Mathematical Modeling of Complex Biological Systems

From Parts Lists to Understanding Systems Behavior

Hans Peter Fischer, Ph.D.

To understand complex biological systems such as cells, tissues, or even the human body, it is not sufficient to identify and characterize the individual molecules in the system. It also is necessary to obtain a thorough understanding of the interaction between molecules and pathways. This is even truer for understanding complex diseases such as cancer, Alzheimer’s disease, or alcoholism. With recent technological advances enabling researchers to monitor complex cellular processes on the molecular level, the focus is shifting toward interpreting the data generated by these so-called “–omics” technologies. Mathematical models allow researchers to investigate how complex regulatory processes are connected and how disruptions of these processes may contribute to the development of disease. In addition, computational models help investigators to systematically analyze systems perturbations, develop hypotheses to guide the design of new experimental tests, and ultimately assess the suitability of specific molecules as novel therapeutic targets. Numerous mathematical methods have been developed to address different categories of biological processes, such as metabolic processes or signaling and regulatory pathways. Today, modeling approaches are essential for biologists, enabling them to analyze complex physiological processes, as well as for the pharmaceutical industry, as a means for supporting drug discovery and development programs. KEY WORDS: Systems biology; human biology; complex biological systems; mathematical modeling; computational models; transcriptomics; proteomics; metabolomics

ver the last decade, DNA- edge of the human genome sequence which genes are active in a given cell sequencing technologies have researchers would be able to readily at a given time, proteomic studies are Oadvanced tremendously, culmi- develop new therapies for treating human discovering which proteins are present nating in the deciphering of the com- disease as yet has only partially been ful- and in what amounts, and analyses of plete human genome in 2001 (Landers filled. The availability of a fully sequenced the metabolome have begun to exam­ et al. 2001; Venter et al. 2001). This human genome is a prerequisite for ine which metabolic processes occur achievement is a major milestone in the elucidating the origins of complex under different conditions. Most understanding of human biology, as the human diseases, such as cancer, obesity, importantly, however, this work has human genome provides a catalogue of Alzheimer’s disease, or alcoholism but highlighted the fact that human genes all human genes and associated molecules unfortunately is by no means sufficient and the proteins they encode do not that are required for creating a living to provide answers to all of the ques­ work in isolation but are connected human being. To date, however, the tions surrounding these diseases. at various levels in networks and availability of this “parts” list specifying In the meantime, further techno­ most human biomolecules, including logical advances have led to a consid­ 1 For a definition of this and other technical terms, see the glossary, p. 84. DNA, proteins, and RNA, has answered erable increase in the understanding only some of the questions concerning of the workings of the human body the complex phenomena of human biol- under normal conditions and in various HANS PETER FISCHER, PH.D, is chief ogy, leaving many others unanswered. disease states. For example, transcrip- scientific officer of Genedata AG, Basel, Moreover, the hope that with the knowl- tomic1 studies are shedding light on Switzerland.

