful for his patience and insights in editing my scientific writings,
which made me a better scientist I thank Dr. Susan M ailery for giving me the
opportunity to study chemistry and biology o f reactive nitrogen and oxygen species in her
lab, which fed to the findings in Chapters 4 and 5. I am greatly appreciative for the
tremendous time and energy that she spent on our co-authored paper. I am very thankful
for her encouragement, patience and advice, i also express my thanks to Ping Pei for
helping me in Dr. Mallery’s lab. I thank Dr. Morse for the insightful comments and
suggestions for my paper and dissertation. I am also grateful to Dr. Chan for his
invaluable suggestions for my dissertation. Full scholarship was granted by the M inistry
o f National Defense in Taiwan. I wish to thank my previous colleagues in National
Defense Medical Center, Drs. O liver Y-P. Hu, An-Rong Lee, Da-Pang Wang, Li-Chien
Chang and Ming-Kuan Hu, who helped and encouraged me during my study in the U.S.
I am deeply indebted to Sbih-Jiuan fo r tremendous help and support, stimulating
discussions and companionship. Last, but not least, I thank my parents for their
unconditional love, fu ll support and understanding.
v
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. VITA
April 28,1967 ------Bom - Taipei, Taiwan
1988 -1989 ------Undergraduate Research, National Defense
Medical Center (NDMC), Taipei, Taiwan
1989 ------B.S. Pharmacy, NDMC
1989-1991 ------Teaching Associate, NDMC
1991 -1 9 9 3 ------Graduate Research, NDMC
1993 ------M.S. Pharmaceutical Sciences, NDMC
1993 - 1997 ------Teaching and Research Associate, NDMC
1997-present ------Visiting Scholarship, The Ohio State University
PUBLICATIONS
Full Papers
1. Teh-Min Hu and W illiam L. Hayton, AUometric scaling o f xenobiotic clearance: uncertainty versus universality. AAPS PharmSci, 3(4) a rticle 2 9 ,20 01.
2. O liver Yoa-Pu Hu, Hung-Shang Tang, H-Y Lane, W-H Chang and Teh-Min Hu. Novel single-point plasma or saliva dextromethorphan method for determining CYP2D6 a c tiv ity . / . Pharm acol Exp.. Ther. 285(3): 955-960,1998
3. Oliver Yoa-PuHil Teh-Min Hri. B-L Chen and K-M Hm, Various o f n»*e and extent o f absorption in bioequivalent study o f norfloxacin tablet. Chin. Pharm. J. 47:363-376,1995
v i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4. Shung-Tai Ho, Jhi-Joung Wang, O liver Yoa-Pu Hu and Teh-Min Hw_ The effect o f aging on the pharmacokinetics o f nalbuphine in rabbits. Biopharm. Drug Dispos. 16: 695-701,1995
5. O liver Yao-Pu Hu, Teh-Min Hu and Hung-Shang Tang, Determination o f galactose in human blood by high performance liquid chromatography: comparison w ith enzymatic method and application to pharmacokinetic study o f galactose in patients w ith liver dysfunction. J. Pharm. ScL 84:231-235,1995
6. An-Rong Lee and Teh-Min H it Determination o f guaiphenesin in anti-tussive pharmaceutical preparations containing dextromethorphan by first- and second- derivative ultraviolet spectrophotometry. /. Pharm. Biomed. Anal. 12:747-752, 1994
7. O liver Yoa-Pu Hu, Teh-Min Hu. Shu-Fen Chiao, Kai-Min Chu, Shu-Fen Chan, Jin- Shing Lai and Ping-Hong Chung, Comparative bioavailability study o f digoxin tablets - an example o f using nonspecific analytical methodology. J. Clin. Pharm. Assoc . 1 :37-47,1992
8. Teh-Min Hn and An-Rong Lee, Simultaneous assay o f aminophylline and phenobarbital in compound tablets by UV spectrophotometry. Chin. Pharm. J. 44: 31-36,1992
A b stra cts
1. Teh-Min Hu Susan R. Mallery and W illiam L. Hayton, Kinetic modeling o f nitric oxide reactions in the celL AAPS Annual Meeting and Exposition, Oct. 21-25,2001, Denver, Colorado, USA.
2. Teh-Min Hu and W illiam L. Hayton, AHometric scaling o f drug clearance: variability versus universality. AAPS Annual Meeting and Exposition, Oct. 21-25,2001, Denver, Colorado, USA.
3. Teh-Min Hu. Oliver Yoa-Pu Hu and Hun-Shang Tang, The kinetics o f urinary excretion o f galactose in normal subjects and patients w ith liver diseases. AAPS Tenth Annual Meeting and Exposition, Nov. 5-9,1995, Miami beach, Florida, USA {Pharmaceutical Research, 12(suppl), 9 : S 103,1995).
F IE L D S O F STU D Y
M ajor Field: Pharmacy
vu
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS
Abstract _____ ....______...______i i
Dedication ------iv
Acknowledgments mw...^.«.»...*...... *m...... v
V it a ______v i
List o f Tables ------x i
List o f Figures ------x ii
Chapters:
1. Introduction ------I
2. Allometric Scaling o f Xenobiotic Clearance: Uncertainty versos Universality
2.1 Introduction ------I I 22. Materials and methods ------13 2.2.1 Data collection and statistical analysis ______13 2 2 2 Monte C arlo sim ulation ______13 2.3 Results ...... 14 2 A Discussion ______....______16 2.5 Summaiy 22 2.6 ...... 23
3. Power-Law Scaling o f the Drug-Drug Interaction Network
3.1 Introduction ______44
vrn
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 3 Materials and methods ______47 3.2.1 Data acquisition ______47 3 3 3 Data analysis __ 48 3 3 3 Theoretical considerations ______49 33 Results ------50 3.4 Discussion ______52 3.5 Conclusion ______60 3.6 Summary ______60 3.7 References ______61
4. Dynamic Biphasic Effect o f Superoxide Dismutases on Nitric-Oxide-Mediated
Nitrosation Reaction
4.1 Introduction ------....------71 43 Materials and methods ______73 43.1 Materials ______73 433 Kinetics of DAN nitrosation ------73 4 3 3 O xidation o f DHR b y SIN-1 ______74 43.4 Cytochrome c reduction assay ______74 43 3 HPLC determination o f SIN-1 degradation kinetics ------75 43.6 Method validation ______....------76 43 Results ------76 4.4 Discussion ------80 43 Conclusion ______88 4.6 Summary ------88 1.7 References ...... 90
5. Kinetic Modeling o f Nitric-Oxide-Associated Reaction Network: Biological
Implications
5.1 Introduction ______106 5 3 M odel ------—...______109 53.1 Reaction chemistry and rate constants ------109 533 Numerical simulations ______110 5 3 R e s u lts ______I I I 53.1 Kinetic profiles ------I I I 5 3 3 GSH as a dynamic sw itch ______111 533 Nonlinear dynamics at high NO and CV input rates ______112 5 3 .4 Phase portraits ..... ______113 5.4 Discussion ______114 5 3 S u m m a ry ______118 ix
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5*6 **H *t**t**H ****H **H *H H tt*t*»H **<*tM ******H ************M «****H «*H ****(**t*(*»(4*M I(|* ^ (S
Appendices
Appendix A MATHEMATICA Program for the Monte Carlo Simulations ___ 133 Appendix B Release Mechanism o f Nitric Oxide and Superoxide from SIN-1 139
BibEograpliy ------...______.... 141
x
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Table Page
2.1 Allometric scaling parameters obtained from linear regressions o f the Iog-!og-transfonned CL versus BW data o f 115 xenobiotics ______33
2.2 Simulated b values in different scenarios w ith varied body weight ranges __ 38
23 Summary ofthe statistical results in Fig. 2.3 ______39
3.1 Basic characteristics o f drug-drug interaction networks ______64
3.2 The top-10 most interacting drugs in the three databases ______65
5.1 The rate constants used for the simulation ------123
5 2 Parameter values for the simulation ______124
x i
Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES
Figpre Page
2.1 The frequency distribution o f the b values for the 91 xenobiotics that showed statistically significant correlation between log CL and log BW in Table 2.1 ------... 40
2 2 The frequency distribution o f the simulated b values in the ten scenarios where the number o f animal species and the range o f body weight were v a rie d ______...__ ___ .... 41
2.3 The relationship between normalized clearances fCI r ^ l and body weights (BW) for the 91 xenobiotics (n = 460) that showed statistically significant correlation between log CL and log BW in Table 2.1 __ .... 42
2.4 The deviation between the fitte d and the observed human C L fo r 68 xi^itics ...... 43
3.1 A model for the drug-drug interaction network ______.... 66
3.2 A drug-drug interaction network consisted o f966 drugs (dots) and 33 interactions (lines) — _____ ..._ 67
3.3 The frequency distribution for the number o f interactions a given drug has. Data were acquired from databases published in 1981 (351 drugs, 3A ), 1991 (636 drugs, 3B) and 1999 (966 drugs, 3C) ______. . . . 68
3.4 The probability degree distributions for the drug-drug interaction networks .... 69
3.5 Cumulative preferential linking for the drug-drug interaction network. The line corresponds to no preferential linking ______.... 70
4.1 The chemical structures o f 3-morphohnosydnommine (SIM-1), 2,3- diaminonaphthalene (DAN) and dihydrorhodamine 123 (D H R ) ______.... 95
xn
Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. 4.2 Nitrosation kinetics o f DAN in the absence and presence o f different levels o f Cn^n-S O D ______96
43 Time- and concentration-dependent, biphasic, dose-response relationship for the effect o f Cu,Zn-SOD on DAN nitrosation ------97
4.4 Effect o f DAN concentration on SOD modulation o f nitrosation kinetics ___ 98
4.5 Time- and concentration-dependent, biphasic, dose-response relationships for the effects o f Mn-SOD and Fe-SOD ______99
4.6 Effect o f intact Cu^n-SOD (•), heat-inactivated Cu^n-SOD (O), BSA (■ ), and metal ions (Cu** A,C uv V ,Z n "r O ) on DAN nitrosation ______100
4.7 Effect o f glutathione (GSH) on Cu^ii-SOD modulation o f DAN nitrosation .. 101
4.8 Effect o f Cu,Zn-SOD on SIN-1 mediated oxidation ofDHR ______102
4.9 Effect o f Cn,Zn-SOD on NO release kinetics o f SIN-1 measured by HPLC __ 103
4.10 Comparison o f the nitrosation kinetics among three SOD isozymes at 1000 U /m l ______104
4.11 Proposed mechanisms for SOD’s biphasic effect on SIN-1-mediated nitrosation reaction ...... 105
5.1 The model ...... i...... 125
5.2 Concentration-thne profiles ofNO, 0 2~, ONOO", N20 3, GSNO, and GSH. Scenarios: (a) kt - k2; (b ) k t - 0.5 k2; (c ) kt = 0.25 k2; (d) k t - 0.125 k2; (e) kt = 0.0625 k2. [GSHjbaai = 10 mM, k2 - 1*10'7 M/s for a ll scenarios ___ 126
53 Concentration-time profiles ofNO , 0>“ ONOO" N203, GSNO, and GSH. Scenarios: (a) kt = k2; (b ) kt = 0 3 k2; (c ) kt = 0.25 k2; (d) kt - 0.125 k2; (e) kt = 0.0625 k2. [GSH]b«sai = I m M , k2 = 1*10*7 M/s for a ll scenarios ____ 127
5.4 Concentration-time profiles ofN O , 0 2_, ONOO", N20 3, GSNO, and GSH. Scenarios: (a) k t = k2; (b ) kt = 0 3 (c ) kt = 0 3 5 k2; (d ) kt = 0.125 k2; (e) k ( = 0.0625 fcj. [GSH]bosai= 0 .1 m M , k2 — 1*10"7 M/s for a ll scenarios __ 128
53 Concentration-time profiles o f N^Oj and GSH at the initial GSH level equal to 1 mM. Arrow: start o f zero-order GSH input (kj). k2 = 6 jiM /m in ; kt = 0 3 k2; ks = (a) 20 tiM/m in; (b) 10 pM/min; (c) 5 pM/min; (d ) 2 3 p M /m in; (e) 135 p M /m in ______129
x iii
Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. 5.6 Concentration-time profiles ofNO , 0 2”, ONOO- , N->03, GSNO, and GSH. Scenarios: (a) k t — k2; (b) kt = 0.5 k2; (c) kt = 0 2 5 k2; (d) kt = 0.125 k2; (e) k [ = 0.0625 k2^ [GSHJbasai = 10 m M , k2 = 1*IQS M/s for all scenarios _ 130
5.7 (A) Phase plane analysis o f [NO]s.s. (B) [NOlss versos k /k 2, k2= 1*10'5 M/s; kf/ky = (a) 4 ; (b) 2; (c) I ; (d) 0.5; (e ) 0 2 5 ; ( f) 0.125 ______131
5.8 (A ) Phase plane analysis o f [NO]s.s. (B) [NOlss versus k /k 2_ k2= 1*10*® M /s; k /k 2 = (a) 4 ; (b) 2; (c) I ; (d ) 0 .5 ; (e ) 0 2 5 ; (0 0.125 ______132
B .l Mechanism for the release ofNO and O f from SIN-1 ______138
B2 HPLC chromatograms for the decomposition kinetics o f SIN-1 ______139
x iv
Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. C H APTER I
INTRODUCTION
Many seemingly unrelated scientific disciplines have recently devoted to study the
emerging properties o f system structures and dynamics.1'15 The system can be as small
and confined as a cell6 or as large and unbounded as the World-Wide Web (WWW).3*5
W hile the interactions among the system elements may be complex and the system
behavior is d ifficu lt to predict, some system properties can be described by a simple
power-law equation.
y=ax* (I)
The idea that one can find sim plicity out o f complexity has attracted scientists from
diverse fields who have pondered how such regularity could exist in nature. A recent
colloquium highlighted the intensity o f growing interests in finding a power-law
relationship in physical, biological, economical and social systems.16
In the pharmaceutical field, a well-known example o f a power-law relationship is
the allometric scaling o f pharmacokinetic (PK) parameters across species.1718 That PK
parameters (clearance, volume o f distribution, half life ) o f a wide variety o f drugs can be
I
Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. scaled by equation I, tnw hichy is the PK parameter andx is the body weight, is itse lf an
astounding, yet useful concept The elimination o f a drag from the body involves
complex physiological processes and is dependent on drug characteristics. The existence
o f a simple power-law relationship in describing PK parameters for a variety o f drugs in
different animal species suggested that macroscopicaily drug elimination is governed by
sim ilar structural and functional attributes among species. Although the underlying
principle remained unknown, the concept o f allometric scaling has been widely applied in
predicting PK parameters in human from parameter values determined in animals.19,20
Accordingly, allometric scaling has been an alternate method used for the prediction o f
the first-time-in-man dose during drug development,21,22 in which case the clearance (CL)
values o f a given drug studied in different species were scaled and, in most cases, the CL
value in human can be extrapolated from the obtained scaling relationship from other
animal species.
One o f the problems in applying allometric scaling for dose estimation is the
uncertainty in determining the b value in equation 1. For example, to obtain the b value
in scaling CL, a common procedure is to use linear regression o f the log-log-transformed
CL versus body weight data. This process is subjected to statistical uncertainty when a
lim ited number o f data points are used. However, to my surprise, most studies reported a
b value without addressing the uncertainty issue. When the literature data were
examined, the b value obtained from the scaling o f CL fo r a variety o f xenobiotics tended
to be scattered. Was the scatter o f b values related to the variability in PK properties
among different drugs? Or was it due to the uncertainty in estimation o f this value? The
answers to these questions are important because they may determine how the allometric 2
Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. scaling is implemented and applied. Specifically, if different drugs should have different
scaling properties, the current practice o f allometric scaling in the pharmaceutical
sciences should focus on improving the experimental design in order to obtain a more
reliable estimate o f the 6 value. Otherwise, one may start to consider the feasibility o f
using a fixed-exponent approach to a specific group o f drugs when allometric scaling is
used for estimation o f the first-time-in-man dose. The question o f whether a universal
exponent exists in scaling drug CL coincides with a century-long quest for a unifying
theory in the allometric scaling o f basal metabolic rate.23*26 Using statistical analyses and
Monte Carlo simulations, Chapter 2 addressed the uncertainty and universality issues in
allometric scaling o f drug clearance.27
Allometric scaling in pharmacokinetics illustrates that drug disposition in complex
physiological systems can give rise to a power-law relationship when the problem was
examined at a global level. It also signifies that one may find the same regularity across
different disciplines, which motivated the study in Chapter 3. The system described in
Chapter 3 was a growing network which consisted o f drugs that interact with each other.
The structure and the dynamics o f the drug-drug interaction network were characterized
and the connectivity o f a given drug (the number o f interaction a given drug has) was
found to follow a power-law distribution, which again can be represented by equation I.
The finding o f a power-law distribution in the drug-drug interaction network concurred
w ith recent m ultidisciplinary interests in analyzing complex networks,1'15 which are
introduced as follows.
Generally speaking, a network is composed o f nodes (vertices) that are connected
by links (edges). The degree o f a node specifies the number o f links that a node has.1 3
Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. Traditionally the study o f complex network has been in the field o f graph theory in
mathematics, h i a random graph, the links are placed randomly among nodes, and the
degree distribution o f a random graph therefore follows a Poisson distribution, which is a
bell-shaped curve w ith a peak at the average degree.1 The question is: are complex
networks in the real world governed by random processes?
Complex networks exist in different forms in nature. For example, the
interconnection o f molecules by chemical reactions inside a cell forms a metabolic
network.6 In a society, networks are formed by direct or indirect interactions o f
individuals.1 Barabasi and Albert2 in 1999 found that for most large real networks the
degree distribution followed power-law degree distribution. In the past three years,
sim ilar findings have been extended to a number o f real networks, such as the WWW3*5
and cellular,6 ecological,7 and scientific collaboration networks8 etc. Moreover,
theoretical models that were able to capture the general feature o f the power-law
distribution have been proposed.9' 14 Two recent reviews1'15 highlighted the intensity o f
growing interest in understanding the topology and evolution o f complex networks.
Drug-drug interaction poses a potential threat to patients who receive treatment with
m ultiple medications. The incidence o f drug interactions w ill be increased when the
number o f co-medicated drugs is increased. The general mechanisms for an interaction
to occur include the pharmacokinetic interactions (or AD ME interactions) by which the
processes o f drug absorption, distribution, metabolism and excretion are affected and the
pharmacodynamic interactions by which the effects o f a drug at its site o f action are
modified.28 Although studies on a particular interaction were occasionally reported and
4
Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. drug-drug interaction information has accumulated over time, there has been lack o f a
systematic approach fo r analyzing the aggregate drug-drug interaction information.
I f the interacting drugs were treated as nodes connected w ith undirected links that
represent the interactions, a drug-drug interaction network can be obtained. Questions
pertaining to network analysis then arise: What is the topology o f the drug-drug
interaction network? How does this network evolve as a dynamic system? The answers
to these questions may provide insights into the nature o f drug-drug interactions. In
Chapter 3, we constructed three drug-drug interaction networks from collective drug
interaction information spanning over two decades. The results indicated that the degree
distribution o f all three networks followed a power law w ith an invariant scaling
exponent close to - 1 3 .
The beauty o f a power taw probably rests on its indication that a complex system is
self-organizing.16 A t a microscopic leveL, the details o f the system may be chaodc so that
one may not have a clear idea about how the system w ill behave. When the system is
examined globally, some governing principles o f the system may be revealed in a simple
form .
However, life is not always as simple as the power-law relationship might have
suggested. This is especially true in biological and ecological systems. How does one
account for a sudden change in an ecological or biological state? Why does the same set
o f genes control different phenotypes? Why does the same molecule play a totally
opposite role in physiological and pathophysiological conditions? For example^ the free
radical nitric oxide (NO) is both a tumor promoter and suppressor.29 Most o f these
questions are d ifficu lt to explore experimentally and systematically, because too many 5
Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. variables are involved. In the NO case, a subsystem can be isolated and examined both
experimentally and theoretically. Sometimes, one may be amazed by how a simple
model system can give rise to diverse outcomes, which lead to a totally opposite notion as
compared w ith that described for power-law relationships.
The complexity o f a system is often reflected by its dynamics, a subject that deals
w ith change, and w ith systems that evolve in time.30 By studying the dynamics o f a
sim plified model, the complex phenomena observed in the real system can be accounted
for. Some examples are: (i) a biochemical gene switch that can be realized by just two
coupled differential equations;30 (ii) complex dynamic transitions in epidemics can be
understood by a simple mathematical model;31 (iii) models o f coupled biochemical
reactions can predict the emergent properties o f biological signaling networks.32 The use
o f theoretical models provides the following advantages when biological complexity is
dealt w ith :33
• It is possible to ask questions that may be inaccessible to experiments or hard to
address experimentally.
• Through modeling, testable predictions can be formed. Counterintuitive
explanations or surprising predictions are also provided.
• Modeling approach allows a rapid exploration o f different mechanisms and o f a
large range o f conditions. It also allows researcher to identify key parameters
o f the system.
• Modeling approach provides a unified theoretical framework that accounts for
available experimental observations and supports or not experimental
conclusions. 6
Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. • Conceptualization by theoretical models leads to clarification o f hypothesis.
• Modeling approach allows analysis o f complex situations in which multiple and
coupled variables are involved, for which sheer intuition provides no insight.
In Chapters 4 and 5, examples were given to demonstrate how systems can be
examined experimentally and theoretically in a dynamic sense. Because the studies were,
by their very nature, dynamic, we were able to identify some important features
associated w ith the enzyme superoxide dismutase and the reactions mediated by NO.
From pharmaceutical perspectives, it is important for pharmaceutical scientists to
have both global and dynamic views on biochemical, cellular and physiological function,
toward the objective o f improved understanding o f the disease state.
References
1. Albert R, Barabasi AL. Statistical mechanics o f complex networks. Mod. Phys. 2002;74:47-97.
2. Barabasi AL, Albert R. Emergence o f scaling in random networks. Science. 1999;286:509-512.
3. Albert R, Jeong H, Barabasi AL. The diameter ofthe world-wide web. Nature. I999;40I:I30.
4. Huberman BA, Adamic LA. Growth dynamics ofthe world-wide web. Nature. 1999;40I:l3l.
5. Adamic LA, Huberman BA. Power-law distribution o f the world wide web. Science. 2000^87:2115.
6. Jeong H, Tombor B, Albert R, Oltvai ZN, Barabasi AL. The large-scale organization o f metabolic networks. Nature. 2000;407:651-654.
7
Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. 7. Montoya JM, Sole RV. Small world patterns in food webs. AxXiv.org e-Print archive. 2000. http://www.arxiv.org/abs/cond-mat/0011195
8. Newman MEJ. The structure o f scientific collaboration networks. Proc Natl Acad SciUSA. 2001;98:404-409.
9. Barabasi AL, Albert R, Jeong H. Mean-fieid theory for scale-free random networks. Physica A. 1999;272:173-187.
10. Krapivsky PL, Redner S, Leyvraz F. Connectivity o f growing random networks. Phys. Rev. Lett 2000;85:4629-4632.
11. Dorogovtsev SN, Mendes JFF, Samukhin AN. Structure o f growing networks with preferential linking. Phys. Rev. Lett 2000;85:4633-4636.
12. Albert R, Barabasi AL. Topology o f evolving networks: Local events and universality. Phys. Rev. Lett 2000;85:5234-5237.
13. Kirillova OV. Communication networks with an emergent dynamical structure. Phys. Rev. Lett 2001;87:06870I;l-4.
14. Dorogovtsev SN, Mendes JFF. Scaling properties o f scale-free evolving networks: Continuous approach. Phys. Rev. E. 200I;63:056I25;l-I9 .
15. Dorogovtsev SN, Mendes JFF. Evolution o f networks. ArXiv.org e-Print archive. 2001. http://www.arxiv.org/abs/ cond-mat/0106144
16. Turcotte DL, Rundle JB. Self-organized complexity in the physical, biological, and social sciences. Proc Natl Acad Sci USA. 20G2;99(suppL 1)^463-2465.
17. Boxenbaum H. Interspecies scaling allometry, physiological time, and the ground plan o f pharmacokinetics. J Pharmacokin Biopharm. 1982;10:201-227.