Vol. 31, No. 1, 2008 49

pathways of varying complexity. A the various components of the plane’s “—Omics” Technologies: deeper understanding of these inter­ controls and the dynamic regulatory The Driving Force Behind actions is pivotal for understanding feedback loops that control this inter­ Systems Biology human diseases and developing appro­ play. Similarly, the processes that occur priate therapeutic approaches. One in living organisms during growth, A major reason for the advent of systems crucial element in this process is the metabolism, and regulation of cell biology activities is that only recently generation of mathematical models functions also are interrelated and analyses at the molecular level of the that capture the often-unexpected require equally tight and coordinated cell have become technically feasible on features of complex biological systems. control mechanisms. a larger scale. With the development of The development of these models is The characteristics of a complex these new, large-scale technologies to intimately linked to the generation of system that arise from the interaction identify and quantify molecules on the experimental data using various high- of various components are referred to DNA, mRNA, protein, and metabolite throughput genomic, transcriptomic, as the emergent properties of the sys­ level, researchers for first time are in a proteomic, and metabolomic experi­ tem. Because they are the result of position to gather comprehensive data mental strategies. interactions between the different parts, on the molecular state of a given bio­ This article summarizes the challenges these emergent properties cannot be logical system in a systematical manner. associated with the study of complex attributed to any single part of the These technologies are sometimes biological systems, the benefits of system. Thus, the ability of a passen­ collectively referred to as “–omics” technologies (see figure 2). In addition, systems biology approaches, and the ger jet to fly is not the consequence new techniques to manipulate cells in ways in which computational models of one particular screw (even though a directed manner allow researchers to can help consolidate and interpret this particular screw may be necessary perturb biological systems under con­ the experimental data obtained using for the plane to function). Similarly, these approaches. These principles are trolled conditions. For instance, single the development of a complex disease genes can be deactivated and the global exemplified by some concrete exam­ (e.g., alcoholism) likely is not caused ples from current research projects. response of the modified cell can be by a single gene, although a particular observed at the protein, transcript, and gene may be one of the elements nec­ metabolite level. Together, these experi­ Blueprints of Life: Emergent essary for the disease to develop. Such mental techniques allow researchers to Properties of a System a system is considered irreducible— obtain a comprehensive picture of the that is, the system is unlikely to be cell’s function as well as of the role of The human body consists of approxi­ fully understood by taking it apart the deactivated gene and its specific mately 1014 individual cells, each of and studying each part on its own. function. Such comprehensive and which is itself a complex system compris­ To understand irreducible systems and accurate experimental data are critical ing thousands of different proteins and fully appreciate their emergent prop­ for developing and testing models of other biomolecules. The information erties, one must study the systems as biological processes, and the data pro­ specifying the composition and struc­ a whole. duced by –omics technologies are ture of virtually all of these molecules The publication of the human expected to guide the development is encoded in the DNA. Although genome sequence provided biological of new and more complex models. researchers now have information on scientists with a list of all the individ­ The new –omics technologies are all genes at hand, they still lack a deeper ual parts that make up the human characterized by three distinct fea­ understanding of many seemingly body. However, just like having a pile tures. First, they allow for analyses on common biological effects. The reason of all the pieces of a passenger jet does different molecular levels, such as the for this can be exemplified by an analogy not allow a technician to put together DNA, RNA, protein, or metabolite with a modern passenger jet, another a functional plane without having a level. These different molecular levels complex, yet man-made, system. Modern blueprint of the wiring scheme, this sometimes behave asynchronously— passenger jets consist of thousands of genome sequence is not sufficient to that is, although some proteins are individual components, such as screws, understand the interactions between highly abundant in a cell, the levels wheels, cables, and other components the genes and their products. Advances of the corresponding mRNAs from that perform a specific function in a over the last few years in transcrip­ which they are produced may be very specific technical context. However, tomics, proteomics, and metabolomics low or vice versa. Because asyn­ knowledge of those individual compo­ that allow investigators to monitor chronous behavior can indicate the nents does not reveal functions that the biological response of cells, how­ effects of complex regulatory interac­ arise through interactions with other ever, will allow studies of physiological tions, it is important to examine the components, such as those related to systems as a whole in order to identify role and degree of synchronization of takeoff, navigation, communication, higher-level biological mechanisms the transcriptome, proteome, and or landing. To understand how a plane encoded in the human genome (Brent metabolome. For example, metabo­ flies, one must know the interplay of 2004) (see figure 1). lites produced in certain biochemical

50 Alcohol Research & Health Mathematical Modeling and Systems Biology pathways sometimes exert a feedback research allow for a broad screen for experimentation has a huge impact on key enzymes in the pathway by unexpected biological side effects caused on how experimental studies are per­ modifying the expression of the genes by new drugs (Ulrich and Friend formed today. For instance, compari­ that encode these enzymes. The –omics 2002; Waters and Fostel 2004). The son of larger numbers of replicate technologies allow researchers to sys­ high degree of parallelization also allows experiments allows researchers to vali­ tematically discover such interactions researchers to elucidate functional date biological effects with a greater and incorporate them into models interactions between different genes statistical certainty. The ease of use of aiming to capture the essential regula­ and proteins and obtain comprehen­ –omics technologies is particularly tory features of a pathway. sive images of emergent properties of relevant for clinical studies, in which Second, –omics technologies are a cell or organism. This is particularly large patient populations must be highly parallelized. This means that important for complex cellular process­ tested to obtain a sound statistical for a single biological sample many es such as the increase in the number basis for confirming drug efficacy and different biological “readouts” can be of cells as a result of cell growth and identifying potential side effects. measured simultaneously. For example, cell division (i.e., proliferation), cell The huge amounts of data gathered with today’s microarrays researchers death (i.e., apoptosis), or the response require tools to automatically process, can simultaneously measure the expres­ to infection, all of which can involve compare, and interpret the data in a sion of virtually all genes of the organ­ several hundred different types of manner that identifies the most relevant ism being studied rather than having molecules. pieces of information and which can be to perform numerous separate experi­ Third, –omics technologies are used to generate models of, for example, ments focusing on different genes. highly standardizable and thus amenable regulatory or metabolic pathways. This parallelization enables scientists to a high degree of automation, allow­ These tools include computerized to detect not only the expected but also ing researchers to handle and process data analysis strategies that result in the unforeseen responses of an organism. large numbers of biological samples. formulation of mathematical models For example, microarrays in toxicology The ease of sample processing and of the biological systems analyzed.

A B

+2.5V +2.5V

Y1 Y2 1 10 R3 2 11 3 12 4 13 5 14 6 15 7 16 C2 C3 8 17 9 18

Y3 Y4 C1 +2.5V

Figure 1 Complex systems and the blueprints used to illustrate the complex interactions that occur between the different components of the systems. A) A modern passenger jet (top) is a complex technical system in which the combination of many parts results in complex technical features (emergent properties), such as flying or navigation. Technical blueprints, such as for the microchip used in the jet’s electronic control system (bottom), allow engineers to get an overview on the wiring scheme of the microchip. B) Human liver cells (top) are complex biological systems. Pathway maps (bottom) provide a high-level view of the complex networks of biochemical reactions (e.g., for detoxification) within liver cells. These pathway maps help researchers to visualize the interplay of the different molecules and understand the cell’s emergent biological properties.

SOURCE: Hepatocytes from http://teaching.anhb.uwa.edu.au/mb140/

Vol. 31, No. 1, 2008 51 Mathematical Models: Tools reaction kinetics—that is, an increase in Mathematical models that take these for Understanding Complex the amount of the starting material of factors into consideration allow researchers Biological Processes the reaction does not necessarily lead to to capture the features of complex bio­ a proportional increase in the amount of logical systems and to understand how Biological systems are inherently complex, the reaction product. Finally, other biological systems respond to external or and many of their emergent properties complexities, such as cell structure and internal signals and perturbations, such as result from the interplay of numerous compartmentalization or random (i.e., different growth or development condi­ molecular components. Moreover, bio­ stochastic) effects, also often result in tions or stress triggered by agents such chemical reactions often obey nonlinear unexpected behavior of the entire system. as alcohol.

Structural Pathway Information

e.g., DNA sequencing, genotyping, ... Genome

Transcription

e.g., microarrays, Transcriptome Structural oligonucleotide chips, ... Pathway Information

Translation e.g., MS-based proteomics, 2-D gel Proteome d electrophoresis, ... = Vprod- Vcons Ci Σ Σ dt j j Reactions V1 = k1 [EGFR] [EGF] - k_1 e.g., mass spectroscopy, nuclear magnetic resonance Metabolome imaging, 13C labeling, ... Mathematical Interactions Representation

e.g., yeast-2-hybrid screens, TAP, ... Interactome 0.03 Integration 0.02 0.01 e.g., gene inactivation, knock-outs, RNAi, ... Phenome 0

Model Data

Dynamic/kinetic information

Figure 2 The –omics technologies gather information on numerous levels, including the genome, transcriptome (entirety of all genes that are converted into transcripts [i.e., mRNA molecules]), proteome (entirety of all proteins found in a given cell or tissue), metabolome (entirety of all metabolism products and intermediates in a cell or tissue), interactome (set of molecules, such as biologically active metabolism products, that interact with a given protein), and phenome (entirety of all observable characteristics of an organism) levels. These data are collected using a variety of complementary technologies such as DNA microarrays or mass spectrometry (MS). The experimental data provide the structural and dynamic information that can then be used to generate mathematical formulas representing the observed reactions, leading to the development of comprehensive models and pathway maps. These in silico models allow researchers to evaluate the potential effects of modifications or perturbations in the system and to design further experiments for analyzing additional biological situa­ tions (e.g., potential side effects caused by a new drug).

SOURCE: Adapted from Fischer, H.P. Towards quantitative biology: Integration of biological information to elucidate disease pathways and drug discovery. Biotechnology Annual Review 11:1–68, 2005.