18. Mordenti J. Man versus beast Pharmacokinetic scaling in mammals. J Pharm Sci. 1986;75:1028-1040.
8
Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. 19. Sawada Y, Hanano M, Sugiyama Y, Iga T. Prediction o f disposition o f beta-Iactam antibiotics in humans from pharmacokinetic parameters in animals. J Pharmacokin Biopbann. 1984;12:241-261.
20. Feng MR, Lou X, Brown RR, Hutchaleelaha A. Allometric pharmacokinetic scaling: Towards the prediction o f human oral pharmacokinetics. Pharm Res. 2000;17:410-418.
21. Bonate PL, Howard D. Prospective allometic scaling: Does the emperor have clothes? J C lin Pharmacol. 2000;40:665-670.
22. Mahmood I. Critique o f prospective allometric scaling: Does the emperor have clothes? J C lin Pharmacol. 2000;40:671-674.
23. West GB, Brown JH, Enquist BJ. A general model for the origin o f allometric scaling laws in biology. Science. 1997;276:122-126.
24. West GB, Brown JH, Enquist BJ. The fourth dimension o f life : Fractal geometry and allometric scaling o f organisms. Science. 1999;284:1677-1679.
25. Banavar JR, Mari tan A, Rinaldo A. Size and form in efficient transportation networks. Nature. 1999;399:130-132.
26. Dodds PS, Rothman DH, Weitz JS. Re-examination o f the "3/4-Iaw" o f metabolism. J Theor Biol. 2001;209:9-27.
27. Hu TM, Hayton WL. Allometric scaling o f xenobiodc clearance: Uncertainty versus universality. AAPS PharmSci. 20013(4), article 29. (http://www.phannsci.org/)
28. Stockley IH. Drug interactions: a source book o f adverse interactions, their mechanisms, clinical importance and management, London, UK: Pharmaceutical Press, 1999.
29. Wink DA, Vodovotx Y, Laval J, Laval F, Dewhirst MW, M itchell JB. The multifaceted roles o f nitric oxide in cancer. Carcinogenesis. I998;19(5):7l 1-721.
9
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30. Strogatz SH. Nonlinear dynamics and chaos. Reading M A: Addison-Wesley Publishing Company, 1994.
31. Earn DJD, Rohani P, Bofker MB, Grenfell BT. A simple model for complex dynamical transitions in epidemics. Science. 2000;287:667-670.
3 2 . Bhalla U S , Iyengar R . Emergent properties o f networks o f biological signaling pathways. Science. 1999;283:381-387.
33. Leloup J-C, Goldbeter A. Modeling the molecular regulatory mechanism o f circadian rhythms in Drosophila. Bioessays. 2000;22:84-93.
10
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H AP TER 2
Allom etric Scaling o f Xenobfotic Clearance: Uncertainty versus Universality
2.1 Introduction
Biological structures and processes from cellular metabolism to population
dynamics are affected by the size o f the organism.1'2 Although the sizes o f m am m alian
species span 7 orders o f magnitude, interspecies sim ilarities in structural, physiological
and biochemical attributes result in an empirical power law (the allometric equation) that
characterizes the dependency o f biological variables on body mass:
Y = a BW b
where Y is the dependent biological variable o f interest, a is a normalization constant
known as the aQometric coefficient. BW is the body weight, and b is the allometric
exponent. The exponential form can be transformed into a linear function:
LogY = Log a + b(LogBW)
and a and b can be estimated from the intercept and slope o f a linear regression analysis.
The magnitude o f b characterizes the rate o f change o f a biological variable subjected to
a change o f body mass and reflects the geometric and dynamic constraints o f the body.3'4
Although allometric scaling o f physiological parameters has been a century-long
II
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. endeavor, no consensus has been reached as to whether a universal scaling exponent
exists. In particular, discussion has centered on whether the basal metabolic rate scales as
the 2/3 or 3/4 power o f the body mass.1'2,3*9
Allometric scaling has been applied in pharmacokinetics for approximately two
decades. The major interest has been prediction o f pharmacokinetic parameters in man
from parameter values determined in animals.10'15 Clearance has been the most studied
parameter, as it determines the drug-dosing rate. In most cases, the pharmacokinetics o f a
new drug was studied in several animal species and the allometric relationship between
pharmacokinetic parameters and the body weight was determined using linear regression
o f the log-transformed data. One or more o f the following observations frequently apply
to the resulting publications: (i) little attention was given to uncertainty in the a and b
values; while the correlation coefficient was frequently reported, the confidence intervals
o f the a and b values were infrequently addressed, (ii) The a and b values were used for
interspecies extrapolation o f pharmacokinetics without analysis o f the uncertainty in the
predicted parameter values, (iii) The b value o f clearance was compared w ith either the
value 2/3 from “surface law” or 3/4 from “Kleiber’s law” and the allometric scaling o f
basal metabolic rate.
This study investigated the possible impact o f the uncertainty in allometric scaling
parameters on predicted pharmacokinetic parameter values. A statistical analysis o f the
allometric exponent o f clearance from I IS xenobiotics and a Monte Carlo simulation was
combined to characterize the uncertainty in the allometric exponent for clearance and to
investigate whether a universal exponent may exist for the scaling o f xenobiotic
clearance. 12
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12 Materials and Methods
2.2.1 D ata c o lle ctio n and s ta tis tic a l analysis
Clearance (CL) and BW data fo r 115 substances were collected from published
studies in which at least three animal species were used for the purpose o f interspecies
comparison o f pharmacokinetics. A total o f 18 species (16 mammals, 2 birds) with body
weight spanning I04 were involved (Table 2.1).16"90 The published studies generally did
not control or standardize across species the (i) dosage, (if) numbers o f individuals
studied per species, (iii) principal investigator, (iv) blood sampling regime, and (v)
gender.
Linear regression was performed on the log-transformed data according to the
equation. Log CL = log a + b * log BW. Values for a and b were obtained from the
intercept and the slope o f the regression, along with the coefficient o f determination (r).
Statistical inferences about b were performed in the following form:
Ho: b = pi
H i:b*pbi«0,I,2
Where po= 0, pi = 2/3 and P? =3/4, respectively. The 95% and 99% confidence intervals
(C l) were also calculated for each b value.
h i addition, the CL values for each individual xenobiotic were normalized so that
a ll compounds bad the same a value. Linear regression analysis was applied to the
pooled, normalized CL versus BW data fo r the 91 xenobiotics that showed sta tistica lly
significant correlation between log CL and log BW in Table 2.1.
2.2.2 M onte C a rlo sim ula tion
13
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The power function CL = a BW b was used to generate a set o f error-free CL
versus BW data (Appendix A). The values for BW were 0.02,0.25,2.5,5,14 and 70 kg,
which represented the body weights o f mouse, rat, rabbit, monkey, dog and human,
respectively. The values o f a and b used in the simulation werelOO and 0.75,
respectively. Random error was added to the calculated CL values, assuming a normal
distribution o f error with either a 20% or a 30% coefficient o f variation (CV), using the
function RANDOM in Mathematics 4.0 (Wolfram Research, Champaign, IL). The b and
r values were obtained by applying linear regression analyses on the log-log- transformed
error-containing CL versus BW data using the Mathematics function REGRESS. Ten
scenarios w ith a variety o f sampling regimens that covered different numbers o f animal
species (3 - 6) with various body weight ranges (5.6 - 3500 fold) were simulated (n =
100 per scenario). The simulations mimicked the sampling patterns commonly adopted
in the published interspecies pharmacokinetics studies.
2 3 Results
The aQometric scaling parameters and their statistics are listed in Table 2.1. O f 115
compounds, 24 (—21%) showed no correlation between clearance and body weight; i.e.,
there was a lack o f statistical significance fo r the regression (p > 0.05). This generally
occurred when only 3 species were used. Among the remaining 91 cases, the mean ±
SJ3. o f the b values was 0.74 ±0.16 with a wide range from 039 to 13, Fig. 2.1. The
frequency distribution o f the b values appeared to be Gaussian. The mean significantly
differed from 0.67 (p < 0.001), but not 0.75. When the b value o f each substance was
tested statistically against both 0.67 and 0.75, the majority o f the cases (81% and 98% at 14
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the level o f significance equal to 0.05 and 0.01, respectively) failed to reject the null
hypotheses raised against both values (Table 2.1); i.e., individual b values did not differ
from 0.67 and 0.75. The wide range o f 95% and 99% C l o f b highlighted the uncertainty
associated with its determination o f b values in most studies.
The ten animal groups studied by Monte Carlo simulation had mean b values (n =
100 per simulation) close to the assigned true value, 0.75, Table 2 2 . However, the 95%
C l in the majority o f the scenarios failed to distinguish the expected value 0.75 from 0.67.
Only Scenario 4 at the level o f 20% CV secluded the possibility that b was 0.67 with
95% confidence. When the experimental error was set at 30% CV, none o f the
simulations distinguished between b values o f 0.67 and 0.75 w ith 95% confidence. The
mean r value ranged from 0.925 to 0.996, suggesting that the simulated experiments w ith
a 20% and a 30% CV in experimental bias were not particularly noisy. The frequency
distributions o f b values are shown in Fig. 2.2.
Fig. 2 3 shows the relationship between normalized clearances and body weights (n
=460) for the 91 xenobiotics that showed a statistically significant correlation in Table
2.1. The regression slope was 0.74 and the 99% C l was 0.71 - 0.76. The normalised
clearances were divided into four groups: 9 proteins (Group I, n =41), 21 compounds
eliminated mainly via renal secretion (Group 2, n = 105), 39 compounds eliminated
mainly via extensive metabolism (Group 3, n = 203), and 22 compounds eliminated by
both renal excretion and metabolism (Group 4, n = 111), Fig. 23. The summary o f the
regression results appears in Table 23. W hile Groups 1,3 and 4 had a b value close to
0.75 and significantly different from 0.67 (p < 0.001), Group 2 had a b value close to
0.67 and significantly different from 0.75 (p < 0.001). 15
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.4 Discussion
Successful prediction o f human clearance values using allometric scaling and
clearance values measured in animals depends heavily on the accuracy o f the b value.
Retrospective analysis o f published results for 115 substances indicated that the
commonly used experimental designs result in considerable uncertainty in this parameter,
Table 2.1.
CL values for twenty-four o f the substances listed in Table 2.1 failed to follow the
allometric equation at the 95% confidence level. The failures appeared to result from the
following: (i) only three species were studied in 16 cases, which severely lim ited the
robustness o f the statistics; in the remaining S failed cases one or more o f the following
occurred: (ii) the species were studied in different labs in 3 cases, (iii) small (n = 2) or
unequal (n = 2-10) numbers o f animals per species were studied in 4 cases, (iv ) different
dosages among species were used in 2 cases, and (v) high interspecies variability in
UDP-glucuronosyltransferase activity was proposed in one case.75 The failure o f these
24 cases to follow the allometric equation appeared for the most part, therefore, to result
from deficiencies in experimental design; i.e., failure o f detection rather than failure o f
the particular substance’s CL to follow the allometric relationship.
How well did allometry applied to animal CL values predict the human CL value?
One indication is how close the human CL value fe ll to the fitted line. O f the 91
substances that followed the allometric equation, 68 included human as one o f the
species. In 41 cases, the human CL value fe ll below the line and in 27 cases it fe ll above,
Fig. 2.4. The mean deviation was only 0.62% and the m ajority o f deviations were less
than 50%. It therefore appeared that fo r most o f the 68 substances studied in which 16
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. human was one o f the species, the human CL value did not deviate systematically or
extraordinarily from the fitted allometric equation. The tendency, noted by othersI0’12, o f
the CL value for human to be lower than that predicted from animal CL values was
therefore not apparent in this large data set
The b values fo r the 91 substances that followed the allometric equation appeared
to be normally distributed around a mean value o f 0.74 although the range o f values was
quite broad, Fig. 2.1. W hile impossible to answer definitively with these data, the
question o f whether there is a “universal” b value is o f interest Does the distribution
shown in Fig. 2.1 reflect a universal value w ith deviation about the mean due to
measurement errors, or are there different b values fo r the various clearance mechanisms
involved in clearance? The Monte Carlo simulations indicated that introduction o f
modest amounts o f random error in CL determinations. Fig. 2.2, resulted in a distribution
o f b values not unlike that shown in Fig. 2.1. This result supported the possibility that a
universal b value operates and that the range o f values seen in Table 2.1 resulted from
random error in CL determination coupled w ith the uncertainty that accrued from use o f a
lim ited number o f species. However, examination o f subsets o f the 91 substances
segregated by elimination pathway showed a b value around 0.75, except fo r substances
cleared prim arily by the kidneys; the b value fo r this subgroup was 0.65 (see below) and
the C l excluded a value larger than 0.70.
The central tendency o f the b values is o f interest, particularly given the recent
interest in the question o f whether basal metabolic rate scales with a b value o f 0.67 or
0.75.3’4’8’9 When examined individually, the 95% C l o f the b values for most o f the 91
substances included both values, although the mean for a ll the b values tended toward 17
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.75. So that a ll CL values could be viewed together, a normalization process was used
that assumed a common a value for a ll 91 substances and CL values were adjusted
accordingly, F ig . 2 3 . F it o f the allom etric equation to th is data set gave a b value o f 0.74
and its C l included 0.75 and excluded 0.67. Normalized CL values randomly scattered
about the line w ith one exception: in the body weight range 20 - 50 kg (dog, minipig,
sheep and goat) the normalized CL values generally fe ll above the line.
The 91 substances were segregated by molecular size (protein) and by major
elimination pathway (renal excretion, metabolism, combination o f both), Fig. 23. With
the exception o f the renal excretion subgroup, the normalized CL values for the
subgroups showed b values sim ilar to the combined group and their CIs included 0.75
and excluded 0.67, Table 23. The renal excretion subgroup (21 substances and 105 CL
values), however, showed a b value o f 0.65 w ith a C l that excluded 0.75. This result was
surprising as it appeared to contradict b values o f 0.77 reported fo r both mammalian
glomerular filtration rate and effective renal plasma flow,91"93 although it was consistent
w ith a b value o f 0.66 reported for intraspecies scaling o f inulin-based glomerular
filtration rate in humans,94 and with a b value o f 0.69 for scaling creatinine clearance.95
Whether the metabolic rate scales to the 2/3 or the 3/4 power o f body weight has
been the subject o f debate fo r many years. No consensus has been reached. The surface
law that suggested a proportional relationship between the metabolic rate and the body
surface area was first conceptualized in the 19th century. It has gained support from
empirical data6’ 96 as w ell as statistical6’ 9 and theoretical6’ 97 results. In 1932, Kleiber's
empirical analysis led to the 3/4-power law, which has recently been generalized as the
quarter-power law by West et al.3’4 Different theoretical analyses based on nutrient- 18
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. supply networks3,8 and four-dimensional biology4 a ll suggested that the quarter-power
law is the universal scaling law in biology.98 However, the claim o f universality was
challenged by Dodds et al.9 whose statistical and theoretical re-analyses cannot exclude
0.67 as the scaling exponent o f the basal metabolic rate.
The logic behind the pursuit o f a universal law for the scaling o f energy metabolism
across animal species is mainly based on the assumption that an optimal design o f
structure and function operates across animal species.3-4-8- 99,101 Given the fact that
mammals utilize the same energy source (oxygen) and energy transport systems
(cardiovascular, pulmonary) and the possibility that evolutionary force may result in a
design principle that optimizes energy metabolism systems across species, the existence
o f such a law might be possible. However, with available data and analyses a conclusion
has not been reached.
A large body o f literature data has indicated that the allometric scaling relationship
applies to the clearance o f a variety o f xenobiotics. It has been speculated that xenobiotic
clearance is related to metabolic rate and clearance b values have frequently been
compared w ith either 0.67 or 0.75. The b values obtained from the scaling o f clearance
for a variety o f xenobiotics tended to be scattered. M y analysis indicated that the b value
generally fe ll within the broad range between 0 and I or even higher. The scatter o f b
values may have resulted from the uncertainty that accrued from the regression analysis
o f a lim ited number o f data points as discussed above. In addition, the scatter may have
involved the variability in pharmacokinetic properties among different xenobiotics. The
latter rendered the prediction o f the b value extremely difficult. Moreover, the discussion
o f “universality” o f the b value was less possible in this regard. From the 19
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. pharmacokinetics point o f view, lack o f a unique b value for a il drugs may be considered
as a norm. In this regard, the uncertainty and variability became a universal
phenomenon. To determine whether a unique b value exists for the scaling o f CL, a more
rigorous experimental design has to be included to control the uncertainty that is possible
to obscure the conclusion, hi doing so, a study that includes the CL data fo r a variety o f
drags covering the animal species in the scope that is sim ilar to its counterpart in scaling
basal metabolic rate might be sufficient but extremely unrealistic. Therefore, from the
perspectives o f pharmacokinetics where drug is the center o f discussion, it is almost
impossible to address whether the b value o f CL tended to be dominated by one or two
values. However, from the perspectives o f physiology where the function o f a body is o f
interest, systematic analysis o f currently available data in interspecies scaling o f CL may
provide some insight into the interspecies scaling o f energy metabolism. The rationale
behind this line o f reasoning was that the elimination o f a xenobiotic from a body is a
manifestation o f physiological processes such as blood flow and oxygen consumption.
Interestingly, the two competitive exponent values, but not others, in theorizing the
scaling o f energy metabolism reappeared in the present analysis. The value 0.75
appeared to be the central tendency o f the b values for the CL o f a majority o f
compounds, except fo r that o f drugs whose elimination was mainly via kidney.
Whether allometric scaling could be used for the prediction o f the first-time-in-man
dose has been o f debate.102*103 Figure 2.4 showed that a reasonable error range could be
achieved when human CL was predicted by the animal data for some drags. However,
the success shown in the retrospective analysis does not necessarily warrant success in
prospective applications. As indicated by my analyses on the uncertainty o f b values and 20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. as illustrated in Bonate and Howard’s commentary,102 caution is needed when allometric
scaling is applied in a prospective manner. Besides, the use o f a deterministic equation in
predicting individual CL data may be questionable because the inter-subject variability
cannot be accounted for. Nevertheless, allometric scaling could be an alternative tool, if
the population mean CL is to be estimated and the uncertainty is adequately addressed.
When the uncertainty in the determination o f a b-value is relatively large, a fixed-
exponent approach might be feasible, fin this regard, 0.75 might be used fo r substances
that are eliminated mainly by metabolism, and by metabolism and excretion combined,
whereas 0.67 might apply for drop that are eliminated mainly by renal excretion.
21
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.5 Summary
Statistical analysis and Monte Carlo simulation were used to characterize
uncertainty in the allometric exponent (b) o f xenobiotic clearance (CL). CL values for
115 xenobiotics wore from published studies in which at least three species were used for
the purpose o f interspecies comparison o f pharmacokinetics. The b value for each
xenobiotic was calculated along w ith its confidence interval (C l). For 24 xenobiotics
(21%) there was no correlation between log CL and log body weight. For the other 91
cases, the mean ±S D oftheb values was 0.74 ±0.16; range: 0.29- 1.2. M ost(8I% )of
these individual b values did not differ from either 0.67 or 0.75 at p = 0.05. When CL
values fo r the subset o f 91 substances were normalized to a common body weight
coefficient (a), the b value for the 460 adjusted CL values was 0.74; the 99% C l was 0.71
- 0.76, which excluded 0.67. Monte Carlo simulation indicated that the wide range o f
observed b values could have resulted from random variability in CL values determined
in a lim ited number o f species, even though the underlying b value was 0.75. From the
normalized CL values, four xenobiotic subgroups were examined: those that were (i)
protein, and those that were (if) eliminated mainly by renal excretion, (iii) metabolism or
(iv) by renal excretion and metabolism combined. A il subgroups except (ii) showed a b
value not different from 0.75. The b value for the renal excretion subgroup (21
xenobiotics, 105 CL values) was 0.65, which differed from 0.75 but not from 0.67.
22
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.6 References
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16 17 17 17 18 19 20 25 21 22 23 24 26 27 23 28 29 30 31 32 32 32 32 33 Rer. BW data (con inued) versus ip , dg, mk, cz mk, dg, , 1 ms. it, mk, dg, hm dg, mk, it, hm ms. cz, dg, mk, it. n, mk, cz, hm cz, mk, n, ( sh dg, rt>, it, ms, it, mk, hm mk, it, hm ms, dg, it>, it, hm ms, dg, it>, it, ms, ib it, ms, hm dg, ib, it, it, ms, sh, ib, ck, pn ck, ib, hm sh, dg, mk, it, dg ms, mk, ib, n, gp, ms, ms, ml, it, ib, hm ib, it, ml, ms, ms, it, ib, hm ib, it, ms, hm mk, ib, it, ms, ms, it, ib, dg, hm dg, ib, it, ms, hm hm mk, ib, mk, it, dg, ib, n, hm mk, ms, dg, ib, it, ms, ms, it, ib, dg, mk, hm mk, dg, ib, it, hm mk, ms, dg, ib, it, ms, ms, it, ib, dg, mk dg, ib, it, ms, m n.d. n.d. n.d. n.d. n.d. 0.54-1.6 0.52-1.4 0.39-1.1 0.37 - 0.78 0.028-1.6 0,047- 1.9 0.016-1.0 0.74 -0.94 m m im m n.d. n.d. n.d. n.d. n.d.'*' n.d. 0.17-1.7 0.16-1.8 0.28-1.2 0.38-1.2 0.27-1.20.48-1.5 n.d. 0.18-1.2 n.d. 0.19-0.73 n.d. 0.53 • 0.840.006-1.1 0.43 - 0.94 0.52-0.81 0.39 - 0.93 0.55 - 0.93 0.52 - 0.830.35 - 0.84 0.43 - 0.93 0.18-1.0 0.20 - 0.94 0.22 0.22 - 0.84 0.72 -1.2 95% Cl orb 99% Cl ofb ow Species 0.77- 0.91 0.45- 0.70 • ♦ * t • • • e ee ee ee ee ee ee M e eee »M ♦ ♦♦ ♦ p««» 0.06 0.15 *** 0.06 r*m 0.976 0.9550.829 0.902 0 .7 5 -1 .4 0.716 0.982 0.924 0.975 0.663 0.945 0.959 0.975 0.917 0.926 0.823 0.849 b l.l 1.0 0.57 0.98 0.96 0.80 0.57 0.56 0.68 0.74 0.59 a 16 0.69 26 47 0.75 0.975 0.59 - 0.92 0.48-1.0 25 1.0 0.67 0.992 3.9 1.5 6.9 2.1 9.6 0.66 0.986 6.7 0.57 6.3 0.53 4.5 0.68 0.41 0.93 0.834 0.39 0.94 0.84 0.988 0 .1 0 0.033 0.53 0.990 G b 1 -Aminocyelopropanecarboxylnte 1 2.6 0.72 Acivin ALQI567 Anti-dinoxin Fab Anti-dinoxin Antipyrine AL0I576ALQI750 Alfentanil B Amphotericin 0.36 AZT Amsacrinc Fab2 Antivenom ApramycinBetamipron Bosentan 38 0.46 2.8 0.906 BSH CaffeineCandoxatrilat CD4*I Cefazolin Cefmetazole 6.3 0.74 12 0.981 Cefodizime Cefoperazone Cofotetan Tabic 2.1 Allometric scaling parameters obtained from linear regressions of the log-log-transformed CL log-log-transformed ofthe Tabic from 2.1 obtained linear parameters regressions Allometric scaling of 115 xenobiotics (a; b; exponent) coefficient; allometric allometric xenobiotics of 115 w w
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Tabic 2.1. (continued) "L "a i o *3 9 m a o « 1 1 95% Cl of b 1 99% Cl of b a 1 R e f. 1 © o € 73 t ■S - r £ « © oo "d « o o - O d •*r i m s o •d cn d £ efi ff- s £ o d d o 4 ■o n U <3 © - r © s o OO SO a a © o © cn t^- © - p oo cn — TT d i ea o s X £ o » » f ■S Os © u o o cn OS s o 00 a cn - r © n* © o *d nr mi mi n* d d » » e • •3 ■s a O © •A N •A © oo cn o © © oo ■d © Os cn o m N d £ efi £ d 1 • ♦ a ■e i JS 5 © © IA SO a © 00 cn « •A © cn © © cn cn SO - r n* d t £ o a « § I i o o •e 73 c— a [ 00 U cn oo 00 © © OO •A © ■d cn ■d - e t£ ea o > e o d d •e •o JS 'C O © © cn ♦ © © © oq •d oo •A °o - p ©' cn d so £ > (A a o C d l e • *o | • • * © d 00 a cn o © IA © © o Co p © < d cn — - e cn d £ m efi E • 1 l •e •3 JS o w d cn d cn •d *d a oo © mi d £ efi £ i a as £ d d 1 40 1 4 73 JS *o IS : j o © * d sO Q cn cn - P a - r d mi cn o d cn cn cn n* d efi £ es s o o i i t ■3 e . o © IA o d cn a TT * - e d cn cn cn ■d - n cn - r d 3 efi £ o cn s es s d i j* •3 JS » : j • DU sO d oo c— *
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23 27 68 69 43 67 31 31 70 43 46 72 23 73 74 31 71 75 76 77 78 79 80 74 Ref. (continued) m Species Species ms, gp, it, rti, mk, dg mk, rti, it, gp, hm ms, dg, mk, rt, ms, rt, mk, dg, hm dg, mk, rt, hm dg, n, mt, it, rt>, dg rt>, it, hm dg, iti, ft, pg mk, rt, ms, ms, n, pn. mk, dg, hm dg, mk, pn. n, ms, hm mk, rt>, n, ms, rt, mk, hm mk, rt, ms, hm hm n, mk, ms, rt>, rt, ms, mk, ml, dg, rt, ms, rt, hs, dg, hm dg, hs, rt, hm ms, dg, rt>, ck rt, pit, pg, rt>, it, rfa, bb rfa, it, dg mk, rt, ms, mk rb, hm rt, dg, ms, rb, mk, it, ms, hm dg, rb, rt, hut dg, rt, ms, rt, dg, hm dg, rt, rt, rb, bb rb, rt, n.d, n.d, n.d. n.d. n.d. n.d. n.d. n.d, n.d. 0.58-1.2 0.37-1.2 0.51 0.51 -0.81 0,31-0.98 m n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. n.d. 0.17-1,1 0,51 0,51 -1,0 0.49-1.4 0.13-1.7 0.26-1.1 0.33-0.95 n.d. 0,55 0,55 - 0,83 0 .36 -1 .0 0,27 - 0.98 0,33-0,95 0,12-1.1 0.24-0,90 0.50-0.79 0.39-0.94 0.034-1.3 0.45 0.45 - 0.97 0.72 -1.1 0.59 - 0,73 ♦ • • • ♦ • ♦t ♦ ♦ ♦ * ♦ •• 0.1 ♦♦♦ 0.1 •t* n"" 95% Cl ofb 99% Cl orb 0.10 0.06 0.07 0.09 0.06 r>(f> 0.946 0.939 0.995 0.992 0.891 0.910 0.999 0.982 0.990 0.964 0.80 0.57 0.71 0.42 0.710 0.89 0.989 0.71 0,9950.67 0.898 0.55-0.87 0.34-1.1 0.64 0.976 0.53 0.62 0.966 0.63 a b 13 11 30 0.69 0.996 98 0.64 0.81 29 50 20 0.66 29 69 28 0.66 0.999 3.4 0.65 7.5 0.64 6.8 7.2 0.16 0.350.78 0.87 0.979 0.10 Phencyclidine 52 0.64 Propranolol lisand-1 filyconrotein P-selcctin 0.0060 0.93 Procalerol PanipenemPefloxacin 12 0.61 0.977 0 .4 8 -0.74 0.39 - 0.82 Recombinant CD4 Recombinant Recombinant growth hormone growth Recombinant V human III factor Recombinant RelaxinRemikiren Remoxipride 6.0 0.80 0.992 0.66 - 0.93 0 .55-1.0 Ofloxacin Oleandomycin Ro 24-6173 Ro Rolitetracycline Sanorg 32701 Sanorg SB-263123Sch27899 34343Sch Sematilide Sildenafil 15 13 0.80 0.812 0.77 0.924 SR 80027 SR SK&F107647 Table (continued) 2,1.