52 Alcohol Research & Health

Mathematical Modeling and Systems Biology

Mathematical models have the big picture of a biological process. And even computer simulations and actual exper­ advantage of being amenable to com­ if it is not clear which components are imental data may help the researcher to puter simulations. Models describing missing from the system under inves­ readily identify such simpler subsys­ biological systems generally are too tigation, the results obtained with the tems that are sufficient to understand complex to be solved analytically mathematical model may help to guide the features of the much more difficult- (“manually”) and therefore typically the design of additional experiments to-treat full biological system. are solved numerically—that is, using to clarify the issue (see figure 3). computers to solve the mathematical Second, mathematical models provide equations that help predict the response a systematic approach for investigating Mathematical Equations of a biological system. With the avail­ systems perturbations—for example, for Modeling Biological ability of computer-based techniques those induced by drug administration, Systems Behaviors for solving mathematical equations, genetic alterations, developmental the response of a biological system to signals, or other factors. To this end, For choosing the optimal modeling different conditions can be relatively scientists can modify the values of the approach it is essential to understand easily simulated in silico once a math­ model parameters (e.g., by introducing the nature of the biological process of ematical model is available. These modified enzyme activities associated interest because different mathematical computer simulations (so-called “dry with alcohol administration) and re-run frameworks have been developed for experiments”) in many cases require the computer simulations. This approach modeling the behavior of different types much lower investment and much less is relatively straightforward once a of biological systems. For example, time compared with the typically reasonable base model is available. most cellular phenomena are governed more time-consuming and expensive Third, mathematical simulations by dynamic processes so that the cell biological experiments (sometimes are not as limited by experimental can adapt to environmental changes referred to as “wet experiments”). constraints as wet experiments. or control inherently dynamic cellular The general approach for creating Computer simulations can quickly functions, such as periodic cell division. and using mathematical models in investigate different experimental For describing such time-dependent biological sciences is similar to the conditions for the biological system phenomena, it is imperative to choose one followed in other scientific disci­ of interest, and only the most relevant mathematical equations that can capture plines such as physics and provides cases can be assessed afterwards in the these dynamic effects. For other biolog­ the basis for communication between laboratory. This allows researchers to ical processes, however, it often is not experimental and theoretical scientists. investigate novel scenarios and to develop necessary to describe all the details of Thus, the theories and mathematical hypotheses to guide the design the underlying dynamics because some formulas developed by theoretical of new and promising experiments. molecules’ concentrations do not change biologists on the basis of existing This approach is particularly helpful over time (i.e., are quasi-stationary). For experimental data can be tested by if the wet experiments are difficult most types of applications, appropriate experimentalists and used to predict the and expensive to perform. The com­ modeling methods have been developed. behavior of biological systems under bination of dry and wet approaches Two examples are described below— as-yet-unexplored conditions. Any is at the heart of systems biology and modeling of metabolic processes and discrepancies between the predicted already is being used widely in the modeling of signaling and regulatory and measured results then need to be metabolic engineering industry, which pathways. resolved, either by extending the the­ uses live cells (e.g., bacteria or cultured oretical framework (i.e., for instance eukaryotic cells) to produce complex Modeling Metabolic Processes by adding new equations to take into chemicals (e.g., precursors of drugs, Metabolic processes are essential for all account other apparently important vitamins, or amino acids) based on living organisms and provide the cell’s molecules that have not been considered fermentation processes. In these cases, energy, deliver building blocks for the in previous versions of the model) or mathematical models are used to sug­ synthesis of larger molecules, or degrade by refining the experimental setup or gest directed genetic modifications toxic substances. Although biological data interpretation. that may improve the productivity research has focused on metabolism for Mathematical models for biological of the microorganisms. several decades, many metabolic pro­ systems and the associated computer Fourth, mathematical models can cesses still are not fully understood, and, simulations offer numerous benefits. be very helpful for systematically in particular, the regulatory mechanisms First, discrepancies between systems determining the relevance of a specific controlling even well-investigated meta­ behaviors predicted by a mathematical molecule or pathway for the overall bolic pathways often are unknown. model and actual behaviors measured behavior of the system. Not all com­ A key parameter in any metabolic in experiments can point to compo­ ponents of a reaction or pathway are study is the metabolic flux—that is, nents that still are missing from the equally important, and many biological the conversion rate of metabolites mathematical model, thereby assisting processes are controlled by relatively along a metabolic pathway. For many in developing a more comprehensive small subsystems. Comparison of research and industrial applications,

Vol. 31, No. 1, 2008 53 it is crucial to predict the metabolic constraints must be solved simultane­ instance, a cell’s carbon flux patterns flux patterns that indicate which bio­ ously, and indeed there are many may be reconstructed by growing chemical routes are utilized (e.g., to well-developed techniques to solve the cells in a medium that contains metabolize nutrients). Modeling tech­ such sets of equations (for reviews, labeled carbon sources (e.g., the so- niques are widely used in the field of see Hornberg et al. 2007; Joyce and called 13C-method) (Wiechert 2002) metabolic engineering to identify any Palsson 2007). Interestingly, because that will be taken up and metabolized steps in the production of a desired stoichiometric constraints allow only by the cells. As the labeled substances molecule by cultured cells or bacteria for relatively few solutions, flux pat­ enter into a metabolic network, their that limit the overall rate with which terns in quasi-stationary networks are flux across several metabolites can be the process occurs (i.e., so-called meta­ relatively limited, which facilitates traced with nuclear magnetic resonance bolic bottlenecks). The results of understanding metabolic processes. or mass spectrometry. By tracing the these analyses can guide researchers The validity of such mathematical labeled atoms across a number of key on how to genetically modify the cells models of metabolic networks can metabolites, scientists can measure or bacteria to optimize the yield of be tested through experiments using the cellular flux distributions, which the desired end product (e.g., see substances that are either radioactively can help validate or disprove meta­ Wendisch et al. 2006). In this setting, labeled or otherwise detectable. For bolic network models. changes in metabolic fluxes over time are not a major concern because the fermenters used in the biotech industry typically operate in a steady-state, continuous flow situation and it there­ Biological phenomenon fore is sufficient for these applications to consider the fluxes in the cell to be quasi-stationary. A well-developed set of mathematical Experimental data methodologies is available for a system­ (Experimental determination of structures, functions, atic analysis of such quasi-stationary and interactions) metabolic phenomena. As an example, consider the process during which sugar is converted to amino acids. In this process, an enzyme called hexoki­ Mathematical model nase adds a phosphate group (i.e., phosphorylates) to the sugar glucose, yielding a compound called glucose- 6-phosphate. This reaction must be New data New data balanced in terms of atoms and elec­ trical charges. In a chemical notation, the balanced reaction is written as 3- 2­ C6H12O6 + ATP � C6H11O6PO3 Hypothesis + ADP2- + H+. This indicates that both sides of the equation are in a stoichiometric balance—that is, they contain the same number of carbon, hydrogen, or phosphorus atoms. Dry Wet When investigating more complex experiment experiment (computer (laboratory metabolic networks, each individual simulation) experiment) chemical reaction contributes a stoi­ chiometric balance constraint that can be formulated as a mathematical equation. However, the individual Figure 3 Schematic representation of the process of knowledge generation in stoichiometric constraints are not systems biology. Experimental data on a given biological phenomenon independent from each other. For serve to derive a mathematical model that leads to hypotheses regarding example, reaction 1 produces a certain the effects of perturbation of the system. These hypotheses are tested in “dry” and “wet” experiments, leading to the generation of new data that number of carbon atoms that then may result in confirmation or modification of the hypothesis and the feed into reaction 2, and so on. underlying mathematical models. Consequently, all mathematical equa­ tions representing the stoichiometric