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18 74 81 82 83 84 41 87 31 86 85 27 88 89 43 48 41 41 90 , hm , ps, hs, 01 it, rb, bb, hm ms, ms, rt, mk, rb, hm rt, dg, rb, hm ms, ms, n, mk, hm rt, dg rb, rt, mk, ds, hm ms, hs, it, hs, ms, rb, mk, dg, hm rt, rb, dg, sh it,ms, rb, bb dg, rt, sp, rb, rt, rb, dg, hm ms, n,dg, hm ms, rt, mk, dg, hm it,ms, hs, ib, dg, mk, hm ms, rt, mk, dg rt, dg, cw ms, it, ct, mk, hm ms, rt,ms, mk, dg, hm ms, ms, rt, ink,rb, hs, hm n.d. n.d. 0.60-1.1 0.66-1.0 0.51 0.51 -1.4 0.28 - 2.0 0.27-0.84 m m m n.d. n.d. n.d. 0.42-1.3 n.d. 0,32-1.3 0.57-1.4 0.32-1.7 0.54-1,1 0,19-1.4 0.62-1.0 0.45-1.2 0,63-1,7 0.30 - 0.79 n.d. 0.30 - 0,97 n.d. 0.36-1.24 n.d. 0.095-1.20.34-0.90 n.d. n.d. 0.40-0.71 0.64 - 0.98 0.57-1.1 0.50 - 0.90 0.39-1.0 0.71 0.71 -1.2 0,71 0,71 *0,97 0.72- 0.95 • « ♦ • * • • •« •» •• ♦♦ •** ♦♦♦ 005 0.053 0.978 0.993 0,971 0,993 0,950 0.919 0.927 0.978 0.942 0.874 0,963 0.993 0.983 0.902 1.0 1.2 0,55 0.84 0.63 0,59 0.65 0.84 0.973 0,79 0.81 0.80 0.69 0.81 0.988 0.70 19 12 17 0.84 0.986 32 61 31 1.9 54 62 0.62 26 0.95 0.981 1.6 0.68 = 0,67 b b « < 0,05 p 0: (♦); < p 0,01 (♦•); p<0,001 (♦*♦) b b = 0,75 and = 0,75 and b b » 0,75 ■ 0,67 b b b pig; ct, cat; cw, cow; gt, goal; ntt, marmoset; hs, hamster hs, marmoset; ntt, goal; gt, cow; cw, cat; ct, pig; rt, rat; rb, rabbit; bb, baboon; mk, monkey; dg, dog; hm, human; ms, mouse; cz, chimpanzee; sh, sheep; ck, chicken; pn, pigeon; gp, guinea pig; pg, pig; guinea gp, pigeon; pn, chicken; ck, sheep; sh, chimpanzee; cz, mouse; ms, human; hm, dog; dg, monkey; mk, baboon; bb, rabbit; rb, rat; rt, Excluding 7) = 0,01 (column 6) and Excluding = 0.05 (column level significance BWthe at and CU between ofcorrelation a lack of because determined not n,d,: determination of Coefficient SR90I07A Stavudine Sumatriptan Talsaclidine 37 Thiopentone 3.5 Tamsulosin Tebufelone Theophylline Zidovudine Tosufioxacin 64 TolcaponeTolterodine TrimethadioneTroglitazone Zalcitabine 12 4.1 15 0.82 Tiludronale activaor Tissue-nlasminojien 1,5 0.56 0.977 Tylosin Zomepirac 10 Table (continued) 2,1, ,M ,ri both Excluding m Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. b r r n Scenarios* ms rt rb mk dg hm range** 20% 30% 20% 30% CV CV CV CV I 0 • • 125 0.75 0.74 0 3 9 6 0 3 8 6 (0.63-0.87) (0.53 - 0 3 5 ) 2 • • • • 250 0.74 0.74 0.994 0 3 8 8 (0.64-0.84) (0.58-0.91) 3 • • • #• 0 700 0.75 0.75 0.996 0 3 9 0 (0.67-0.83) (0.62 - 0.88) 4 3500 0.75 0.75 0.996 0 3 8 9 (0.69-0.81) (0 .6 2 - 0.88) 5 •• • 20 0.76 0.72 0.992 0 3 5 4 (0.57-0.94) (0 .2 9 -1 .2 ) 6 •• 0 0 56 0.75 0.73 0 3 9 0 0 3 6 8 (0 .6 0 - 0.8 8 ) (0 .5 0 - 0.95) 7 •• 0 0 0 280 0.75 0.76 0 3 9 2 0 3 8 0 (0.65-0.85) (0 .5 8 - 0.93) S • 0 0 5.6 0.80 0.74 0 3 7 4 0.925 (0 .5 0 -1 .1 ) (023 - 13) 9 • 0 0 0 28 0.74 0.75 0 3 8 7 0371 (0.58-0.90) (0 .4 7 -1 .0 ) 10 0 0 0 14 0 .74 0.73 0388 0 3 6 9 (0.50-0.98) (0 .4 4 -1 .0 ) T able 2 2 Simulated b values In different scenarios w ith varied body weight ranges ms: mouse, 0.02 kg; rC rat, 0.25 kg; rb: rabbit. 2.5 leg; mk: monkey, 5 kg; dg; dog, 14 leg; hm: human, . . 7 0 k g . ** Range= maximum body weight/minimum body weight in each scenario f The mean b value with 95% confidence interval (boldface in the parenthesis) was obtained from 100 simulations where linear regression analyses were applied to the log-log-transformed CLversus BW data with either a 20% or a 30% coefficient of variation (C V ) in CL. n The mean correlation coefficient (r) o f linear regression from 100 simulated experiments per scenario 38 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Group* no. o f no. o f slope, b (95% C l) (99% CD xenobiotics data points I 9 41 0.78 0 .7 3 -0 .8 3 0 .7 2 -0 .8 4 2 21 105 0.65 0.62-0.69 0.61 -0.70 3 39 203 0.75 0.72-0.78 0.70-0.79 4 22 111 0.76 0.71 -0.81 0.70-0.82 O verall 91 460 0.74 0.72-0.76 0.71-0.76 Table 23. Summary o f the statistical results in Fig 23 * Group I = protein; group 2 = xenobiotics that were eliminated mainly by renal excretion; group 3 = xenobiotics that were eliminated mainly by extensive metabolism; group 4 = xenobiotics that were eliminated by both renal excretion and non-renal metabolism. 39 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30 Mean = 0.74. SD = 0.16 Nonnal distribution 25 - 20 - o>» c © 3 Er ^ 10 5 - i i 0.0 0-1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Allometric exponent Figure 2.1. The frequency distribution o f the b values fo r the 91 xenobiotics that showed statistically significant correlation between log CL and log BW in Table 2.1. The frequency o f the b values, at an interval o f 0.1, from 0.2 to 1.2 was plotted against the midpoint o f each interval o f b values. The dotted line represents a fitted Gaussian distribution curve. 40 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. m too so as 60 40 4 0 20 20 0 0 338S23S35g3 mouse. rwL mbttt. monkey, dog m o urn ra t. m b t*. mortmy. dog. hunan 6 0 4 0 20 0 3333S38SS8S1 SS3S888SS8 mtmooitmortmy rmt, nobt nonhtyjjoB »> O — 30% CV — 20% CV O’ & u. 33S88SS83 HUS3S8SU 1Q0 wtmted monte* dog, numm ^ ^ roote. monte* dog i 60 6 0 4 0 20 0 - 3SS388S33i 33S3S388S83 too monte*, dofc. o m it 6 0 6 0 4 0 20 :LJI l a , h j J l f c . 888388S88 33S8S3S8S88 Exponent F ig u re 2 2 . The frequency distribution o f the simulated b values in the ten scenarios where the number o f animal species and the range o f body weight were varied. The b values were obtained by applying linear regression analyses on the Iog-Iog- transfbrmed, error-containing CL versus BW data w ith either a 20% (gray) or a 30% (black) coefficient o f variation (CV) in CL. 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1000 100 o *N o E 0.01 r 0.001 0.001 0.01 1 10 100 1000 10000 Body Weight (kg) Figure 23. The relationship between normalized clearances fCL and body weights (BW) fo r the 91 xenobiotics (n = 460) that showed statistically significant correlation between log CL and log BW in Table 2.1. The relationship follows the equation: log C[.normalized = 0.74 log BW +• 0.015. r = 0.917. The 99% confidence interval o f the regression slope was 0.71 - 0.76. The different colors represent different subgroups o f xenobiotics: red. protein: blue, xenobiotics that were eliminated mainly (>70%) by renal excretion: green, xenobiotics that were eliminated mainly (>70%) by metabolism: black, xenobiotics that were eliminated by both renal excretion and metabolism. The result o f each subgroup can be viewed in the web version by moving the cursor to each symbol legend. 42 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -150 -100 -50 0 50 100 150 % Deviation Figure 2.4. The deviation between the fitted and the observed human CL for 68 xenobiotics. The fitted human CL o f each xenobiotic was obtained by applying linear regression on the log-log-transformed CL versus BW data from d iffe re n t animatspecies including human. The deviation was calculated as I00*(C LObsen,ed - CLfioed)/CLgned- The mean deviation was 0.62%. 43 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 3 Power-Law Scaling of the Drng-Drug Interaction Network 3.1 Introduction Many complex natural phenomena could be described by a simple power-Iaw equation. The question as to how such regularity existed in Nature has intrigued many scientists in various disciplines. For example, in a recent colloquium 1 on “ self-organized complexity in the physical, biological, and social sciences” held by the National Academy o f Sciences (NAS) o f the United States, power-Iaw scaling was ubiquitous in many examples presented therein, ranging horn allometric scaling in biology to social networks. A power-Iaw relationship between a measured quantity y and an independent variable x is o f the form: y = a x b ( 1) where a and b are constants. The scaling exponent b characterizes the rate o f change in y w ith respect to the change o f x, since (2) d \n x The b value could be either positive or negative, depending on the variables o f interest. 44 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. For example, the ailometric scaling o f metabolic rate 2 and xenobiotic clearance 3 has a positive scaling exponent, whereas the exponents for the ailom etric scaling o f the cardiac frequency and the half-life o f drugs are negative .2 Another example that w ill give rise to a negative b value is the power-Iaw frequency-size distribution feund in many fields, such as the frequency distribution for the rupture area o f earthquakes 1 and for the size o f companies .4 Besides the sign o f the b value, its absolute magnitude is o f particular importance, as it could be a manifestation o f the topology o f a system or o f the underlying mechanism o f a process. Complex networks can be found in systems as small as a cell and in those as large as the human society: In the former, the interconnection o f molecules by chemical reactions was considered as an intricately-woven web; in the latter, complex social networks can be formed by direct or indirect interactions o f human beings. Generally speaking, a network is composed o f nodes (vertices) that are connected by links (edges ).5 The degree o f a node specifies the number o f links that a node has. Before 1999, the real networks mentioned above would be realized by the random graph theory in which the connections o f nodes are considered as a random process .5 Accordingly, the theory would predict that the probability o f a randomly selected node w ith exactly k links (degree &), P(k), fellows a Poisson distribution, which is a bell-shaped curve with a peak a t the mean k. However, the seminal work by Barabasi and Albert in 1999 indicated that real networks including the World-Wide Web (WWW) have their degree distribution significantly deviated from a Poisson distribution .6 In their empirical results, the degree distribution o f the real networks was extremely skewed w ith the ta il following the power law : P {k ) °c fc~T (3) 45 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In the past 3 years, the power-Iaw degree distribution has beat described fo r a number o f real networks, such as the WWWM and cellular , 10 ecological , 11 and scientific ty e collaboration networks etc. Moreover, theoretical models that were able to capture the general feature o f the power-Iaw distribution have been proposed . 13*18 Two recent reviews 5’19 highlighted the intensity o f growing interests in understanding the topology and evolution o f complex networks. Drug-drug interaction poses a potential threat to patients who receive treatment with multiple medications. Whether two co-medicated drugs w in interact with each other depends on many factors: the drug properties (physicochemical, pharmacokinetic and pharmacodynamic), the basic characteristics o f patients (age, sac, race etc) and the disease states. The general mechanisms for an interaction to occur include the pharmacokinetic interactions (or ADME interactions) by which the processes o f drug absorption, distribution, metabolism and excretion are affected and the pharmacodynamic interactions by which the effects o f a drug at its site o f action are modified .20 Although some drug interactions may produce a beneficial effect, most interactions resulted in either unwanted adverse reactions or reduced efficacy. While adverse drug reactions may be due in part to elevated drug concentrations, additive or synergistic interactions and combined toxicities, factors such as reduced chug concentrations or antagonistic interactions may cause a reduction in efficacy .20 Sometimes the interactions are severe or even fetal so that a drug is withdrawn from the market. Therefore, the detection o f potential drug interactions has become an important part o f drug safety evaluation in the drug development process, during which a new drug entity (NDE) must be tested for its ability to modulate the pharmacokinetics or pharmacodynamics o f those frequently co- 46 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. prescribed drags .21 Furthermore, the detection o f drug interactions extends over the post market period. Currently, a substantial amount o f information about drug-drug interactions has accumulated. I f one treats the interacting drugs as nodes and connect those nodes w ith undirected links that represent the interactions, a drug-drug interaction network can be obtained. Interesting questions pertaining to network analysis then arise: What is the topology o f the drug-drug interaction network? How does this network evolve? The answers to these questions may provide a heuristic view towards the nature o f drug-drug interactions. 3.2 Materials and Methods 3.2.1 Data acquisition The drug-drug interaction information was retrieved from a comprehensive source reference-Drz/g Interactions: a source book o fadverse interactions, their mechanisms, clinical importance and management by Stockley,20' “ *23 which was first published in 1981 and was continuously updated since then. Besides its comprehensiveness, the information covered was mainly based on the published primary references in which clinical and experimental evidences were provided. To investigate the evolution o f the drug-drug interaction networks and the effect o f network size on its topology, we extensively surveyed the source reference’s firs t (1981),23 second (1991)22 and fifth (1999)20 editions, which were separated by a time interval o f 8 —10 years and had about 600,1200 and 2400 monographs, respectively. The source references included not only the interaction cases, but also those that showed a lack o f interaction. The quality o f interaction information varied widely (controlled versus uncontrolled clinical trials, case 47 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. reports, in vitro studies, animal studies ere), and it was therefore imperative to establish inclusion and exclusion criteria. I only considered the drug-drug interactions that have been detected in patients or healthy subjects and excluded (I) those where only in v itro data were reported; (if) those where only animal studies were conducted; (iii) manufacturer’s statements and generalized claims; (iv) those where the interactions were found when more than 2 drugs were co-medicated and there was no further evidence to support interaction for any particular pair o f drugs. Furthermore, pharmacokinetic interaction between a pair o f drugs was considered only when the change o f mean pharmacokinetic parameters in either drugs exceeded 20%. Overall, I obtained three databases that consisted o f351,636 and 966 drugs and 742,1858, and 3351 pairs o f interaction, respectively 3.2.2 Data analysis Based on the drug-drug interaction information from the databases, I prepared histograms that describe the frequency distributions for the number o f interactions that a given drug has. Dividing each element o f the histogram into the total number o f drugs in the database, the p ro b a b ility that a given drug has k interactions, P (k), can be obtained. A. logarithmic binning approach ,24 w hich can smooth the obtained distributions fo r larger values o f k while retaining the nature o f the distribution, was used according to the following rule: P j k ) = (4) l(k r,*D 48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. w h e re ^ Pn(k ) is the summed p ro b a b ility in the nth b in and the b in w id th /^ ^ "* ,k ™ ) is the number o f integers in the range k™ to . For the logarithmic binning I set bin w idths w ithk™ I k™ = constant. To obtain the power-Iaw exponent, the log-Iog- transformed data points ( log£„, log Pn) were fitted to a straight line using linear regression, where logfc„ = log iy f k ^ k ^ } . PAJEfC, a program for large-network analysis and visualization, was used for constructing the drug-drug interaction network. This program is available at http://vIado-rmfuni-Ii.si/pub/networks/paiek/ 3.23 Theoretical considerations The drug-drug interaction network consisted o f two basic elements: a node (vertex) representing a given drug that has one or more interaction(s) w ith other drugs and a lin k (an edge) representing the interaction between two drugs. The degree (ki) o f a node i in the network was defined as the number o f links that this node has. Thus, the degree (£,) o f a given drug in the drug-drug interaction networks described the number o f interactions that link to this drug. The evolution o f a network is a dynamical process, w hich im plies that the degree o f a node changes over time. Considering a model for drug-drug interactions (F ig 3.1), the degree (kt ) o f drug i w ill increase every tune a new interaction that associates w ith this drug is detected. The new interaction may come from a drug that had never been detected previously. The probability o f this process, is proportional to the degree o f drug /, k*. Moreover, the 49 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. new interaction may derive from a drag, say/, which already existed in the network, hi this case, the probability o f interaction, denoted as the degrees o f drug i and j , ktk j. The probabilities that assign to the above tw o processes are based on the assumption that a drug has a higher chance to interact w ith drugs that have a higher number o f interactions detected previously. This is the so-called “ rich-get- richer” or preferential linking - a common phenomenon in other real networks .5 The size o f the network is continuously growing as the numbers o f its nodes (drugs) and links (interactions) increase over time. After a relatively long period o f evolution, the network may self-organize into a structure that can be characterized by the probability distribution o f the degree (&), P(k), which by definition is the probability that a given node has k lin ks (k > I). The empirical results o f the present study indicated that P(k) follows a power-Iaw distribution, P(k) <* k' r , where yean be predicted using the continuum approach 13*18 that was successfully applied to modeling the scientific collaboration network by Barabasi et ah 25 and the web o f English words by Dorogovtsev and Mendes .6 3 3 Results The drug-drug interaction network is graphically represented in Fig. 33. The network, consisting o f966 drugs and 3351 pairs o f interactions, was generated from the updated drug-drug interaction information up to 1999. The dots represent the interacting drugs and the lines the interactions that have been detected for any given pairs o f drugs. This is a highly inhomogeneous network, w ith a dense interior fille d with highly 50 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. interacting drugs and a sparse exterior comprised o f a large number o f drugs that sparsely interact The heterogeneity o f the network could be further exemplified by the following observation: The top 40 most interacting drugs (red dots), while represented only 4.1 % (40/966) o f all the drugs in the entire network, have their number o f interactions > 30 per drug and together contributed more than 36 % (2421/6702) o f the interactions. In contrast, as many as 696 (hugs (72 %) have 5 interactions or less per drug, which constituted only 21 % o f all the interactions (1438/6702). The data suggested that the network behavior was dominated by a small fraction o f drugs that exhibited a higher tendency to interact with other drugs - a “rich-get-richer” phenomenon in the drug-drug interaction network. The frequency distributions for the number o f interactions a given drug has is shown in Fig. 33, where the data were retrieved from the three drug-drug interaction databases w ith the number o f interacting drugs increasing from 351 (Fig. 33A) to 966 (Fig. 33Q and the total number o f interactions for all drugs increasing from 1484 to 6702. The bar charts illustrated nearly L-shaped histograms, which upon log-tog transformation corresponded to the scatter plots shown in the insets. By visual examination, the scatter plots could be described by straight lines, hi addition, the distribution was “fat-tailed” , which is one o f the characteristics o f a power-Iaw distribution. To estimate the power-Iaw exponent and to compare the degree distribution P(k) o f the three databases, the frequency data in Fig. 33 were transformed to probabilities and the resulting probability distributions were smoothed fo r larger k(k> 4) using the logarithmic binning approach described in Materials and Methods. It is remarkable that 51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the probability degree distributions fo r the three networks w ith different sizes were superimposed and followed a straight line with a slope close to -1.5 on a Iog-Iog plot, Fig.. 3.4. The basic characteristics o f the drug-drug interaction networks studied are summarized in Table 3.1. Notably, the average number o f interactions per drag (the density o f the network), <&>, increased as the network size was enlarged, suggesting that the network was subject to a non-linear growth. Nevertheless, the network exhibited scale-free characteristics as it followed a power-Iaw degree distribution w ith an almost invariant scaling exponent. The top-ten most interacting drags in the three databases are listed in Table 32.. The members o f the top-ten lists during the evolution o f the network only changed to a slight extent: Four members (phenylbutazone, probenecid, tolbutamide, and Ievadopa) in the 1981 database fe ll out and were replaced by 4 new members (cimetidine, cyclosporin, propranolol and theophylline) in the 1991 database, whereas 2 members (phenobarbital, digoxin) in the 1991 databases were replaced by the other tw o new members (carbamazepine, rifam picin). 