54 Alcohol Research & Health

Mathematical Modeling and Systems Biology

Modeling Signaling and Regulatory Obviously, signal transduction is an ity have not yet been performed). But Pathways inherently dynamic phenomenon, as even if the kinetic parameters have Signaling pathways serve as the cell’s the cell has to be able to flexibly respond been measured, these data often are central control machinery, which tightly to changes within the organism and in based on experiments performed in a regulates the cell’s response to external the environment. To model the dynam­ test tube with purified enzymes (i.e., in vitro), and it is unlikely that the and internal stimuli. These pathways ics of signaling cascades such as those enzymes behave similarly under the involve the transmission of external and described above, researchers primarily conditions found in a living internal signals through the cell’s mem­ rely on so-called differential equations cell (i.e., in vivo). To overcome this brane and interior into the cell’s nucleus, (technically known as time-dependent limitation, one can use dynamic where they activate or deactivate specific ordinary or partial differential equa­ measurements of the overall system. sets of genes. All of these processes are tions). Such differential equations are used to model the dynamic behavior Computational procedures are avail­ inherently dynamic events that require able to estimate the appropriate model different mathematical modeling strate­ of, for example, the changes in the concentration of signaling molecules parameters by testing different para­ gies than the quasi-stationary (meta­ meter sets until they fit the available bolic) processes discussed above. over time as well as the signaling molecules’ distribution across different experimental data. However, this pro­ Many signaling pathways are trig­ cellular compartments. Modeling of cess is critically dependent on the gered by the binding of extracellular even relatively simple signaling networks quality of the experimental data, and biomolecules (e.g., hormones or growth has revealed that signal transmission unreliable experimental data will lead factors) to a docking molecule (i.e., through the cell often shows unexpected to unreliable predictions of kinetic receptor) embedded in the membrane behaviors, such as periodic activation parameters and therefore to models surrounding the cell. Receptors are patterns or enhancement (i.e., amplifi­ of very limited value (Schilling et al. proteins, often spanning the mem­ cation) of the initial signals (Hoffmann 2005). The lack of sufficiently large, brane, which expose one part of their et al. 2002; Swameye et al. 2003). A high-quality experimental datasets structure to the exterior environment specific example of how regulatory pro­ still is a major hurdle in developing (i.e., the extracellular space) and one cesses are being modeled is described models even for relatively simple part to the cell’s interior (i.e., the in the accompanying sidebar, p. 56. signaling networks. cytoplasm). If a signaling molecule It must be pointed out that some binds to the extracellular region of Identifying Model Parameters biological phenomena cannot be the receptor, the receptor’s three- described by using models that are dimensional structure may change— Any equation in a mathematical model just based on continuous concentra­ a process that can trigger cascades of will contain one or more parameters that tion fields (described, for example, biochemical reactions within the cyto­ describe certain biophysical characteris­ by partial differential equations), plasm. These cascades often involve tics of the molecules involved in the ignoring the existence and relevance specialized signaling molecules such reaction or pathway being studied. For of individual molecules. For instance, as enzymes known as kinases, which example, when modeling the dynamics on a molecular scale random molecular transfer phosphate groups from one of a network of biochemical reactions, movements can have a major impact molecule (the donor) to a specific target the mathematical equations must on cellular processes. The molecules molecule (the substrate) and which incorporate parameters that reflect in a cell are closely packed, and ther­ are used extensively to transmit and the kinetic properties of the involved mally induced random movements of integrate signals to control complex enzymes—for example, the number these molecules as well as interactions cellular processes. In many cases, of reactions the enzyme can perform between them can strongly affect the kinases act on and modify the activity during a given period of time (i.e., the transmission of signals. To account for of specific proteins. The addition of rate constant). Researchers must know such effects, a random (i.e., stochastic) the phosphate group changes the sub­ these kinetic parameters before they component must be integrated into strate protein’s biochemical behavior can set up well-defined systems of dif­ the mathematical equations of the so that it, in turn, can modify addi­ ferential equations representing appro­ model. Particularly for rare signaling tional signaling molecules in the sig­ priate models of biological processes. molecules, of which only a few copies naling cascade. Ultimately, this chain In principle, the kinetic parameters may be present in the cell, the effects reaction results in the activation of for all the relevant enzymes can directly of such a stochastic component are proteins called transcription factors be experimentally determined. In significant and must not be neglected. that bind in the cell nucleus to DNA, practice, however, many kinetic Another issue that complicates triggering expression of distinct sets parameters, even for otherwise well- modeling of biological systems is that of target genes. It is this gene activa­ investigated enzymes, still are unknown, the different components of a path­ tion that alters the cell’s behavior and primarily because the relevant experi­ way often act over different time and represents the cell’s response to the mental data are lacking (i.e., the actual distance scales. For example, metabolic initial stimulus. direct measurements of enzyme activ­ reactions can happen within seconds

Vol. 31, No. 1, 2008 55 Example for the Mathematical Modeling of a Signaling Pathway