3.4 Discussion Many seemingly unrelated scientific disciplines have recently arrived at an intersecting point - the discovery o f power-Iaw scaling. Especially, numerous power-Iaw frequency distributions have been described for various attributes in diverse systems. Examples are the number o f pages w ithin a WWW site 8 or the number o f links to a web page ,7 the number o f chemical reactions in which a metabolic substrate participates , 10 the month-to-month variation o f a hospital waiting list ,27 and the size o f a company .4 A 52 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. distribution in a power-Iaw form is free o f scale and often implies non-randomness .5 To pharmaceutical scientists, a fam iliar example o f power-Iaw scaling is the ailometric scaling o f a pharmacokinetic parameter (e.g., clearance) in different species with body sizes spanning over many orders o f magnitude .3 In this chapter, I described a drug-drug interaction network in which the interacting drugs were treated as nodes and were connected w ith undirected links that represent interactions. The degree (the number o f interactions that a drug has) o f the resulting network followed a power-Iaw distribution. The scaling exponent was close to -1.5 and independent o f the network size. The power-Iaw degree distribution o f the drug-drug interaction network can be derived according to the model in Fig. 3.1. The network was assumed to be governed by the mechanism o f preferential linking, which suggested that highly interacting drugs have a higher tendency than less interacting drags to acquire a new interaction. During the time evolution, the number o f interaction (£,) o f drug i increased as a result o f newly detected interactions that associated with it. The interaction occurred either with drugs that had never been identified for any interaction or with drugs that had existing interactions. The probability for the two interaction sources was denoted as & and respectively, which are o f the following forms 25 (5) and (6 ) 53 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Accordingly, the evolution o f the number o f interactions (£;) that drag i has can be described as: (7 ) dN dM where is the rate o f acquired interactions from new incoming drugs and - j - represents the rate o f newly identified interactions among existing drugs in the network. Note that the factor 2 in equation (7) implies that inside a network any given link has 2 equal ends that are distributed preferentially among the existing nodes. We assumed that new incoming (hugs jo in the drug-drug interaction network at a constant rate; therefore, dN - - a . (8) Furthermore, I considered that the flux o f new interactions inside the existing network increased nonlinearly and was proportional to tb, where b> 0 . Thus, (9) where a and f i in ( 8) and (9) are positive constants. The cumulative probability in (7) is approximately equal to tp-„ if we assumed that m ultiple links (between the same pah o f drugs) were absent in the drug-drug interaction network and applied the procedures taken by Barabasi et al .25 Using (5), ( 8), (9) and the approximation for ^ <1* ^ , equation (7 ) can be w ritte n as: (10) 54 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where the total degree o f the n e tw o r k , £ tfj , can be derived from ( 8) and (9 ): (II) Substituting (11) into (10), we obtained dki _ a +2 fit* (12) d t . I I According to my empirical data, > 90% o f drug interactions in a new database resulted from interactions among drugs that were members o f the old database. Therefore, one ft can a s s u m e ^ j-t **1 » a t for large t and equation ( 12) can be sim plified as: f= (7 h ‘>- (i3> The solution o f (13) with an in itia l condition ytj(/j) = I for the degree o f drug / at t = tt is: (14) \ / It remained to know the probability distribution o f tiy which was assumed to be uniform ly distributed in the [ 0, t] interval because the interacting drags joined the network randomly at a constant rate. Therefore, the probability distribution o f 4 was given as: 1 g iO = 7 - (15) Using (14) and (15) and the change o f variable technique ,28 the degree distribution, P (k), can be obtained as follows: 55 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. P ( * ) = g ( r f> fAl |=_i—fc^1+ST) (16) L ^ J U w l 6+1 Accordingly, (17) Compared w ith (3), yin the power-Iaw exponent is o f the following form: Obviously, l empirical finding. I used the three databases to examine the assumptions o f preferential linking and nonlinear growth in the interaction network. The average degree, network size enlarged (Table 3.1), which implied that the total number o f interactions in the drug-drug interaction network increased noniineariy over time. The data suggested a nonlinear growth o f the network. To demonstrate that preferential linking operated in the interaction network, 1 evaluated the probability distribution o f a given drug w ith kt interactions to acquire a new interaction. In so doing, the number o f drug interactions was compared fo r drugs that appeared in two databases published at different times (e.g., 1981 versus 1991,1991 versus 1999). The cumulative probability distribution was calculated as follows :5 (19) 56 I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where M , is the number o f interactions added in the later database for drugs that have k, interactions in the earlier database, and Ak is the total number o f interactions added to the previous database. By plotting r(k) versus k in a log-Iog plot, whether preferential linking existed can be determined from the slope o f the plot. If the slope is equal to I, it indicates no preferential linking because M , /A k would be a constant in this case. However, if the slope is greater than I, which may imply Akt / Ak <* k s (s > 0), and that preferential linking occurs .3 O ur analyses showed that the slope o f the cum ulative probability distributions in the log-log plots was larger than I (Fig. 3.5), thereby suggesting that preferential linking operated in the drug-drug interaction network. Moreover, the result was robust, regardless o f how the networks were compared. The consistency o f this finding in conjunction w ith the invariant power-Iaw scaling o f the degree distribution suggested that the global properties o f drug-drug interaction have remained unchanged over the past decades, even though, at the microscopic level, new drugs and new interaction mechanisms have emerged. The present study demonstrated that power-Iaw frequency distribution exists in the pharmaceutical system, which coincided w ith recent multidisciplinary interests in network analysis and power-Iaw scaling. It was interesting to find that the evolution o f the drug-drug interaction network was sim ilar to many complex networks that exhibited scale-free characteristics .5 However, to many pharmaceutical scientists, a more intriguing question could be: how could the current analysis add to our knowledge about drug-drug interaction? Specifically, what does preferential linking implicate in drug interactions? 57 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. What i f the probability fo r a drug to interact w ith any other drugs follows a Poisson distribution? This would im ply that the process is random and the majority o f drugs have the number o f interaction close to a characteristic (mean) value, which is the central tendency phenomenon. The Poisson distribution would further im ply that it is exponentially rare fo r a drug to have an extremely large (or small) number o f interactions, say S standard deviations away from the mean. Were this the case, drug-drug interactions would be much more d ifficu lt than is currently the case for researchers, health care practitioners, and regulatory agencies to predict, prevent and set guidance for. Indeed, we know the existence o f some classes o f drugs that have higher chance than others to cause an interaction. This is strikingly similar to social networks in which a small number o f individuals have disproportionately high popularity. Once a person has been recognized for his/her success, the chance for this individual to get connected increases. Eventually, the connectivity in the social network becomes inhomogeneous and the degree distribution may follow the power law. Similar situations apply for the drug-drug interaction network. The heterogeneity o f the drug-drug interaction network could be understood as the consequence o f at least two driving forces: the feature o f a drug and the decision-making o f individuals who participate in the field. Like the social networks, the characteristics o f a given drug may determine its detectability in a potential drug-interaction context. By examining the lists for the top-10 most interacting drugs (Table 3.2), one finds that 4 compounds (phenytoin, alcohol, warfarin and lithium ) have remained on the list since 1981. Among them, phenytoin, warfarin and lithium are drugs w ith extremely narrow therapeutic windows and are frequently used fo r diseases that require polypharmacy 58 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. treatment. Alcohol, though not a chug by a strict definition, is pharmacologically sim ilar to many drugs that depress the CNS. The prevalence o f alcohol consumption and the potential o f an interaction among alcohol and CNS depressants may have resulted in alcohol being on the top lists over decades. Although drugs w ith a low therapeutic index, such as digoxin, theophylline and those mentioned above, tended to have high incidences o f drug interaction, cim etidine, a drug on the top-ten lists in the 1991 and 1999 databases, reflected that the research on drug interactions has undergone a significant transformation in recent years. When taken alone, cimetidine is a rather safe drug. However, it inhibits the metabolism o f certain coadministered drags, thereby increasing the potential fo r adverse drag reactions .29 The ability o f cimetidine to inhibit the cytochrome P450 (CYP) fam ily o f enzymes, especially CYP3A4 and CYP2D6, may contribute to its high propensity to cause an interaction .29 Recently, metabolic drug-drug interactions associated w ith CYP have become the central issue o f drag interaction studies, partly due to the advances in the molecular biology o f CYP and the development o f in v itro methodologies that facilitate the detection o f a potential interaction .21 The rapid expansion in detecting CYP-related interactions was evident by the addition o f carbamazepine (a substrate and an inducer fo r CYP3A4 )30 and rifampicin (an inducer for CYP3A4, CYP2C9 and CYP2C19)30 to the top-10 list the first time in the 1999 database (Table 3.2). Moreover, 9 o f the top 10 drags in the 1999 databases (Table 3.2) have been identified as substrates, inducers o r inhibitors o f the CYP isozymes. 30 Human factors might play an important role in orchestrating the structure o f the drug-drug interaction network, because the decision-making process o f researchers was 59 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. involved. Specifically, the decision o f winch drug interactions are to be investigated, a small number o f drugs were more frequently identified for consideration than were others. For example, a recent survey o f new molecular entities approved from 1987 to 1997 indicated that the most commonly studied interacting drugs did not change over this period, w ith cimetidine and digoxin being the top 2 drugs o f choice for drug interaction studies .31 These drugs were popular because either their unique characteristics in causing an interaction have been long recognized or the chance o f these drugs to be coadministered w ith the new chemical entities is high. The results suggested that the decision-making process o f researchers was based on drug interaction information that was biased toward more recognizable drugs. It was possible that this process might contribute to the “rich-get-richer" phenomenon in the drug-drug interaction network. 3.5 Conclusion This study from a network standpoint provided a heuristic view on drug-drug interactions. W hile thug interaction information has continuously accumulated and the nature o f interactions has been modified over the decades, the structure o f the drug-drug interaction network remained robust with the degree distribution o f the network following a power law w ith an invariant scaling exponent. A dynamic model was proposed to account for the observed scale-free structure o f the network. 3.6 Summary Using drug interaction information that spanned decades, a drug-drug interaction network was described in which the interacting drugs were treated as nodes and were 60 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. connected w ith undirected links that represented interactions. The degree (the number o f interactions that a drag has) o f the resulting network followed a power-Iaw distribution. The scaling exponent was close to -1.5 and independent o f the network size. A dynamic model was proposed to account for the observed scale-free structure o f the network. This study from a network standpoint provided a heuristic view on drug-drug interactions. While drag interaction information has continuously accumulated and the nature o f interactions has evolved over the decades, the structure o f the drug-drug interaction network remained robust with the degree distribution o f the network following a power law w ith an invariant scaling exponent. 3.7 References 1. Turcotte DL, Rundle JB. Self-organized complexity in the physical, biological, and social sciences. Proc Natl Acad Sci USA. 2002;99(suppL l):2463-2465. 2. West GB, Brown JH, Enquist BJ. A general model for the origin o f ailometric scaling laws in biology. Science. 1997;276:122-126. 3. Hu TM, Hayton WL. Ailometric scaling o f xenobiotic clearance: Uncertainty versus universality. AAPS PharmSci. 2001^(4), article 29. (http://www.pharmsci.org /1 4. Axtell RL. Zipf distribution o f U.S. firm sizes. Science. 2001;293:1818-1820. 5. Albert R, Barabasi AJL. Statistical mechanics o f complex networks. Mod. Phys. 2002;74:47-97. 6 . Barabasi AL, Albert R. Emergence o f scaling in random networks. Science. 1999;286:509-512. 7. Albert R. Jeong H, Barabasi AL. The diameter o f the world-wide web. Nature. 1999;40I:I30. 8. Huberman BA Adamic LA. Growth dynamics o f the world-wide web. Nature. 1999;401:I3I. 61 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9. Adamic LA, Huberman BA. Power-Iaw distribution o f tbe world wide web. Science. 2000287:2115. 10. Jeong H, Tombor B, Albert R, Oltvai ZN, Barabasi AL. The large-scale organization o f metabolic networks. Nature. 2000;407:651-654. 11. Montoya JM, Sole RV. Small world patterns in food webs. ArXiv.org e-Print archive. 2000. http://www.arxiv.org/abs/eond-mat/ 0 0 l 1195 12. Newman MEJ. The structure o f scientific collaboration networks. Proc Natl Acad Sci USA. 2001;98:404-409. 13. Barabasi AL, Albert R, Jeong H. Mean-field theory for scale-free random networks. PhysicaA. 1999272:173-187. 14. Krapivsky PL, Redner S, Leyvraz F. Connectivity o f growing random networks. Phys. Rev. Lett. 2000;85:4629-4632. 15. Dorogovtsev SN, Mendes JFF, Samukhin AN. Structure o f growing networks with preferential linking Phys. Rev. Lett. 2000;85:4633-4636. 16. Albert R, Barabasi AL. Topology o f evolving networks: Local events and universality. Phys. Rev. Lett. 2000;85:5234-5237. 17. Kirillova OV. Communication networks with an emergent dynamical structure. Phys. Rev. Lett. 2001;87:068701-+. 18. Dorogovtsev SN, Mendes JFF. Scaling properties o f scale-free evolving networks: Continuous approach. Phys. Rev. E. 200l;6305:6l25-+. 19. Dorogovtsev SN, Mendes JFF. Evolution o f networks. ArXiv.org e-Print archive. 2001. http://www.arxiv.org/abs/cond-mat/Q 106144 20. StockleylH. Drug interactions: a source book o f adverse interactions, their mechanisms, clinical importance and management, London, UK: Pharmaceutical Press, 1999. 21. Thummel KE, Kunze KL, Shen DD. Metabolically-based drug-drug interactions: principles and mechanisms. In: Levy RH, Thummel KE, Trager WF, Hansten PD, Eichelbaum M , eds. Metabolic drug interactions, Philadelphia, PA: Lippincott Williams & W ilkins, 20002-19. 22. StockleylH. Drug interactions: a source book o f adverse interactions, their mechanisms, clinical importance and management, Oxford, UK: Blackwell Scientific Publications, 1991. 62 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23. StockleylH. Drag interactions: a source book o f adverse interactions, their mechanisms, clinical importance and management, Oxford, UK: Blackwell Scientific Publications, 1981. 24. MeakmP. Fractals, scaling and growth far from equilibrium, Cambridge, UK: Cambridge University Press, 1998. 25. Barabasi AL, Jeong H, Neda Z, Ravasz E, Schubert A, VicsekT. Evolution o f the social network o f scientific collaborations. ArXiv.org e-Print archive. 2001. httpjVwww.arxiv.org/abs/cond-mat/0104162 26. Dorogovtsev SN, Mendes JFF. Language as an evolving word web. Proc R Soc LondB. 2001;268:2603-2606. 27. Smethurst DP, Williams HC. Power laws: are hopital waiting lists self-regulating? Nature. 2001;410:652-653. 28. Hoel PG. Introduction to mathematical statistics, New York, NY: John Wiley & Sons, Inc, 1962. 29. Paine MF. H2-receptor antagonists. In: Levy RH, Thummel KE, Trager WF, Hansten PD, Eichelbaum M, eds. Metabolic drag interactions, Philadelphia, PA: Lippincott W illiams & Wilkins, 2000;653-659. 30. Papp-Jambor C, Jaschinski U, Forst H. Cytochrome P450 enzymes and their role in drug interactions. Anaesthesist. 2002;51:2-15. 31. Marroum PJ, Uppoor RS, Parmelee T, Ajayi F, Burnett A , Yuan R, Svadjian R, Lesko LJ, Balian JD. hi vivo drug-drug interaction studies-a survey o f all new molecular entities approved from 1987 to 1997. Clin Pharmacol Ther. 2000;68:280-285. 63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DATABASE Y E A R tB> N ™ k W I 1981 351 1484 4 2 1.48 2 1991 636 3716 5.8 1.50 3 1999 966 6702 6.9 1.44 Table 3.1. Basic characteristics o f drug-drug interaction networks (a> Year o f publication <6) Total number o f interacting drugs (c) Total number o f interactions for a ll drugs w Average interactions per drug, 64 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1981 1991 1999 RANK DRUG k ,' DRUG fc1 DRUG I A lcohol 53 Phenytoin 107 Phenytoin 153 2 Phenytoin 51 W arfarin 102 A lcoho l 135 3 W arfarin 44 A lcohol 101 C im etidine 133 4 Phenobarbitai 26 Cimetidine 80 W arfarin 133 5 Lithium 24 Cyclosporin 56 Cyclosporin 120 6 Phenylbutazone 24 Propranolol 54 Carbamazepine 98 7 Probenecid 24 Lith ium 52 R ifam picin 96 8 Tolbutamide 23 Phenobarbitai 52 Lith ium 91 9 Levodopa 22 Theophylline 52 Theophylline 86 10 D igoxin 20 D igoxin 51 Propranolol 75 Table 3.2. The Top-10 Most Interacting Drugs in the Three Databases ^Number o f interactions i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.1. A model fo r the drug-drug interaction network. Each node represents a drug. The line between two nodes represents an interaction. A t each time step, a given drug i inside an existing interaction network, can interact with a new interacting drug (blue nodes) outside the network, with a probability 66 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.2. A drug-drug interaction network consisted o f966 drugs (dots) and 3351 interactions (lines). Red dots represented the top 40 most interacting drugs. PAJEK. a program for large-network analysis and visualization, was used for constructing the drug- drug interaction network. This program is available at http://viado.finf.uni- ii.si/pub/networks/paiek/ 67 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ISO 1000 100 D o $ too o c © 10 \ 9 t OS GD 50 1 at to too TOGO 20 40 60 SO 100 120 t40 160 180 Number of Interactions B 250 1000 200 too >» c tso © 3 g too i t at 50 i to too taoo 20 40 60 80 100 120 140 160 180 Number of Interactions 350 1000 300 too 250 o>» c 200 © 3 V 150 9 100 at too tooo a 20 40 60 80 100 120 140 160 180 Number of Interactions Figure 33. The frequency distribution for the number o f interactions a given drug has. Data were acquired from databases published in 1981 (3S1 drugs, A ), 1991 (636 drugs, B) and 1999 (966 drugs, Q . 68 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 0.1 0.01 CL o 1981 0.001 V 1991 □ 1999 Slope ~ -1.49 0.0001 1 10 100 Figure 3.4. The probability degree distributions for the drug-drug interaction networks. 69 I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 0 • 1981-1991 O 1991-1999 Slope = 1 0.1 £ U 0.01 0.001 0.0001 1 10 100 Number of pre-existing interactions (k) Figure 35. Cumulative preferential linking for the drug-drug interaction network. The tine corresponds to no preferential linking. 70 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 4 Dynamic Biphasic Effect o f Snperoxide Dismutases on Nitric-Oxide-Mediated Nitrosation Reaction 4.1 Introduction The free radical nitric oxide (NO) contributes to diverse physiological and pathophysiological processes. NO is synthesized from L-arginine by three types o f nitric oxide synthase (NOS).1 W hile nNOS (NOS I) and eNOS (NOS HI) are constitutive isoforms first found in neurons and endothelial cells, respectively, iNOS (NOS II) is an inducible isofrom present in a wide range o f cells and tissues, especially during proinflammatory conditions.2*3 Despite over a decade o f intense research, many aspects o f NO physiological chemistry remain both paradoxical and controversial.4 A t low concentrations (~ nM), NO modulates normal physiological functions such as regulation o f vascular tone and intracellular signaling via a direct interaction with its targets/ However, high NO levels (~ftM ) can induce cytotoxicity, presumably attributable to oxidative and nitrosative stresses.5 While generally slow in its reactions w ith many molecules, NO reacts rapidly w ith reactive oxygen species.6 The concurrent production o f O f and NO during inflammatory and immunological reactions has complicated an understanding o f the pathological mechanisms related to 71 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. these two free radicals. In addition, complexity is introduced by other cellular factors that can modulate the abundance o f both reactive species. Accordingly, the consequences o f oxidative and nitrosative chemistry may depend heavily on a delicate balance among the processes that govern the formation and elimination o f both causative agents. Elevated NO levels present at inflammatory sites provide the opportunity for NO to successfully compete w ith superoxide dismutase (SOD) for reaction w ith O 2', thereby generating the highly reactive and cytotoxic peroxynitrite (ONOO~) molecule.6 While O f reduces NO-mediated oxidation,7 hydroxylation7 and nitrosation reactions,8-9 SOD attenuates the inhibitory effect o f O 2'.8-9 SOD therefore plays a pivotal role in modulating the consequences o f oxidative and nitrosative chemistry. SOD sometimes demonstrates anomalous bell-shaped, dose-response relationship.10 W hile low concentrations o f SOD are cardioprotective, higher levels can exacerbate acute cardiac injury.1 M3 Several mechanisms have been proposed to explain SOD's biphasic effects including increased hydrogen peroxide production resulting from dismutation o f Oj-m-w soD's peroxidase activity,19 and the dual roles o f superoxide in initiating and terminating radical chain reactions.20 Recently, studies by O ffer et a I.21 showed that low levels o f Cu,Zn-SOD inhibited Oj'-induced ferrocyanide oxidation, while its antioxidative effect was lost at high [Cu,Zn-SODj. The authors proposed that in its oxidized form Cu,Zn-SOD oxidizes the target molecule that it was supposed to protect.21 Related studies by Liochev and Fridovich22 implied that Cu^n-SOD functions both as a superoxide reductase and a superoxide oxidase. Consequently, the findings o f Offer et al. were attributed to the increase in SOR activity that accompanied increased [Cu,Zn-SOD]. 72 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SOD may affect NO bioavailability via a mechanism other than the dismutation o f Q f- Indeed, an Of-dismutation-independent mechanism has been implicated in SOD’s capability to (i) reversibly convert nitroxyl anion (NO") to NO,23 and (ii) enhance the formation o f free NO from L-argmme by NOS.24 These findings suggest that SOD might directly affect the reaction kinetics o f reactive nitrogen oxide species. Therefore, a complex dose-response relationship may be anticipated fo r SOD in NO-mediated nitrosative chemistry. This study used NO-donor-based kinetic analyses to investigate the effect o f SOD on NO-mediated nitrosation reactions. The present findings depict for SOD a novel dose-response relationship, which underwent dynamic transformations and was highly sensitive to the substrate concentration. 4.2 Materials and Methods 4.2.1 Materials SIN-1 was purchased from Calbiochem (La Jolla, CA). Cu,Zn-SOD, Mn-SOD, Fe- SOD, catalase, diaminonaphthalene (DAN), dihydrorhodamine 123 (DHR), glutathione (GSH), diethyltriaminepetaacetic acid (DTPA) and a ll other chemicals were purchased from Sigma Chemical Company (St. Louis, MO). The chemical structures o f SIN-1, DAN and DHR are shown in Fig. 4.1. 4.2.2 Kinetics of DAN nitrosation The nitrosation kinetics o f DAN was studied using a fluorescence spectrometer (Perkin Elmer LS 50B, Norwalk, CT). Reactions were performed in a 96-well microtiter plate format at 25 ± I °C in the sample chamber. The fluorescence intensity o f nitrosated DAN was measured at excitation and emission wavelengths o f375 and 430 nm, 73 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. respectively. A. stock solution o f DAN (30 mM) was freshly prepared in dimethyl sulfoxide (DMSO), protected from light exposure and stored at 4 °C. The dynamic range o f DAN in the nitrosation kinetics was studied by varying the concentration o f DAN (0.78 — 300 pM ) in 200 p i o f phosphate-buffered saline (pH 7.4) that contained 0.1 mM DTPA and 120 U/ml catalase to eliminate hydrogen peroxide. Reactions were initiated by adding an aliquot o f 4 p i SIN-1 stock solution (5 mM in DMSO) into 200 pi DAN-containmg reaction buffers. The fluorescence intensity after the addition o f SIN-1 was measured at 10-min intervals. The nitrosation o f DAN in the presence o f SOD (0 - 1000 U/ml) and SIN-1 (100 pM ) was studied in the same pH 7.4 reaction buffer at 25 ± I °C by measuring the increase in fluorescence every 10 min up to 8 hr. 4.23 Oxidation of DHR by SIN-l The oxidation o f DHR was determined at 25 ± I °C in the above-mentioned reaction buffer except that DAN was replaced by DHR (10 mM stock in dimethyiformamide stored at -20 °C and protected from light). The fluorescence o f rhodamine 123 generated from the oxidation reaction was measured at excitation and emission wavelengths o f S00 and 530 run, respectively. The effect o f SOD (0 - 1000 U/ml) on SIN-I mediated DHR oxidation was studied in 200-CI DHR-containing reaction buffer, where the DHR concentration (0.39 DM in the final reaction mixture) was chosen based on a pilot experiment in which the dynamic range o f DHR was determined. The oxidation kinetics o f DHR was typically monitored every 5-min up to 4 hr. 4 2 4 Cytochrome c reduction assay 74 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The activity o f Cu,Zn-SOD, Mn-SOD and Fe-SOD was determined by measuring the ability o f SOD to inhibit the reduction o f acetylated ferricytochrome c by O f generated from xanthine/xanthine oxidase.23 Reaction buffers (50 mM phosphate buffer/0.1 mM EDTA, pH 7.8) containing xanthine (500 pM ), ferricytochrome c (4 pM) and SOD at various concentrations (0,0.05,0.1,0.5,1 U/ml) were prepared. The reaction was initiated by adding 17 p i xanthine oxidase solution (~L U/m l) into 830 pi reaction buffer. The change o f absorbance at 550 nm was measured fo r 3 min at 25°C. 4.25 HPLC determination o f S IN -l degradation kinetics An HPLC method26 was modified to study the effect o f SOD on the degradation kinetics o f SIN -l (Appendix B). The method consisted o f a reversed phase column (Waters Nova-Pak Ctg3.9 x 300 mm), a mobile phase (10 mM sodium acetate buffer (pH3. lyacetonitrile/methanol = 92/6.4/1.6, flow rate = I ml/min), and UV detection at 254 nm. SIN -l was separated from its two degradation products, SIN-l A and SIN-IC, with retention times o f 4.0,9.0 and 9.8 min for S IN -l, SIN -l A and SIN-IC, respectively. The kinetics o f the SIN -l degradation at 25 °C was studied by serial sampling (0,30,60, 90,120,180,240,300,360,480 min), with an initial [S IN -l] o f 100 pM, with and without 1000 U/ml Cu,Zn-SOD in the same reaction buffer as described in the nitrosation kinetics section. The dose-response relationship o f Cn,Zn-SOD for the degradation o f S IN -l was further investigated by determining the relative quantity (expressed as % control) o f SIN-I and its degradation products after 4 hr incubation in reaction buffer containing 100 pM SIN-I and various concentrations o f Cu^Zn-SOD (1000,250,62.5, 15.6,3.13,0.78 U/ml). 75 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.2.6 Method validation The concentrations o f DAN and DHR used in the study were determined in pilot studies to exclude the possibility o f fluorescence quenching. In addition, nitrogen oxide species such as N O f, N Q r and ONOCF, which were likely generated during the reaction, were evaluated and shown not to nitrosate DAN. SOD was also shown not to affect the fluorescence o f DAN and DHR. Nevertheless, suitable controls (e.g., SOD/DAN for SIN-1-mediated nitrosation kinetics, SOD/DHR for oxidation kinetics) were included in each experimental run and the fluorescence reported was after subtracting out the background fluorescence o f the controls. 4 3 Results Kinetics o f DAN nitrosation. The kinetic profile o f SIN-1-mediated DAN nitrosation, Fig. 42, was characterized by the formation o f fluorescence a t430 nm. The nitrosation for the control (curve L) peaked a t- 180 min after the addition o f SIN-1 (100 pM). After the maximum, the fluorescence intensity tended to decline gradually. W ith increasing concentrations o f Cu^n-SOD up to 15.6 U/ml, the rate and extent o f DAN nitrosation increased disproportionately, curves 2-6 o f Fig 42A. hi constrast, [Cu,Zn- SOD] above 15.6 U/ml increasingly attenuated DAN nitrosation, curves 7-11 o f Fig 42B. The kinetics o f fluorescence formation was dramatically affected by the presence o f the highest [Cu, Zn-SOD], at which the fluorescence intensity accumulated in a slow and sustained fashion (curve 11, Fig 42B). 76 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SOD modulated SIN-l-mediated DAN nitrosation in a biphasicfashion. To farther characterize the interaction between SOD and DAN nitrosation, a dose-response relationship was constructed in accordance w ith the relative degree o f nitrosation compared w ith the control versus [CuyZn-SOD] at different measurement times. Remarkably, m ultiple biphasic dose-response curves characterized by a dynamic transition among those curves emerged (Fig. 43 A). Furthermore, these data enabled a 3- D representation o f the dynamic dose-response relationship (Fig. 43B). Based on Fig. 43, the maximum stimulatory effect o f SOD occurred initially at [Cu^n-SOD] < 10 U/ml, which corresponded to a hump in this dose region at early incubation time. Furthermore, the size o f the hump in this region diminished and then disappeared at - 180 min. A fter this mark, the dose-response curve in the low Cu,Zn-SOD concentration region changed insignificantly along time and became the ascending part o f a new emerging hump whose size grew continuously and the concentration o f CtiyZn-SOD corresponding to the hump also tended to increase. In contrast w ith the low concentration region, the dose-response relationship in the high concentration region (30 -1000 U/ml) appeared to be steady in the early period while changing substantially in the later period. Notably, high [Cu,Zn-SOD] reduced N-nitrosation to the extent that DAN nitrosation levels were generally below control levels. DAN concentrations affected SOD modulation o f nitrosation kinetics . To investigate whether the substrate concentration affected the observed dose-response phenomena, the concentration o f DAN was halved or doubled while keeping other experimental conditions unchanged. Fig. 4.4 depicts the sharp contrast between two experiments that used 4-fold differences o f [DAN]. W hile the time-dependent, bell- 77 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. shaped, dose-response relationship remained in both cases, there was a fundamental difference in the way in which N-nitrosation was affected by the presence o f Cu,Zn-SQD. A t [DAN] = 1.56 pM, Fig. 4.4A, the hump in the higher SOD region dominated that in the lower region (~ 600 % at [Cu,Zn-SOD] ~ 30 U/mi at 480 min versus ~ 450 % at [Cu,Zn-SOD] ~ 3 U/ml at 45 mm). In addition, the dynamic transition between the two regions in Fig. 4.4A occurred much earlier than that in Fig. 43. However, the result was somewhat reversed when [DAN] was increased by 4-fold (Fig. 4.4B). The effect o f Ct^Zn-SOD peaked at the in itia l period and then dropped more slowly until it achieved a second phase in which the maximum effect was shifted to the right (Fig. 4.4B). Moreover, the dose-response relationship at [CnZn-SOD] > 100 U/ml was less perturbed during the reaction period (Fig. 4.4B). To account for this observation, the kinetic profiles for the three controls w ith different levels o f DAN were compared (Fig. A AC). The time to attain maximum nitrosation appeared to be increased from ~ 2 hr for the control with the lowest [DAN] to ~ 3 hr and ~ 5 hr for the control with two- and four-fold higher [DAN], respectively. The extent o f nitrosation increased almost linearly. A ll SOD isoforms demonstrated biphasic reaction kinetics. A lso examined was whether Mn- and Fe-SOD elicited a biphasic effect sim ilar to that o f Cu,Zn-SOD. A sim ilar dose-response relationship occurred for these SOD isoforms as well (Fig. 4.5), although a smaller inhibitory effect was observed for both high [Mn-SOD] and [Fe- SOD]; the maximal effective concentration at t= 480 min was increased from 313 U/ml for Cu,Zn-SOD (Fig. 43 A) to 62.5 U/ml for both Mn- and Fe-SOD (Figs. 4.5A and 4 3 B ). 78 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Functional SOD was required fo r the biphasic effect. Heat inactivated (> 90 °C , 2 hr) Cu,Zn-SOD lost both its stimulatory and inhibitory effects on N-nitrosation (Fig. 4.6). Free metal ions such as C u\C u"” andZn^ also had no effect on N-nitrosation (Fig. 4.6). Bovine serum albumin (BSA) was used to test whether a nonspecific protein effect might have been involved in the reaction. W hile BSA had no effect on nitrosation at low concentrations, it inhibited the reaction to some extent at concentrations > 1 pM (Fig. 4.6). Glutathione modulated the biphasic effect o f Cu,Zn-SOD in a concentration- dependentfashion. Glutathione (GSH), a reduced thiol and an antioxidant, is an “NO sink” that modulates cellular redox reactions. It was therefore postulated that GSH would modify the effect o f SOD on the NO-mediated N-nitrosation reaction. Experiments were designed (i) to determine the effect o f GSH on SIN-1-mediated N-nitrosation in the absence o f SOD and (if) to investigate the dose-response relationship o f Cu^n-SOD on N-nitrosation in the presence o f three levels o f GSH. GSH at or above 0.5 mM inhibited SIN-1-mediated N-nitrosation by > 90% (Fig. 4.7A). Accordingly, the effect o f Cti,7n- SOD was examined in the presence o f 0.2 ,1 and 5 mM GSH, which represented low, intermediate and high physiologically relevant levels. While the biphasic effect o f CuZn-SOD was retained at 0.2 mM GSH, it disappeared with higher [GSH] (Fig. 4.7B). When the data were expressed as % control and compared w ith the dose-response curve obtained from the experiment in which GSH was absent, it was remarkable that the effect o f Cu,Zn-SOD was enhanced by the presence o f increasing [GSH] (up to I mM), which was reflected in the upward shift o f the entire dose-response curve (Fig. 4.7Q . However, the stimulant effect o f GSH disappeared at 5 mM GSH. 79 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The effect o f Cu,Zn-SOD on SIN-I-mediated oxidation o f DHR was monophasic. To investigate whether the biphasic effect o f SOD m ight be observed in other reactions mediated by NO and 02“, SIN-1-mediated oxidation o f the fluorescence dye DHR 123 was studied in the presence o f various levels o f CiiZn-SOD. Cu^Zn-SOD inhibited the SIN-1-mediated oxidation o f DHR and the IC 50 increased over time (Fig. 4.8). Unlike N- nitrosanon, Cu^Zn-SOD did not stimulate SIN-I-mediated oxidation o f DHR. Cu,Zn-SOD inhibited the release o f NO from SIN-L An HPLC method was used to follow S IN -l as w ell as its degradation intermediate, SIN-1 A. and its stable end product, SIN-IC, whose formation was indicative ofNO release from SIN -I. Inclusion o f 1000 U/m l CaZn-SOD significantly inhibited the formation o f SIN-IC and thereby the release o f NO (Fig. 4.9A). This inhibitory effect required functional Cu,Zn-SOD, as indicated from the heat-inactivation result (Fig. 4.9B). To construct a dose-response curve over the same concentration range o f Cu^Zn-SOD studied in the previous experiments, the peak intensities o f S IN -l, SIN-I A and SIN-IC were measured after 4 hr incubation o f SIN -I. High [Cu^n-SOD] preserved SIN-L and inhibited the formation o f SIN-IC (Fig. 4.9Q. However, Cu^n-SOD had no effect on the degradation o f SIN-I and the formation o f its degradation products at the low concentration range, during which Cu^n-SOD stimulated the N-nitrosation reaction. 4,4 Discussion The biological importance o f SOD was attributed to its ability to catalyze the dismutation reaction o f superoxide. SOD was implicated in many diseases, including cardiac or cerebral ischemia and neurodegeneration.27 However, some studies11"13 80 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. indicated that the beneficial effects o f SOD at low concentration were reversed at high concentration, which resulted in a bell-shaped dose-response curve. Moreover, SOD can both potentiate28"30 and attenuate31'33 NO-mediated toxicity. SOD effectively removes 0?~, thereby preventing the O^'-mediated damage that could be sustained during normal c e llu la r oxidative metabolism as w e ll as during inflam m ation, h i addition, the removal o f O2' by SOD may diminish peroxynitrite (ONOO~), a deleterious pro-oxidative molecule formed by the direct reaction ofNO and O 2". These findings suggested a far more complex role for SOD in the cellular m ilieu than was first appreciated. The present study used S IN -l as a donor o f both NO and Oz~, to mimic a scenario in which both free radicals were coexistent and sustainable, as might occurred in activated macrophages. The bell-shaped dose-response relationship that characterized the effect o f SOD on N-nitrosation o f DAN was consistent among the three isoforms o f SOD (CuZn, Mn, Fe), although there existed subtle differences. Low levels o f SOD enhanced the N-nitrosation o f DAN, which seemed to agree with the role o f SOD; i.e., SOD dismutated O f, thereby increasing the availability o f NO for the N-nitrosation reaction. Nevertheless, increasing levels o f SOD did not further increase the N-nitrosation, but rather significantly inhibited it This observation suggested that additional activities operated at high levels o f SOD. Varying the DAN concentration resulted in qualitatively and quantitatively distinct bell-shaped, dose-response curves, suggesting that second- order or other complex kinetics might be involved in DAN nitrosation. SOD affected both the rate and extent o f the N-nitrosation kinetics. As for C.n /n - SOD, low levels (up to 7.8 U/ml) increased the build-up rate o f DAN nitrosation, which was indicated by the increased steepness o f the in itia l slope along w ith a shortened time SI Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. interval to reach the steady-state (Fig. 4.2A). In addition, the extent o f DAN nitrosation was enhanced by increasing [Cu,Zn-SOD] (Fig, 4.2A). Remarkably, [Cn^Zn-SOD] as low as I U/m l was enough to cause more than a 2-fold enhancement, which correlated w ith the O f scavenging activity o f Cu^Zn-SOD. A t I U/ml, Cu,Zn-SOD resulted in —50% inhibition o f ferricytochrome c reduction in the xanthine/xanthine oxidase system (data not shown). When [Cu,Zn-SOD] reached 15.6 U/m l (Fig. 4.2A, curve 6), the kinetic profile o f DAN nitrosation started to deviate from those obtained at lower concentrations. This was considered to be a transition point at which the effect o f SOD at high levels was distinct from that at low levels. A t [CurZn-SOD] > 15.6 U/ml, the rate and extent o f the DAN nitrosation was constantly reduced by increasing [Cu,Zn-SOD] (Fig. 4.2B). Compared with the control (Fig. 4.2A, curve 1), the kinetic profiles in curves 7-11 featured a much slower build-up o f the fluorescence intensity, thereby resulting in a non-steady-state, dose-response relationship in the high [Cu,Zn-SOD] region (Fig. 43). The slow DAN nitrosation rate could be partly attributed to a slow NO release rate imposed by high [Cu,Zn-SOD] (Fig. 4.9). Can the impediment o f NO release by high [SOD] fu lly account for the descending part o f the bell-shaped dose-response curves? Is [SOD] itse lf a target o f nitrosation or can it act as an “ NO sink” via other reactions? These are important questions associated with the findings. SOD is a class o f metalloprotein consisting o f three isoforms that vary in their metal centers. NO interacts with copper ions in Cu-containing proteins, such as Cu.Zn-SOD23 and cytochrome c oxidase;34 it also interacts w ith Fe-containing proteins, such as guanylyl cyclase35 and hemoglobin.36 It is therefore likely that via a direct interaction between NO and metal centers imbedded in SOD the availability ofNO for 82 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DAN nitrosation is lim ited. Besides metal centers, the protein structure o f SOD may provide other functional groups to react w ith NO, thus serving as an NO sink.36 High [BSA] inhibited DAN nitrosation to some extent (Fig. 4.6). Since the concentration range o f BSA to inhibit the nitrosation was sim ilar to that o f [Cu,Zn-SOD], I investigated whether the protein nature o f SOD played a role. BSA is a target o f NO- mediated S-nitrosation,37 which might allow BSA to compete w ith DAN for nitrosation. Furthermore, the inhibitory effect o f BSA and Cu,Zn-SOD only occurred over the concentration range (1- 10 pM), which was comparable with that o f DAN (3.13 pM ) and supported the competition mechanism. I f high levels o f SOD competed w ith DAN for nitrosation, it was possible that the competition could be abrogated by another nitrosation target I chose GSH to test this hypothesis, because (i) GSH is a target fo r the NO-mediated S-nitrosation reaction in vivo;38 (ii) GSH is a crucial antioxidant that may function together w ith SOD in diminishing or eliminating oxidative and nitrosative stresses;39 (iii) the biologically relevant concentrations o f GSH range from 0.5 pM to 10 mM;40 and (iv) it is important to know how the apparent biphasic effect o f SOD w ill be modulated by GSH in different physiological conditions. GSH effectively abolished DAN nitrosation in the physiologically relevant concentration range (Fig. 4.7). Moreover, the biphasic effect o f Cu,Zn-SOD was modulated by GSH in a nonlinear fashion. A t low [GSH] (0.2 mM), the bell-shaped dose-response relationship was retained; however, the maximum response was increased from - 400% (without GSH) to ~ 800% (w ith GSH) and the concentration o f Cu^nrSOD to reach the maximum response was also increased about 10-fold (Fig. 4.7Q . When [GSH] was elevated to I mM, the maximum response was boosted by— 83 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1500% and the bell-shaped character o f the profile disappeared (Fig. 4.7Q . These findings suggested that GSH might attenuate the apparent inhibitory effect o f CuJZn-SOD on DAN nitrosation, thus revealing the stimulatory effect o f Cu^Zn-SOD. hi other words, excess GSH might mask the reaction between SOD and NO by acting as an NO sink. Surprisingly, the whole dose-response curve o f Cu^Zn-SOD fe ll dramatically at 5 mM GSH (Fig. 4.7Q . This result may be explained by the fact that the maximum inhibitory effect o f GSH on DAN nitrosation was achieved at [GSH] ~ I mM (Fig. 4.7A). Above this level, the detection lim it might be approached; therefore, no further inhibition was observable for the baseline. In this case, normalization may have resulted in an underestimation o f the actual effect o f GSH on the Cu^n-SOD-mediated response. Nevertheless, the data were consistent w ith the hypothesis that excess GSH may attenuate interaction between SOD and NO. This result also identified a potential mechanism by which SOD at high levels competed with DAN for nitrosation, and thereby reduced DAN nitrosation. A ll three SOD isoforms elicited the biphasic effect on the nitrosation reaction. It was conceivable that the bell-shaped dose-response curve was a manifestation o f certain intrinsic characteristics o f these enzymes. For example, the stimulatory effect o f SOD on the nitrosation could be attributed to the Oi'-scavenging effect o f SOD.8,9 W hile the nitrosation o f DAN is suppressed by the presence o f O f,8 later results9 demonstrated that increasing concentrations o f O f dramatically reduced the nitrosation o f both DAN and GSH in a buffer system in which DEA/NO was used as an NO donor and O f was generated by the xanthine/xanthine oxidase reaction. The inhibition o f nitrosation by O f was reversed by SOD.9 In the present study, SIN -I was used as both an NO and an O f 84 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. donor, because S IN -l releases NO and 02” at a 1:1 ratio.26,41 fa the presence o f SOD, the NO/Q?~ molar ratio may be increased due to the elimination o f 02” by SOD. Excess NO may undergo autooxidation in the presence o f molecular oxygen to farm nitrogen oxides that are potent nitrosatfag agents.42 Therefore, the result was in concert w ith the previous findings fa the sense that SOD stimulated N-nitrosation via elimination o f O 2'. The earlier study did not report the biphasic effect o f SOD on N-nitrosation,9 and it is unclear whether different NO and O 2" donor systems led to this discrepancy. The systems differ fa their rates o f generation o f these species, w ith generation ofN O from DEA/NO and from xanthine/xanthine oxidase being much faster than their generation from S IN -l. For example, SIN-l generates NO and O 2'w ith a rate constant o f 0.0017 m in1 (current study) whereas the rate constant for the formation o f NO from DEA/NO9 was 0.3 m in'1. Moreover, the stoichiometry o f SOD and DAN may have contributed to the contradictory results. The concentration o f DAN used fa the previous study was 200 pM, which was much higher than that o f SOD. fa contrast, the concentrations o f DAN used fa this study (1.56 - 6.25 pM) were comparable to the high concentration range o f SOD (0.5 —10 pM). Accordingly, if SOD can act as an NO sink, excess DAN may produce a masking effect sim ilar to that o f high [GSH] as discussed above. I did not test this conjecture because from the method validation I found that SIN-1-mediated DAN nitrosation may undergo self-quenching at DAN concentrations above 25 pM . fa fact, the entire experiment was designed to avoid possible fluorescence quenching caused by high dye concentrations. Distinctions among the three SOD isoforms were o f interest, especially since Mn- and Fe-SOD, as compared w ith Cu,Zn-SOD, exerted a smaller inhibitory effect on 85 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. nitrosation at high concentrations (Fig. 4.5). Based on the kinetic profiles o f DAN nitrosation in the presence o f 1000 U/ml SOD (Fig. 4.10), Mn- and Fe-SOD did not produce either the stimulatory or inhibitory effect during the early period up to 150 min. However, unlike the control, nitrosation in the presence o f Mn- and Fe-SOD did not level o ff after 150 min. This could be interpreted by a mechanism in which the stimulatory effect o f SOD was counteracted by an inhibitory effect at high concentrations. It was apparent that Cu,Zn-SOD was more potent in terms o f its inhibitory action. While the present study did not definitively answer the question as to how the differences among the three SOD isoforms emerged, possibility that the difference resulted from differences in Os'-scavengmg activity (data not shown) was eliminated. A schematic mechanism was proposed to delineate the biphasic effect o f SOD on SIN-1-mediated nitrosation (Fig. 4.11). SIN-1 releases NO and O?- and the two free radicals react to form ONOO- at a nearly diffusion-lim ited rate .5 Since the second-order rate constant fo r SOD's dism utation o f Qz~ is about 1/3 o f that o fN O / O 2- reaction ,5 the finding that low levels o f SOD (< 10 nM) were sufficient to stimulate the nitrosation reaction is perplexing. However, it suggested that mechanisms in addition to O f scavenging may promote the pro-nitrosative effect o f SOD. It has been shown that the nitrosation reaction is enhanced w ithin protein hydrophobic moieties .37 Therefore, SOD may entrap and concentrate nitrosating species (e.g. N 2O3) as well as DAN, consequently accelerating nitrosation kinetics, hi addition. SOD itse lf may be nitrosated through autocatalyzation .57 As SOD concentrations increased. I speculated that SOD acts as a nitrosating species sink, which competes w ith DAN for reaction w ith the nitrosating 86 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. species, N 2O3- High levels o f GSH would modify these interactions, since GSH has high affinity towards N 2Q1. My data, which showed that GSH effectively quenched DAN baseline GSH nitrosation and intensified SOD's pro-nitrosative effects, supported this premise. Furthermore, given that NO interacts with copper ions in Cu-containing proteins, such as Cu^Zn-SOD (23) and cytochrome c oxidase (34), CuZnSOD may also lim it the NO availability via a direct interaction between its metal center and NO. My data also support this concept Finally, NO availability can also be reduced by SOD’s inhibitory effect on the kinetics o f NO release. However, this pathway cannot fully explain the inhibitory effect o f SOD on N-nitrosation as indicated in Fig. 4.9. Overall, the net effect o f SOD on nitrosation is determined by the counterbalance o f SOD’s abilities to both promote and quench reactive species chemistry. SOD elicits multiple (^'-independent actions that are related to NO: (t) CtiyZn- SOD can reversibly convert nitroxy anion (NO") to NO;23 (ii) SOD can enhance free NO formation from L-arginine by NO synthase;24 (in ) SOD catalyzes the decomposition o f S- nitrosoglutathione, resulting in the sustained production o f NO;43 and (iv) peroxynitrite- mediated tyrosine nitration is catalyzed by SOD.44 Moreover, recent in v itro cell culture studies have implicated a potential role for SOD in many biological functions linked to NO. For example, the Cu,Zn-SOD gene in keratinocytes can be regulated by NO.45 (XZn-SOD was associated w ith NO-mediated apoptotfc cell death.46"48 Altogether, these findings suggested that NO-mediated activities may be highly regulated by SOD or vice versa. It was therefore conceivable that temporal and spatial distribution o f SOD in the cellular m ilieu may play a significant role m NO-mediated reactions. The presence o f biomolecules that are capable o f interrupting direct or indirect NO-SOD interactions 87 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. would further increase the complexity o f this system. That GSH can modulate the biphasic effect o f SOD on N-nitrosation supported this view. Recently, nitros(yl)ation has been considered as a prototypic redox-based signaling mechanism;49 proteins involved in the signal transduction pathway can be regulated by NO via the modification o f cysteine thiols and transition metal centers.49 Hence, SOD may modulate the dynamic regulation o f NO-related posttranslational modifications o f proteins. 4 i Conclusion This study pinpointed some intriguing aspects o f the action o f SOD on the NO- mediated nitrosation reaction. SOD showed a concentration-dependent biphasic effect on nitrosation. Its effects were sustained and underwent dynamic transformations. Finally, SOD itse lf may serve as a substrate for the nitrosation reactions, depending on the relative abundance o f other biomolecules. Overall, the kinetics were made complex because more than one function o f SOD was involved, which may account for the bell shaped, dose-response relationship. This study provided insights into the unsettled nature o fN O and O 2' in the cellular m ilieu, where the distribution and proportions o f reactants may affect NO-mediated nitrosation in a nonlinearfashion. 4.6 Summary N itric oxide (NO) and superoxide (O f) are two important radicals involved in many physiological and pathological functions. SOD’s removal o f superoxide may reduce the prochiction o f the deleterious molecule, peroxynitrite (ONOOr). While low levels o f SOD are anti-oxidative, high levels o f SOD are pro-oxidative. However, the 88 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. mechanism underlying this idiosyncratic bell-shaped dose-activity relationship o f SOD remains elusive. 3-Morpholinosydnonimine (S IN -l) was used to generate NO and Oz~ simultaneously in PBS buffer at pH 7.4. Diaminonaphthalene (DAN) and dihydrorhodamine 123 (DHR) were used as molecular probes fo r assessment o f the nitrosation and oxidation reactions, respectively. The effect o f SOD on SIN-1-mediated nitrosation o f DAN and oxidation o f DHR was determined by kinetic measurements o f the formation o f the florescent products o f DAN and DHR. SOD's effect on NO release was studied by HPLC. The results showed that: (i) the biphasic effect o f Cu,Zn-SOD in the nitrosation o f DAN mediated by SIN -l is time- and substrate concentration- dependent; (ii) Mn-SOD and Fe-SOD exhibited sim ilar biphasic dose-response phenomena; (iii) the biphasic effect o f SOD required functional enzyme; (iv) notably, the effect o f Cu,Zn-SOD on S IN -l- mediated oxidation o f DHR was monophasic; (v) high [CuZnSOD] inhibited the NO release rate; (vi) reduced glutathione (GSH) modulated the biphasic effect o f SOD. These findings suggest that SOD’s superoxide scavenging effect prevents NO from reacting with superoxide and thus increases the availability ofN O for the nitrosation reaction. Moreover, SOD may also serve as an NO sink, thereby reducing the N-nitrosation w ithin the physiological concentration range. Overall, complex kinetics involving more than one function o f SOD may account for the observed bell-shaped dose-response relationship. This study provides insights into the unsettled nature o f NO and Oz~ in the cellular m ilieu where, the distribution and proportions o f reactants may affect the outcome NO-mediated reactions in a nonlinear fashion. 89 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgments This work was supported by NIH/NIDCR P01 DE 12704, P30CA16058. The majority o f this work was conducted in Dr. Mallery’s lab. 4.7 References 1. Masters BS. Structural variations to accommodate functional themes o f the isoforms o f NO synthases, hi: Ignarro LJ. eds. N itric Oxide: Biology and Pathobiology 1st Ed., San Diego: Academic Press, 2000:91-104. 2. Szabo C. Pathophysiological roles o f nitric oxide in inflammation. In: Ignarro LJ. eds. N itric Oxide: Biology and Pathobiology 1st Ed., San Diego: Academic Press, 2000:841-872. 3. Ganster RW, Geller DA. Molecular regulation o f inducible nitric oxide synthase. In: Ignarro LJ. eds. N itric Oxide: Biology and Pathobiology 1st EcL, San Diego: Academic Press, 2000:129-156. 4. Grisham MB, Jourd'heuil D, Wink DA. N itric oxide. I. Physiological chemistry o f nitric oxide and its metaboIites:impiications in inflammation. Am. J. Physiol. 1999;276:G315-321. 5. Miranda KM, Espey MG, Jourd’heuil DJ, et al. The chemical biology o f nitric oxide, ha: Ignarro LJ. eds. N itric Oxide: Biology and Pathobiology 1st EcL, San Diego: Academic Press, San Diego, 2000:41-55. 6. Patel RP, McAndrew J, SeDak H, et al. Biological aspects o f reactive nitrogen species. Biochim. Biophys. Acta. 1999:1411:385-400. 7. Miles AM, Scott Bohle D, Glassbrenner PA, et al. Modulation o f superoxide- dependent oxidation and hydroxylation reactions by nitric oxide. J. Biol. Chem. 1996;271:40-47. 8. Miles AM, Gibson MF, Kirshna M, Cook JC, et al. Effects o f superoxide on nitric oxide-dependent N-nitrosation reactions. Free Rad. Res. 1995;23:379-390. 90 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9. Wink DA, Cook JA, Kim SY, et al. Superoxide modulates the oxidation and nitrosation o f thiols by nitric oxide-derived reactive intermediates. J. Biol. Chem. 1997;272:11147-11151. 10. Weber GF, Bruch HP. Pharmacology o f snperoxide-dismutase. Pharmazie. 1992;47:159-167. 11. Bernier M, Maiming AS, Hearse DJ. Reperfusion arrhythmias: dose-related protection by anti-free radical interventions. Am. J. Physiol. 1989^56:1344-1352. 12. Omar BA, McCord JM. The cardioprotective effect o f Mn-superoxide disinutase is lost at high doses in the postxschemic isolated rabbit heart. Free Rad. B iol. Med. 1990;9:473-478. 13. Omar BA, Gad NM, Jordan MC, et al. Cardioprotection by CtCZn-superoxide dismutase is lost at high doses in the reoxygenated heart Free Rad. BioL Med. 1990;9:465-471. 14. Mao GD, Thomas PD, Lopaschuk GD, Poznansky MJ. Superoxide dismutase (SOD)-catalase conjugates. J. BioL Chem. 1993;268:416-420. 15. Norris BCH, Hornsby P. Cytotoxic effects o f expression o f human superoxide dismutase in bovine adrenocortical cells. M utat Res. 1990;237:95-106. 16. Ishii T, Iwahashi H, Sugata R, Kido R. Superoxide dismutase enhances the toxicity o f 3-hydroxyanthranilic acid to bacteria. Free Rad. Res. Commun. 1991; 14:187- 194. 17. Scott MD, Meshnick SR, Eaton JW. Superoxide dismutase-rich bacteria. Paradoxical increase in oxidant toxicity. J. BioL Chem. 1987;262:3640-3645. 18. Kedziora J, Bartosz G. Down’s syndrome: a pathology involving the lack o f balance o f reactive oxygen species. Free Rad. BioL Med. 1988;4:317-330. 19. Yim MB, Chock PB, Stadtman ER. Copper, zinc superoxide dismutase catalyzed hydroxy radical production from hydrogen peroxide. Proc. Natl. Acad. Sci. USA I990;87:5006-5010. 91 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20. McCord JM. The importance o f oxidant-antioxidant balance, hr Montagnier L, O livier R. PasquierC. eds. Oxidative Stress in Cancer, AIDS, and Neurodegenerative Diseases, New York: Marcel Dekker, 1998; I-7. 21. Offer T, Rosso A, Samuni A. The pro-oxidative activity o f SOD and nitroxide SOD mimics. Faseb J. 2000;14:1215-1223. 22. Liochev SI, Fridovich L Copper- and zinc-containing superoxide dismutase can act as a superoxide reductase and a superoxide oxidase. J. BioL Chem. 2000;275:38482-38485. 23. Murphy ME, Sies H. Reversible conversion o f nitroxyl anion to nitric oxide by superoxide dismutase. Proc. Natl. Acad. Sci. USA 1991;88:10860-10864. 24. Hobbs AJ, Fukuto JM, Ignarro LJ. Formation o f free nitric oxide from L-arginine by nitric oxide synthase: Direct enhancement o f generation by superoxide dismutase. Proc. NatL Acad. ScL USA I994;9l: I0992-I0996. 25. Mallery SR, Landwehr DJ, Ness GM, Clark YM, Hohl CM. Thiol redox modulation o f tumor necrosis factor-a responsiveness in cultured AIDS-reiated Kaposi’s sarcoma cells. J. Cell. Biochem. 1998;68:339-354. 26. Feelisch M, Ostrowski J, Noack EJ. On the mechanism o f NO release from sydnonimines. Cardiovasc. Pharmacol. !989;14(SuppL 11):S13-S22. 27. Beckman JS, Chen J, Crow JP, Ye YZ. Reactions o f nitric oxide, superoxide and peroxynitrite w ith superoxide dismutase in neurodegenration. Prog. Brain. Res. 1994;103:371-380. 28. Oury TD, Ho Y-S, Piantadosi CA, Crapo JD. Extracellular superoxide dismutase, nitric oxide, and central nervous system 02 toxicity. Proc. NatL Acad. ScL USA 1992;89:9715-9719. 29. Assreuy T, Cunha FQ, Epperfein M, Noronha-Dutra A , O’Donnell CA, Liew FY, Moncada S. Production o f nitric oxide and superoxide by activated macrophages and killin g o f Leishmania major. Eur. J. Immunol. 1994;24:672-676. 92 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30. Gergel D, M isik V, Ondrias BC, Cederbaum AL Increased cytotoxicity o f 3- Morpholinosydnonimine to HepG2 cells in the presence o f superoxide dismutase. J. BioL Chem. 1995;270:20922-20929. 31. Bruneili L, Crow JP, Beckman JS. The comparative toxicity o f nitric oxide and peroxynitrite to Escherichia coii. Arch. Biochem. Biophys. 1995;316:327-334. 32. Lipton SA., Choi Y-B, Pan Z-H, Lei SZ, Chen H-SV, Sucher NJ, Loscalso J, Singe! DJ, Stamler JS. A redox-based mechanism for the neuroprotective and neurodestructive effects o f nitric oxide and related nitroso-compounds. Nature 1993;364:626-632. 33. Siegfried MR, Erhardt J, Rider T, Ma X-L, Lefer AM. Cardioprotection and attenuation o f endothelial dysfunction by organic nitric oxide donors in myocardial ischemia-reperfusion. J. Pharmacol. Exp. Ther. 1992;260:668-675. 34. Cooper CE. N itric oxide and cytochrome oxidase: Substrate, inhibitor or effector? Trends Biochem. ScL 2002;27:33-39. 35. Koesling D, Friebe A. Structure-function relationships in NO-sensitive guanytyt cyclase. In: Ignarro LJ. eds. N itric Oxide: Biology and Pathobiology 1st Ed., San Diego: Academic Press, 2000^69-379. 36. Lancaster Jr. JR. The physical properties o f nitric oxide: determinants o f the dynamics ofNO in tissue. In: Ignarro LJ. eds. N itric Oxide: Biology and Pathobiology 1st Ed., San Diego: Academic Press, 2000^209-224. 37. Nedospasov A, Rafikov R, Beda N, Nudler E. An autocatalytic mechanism o f protein nitrosylation. Proc. Natl. Acad. ScL USA 2000;97:13543-13548. 38. Gaston B. N itric oxide and thiol groups. Biochhn. Biophys. Acta I999;I411:323- 333. 39. Calabrese V, Bates TE, Stella AMG. NO synthase and NO-dependent signal pathways in brain aging and neurodegenerative disorders: The role o f oxidant/antioxidant balance. Neurochem. Res. 2000;25:1315-1341. 93 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40. G riffith OW. Biologic and pharmacologic regulation o f mammalian glutathione synthesis. Free Rad. B iol. Med. 1999;27:922-935. 41. Bohn H, Schonafinger BC. Oxygen and oxidation promote the release o f nitric oxide from sydnonimines. J. Cardiovasc. Pharmacol. !989;l4(SuppI. 11): S6-SI2. 42. Marietta MA, Mammalian synthesis o f nitrite, nitrate, nitric oxide, and N- nitrosating agents. Chem. Res. Toxicol. 1988;1:249-257. 43. Jourd’heuil D, Stephen Laroux F, Miles AM, Wink DA, Grisham MB. Effect o f superoxide dismutase on the stability o f S-nitrosothiols. Arch. Biochem. Biophys. I999;36l;323-330. 44. Ischiropoulos H, Zhu L, Chen J, Tsai M, Martin JC, Smith CD, Bechman JS. Peroxynitrite-mediated tyrosine nitration catalyzed by superoxide dismutase. Arch. Biochem. Biophys. 1992;298:431-437. 45. Frank S, Kampfer H, Podda M, Kaufinann R, Pfeilschifter J. Identification o f copper/zinc superoxide dismutase as a nitric oxide-regulated gene in human (HaCaT) keratinocytes: Implications for keratinocyte proliferation. Biochem. J. 2000;346:719-728. 46. Troy CM, Derossi D, Prochiantz A, Greene LA, Shelanski ML, Downregulation o f Cu/Zn superoxide dismutase leads to cell death via the nitric oxide-peroxynitrite pathway. J. Nerurosci. 1996;16:253-261. 47. Morrison BM, Morrison JH, Amyotrophic lateral sclerosis associated with mutations in superoxide dismutase: a putative mechanism o f degeneration. Brain Res. Rev. 1999;29:121-135. 48. Ciriolo MR, De Martino A, Lafavia E, Rossi L» Carri MT, Rotilio G. Cn,Zn- superoxide dismutase-dependent apoptosis induced by nitric oxide in neuronal cells. J. BioL Chem. 2000;275:5065-5072. 49. Stamler JS, Lamas S, Fang FC. Nitrosylation: The prototypic redox-based signaling mechanism. CeO, 2001;106:675-683. 94 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -14— 0 3-Morpholinosydnonimine (SIN-l) NH2 n h 2 2,3-Diaminonaphthalene (DAN) NH Dihydrorhodamine 123 (DHR) Figure 4.1. The chemical structures of 3-morphoIinosydnonimine (S IN -l), 23- diaminonaphthalene (DAN) and dihydrorhodamine 123 (D H R ). 95 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A 5 0 0 400 6 5 300 4 3 7 200 E c e too 5? ✓ Q 0 0 too 200 300 400 500 >* •* c £c B 500 1 400 7 8 s 9 o 300 200 10 too tt 0 100 200 300 400 500 Time (min) Figure 4.2. Nitrosation kinetics o f DAN in the absence and presence o f different levels o f CiijZn-SOD. The reactions were performed in a 96-well microtiter plate form at SIN -l (100 pM) was added to PBS-based reaction buffer containing 3.13 pM DAN, 0.1 mM DTP A, 120 U/ml catalase and CitZn-SOD (0 - 1000 U/ml>, pH 7.4, at 25 ± I°C . The fluorescence intensity after the addition o f SIN -l was measured at 10-min intervals by fluorescence spectroscopy. Data represent the mean o f three measurements. Each curve represents a different [Cu,Zn-SOD]: I, control; 2,0.98 U/ml; 3,1.95 U/ml; 4, 3.9 U/ml; 5,7.8 U/ml; 6,15.6 U/ml; 7 ,31J2 U/ml; 8,62.5 U/ml; 9,125 U/ml; 10,500 U/ml; 11,1000 U/mL 96 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A 5 0 0 o 1 10 100 1000 Cu.Zh-SOD (U/ml) B Figure 43. Time- and concentration-dependent, biphasic, dose-response relationship fo r the effect o f Cu,Zn-SOD on DAN nitrosation. A. The fluorescence intensities at the same time point in FIG. 42. were expressed as % control and plotted against [Cu,Zn-SOD], Each curve (n = 3} represents the dose-response relationship at 20-mm intervals. The arrows indicate the direction o ftone progression starting at 45 min and ending a t485 min. B. Saddle-like dose-response surface was generated by plotting the relative fluorescence intensities against [Ct^Zn-SOD] and the reaction time. 97 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A C 400 10 100 100 0 Cu,Zh-SOD (U/ml) B ~ 500 C 1 00 10 100 100 0 Cu,Zh-SOD (U/ml) f 250 • - [D A N ] - 1 a |lM 200 -■>- [O M f-X TlllM .*■ * 150 .iT 100 200 300 Tim* On In) Figure 4.4. Effect o f DAN concentration on SOD modulation o f nitrosatiott kinetics. Procedures were as described in FIG. 4.2, except (A ) Vz x [DAN] or (B) 2 x [DAN] was used. Mean dose-response curves (n = 4 ) were obtained by plotting the relative fluorescence intensities (% control) against [Cu^n-SOD]. The time interval for each curve is 20 min. The arrows indicate the direction o f time progression starting at 45 min and ending at 485 min. (Q The kinetics profiles for the three controls with different levels o f DAN . 98 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A 500 s c o 400 3? c 300 o 200 c 100 z < Q 1 10 100 1000 Mn-SOD (U/ml) B 500 2 c o 400 S! 300 200 e z 100 < Q 1 10 100 1000 Fe-SOD (U/ml) Figure 4.5. Time- and concentration-dependent, biphasic, dose-response relationships fo r the effects o f Mn-SOD and Fe-SOD. Procedures were described in FIG . 42. and FIG. 43, except (A ) Mn-SOD and (B) Fe-SOD were studied. Reactions were initiated by adding S IN -l (100 |iM ) to PBS-based reaction buffer containing 3.13 pM DAN, 0.1 mM DTPA, 120 U/ml catalase and various activities o f SOD (0 —1000 U/m l). Values represent the mean o f three measurements. 99 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 400 0 350 1 300 o ^ 250 c o 3 200 CO (A 2 150 z < o 0.01 0.1 1 10 Concentration ftiM) Figure 4.6. Effect o f intact Cu^Zn-SOD (•), heat-inactivated Cu,Zn-SOD (O), BSA (■), and metal ions (C u^ A , Cu+ V , ZnM" O ) on DAN nitrosation. The experiment followed the typical nitrosation kinetics procedures for Cu,Zn-SOD, accept Cn,Zn-SOD was replaced by heat-inactivated enzyme, BSA, Q 1SO4, CuCI or ZnCh- Equal molar concentration range (0.01 -1 0 pM) for all species was used. Dose-response curves were compared at 4 hr. 100 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. i n 140 i 120 i n n 40 o 2 4 S S 12 GSH (mM) B 10 333 i n 333 io n Cu£h-SOD(Uftnl) 1300 _ te n >aii 1 u n I 1200 f 1000 I m 1 s n 2n i 10 i n io n Cu.2n-SOO(U/ml) Figure 4.7. Effect o f glutathione (GSH) on Ci^Zn-SOD modulation o f DAN nitrosation. (A ) SIN-l (100 pM ) was added to PBS-based reaction buffer pH 7.4 containing 3.13 pM DAN. 0.1 mM DTPA, 120 U/ml catalase and GSH (0 - 10 mM). at 25± i°C . The fluorescence intensity after the addition o f SIN-1 was measured at 4 hr and was plotted against [GSH]. (B) A t three fixed GSH levels (0.2 mM, I mM, 5 mM), DAN nitrosation was studied in the absence and the presence o f 10,333,100,333 and 1000 U/ml QivZiv-SOD. Fluorescence intensity at 4 hr fo r each group was plotted against [Cu^n-SOD]. Values represent the mean ± SD (n =4). (C) The data in B were expressed as % controL The dose-response curve at t = 4 hr for Cu^n-SOD in the absence o f GSH was included fo r the purpose o f comparison. 101 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o 120 Cu, Zn-SOD (U/ml) Figure 4.8. Effect o f Cu^Zn-SOD on SIN -l mediated oxidatioii o f DHR. SIN-I (100 p M ) was added to pH 7.4 PBS b u ffe r containing 0 3 9 pM DHR. 0.1 mM DTPA. 120 U/ml catalase andCu,Zn-SOD (0 -1000 U/mI)», at 25 ± I°C . The fluorescence intensity after the addition o f S IN -l was measured at a 5-min interval; fluorescence was expressed as % control (n = 4 ± SD) and plotted at a 20-min intervals against [CuyZn-SOD]. The arrows indicate the direction o f time progression starting at 25 min and ending at 245 m in. 102 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A 3 .0 C o n tro l 2.S -O- - Co. Zn-SOD 1000 U/ml 5 2 .0 1.0 0 .5 0 too 200 3 00 4 0 0 500 T lm o (m in ) B 2 .0 Control CuZivSOD H.L- C tO n-S O O C 200 150 2 too 1 10 too 1000 Cu2n4QO (U/ml) Figure 4.9. Effect o f Cu,Zn-SOD on NO release kinetics o f S IN -l measured by HPLC. SIN -i (100 |lM ) was added to a pH 7.4 PBS buffer containing 0.1 mM DTPA and 120 U/ml catalase, at 25 ± I°C. SIN -l and its degradation products (SIN-1A and SIN-IC) were determined by HPLC. (A ) SIN-IC formation in the absence and the presence o f 1000 U/ml CuyZn-SOD. (B) SIN-IC formation at 4 hr in the absence or presence o f either intact Cn,Zn-SOD (1000 U/m l) or heat-inactivated (ELL) Ca1Zn-SOD. (Q CuZn-SOD (I —1000 U/ml) was included; the solutions were incubated for 4 brand the peak intensity o f SIN -l and its degradation products were determined. Mean data were presented as %control, n = 3 ± SD. 103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Control O Cu, Zn-SOD (1000 U/ml) A Mn-SOD (1000 U/ml) □ Fe-SOD (1000 U/ml) R 250 200 300 500 Tim e (m in ) Figure 4.10. Comparison o f the nitrosation kinetics among three SOD isozymes at 1000 U/mL SIN-1 (100 pM ) was added to the PBS pH 7.4 bufier containing 3.13 pM DAN, 0.1 mM DTP A, 120 U/ml catalase and SOD (1000 U/ml), at 25 ± l°C . The fluorescence intensity was measured at 10-min intervals; values represent the mean ± SD, n = 3. 104 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SCO GSH DAK SOD SIN-l - GSNO GSH SOD Figure 4.11. Proposed mechanisms fo r SOD’s biphasic effect on SIN-l-mediated nitrosation reaction 105 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTERS Kinetic Modeling of Nitric-Oxide-Associated Reaction Network: Biological Implications 5.1 Introduction The free radical nitric oxide (NO) mediates a large number o f physiological and pathophysiological processes. Despite more than a decade o f intense research, many aspects o f NO physiological chemistry remain both paradoxical and controversial. A t low concentrations (~ nM), NO modulates normal physiological functions such as regulation o f vascular tone and intracellular signalingvia a direct interaction w ith its targets.1 However, high NO levels can induce cytotoxicity, presumably attributable to oxidative and nitrosative stresses.1 Elevated NO levels present at inflammatorysites provide the opportunity for NO to compete w ith superoxide dismutase (SOD) for reactions with superoxide (O O , thereby generating the highly reactive and cytotoxic peroxynitrite (ONOO~) molecule.2 The findings in the previous chapter highlighted the complexity o f NO-mediated chemical reactions. Because o f the complex nature ofNO and technical difficulties in studying its biological features, computational modeling has been used as an alternative tool fo r understanding diverse aspects ofN O , which included (i) the biotransport o f NO;3"7 (if) 106 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. kinetics related to the generation and reaction ofNO;®"15 (iii) functions ofN O in physiological and pathophysiological processes, such as neural signaling16 and wound healing17 (iv) mechanistic role ofNO on the activation o f soluble guanyiyl cyclase.18 For example, mathematical modeling ofN O diffusion predicted that NO is not a locally acting mediator, due to its rapid and wide spread d iffiisib ility. Thus, one NO-producing cell can affect many hundred o f its neighboring cells.19 Modeling approaches were also applied to examine the processes in the interaction o f ONOO" with Iow-density lipoproteins (LDLs) in the plasma.11*13 The kinetic model predicted that plasma \ONOO~J should be in nM range and ONOO" is a potential candidate for initiating peroxidation o f LDLs.11 Once ONOO~ is formed, antioxidants have little effect on the ONOO" level.13 Furthermore, a reaction/diffusion model was used to explore the movement o f ONOO' into the LDL particle.12 The coexistence o fN O and O 2" in the physiological m ilieu gives rise to intricate oxidative and nitrosative reactions. As described in Chapter 4, low \SOD\ stimulated, whereas high [SOD] attenuated, NO-mediated nitrosation reaction. Glutathione (GSH) modulated the biphasic effect o f SOD. The results, therefore, suggested that the consequences o f oxidative and nitrosative chemistry may depend heavily on a delicate balance among the processes that govern the formation and elimination ofN O and O f. The formation ofNO in the tissue is catalyzed by nitric oxide synthases (NOS), which are heme-containing enzymes. The expression o f the different NOS isoforms is regulated by diverse mechanisms.20 W hile NOS I [NOS 1, neuronal NOS (nNOS)] and NOS3 [NOS in , endothelial NOS (eNOS)] are low-output, constitutive enzymes whose 107 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. activities are regulated by Ca2+ and calmodulin, NOS2 (NOS H, inducible NOS (iNOS)) is a high-output enzyme, which after induction can produce a large amount ofN O in a Ca2+-independent fashion.20 Apparently, the amount ofN O produced in tissues is a dynamic process that depends on which enzyme is involved, and where and when the enzyme is expressed. La tissues, NO has an extremely short half-life, on the order o f seconds.21 In addition to the high mutual reactivity between NO and OT,22 NO also undergoes autooxidation w ith a rate that is dependent on the concentration o f oxygen.21 Thus, both Q» and O 2" play an important role in the rapid scavenging ofNO . The respective reaction intermediates, N 2O3 and ONOO", fo r NO-O 2 and N O -O f reactions were attributed to the indirect cytotoxic actions ofN O .1 While N 2O3 was believed to be a strong nitrosating agent towards targets, such as DNA and proteins, ONOO- is a potent oxidant and has been shown to react w ith a large number o f biomolecules in vitro. The oxidative activity o f ONOO- contributes substantially to tissue damage in inflammatory and infective diseases.1 hi this study, I integrated key reaction pathways associated with NO-mediated nitrosative and oxidative chemistry into a reaction network. The dynamics o f this network was investigated. Two specific questions were examined: (i) what is the role o f GSH in modulating nitrosative and oxidative species, such as N 2O3 and ONOO"? and (ii) how does the system behave when the generation rate ofN O and O 2- varies? 108 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.2 Model Fig. 1 integrated the reaction pathways related to NO and its reaction products, N2O3, ONOO" and nitroso glutathione (GSNO). The concentrations o f NO, N 2O3, ONOO- and GSNO as w ell as the free radical 0z~ and antioxidant GSH were simulated. The general procedure was firs t to write a set o f coupled differential equations based on the law o f mass action. The differential equations were then solved simultaneously by numerical methods. Since the reaction kinetics o f the integrative system was the main interest o f this study, transport and diffusion processes were not included in the model. 5.2.1 Reaction chemistry and rate constants The NO production rates were estimated to be in the range from I x I O'10 to 1.6 xiO** M/s fo r adherent cells expressing iNOS.ts Using mathematical modeling, Vaughn et al.14 predicted the rate o f NO production by vascular endothelium o f ~ I0 's M/s. In addition, the NO production rate by basal epidermal cell was estimated to be 1.7 x 10~7 M/s.23 Cultured keratinocyte cells24 and fibroblasts25 generated Q f at a rate o f ~ I O'6 M/s and - I O'5 M/s, respectively. The rate constants were summarized in Table I.26"36 The rate equations for NO, O 2-, ONOO- GSNO, N2O3, GSNO and GSH were: ^ Q = k l +kia[GSNO]1[o;]-/ct[NO][o;]-ict,[m }2[o,] (I) at = kz -^[VO ][C>;]-Ar5[O;][5OO]-^I0[G SVO l2[O 2-l (2) d[ONOCT] = kt[NO][O;}-kflON0Gr][GSH]-(kT[GPX] dt (3) +k*[COz]+ k9[cyt cWONOOr] 109 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ^^^=k,[0N 0(T\[G S H \+klS.NM[GSH\-kw[GSN0f[0-1[ (4) at ^ ^ = k aim nO t}-k„lN,0,\lGSH\-kJ_N,p,} (5) ^ p . = k , -(*l[0W00-][CSHl+t„[iV!0J][C O T ])+ -^^P - (6) at Km +[G5oC/| [GSSG]= [G S H \ - [G S H ] - [GSNO] (7) S J tl Numerical simulations Numerical simulations o f the model (equations 1 -7 ) were carried out using NDSolve in Mathematica 4.0 [W olfram Research, Champagne, EL]. NDSolve can solve s tiff differential equations using Backward Differentiation Formulas (or Gear Formulas). The approximation error in NDSolve is controlled by two built-in functions o f Mathematica, AccuracyGoal and PrecisionGoal, which specify absolute and relative error, respectively. NDSolve attempts to calculate a solution, y(x) , w ith error less than 10'“ +|y(x)[ I0~p, where a and p are positive integers that represent the settings for AccuracyGoal and PrecisionGoal, respectively.37 For this study, the error was set to no more than I O'15. The model consisted o f 7 dependent variables, which were the chemical species to be simulated. The rate constants k i to k j were subjected to variation, while kt to £ /j were fixed as constant parameters. Other constants were Vm> Km, [O ?], [CO>]»[cyt c], [SOD], [GPX\. The values for these constants were shown in Table 2 .22-36*38-39 110 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 3 Results 533 Kinetic profiles Figs 2-4 show the concentration-time profiles for NO, O 2-, ONOO-, N2O3, GSNO and GSH in 3 separate simulations where the in itia l GSH level was varied. For each simulation, 5 scenarios were considered. Each scenario had a 2-fold difference in the generation rate o f NO, £/. The results indicated that changing basal GSH levels did not alter the kinetics o f NO, O?-, and ONOO-, w ith the steady-state concentrations being in the (jM , pM and nM range, respectively (left panels. Figs 2-4). The kinetics o f the three species reached steady state w ithin 10 mm. The steady-state concentrations decreased (NO and ONOO- ) o r increased (O 2-) corresponding to the reduction o f kt. The kinetic profiles ofN jO j, GSNO and GSH were sensitive to the variation o f basal GSH levels (right panels, Figs 2-4). The profiles were consistent in a sense that [GSNO] continuously increased at the expense o f GSH and N 2O3. As a result, [GSH] was depleted and the time for a complete depletion depended on the basal level o f GSH (Figs 2-4) and the input rate o fNO (individual curves in each figure). It is interesting to note that GSH and GSNO followed zero-order kinetics before GSH was exhausted, which disobeyed second-order rate equations for these two species. This discrepancy w ill be discussed later. 5 3 3 GSH as a dynamic switch As indicated in the model (Fig. I), the continuous generation o f NO contributes to the formation o f^O ? , a potential nitrosating agent. Strikingly, N 2O3 was kept at an extremely low level due to the presence o f GSH (Fig. 2). An instantaneous elevation o f [N 2O3 } was apparent when [GSH] approached a value o f zero (Fig. 2). The kinetic III Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. profiles were therefore step-like. Moreover, the slower the NO-generation rate was, the longer fo r this phenomenon to be initiated, and the lower was the new steady-state [NzOj[. When the basal [GSH] was reduced to I and 0.1 mM (Figs 3 and 4), GSH was depleted much more quickly, followed by much earlier switching o f than it was at 10 mM. To further explore the switch-like phenomenon, a zero-order input o f GSH was started at a given time after GSH was depleted. The result showed that the system responded in a switch-like fashion (Fig. 5). [NjOj] was sensitive to the perturbation and was reduced to a new steady state immediately. Overall, the data suggested that GSH acted as a dynamic switch in the reaction network. 53 3 Nonlinear dynamics at high NO and Ch~ input rates To study the system behavior at high NO and Ch~ input rates, simulations were conducted by setting k{ an dk> 100 times higher, w hile keeping kjkz ratios and other parameters the same as in Fig. 2. The results were surprising because the dynamic patterns in Fig. 6 significantly deviated from those in Fig. 2. The concentrations o f NO were below S pM for all simulations with ki/kz ratios in the range o f0.0625 — 0.5, but at equal NO and QT input rate, [NO] reached to 70 pM at steady state (Fig. 6). Compared with Fig. 2, [NO] was relatively lower while [O f]was higher in a ll scenarios in Fig. 6. The result suggested that O f outcompeted w ith NO when both NO and O 2- input rates were high. It further implied that an increase in NO production couldn’t guarantee an increase in [NO] as long as the input o f O f was not fixe d . Another interesting result, as compared with Fig. 2, was the elevation o f [ONOO-] in Fig. 6, which suggested that the 112 1i i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. system was more efficient in terms o f the generation o f ONOO . Finally, the kinetics o f N2O3, GSNO and GSH in the right panel o f Fig. 6 coincided w ith the role and the kinetics o fN O . 53.4 Phase portraits'*0 A phase-portrait approach was used to account fo r the nonlinear dynamics illustra ted in Fig. 6 . To construct a phase portrait, the relationship between and dt [NO\ was plotted according to equation 1, assuming that the contribution o f GSNO to the kinetics o f NO was negligible under the simulation conditions. Hence, equation I became -MWOlton-MiTOfto,!. (8) The steady-state O -f concentration with the same assumption was [OT] = . (9) * k&NOl+kJiSODl Substituting (9) into ( 8), equation I became Kk£NO\ * (10) dt ^ kt[NO]+k5[SOD] u Since k<, £ j, k i2 , [SOD] and [O2 ] were known parameters, by varying the ratio ki/kz and p lo ttin g the data ( versus [M?D, a set o f curves was obtained (Fig. 7A). The x- dt axis intersect implies = q , ^ corresponding value on x-axis being the d t steady-state concentration o f NO, [#£)]». By plotting [MTJj, versus k//%>, a nonlinear curve was obtained. This curve captured the essence o f nonlinearity in NO kinetics in 113 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 6 ; if £( < 0 .5 ^, [iVO^s was low and insensitive to the variations in £ 7 ; nevertheless, EM?]** increased disproportionately as jfc> increased beyond 0.5 cjI. For the purpose o f comparison, Fig. 8 showed a scenario where the dynamics was approximately linear. 5.4 Discussion Using mathematical modeling, this study examined two questions related to the reaction kinetics o f nitrogen oxide species (NO*) in an integrative dynamic system: (i) what is the role o f GSH in modulating nitrosative and oxidative species, such as N 2O3 and ONOO"? (ii) how does the system behave when the generation rate o f NO and O 2" varies? It is d iffic u lt to study these types o f questions using experimental approaches, since it may require simultaneous measurements o f multiple short-lived species at extremely low concentrations, in complex physiological matrices. Nevertheless, one can gain a reasonable picture o f the behavior o f an in vivo system by using a modeling approach to integrate the knowledge about individual elements (reactions) o f the system. The underlying rationale was that the behavior o f a complex system usually is not determined by an additive process. Glutathione (GSH), the major low-molecular-weight thiol compound in the cell, is best known fo r its role as a superoxide scavenger in mediating cellular redox reactions .41 Since cellular GSH levels are as high as 10 mM and GSH reacts w ith ONOO" and N 1O3 in aqueous media, it was suggested that GSH is a scavenger fo r reactive NO* as well .42 Moreover, the S-nitrosation product o f GSH, S-nitrosoglutathione (GSNO) was considered as a possible carrier molecule fo r NO .43 In Chapter 4, GSH was shown to diminish the NO-mediated nitiosation reaction. It also modulated the biphasic dose- 114 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. response relationship for the effect o f SOD on NO-mediated nitrosation. Since \GSH\ ranges from several hundred [iM (extracellular) to 10 mM (intracellular), the effect o f GSH on the kinetics ofNOx was simulated w ith initial [GSH\ = 0.1,1 and 10 mM, respectively. That GSH didn’t affect the kinetic profiles o fNO and ONOO- (Figs 2 -4 ) reflected the fact that in the model GSH does not react w ith NO directly, and the GSH pathway is not the predominant route for the elimination o f ONOO-. Besides GSH, ONOO- also reacts w ith a w ide variety o f biomolecules. In th is study, the reactions o f ONOO- w ith CO2, cytochrome c (cyt c) and glutathione peroxidase (GPX) were only included because o f the relative importance o f these reactions (Fig. I). ONOO- reacts rapidly w ith CO 2 (k = 5.8 x 104 W V 1) to generate nitrosoperoxycarbonate adduct, which decomposes to NO 3' and CO 2 in the absence o f other reactive molecules .30*44 ONOO-+CO, -* ONO,CO; ( 11) ono,co; -> no;+co 2 ( 12) Since COWbicarbonate/carbonate is an important buffering system in vivo and the concentrations o f CO 2 (13 mM in plasma) and bicarbonate (12 mM in intracellular fluid and 25 - 30 mM in plasma) are high, the reaction between ONOO- and CO 2 could be the major route o f ONOO- disappearance in vivo .44*45 Although the rate constants for the reactions between ONOO- and GPX (2 x 106 M 'V 1),29 and between ONOO- and cyt c (2 x 105 M 'V 1)31 are re la tive ly higher than that fo r the ONOO- - CQ» reaction, the contribution o f GPX and cyt c in eliminating ONOO- could be less significant due to their relatively lower concentrations in biological fluids (Table 2). The rate constant for the reaction between ONOO- and GSH is 135 x IQ 3 M 'V 1,28 which is the smallest 115 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. compared w ith those o f the abovementioned reactions. Therefore, GSH w ill be far less effective than COz in modulating ONOO- levels in the physiological environment, where GSH is less abundant, e.g. blood plasma. In contrast, GSH may become important inside the cells because o f its high intracellular concentration (10 mM). The reason that [ONOO~[ in Fig.2 was comparable to that in Figs 2-3 was because the reaction rate o f ONOO- with I mMCOz was s till at least 4-fold larger than that with GSH, even though [GSH] was as high as 10 mM. Zero-order kinetics was observed fo r GSH and GSNO, which disobeyed the rate laws for both species. Since ONOO- and N 2O3 were the two molecules responsible for the depletion o f GSH and the accumulation o f GSNO in the model, the discrepancy was resolved when the kinetics o f ONOO- and N 2O3 was examined. While [ONOCT] reached steady state w ith in 10 m in, [W2O3] was kept at nearly constant and extremely low levels before GSH was completely depleted (Fig. 2). Therefore, d[iV,0 2 ] ^ dt dt approximately zero in the early period. From (3) and (5), one immediately obtains: k£ONOCr\[GSH\ = £4[tf0][< X I-(fc7[GPXl+fcg[C02]+ k jc y t cD[OWOO‘ ] (13) ktI[Af,0J][GSH]=^2[iV0f(02]-kl3[N20J] (H) Since [M 7j and [O f] also reached steady states very quickly (Fig. 2), and [GPX], [CO?], [ 0 ?] and [cyt c] are constants, it implies that the term k,[ONOOr][GSH\^iNMiGSH\ in (4 ) and ( 6 ) is close to a constant and, therefore, the elimination o f GSH and the formation o f GSNO foDowed zero-order kinetics. 116 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The current study proposed that GSH can act as a dynamic switch that controls the concentration ofN iG s, which is an intriguing phenomenon from both kinetic and biological standpoints. Kinetically, the switch suggested an almost discontinuous solution to the differential equations, which is counterintuitive because the processes were considered continuous. How could it happen? By closely examining equation 5 and the rate constants (Table 1), one finds that kn[GSH] »kn when [GSH] = 1 -1 0 mM. Accordingly, the elimination o f N 2O3 was controlled by GSH at high levels. Under this circumstance, the hydrolysis o f N 2O3 (ku) becomes a redundant e lim ination pathway that contributes insignificantly to the whole process. The concentration o f N 2O3 remained quite low due to the presence o f sufficiendy high levels o f GSH (Fig. 2 or Fig. 3). However, the once redundant pathway became increasingly important as GSH approached a depletion point at which the alternate elimination pathway took over and a new steady state switched on. The nearly instantaneous occurrence o f the new steady- state can be attributed to the first-ord er rate constant ku (Table I), which corresponds to a h a lf-life as short as 0.4 ms. From a biological standpoint, a sudden elevation o f a reactive NOx in a physiological system could be catastrophic. N-nitrosation may result in the deamination o f DNA bases .38 Furthermore, S-nitrosation o f proteins was attributed to the inhibition o f some enzymes, such as glyceraldehydes-3-phosphate dehydrogenase 46 and the DNA repair enzyme 0 5-methylguanine-DNA-methyitransferase .47 A brupt changes in S- nitrosation status may also disrupt redox-based signaling transduction pathways .48 GSH, therefore, may play an important role in modulating NOx-mediated cytotoxicity. For example, the NO donor DEA/NO only caused a modest toxicity in Chinese hamsterV79 117 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. cells.42 However, the toxicity was dramatically increased when GSH was depleted in these cells. Recently, cellular GSH status was linked to the differential iNOS regulation in hepatocytes and inflammatory cells.49 W hile iNOS induction in hepatocytes in vivo and in vitro was dependent on the intracellular GSH status and correlated w ith NF-kB binding, GSH-depletion had no eflect on the expression o f iNOS in inflammatorycells.49 5.5 Summary Kinetic modeling was used to explore the reaction network associated w ith the flee radicals NO and O 2” Numerical simulations provided two testable predictions: (i) GSH may modulate the nitrosation reaction in a switch-like fashion; (ii) Concurrently high NO and Oz~ generation may result in nonlinear dynamics o f nitrogen oxide species. 5.6 References 1. Miranda KM, Espey MG, Jourd’heuil DJ, et al. The chemical biology o f nitric oxide. In: Ignarro LJ. eds. N itric Oxide: Biology and Pathobiology 1st Ed., San Diego: Academic Press, San Diego, 2000;4l-55. 2. Patel RP, McAndrew J, SeOak H, et al. Biological aspects o f reactive nitrogen species. Biochim. Biophys. Acta. 1999;1411:385-400. 3. Burek DG. Can we model nitric oxide biotransport? A survey o f mathematical models fora simple diatomic molecule w ith surprisingly complex biological activities. Annu. Rev. Biomed. Eng. 2001;3:109-143. 4. Lancaster Jr. JR. Simulation o f the diffusion and reaction o f endogenously produced nitric oxide. Proc. Natl. Acad. Sci. USA 1994;91:8137-8141. 5. Lancaster Jr. JR. A tutorial on the diffusibility and reactivity o f free nitric oxide. N itric Oxide: Biology and Chemistry. t997;l(l):l8-30. 6. Vaughn MW, Kuo L, Liao JC. Effective diffusion distance o f nitric oxide in the microcirculation. Am. J. Physiol. 1998;274(5):H1705-K1714. 118 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7. Shin H-W, George SC. Microscopic modeling o f NO and S-nftrosoghrtathione kinetics and transport in human airways. J. AppL Physiol. 2001;90:777-788. 8. Chen B, Deen WM. Analysis o f the effects o f ceil spacing and liquid depth on nitric oxide and its oxidation producs in cell cultures. Chem. Res. Toxicol. 2001;14:135- 147. 9. Goss SPA, Hogg N, Kaiyanaraman B. The effect o f nitric oxide release rates on the oxidation o f human low density lipoprotein. J. BioL Chem. 1997;272:21647-21653. 10. Stanbro WD. A kinetic model o f the system: Tyrosy I radical-nitrogen oxide- superoxide ion. J. Theor. BioL 1999;197:557-567. 11. Stanbro WD. Modeling the interaction o f peroxynitrite with Iow-density lipoproteins. I. Plasma levels o f peroxynitrite. J. Theor. B iol. 2000;205:457-464. 12. Stanbro WD. Modeling the interaction o f peroxynitrite with Iow-density lipoproteins. IL Reaction/diffusion model o f peroxinitrite in Iow-density lipoprotein particles. J. Theor. B iol. 2000;205:465-471. 13. Stanbro WD. Modeling the interaction o f peroxynitrite with Iow-density lipoproteins. IIL The role o f antioxidants. J. Theor. Biol. 2000;205:473-482. 14. Vaughn MW, Liao JC. Estimation o f nitric oxide production and reaction rates in tissue by use o f a mathematical modeL Am. J. Physiol. 1998;274(6):H2163-H2176. 15. Laurent M, Lepoivre M, Tenu J-P. Kinetic modeling o f the nitric oxide gradient generated in vitro by adherent cells expressing inducible nitric oxide synthase. Biochem. J. 1996314:109-113. 16. Philippides A, Husbands P, O’Shea M . Four-dimensional neuronal signaling by nitric oxide: A computational analysis. J. Neurosci. 200030(3): 1199-1207. 17. Cobbold CA, Sherratt JA. Mathematical modeling o f nitric oxide activity in wound healing can explain keloid and hypertrophic scarring. J. Theor. BioL 2000304357- 288. 18. Bellamy TC, Wood J, Garthwaite J. On the activation o f soluble guanytyl cyclase by nitric oxide. Proc. NatL Acad. ScL USA 2002;99( I):507-510. 19. Lancaster Jr. JR. The physical properties o f nitric oxide: Determinants o f the dynamics o f NO in tissue. In: Ignarro LL eds. N itric Oxide: Biology and Pathobiology 1st Ed., San Diego: Academic Press, 2000309-224. 20. Kleinert H, Boissel J-P, Schwarz PM, Fbrstermann U. Regulation o f the expression o f nitric oxide synthase isoforms. In: Ignarro LJ. eds. N itric Oxide: Biology and Pathobiology 1st Ed., San Diego: Academic Press, 2000;105-128. 119 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21. Thomas DD, Liu X, Kantrow SP, Lancaster Jr. JR. The biological lifetim e o f nitric oxide: Implications fo r the perivascular dynamics ofN O and O 2- Proc. Natl. Acad. ScL USA 2001^8(1)355-360. 22. Beckman JS, Koppenol WH. N itric oxide, superoxide, and peroxynitrite: the good, the bad, and the ugly. Am. J. PhysioL 1996;271:C1424-C1437. 23. Savill NJ, Weller R, Sherratt JA. Mathematical modeling o f nitric oxide regulation o f rete peg formation in psoriasis. J. Theor. B iol. 2002;214: 1- 16 . 24. Turner CP, Toye AM, Jones OTG. Keratinocyte superoxide generation. Free Rad. BioL Med. l998;24(3):40l-407. 25. O’Donnell VB, Azzi A. High rates o f extracellular superoxide generation by cultured human fibroblasts: Involvement o f a lipid-metabolizing enzyme. Biochem. J. 1996318:805-812. 26. Huie RE, Padmaja S. The reaction o f NO w ith superoxide. Free. Rad. Res. Common. 1993;18:195-199. 27. Fiefden EM, Roberts PB, Bray RC, Lowe DJ, Mautner GN, Rodlio G, Calabrese L. The mechanism o f action o f superoxide dismutase from pulse radiolysis and electron paramagnetic resonance. Biochem. J. 1974;139:49-60. 28. Koppenol WH, Moreno JJ, Pryor WA, Ischiropoulos H, Beckman JS. Peroxynitrite, a cloaked oxidant formed by nitric oxide and superoxide. Chem. Res. Toxicol. 1992;5:834-842. 29. Sies H, Sharov VS, Klotz L-O, Briviba K. Glutathione peroxidase protects against peroxynitrite-mediated oxidations. J. Biol. Chem. 199737237812-27817. 30. Denicola A, Freeman BA, Trujillo M, Radi R. Peroxynitrite reaction with carbon dioxide/bicarbonate: kinetics and influence on peroxynitrite-mediated oxidations. Arch. Biochem. Biophys. 1996333:49-58. 31. Thomson L, Trujillo M, Telleri R, Radi R. Kinetics o f sytochrome c2~ oxidation by peroxynitrite: Implications for superoxide measurements in nitric oxide-producing biological systems. Arch. Biochem. Biophys. 1995319:491-497. 32. Jourd’heuil D, Mai C, Laroux F, W ink DA, Grisham MB. The reaction o f S- nitrosoglutathione with superoxide. Biochem. Biophys. Res. Common. 1998;244:525-530. 33. Keshive M , Singh S, Wishnok JS, Tannenbaum SR, Deen WM. Kinetics o f S- nitrosation o f thiols in nitric oxide solutions. Chem. Res. ToxicoL 1996;9:988-993. 120 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 34. W ink DA, Darbyshire JF, Ninas RW, Saavedra IE , Ford PC. Reactions o f the bioregulatoty agent nitric oxide in oxygenated aqueous media: Determination o f the kinetics fo r oxidation and nitrosation by intermediates generated in the NO/CK reaction. Chem. Res. ToxicoL 1993;6:23-27. 35. Licht WR, Tannenbaum SR, Deen WM. Use o f ascorbic acid to inhibit nitrosation: kinetic and mass transfer considerations for an in vitro system. Carcinogenesis. 1988;9:365-372. 36. Antunes F, Salvador A, Marinho HS, Alves R, Pinto RE. Lipid peroxidation in metochondrial inner membranes. I. An integrative kinetic model. Free Rad. Biol. Med. l996;2I(7):9I7-943. 37. Coombes KR, Hunt BR, Lipsman RL, Osbom JE, Stuck GJ. Differential equations with Mathematica. 2nd ed. New York: John W iley & Sons, Inc., 38. Radi R, Denicola A, Alvarez B, Ferrer-Sueta G, Rubbo H. The biological chemistry o f peroxynitrite. hi: Ignarro U . eds. N itric Oxide: Biology and Pathobiology 1st Ed., San Diego: Academic Press, San Diego, 2000;57-82. 39. G riffith OW. Biologic and pharmacologic regulation o f mammalian glutathione synthesis. Free Rad. Biol. Med. 1999;27:922-935. 40. Strogatz SH. Nonlinear dynamics and chaos. Reading MA: Addison-Wesley Publishing Company, 1994. 41. Sies H. Glutathione and its role in cellular functions. Free Rad. Biol. Med. 199927:916-921. 42. Wink DA, Nims RW, Darbysbire JF, et al. Reaction kinetics for nitrosation o f cysteine and glutathione in aerobic nitric oxide solutions at neutral pH. Insights into the fate and physiological effects o f intermediates generated in the NO/Oj reaction. Chem. Res. ToxicoL 1994;7:519-525. 43. Gaston B. N itric oxide and thiol groups. Biochimica et Biphysica Acta. 1999;1411:323-333. 44. Pfeiffer S, Mayer B, Hemmens B. N itric oxide: chemical puzzles posed by a biological messenger. Angew. Chem. Int. Ed. 1999;38:1714-1731. 45. Murphy MP, Packer MA, Scarlett JL, Martin SW. Peroxynitrite: a biologically significant oxidant. Gen. Pharmac. 199821:179-186. 46. Vedia VL, McDonald B, Reet B, et al. N itric oxide-induced S-nitrosylation o f glyceraldehydes-3-phosphate dehydrogenase inhibits enzymatic activity and increases endogenous ADP-riboxylation. J. Biol. Chem. 199226724929-24932. 121 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47. Laval F, Wink DA. Inhibition by nitric oxide o f the repair protein, O6- methylguanine-DNA-methyltransferase. Carcinogenesis. 1994;15:443-447. 48. Stamler JS, Lamas S, Fang FC. Nitrosylation: The prototypic redox-based signaling mechanism. C ell, 2001;106:675-683. 49. Vos TA, van Goor H, Tuyt L, et al. Expression o f inducible nitric oxide synthase in endotoxemic rat hepatocytes is dependent on the cellular glutathione status. Hepatology. l999;29(2):42l-426. 122 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CONSTANT VALUEREFERENCES ki »IQ'S M s 1 Vaughn et aL,1* Laurent et al.,0 Savill et aL" k2 10"*—>I0‘sM s'1 Turner et a!..-* O’Donnell and A2 zf“ kj varied k* 6 .7 x to’ v r V Huie and Padmaja2* k* 2.4 x tO’tiT's1 FieldenetaL" k& 1.35 x tO1 MTl s‘l Koppenol et aL2* k7 2 x I0 6M-l s ‘ SiesetaL2* k* 5.8 x to4 VT1 s l Denicolaetal." k» 2.5 x 10* NT's'1 Thomson et aL“ kio 6 x I0 *V T V Jourd’heuil et aL“ k» 5.6 x I07W ' s ‘ Keshive et al.0 ku 6 xI06 O T V WinketaL** k ij 1.6 x 1 0 V Licth et aL" v» 3.2 x 10"1 M s 1 AntunesetaL* Table 5.1. The rate constants used fo r the simulation. 123 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PARAMETERVALUEREFERENCE m 3 5 *iM Antunes et a l.^ [CO,] 1-25 mM Radi et a l.34 C yt c1^ 400 p M Radi et a l.J8 [SOD] I - 10 |iM Beckman22 [GPX] 5.8 Antunes e t a l.36 Km 50 |lM Antunes e t a l/6 [GSH] I -10 mM G r iffith " Table 5.2. Parameter values fo r the simulation. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 5.1. The Model GPX: Ghitathtone peroxidase Cyt c: Cytochrome c 125 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100 80 O w z 20 10 200 400 600 8QQ 1000 T im e (m in ) 4 . 10 . 8 3 . . & S. 2. O 4 . «Z 1. O 2. 0 200 400 600 800 1000 T im e (m in ) 10 . 0 .5 a. 6. 0 .3 o 0 .2 « (9 0.1 2. 0 200 400 600 800 1000 T im e (m in ) Figure 5.2. Concentration-time profiles o f NO, 0 2-, ONOO-, N20 3, GSNO, and G SH . Scenarios: (a) k( = k2; (b ) kt = 0.5 k2; (c> kt -0 2 5 k2; (cl) kt = 0.125 k2; (e) k, - 0.0625 k3, [GSHJbasai = 10 m M , k2 = 1*10'7 M/s for all scenarios. 126 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IQQ 0 .5 80 r c a. ~0.3 o 40 &M 0.2 z z 20 0.1 0 0 200 400 600 800 1000 T im e (m in ) 4 l . 3 ^0.8 S £ 0 .6 2 g 0 .4 o M « 1 0 0 200 400 600 800 1000 T im e (m in ) o.s l. 0 .5 0 .8 C 0 *4 f 0.6 , 0 .3 Cu£ 3** 0.2 O 0.1 0 .2 a 10 0 200 400 600 300 1000 T im e (m in ) F ig ure 53 . Concentration-time profiles o f NO, 0 2 , ONOO , N20 3, GSNO, and GSH. Scenarios: (a) k, = k2; (b ) k, = 0.5 k2; (c ) k, = 0.25 k2; (d ) kt = 0.125 k2; (e) k, = 0.0625 k2. [GSIfJbosai = I m M , k2 = I*10'7 M/s for all scenarios. 127 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. too 0 .5 80 SO 40 20 0 .1 0 200 400 SOO 800 1000 T im e (m in ) 4 0.1 0.08 3 S. 0.06 2 s M i 0 .04 o « 1 ° 0.02 200 400 SOO 800 1000 T im e (m in ) 0.1 0 .5 mX 0.04 (3 0.02 200 4QQ S0Q 800 1000 T im e (m in ) Figure 5.4. Concentration-time profiles o f NO, 0 2", ONOO", N20 3, GSNO, and GSH. Scenarios: (a) k, = k2; (b ) kt = 05 k2; (c) k, = 0.25 k2; (d ) kt = 0.125 k2; (e) kt = 0.0625 k2, [GSHjbasai = 0.1 m M , k2 = I*1Q7 M/s for all scenarios. 128 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0 .2 5 0.2 C 0 .1 5 N 0 .0 5 0 200 400 600 800 1000 Time (min) 0.8 0.6 = 0 .4 0.2 0 200 400 600 800 1000 Time (min) Figure 5.5. Concentration-time profiles of N20 3 and GSH at the initial GSH level equal to 1 mM. Arrow: start of zero-order GSH input (£3). k2 = 6 |jM /m in ; kt = 0.5 k2; k3 = (a) 20 JiM/min; (b) 10 |iM/min; (c) 5 {iM/min; (d) 2.5 |iM/m in; (e) 1.25 pM/min. 129 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TO. O 0.2 10 . 0 b .c .d .i 200 400 600 300 1QQQ T im e (m in ) 400 300 * i — 200 o2 a t ° 100 (9 Q 2 4 6 8 10 200 400 600 300 1000 T im e (m in ) T im e (m in ) 10 . 5 0 . 8. r 40. ~ 3 0 . b 4 . o 20. a t 19 2 1 0 . d ------. 0 0 200 400 600 800 1000 T im e (m in ) Figure 5.6. Concentration-time profiles of NO, 0 2~, ONOO', N20 3, GSNO, and G SH . Scenarios: (a) k, - k2; (b ) kt = 0.5 k2; (c) kt = 0.25 fc2; (d ) k, = 0.125 fc2; (e) kt = 0.0625 k2, [GSHJbasai= 10 m M , k2 = l*10‘s M/s for all scenarios. 130 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1400 2200 1000 o 800 5 600 u_t 400 200 100 200 300 400 500 MO (pM) 500 * 4 0 0 *3 0 0 « 2 200 100 0.5 t. 1.5 2. 2.5 3. 3.5 4. fcl/kz Figure 5.7. (A) Phase portraits o f [NOl (B) [NOlss versus k /k 2. k2= L*10‘5 M/s; k /k 2 = (a ) 4; (h ) 2; (c> I ; (d ) 0.5; (e) 0 2 5 ; (f) 0.125 I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 .5 2 4 S 8 10 12 L4 16 18 20 NO (^ M ) 4 Z 0.5 1. 1.5 2. 2.5 3. 3.5 4. k i / k 2 Figure 5.8. (A ) Phase portraits o f [NOl (B) [NOlss versus k /k 2. k2= 1*10^ M/s; k /k 2 = (a) 4; (b) 2; (c) 1; (d) 0.5; (e) 0.25; (f) 0.125 132 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APP E N D IX A MATHEMATICA Program for the Monte Carlo Simulations Needs["Statistics’ContinuousDistributions'"]; Needs["Graphics'Graphics'"]; Needs["Statistics'LinearRegression'"]; Needs["Statistics'ConfidenceIntervaIs'"]; Needs ["Graphics' M uItipleListPlot' "]; Needs["Statistics'DataManipuIation'"]; Needs["Statistics'ContinuousDistributions'"]; f[x j := 100*XA0.75; MassLst= {0.02,0.25,2.5,5,14,70}; RunMonteCarlo [n_, file_, cv_] — ModuIe[{data, m =0}, W hile[m < n, m ++; data= {m ,TabIe[{xLst[[fl], RNDdataft,cv][U|]}, {j, I, k }]}; RecordData[data, file , m]; If[Mod[m, 10] = 0, ReportProgress[m, a]]]; stream = O penRead[fiIe]; answer = ReadList[stream, Expression]; CIose[fiJe]; answer ] RNDdata[i_, cv_j := TabIe[Random[NonnalDistribution[yLst[[i]], cv*yLst[[i]]]], {i, I, k}]; RecordData[data_, file_, current_j — Module[ {stream}, stream = OpenAppendffile]; Write[stream, data]; Qose[fiIeQ ReportProgress[current_, n_J — Prmt["Monte Carlo is ", N[Round[I00 current/n]],"% complete."] ExponentList[n_] — ModuIe[ {exponentdata= {}, Ioglogregress, tempLst, m = 0}, While[m < n, m++; foglogregressfm] = Regress[Log[answer[[m]][[2]]], { I, x }, x j; tempLst[m] = {ParameterTable /. IogIogregress[m]}; exponentdata= AppendTo[exponentdata, te m p L st[m ][[I]][[I]][[2 ]][[I]]] I; exponentdata IB Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I RsquareListfnJ := ModuIe[{Rsquaredata = {}, loglogregress, m = 0}, W hile[m < a, m++; loglogregress[m] = Regress[Log[answer[[m]][[2]]], {1, x }, x]; Rsquaredata = AppendTo[Rsquaredata, RSquared /. loglogregress [m ]] 1; Rsquaredata ] 1. mouse to rabbit scaling (M oujtat, Rab) ClearAII[xLst, yLst, ErrorFreeData]; xLst = Take[MassLst, 3]; yLst = fix ] I. x -> xLst; k = LengthfxJLst]; ErrorFreeData = TabIe[{xLst[[t]],yLst[[i]]}, {iT I, k}] RunMonteCarIo[ 100, "MouRbDatal.dta", 0.2]; MouRbDatal = ExponentList[ 100] RunMonteCarIo[ 100, "MouRbData2.dta", 0 3 ]; MouRbData2 = ExponentList[ 100] midpoints = , 035,"", 0.55,"", 0.75, "*, 0.95, "", 1.15,"", 1 3 5 }; MouRbcountsI = BinCounts[MouRbDatal, {0 3,1 .4 ,0 .!}]; MouRbcounts2 = BinCounts[MouRbData2, {0 3 ,1 .4 ,0 .!}]; mourbplot = BarChartfMouRbcounts I , MouRbcounts2, Bar Labels -> midpoints, PlotLabel-> {"mouse,rat^abbit"}, PIotRange-> {A il, {0,80}}, BarStyle -> {RGBColortf),0,0], RGBCoIorfl, I, I]}] 2. mouse to Monkey scaling (Mou,Rat, Rab,Mon) ClearAll[xLst, yLst, ErrorFreeData]; xLst= Take[MassLst, 4]; yLst = f[x ] /. x -> xLst; k = Length[xLst]; ErrorFreeData= Table[{xLst[[i]], yLst[[i]]}, {i, I,k }] RunMonteCarlo[ 100, "MouMnData I .dta”, 0 3 ]; MouMnDatal = ExponentList[ 100] RunMonteCarIo[100, "MouMnData2.dta", 0 3 ]; MouMnData2 = ExponentList[ 100] MouMncounts! = BinCountsfMouMnDatal, {0 3,1 .4,0 .!}]; MouMncounts2 = BinCounts[MouMnData2, {0 3 ,1 .4 ,0 .!}]; m oum nplot= BarChart[MouMncounts 1, MouMncounts2, BarLabels -> midpoints, 134 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PIotRange -> {A ll, {0,80 }}, PIotLabel -> {"mouse.raLrabbiLmonkey"}, BarStyle -> {RGBCoIor£0,0,0], RGBCoIor[l, I, I}}] 3. mouse to Dog scaling (MouRat, Rab,MonJ>) DeIeteFile[”MouDoDataI .dta"] DeIeteFiIe["MouDoData2.dta'’] ClearAl![xLst, yLst, ErrorFreeData]; xLst= Take[MassLst, 5]; yLst = f[x ] /. x -> x L st; k = Length[xLst]; ErrorFreeData=TabIe[{xLst[[i]],yLst[[i]]}, {i, I,k }] RunMonteCarIo[IOO, "MouDoDatal .dta", 0 2 ]; MouDoDatal = ExponentList[ 100] RunMonteCarIo[lOO, ,'MouDoData2.dta", 0.3]; MouDoData2 = ExponentList[ 100] MouDocountsI = BinCounts [MouDoDatal, {0.2,1.4,0.!}]; MouDocounts2 = BinCounts[MouDoData2, {02, 1.4,0.!}]; moudoplot = BarChart[MouDocounts I , MouDocounts2, Bar Labe Is -> midpoints, PIotRange-> {A ll, {0,100}}, PIotLabe! -> {"mouse,rat/abbiLmonkey,dog"}, BarStyle -> {RGBColor[0,0,0], RGBCoIor[I, I, I]}] 4. mouse to human scaling (MouRat, Rab, Mon, D, H) DeIeteFiIe[”allsca!e I .dta”] DeIeteFiIe[,,alIsca!e2.dta"] CIearAIl[xLst, yLst, ErrorFreeData]; DeleteFiIe["aIIscaIe.dta"]; xL st = MassLst; yLst = f[x ] /. x -> xL st; k = Lengtb[xLst]; ErrorFreeData = TabIe[{xLst[[i]],yLst[[i]]}, {i, l,k }] RunMonteCarIo[ 100, "allscalel.dta”, 02 ]; allscaledatal = ExponentList[I00] RunMonteCarIo[ 100, ”allscale2.dta'\ 0 3 ]; allscaledata2 = ExponentList[ 100] allscalecountsl = BinCounts[al!scaIedataI, {0 2 ,1 .4 ,0 .!}]; a!Iscalecounts2 = BinCounts[alIscaIedata2, {02,1.4,0.1}]; allscaleplot= BarChart[aIIscaIecounts I, a!IscaIecounts2, BarLabels -> midpoints, PIotLabel -> {"mouse,rat^abbiLxnonkey,dogRuman"}, PIotRange •> {AIL (0,100}}, BarStyle -> {RGBCoIor[0,0,0], RGBCoIor{l, I, I]}] 135 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5. cat to Monkey scaling (Rat, Rab,Mon) ClearAll[xLst, yLst, ErrorFreeData}; xLst= Take[MassLst, {2 ,4 ,1}]; yLst = f [x ] /. x -> xLst; k=Length[xLst]; ErrorFreeData= Table[{xLst[[i]], yLst[[i]]}, {i, I, k}] RunMonteCarIo[iOO, "RatMnDatal .dta", 0.2]; RatMnDatal = ExponenlList[ 100] RunMonteCarlo [100, "RatMnData2.dta”, 0 3 ]; RatMnData2 = ExponentList[ 100] RatMncountsI = BmCounts[RatMnDatal, {03,1.4,0.1}]; RatMncounts2 = BinCounts[RatMnData2, {03,1.4,0.1}]; ratm nplot= BarChart[RatMncounts 1, RatMncounts2, BarLabels -> midpoints, PIotRange -> {AD, {0,60}}, PIotLabel -> {"rat^rabbiunonkey"}, BarStyle-> {RGBCoIor[0, 0,0], RGBCoIor[I, I, I]}} 6. ra t to Dog scaling (Rat, Rab,Mon,D) CIearAlI[xLst, yLst, ErrorFreeData]; xLst= Take[MassLst, (2, 5 ,1}]; yLst = f[x ] /. x -> xLst; k = Length[xLst]; ErrorFreeData= TabIe[{xLst[[i]], yLst[[i]]}, {i, I, k}] DeleteFile["RatDoData.dta"]; RunMonteCarIo[I00, "RatDoDatal.dta”, 03 ]; RatDoDatal = ExponentListf 100] RunMonteCar!o[100, "RatDoData2.dta’\ 0 3 ]; RatDoData2 = ExponentList[ 100] RatDocountsI = BinCounts[RatDoDataI, {0 3 ,1 .4 ,0 .!}]; RatDocounts2 = BinCounts[RatDoData2, {0.2,1.4,0.1}]; ra tdop lot= BarChart[RatDocounts I, RatDocounts2, BarLabels -> midpoints, PIotRange -> {A ll, {0,60}}, PIotLabel -> {"ratjabbit^nonkey.dog"}, BarStyle -> {RGBCoIor[0,0,0], RGBCoIor[I, I, I]}] 7. rat to Human scaling (Rat, Rab>fonJDJH) DeleteFiIe["RatHuDatal.dta”] DeIeteF9e[nRatHuData2.dtan] ClearAII [xLst, yLst, ErrorFreeData]; 136 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. xLst= TakefMassLst, {2,6,1}]; yLst= f[x] /. x -> xLst; k = Length[xLst]; ErrorFreeData= TabIe[{xLst[[i]], yLst[[i]]}, {i, l,k }] RunMonteCarlo[100, "RatHuDatal .dta1’, 0 3 ]; RatHuDatal = ExponentList[ 100] RunMonteCar lo [100, "RatHuData2.dta", 0.3]; RatHuData2 = ExponentList[ 100] RatHucountsI = BinCounts[RatHuDatal, {03, 1.4,0.1}]; RatHucounts2 = BinCounts[RatHuData2, {03, 1.4,0.1}]; rathuplot = BarChart[RatHucounts I, RatHucounts2, BarLabels -> midpoints, PIotRange -> {A ll, (0 ,8 0 }], PIotLabel -> {"raLrabbiMnonkey,dog,human”}, BarStyle -> {RGBCoIor[0,0,0], RGBCoIor[l, I, I]}] 8. rabbit to Dog scaling (Rab,Mon, D) ClearAII[xLst, yLst, ErrorFreeData}; xLst= Take[MassLst, {3,5,1}]; yLst = fix ] /. x -> xLst; k = Length[xLst]; ErrorFreeData=TabIe[{xLst[[i]],yLst[[i]]}, (i, I, fc}] RonMonteCarIo[lOO, "RabDoDatal.dta”, 0.2}; RabDoDatal = ExponentList[ 100} RunMonteCarlo[lQ0, ”RabDoData2.dta", 0 3 ]; RabDoData2 = ExponentList[ 100] RabDocountsl = BinCounts[RabDoDatal, {0.2,1.4,0.!}]; RabDocounts2 = BinCounts[RabDoData2, {0 3 ,1 .4 ,0 .!}]; rabdoplot = BarChartfRabDocountsl, RabDocounts2, BarLabels -> midpoints, PIotRange -> {A ll, {0,80}}, PIotLabel -> {"rabbit^nonkey,dog”}, BarStyle-> {RGBColor[0,0,0], RGBCoIor[l, I, I]}] 9. Rabbit to human scaling (Rab, Mon, D, H) ClearAU[xLst, yLst, ErrorFreeData]; xLst= TakefMassLst, -4]; yLst=f[x] /. x -> xLst; k = Length[xLst}; ErrorFreeData= TabIe[{xLst[[i]], yLst[[i]]}, {i, l,k }] RunMonteCarIo[100, "RabHuDatal .dta”, 0 3 ]; RabHuDatal = ExponentList[ 100] RunMonteCarIo[100, ”RabHuData2.dta”, 0 3 ]; RabHuData2 = ExponentList[ 100] RabHucountsl = BinCounts[RabHuDataI, {0 3 ,1 .4 ,0 .!}]; 137 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. RabHucounts2= BinCounts[RabHuData2, (02, 1.4,0.1}]; rabhuplot= BarChart[RabHucounts I, RabHucounts2, BarLabels -> midpoints, PIotRange -> {A ll, {0,80}}, PIotLabel -> {"rabbitjnonkey,dog,human"}, BarStyle-> (RGBCoIorfl), 0,0], RGBColor[l, I, I]}] 10. Monkey to Htonan scaling CIearAH[xLst, yLst, ErrorFreeData]; xLst= TakefMassLst, -3]; yLst= fix ] /. x -> xLst; k = Length[xLst]; ErrorFreeData= TabIe[{xLst[[i]], yLst[[i]]}, {i, 1, k}] RunMonteCarlo [ 100, "MonHuDatal.dta”, 02]; MonHuDatal = ExponentList[ 100] RunMonteCarIo[ 100, ”MonHuData2.dta", 0.3]; MonHuData2 = ExponentList[ 100] MonHucountsI = BinCounts[MonHuDataI, {02, 1.4,0.1}]; MonHucounts2 = BinCounts[MonHuData2, {0.2,1.4,0.1}]; m onhnplot= BarChart[MonHucounts I, MonHucounts2, BarLabels -> midpoints, PIotRange -> {A ll, {0,80}}, PIotLabel -> {"monkey,dog^iuman"}, BarStyle -> {RGBCoIor[0,0,0], RGBCoIor[I, I, I]}] Show[GraphicsArray[{{mourbpIot, moumnplot}, {moudoplot, allscaleplot}, {ratmnplot, ratdoplot}, {rathuplot, rabdoplot}, {rabhuplot, monhuplotj}]] 138 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A PP E N D IX B Release Mechanism o f N itric Oxide and Snperoxide from SIN-1 o tr ONOO- ,0 . SIN -1 SIN-ia n o x NO* 0 N -N=C— CN r r * % cN SIN-1 SIN -1C Figure B .l. Mechanism fo r the release o f NO and O j' from SIN-1 139 i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure B J. HPLC chromatograms for the decomposition kinetics o f SIN-I 140 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. BIBLIOGRAPHY Adamic LA, Huberman BA. Power-law distribution o f the world wide web. Science. 2000^87:2115 Adolph EF. Quantitative relations in the physiological constituents o f mammals. Science. 1949;109:579-585. Ahr HJ, Boberg M, Brendel E, Krause HP, Steinke W. Pharmacokinetics o f m iglitol: Absorption, distribution, metabolism, and excretion following administrationto rats, dogs, and man. Arzneim Forsch. 1997;47:734-745. Albert R, Barabasi AL. Statistical mechanics o f complex networks. Mod. Phys. 2002;74:47-97. Albert R, Barabasi AL. 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