One important signaling factor is nuclear factor kappa B activation leads to production of new IκBα, which can (NFκB), which regulates numerous processes relevant then bind to NFκB and shut off the NFκB pathway. for inflammatory reactions, immune responses, cell pro­ This is known as a negative feedback loop. Continuous liferation, and survival of the cell. NFκB is a transcription cycles of IκBα degradation and synthesis give rise to reg­ factor—that is, it activates specific genes required for these ular changes (i.e., oscillations) in NFκB activity that can processes by binding to the DNA in front (i.e., upstream) be observed experimentally. Mathematical models have of these so-called target genes. been used to investigate these oscillations in more detail, Because of its important functions in the cell, the and comparisons between “dry” and “wet” experimental κ levels and actions of NF B must be tightly regulated. results generally have shown good agreement. The math­ NFκB normally is found in the fluid filling the cell (i.e., ematical equations for modeling NFκB activation also the cytoplasm) and must move to the nucleus to exert its effects on its target genes. To prevent inappropriate have been used to identify potential contributions of movement of NFκB to the nucleus, the molecule other molecules that are thought to modulate the normally is linked to a phosphate group (i.e., is phos­ NFκB/IκB-mediated regulatory process. For example, phorylated) and interacts with proteins called inhibitory modeling approaches using experimental data derived molecules of NFκB (IκBs). When the NFκB pathway from mice in which specific IκB genes had been inacti­ is activated by another signaling molecule, IκBs are vated (i.e., knocked out) demonstrated that certain IκBs degraded, allowing NFκB to move to the nucleus and had a damping effect on cyclic NFκB/IκBα oscillations activate its target genes. One of these target genes codes (i.e., that the changes in NFκB/IκB activity became for one of the inhibitory molecules, IκBα. Thus, NFκB smaller over time) (Hoffmann et al. 2002).

TNF cell membrane A20 IKKα

IKKα IKKi

IkBa IkBα IRBαNF-kB cytoplasm nucleus NF-kB IkBα IkBαNF-kB A20 mRNA

IkBα mRNA

As shown in the upper left panel, NFκB is part of a complex regulatory network that is, in part, controlled by the inhibitory fac­ tor IκBα. The cellular concentrations of the relevant molecular players over time can be expressed by formulas such as the one shown in the upper right panel. Experimental analyses of NFκB/IκBα activity over time found that the changes in NFκB/IκB activity became smaller over time (bottom left panel), in agreement with the predictions of the mathematical model. This temporal behavior of the pathway also can be expressed graphically (bottom middle panel), and detailed analysis of these experimental data and resulting graphs (bottom right panel) led to further refinement of the mathematical model.

SOURCES: Hoffman et al. 2002, Lipniacki et al. 2004.

56 Alcohol Research & Health Mathematical Modeling and Systems Biology or minutes, whereas genetic regulatory existing drugs), which is considered an ingly important role in this process, processes that are induced by these indicator of the innovation potential of and the pharmaceutical industry is metabolic reactions may occur over pharmaceutical research, is only slowly greatly interested in establishing new several hours or even days. Similarly, growing (Lindsay 2003). The whole predictive, computer-supported meth­ some regulatory reactions occur over process of developing, testing, and ods to systematically identify the most small distances (e.g., across the width obtaining approval for a new drug now promising drug candidates. In this of the membrane surrounding a cell), costs an average of approximately $900 context, a number of pharmaceutical whereas others involve greater distances million for each drug that makes it to companies recently have initiated dedi­ (e.g., the entire cytoplasm of the cell, the market (Service 2004) and the pro­ cated systems biology programs to sup­ or between tissues where blood circu­ cess can take more than a decade. As a port their in-house drug discovery and lation may transport signaling molecules result, companies look for more cost- development programs (Mack 2004). such as hormones and activate specif­ effective and less time-consuming alter- At the same time, an increasing ic cell types in remote tissues). To number of publicly and privately couple relevant effects occurring on funded initiatives and consortia aim very different length and time scales, A number of at establishing systems biology in dif­ researchers use so-called multiscale ferent domains of biological research models as a compromise to avoid pharmaceutical to elucidate, for example, the func­ making the model overly complex. companies recently tions of specific cell types relevant for Finally, it is important to recognize medical applications or to develop that any model can be only as good have initiated comprehensive systems biology appli­ as the assumptions upon which it is cations for metabolic engineering. In based. By definition, any model is an dedicated systems most cases, multiple research centers abstraction and simplification of real­ biology programs to or companies are integrated in a ity. All currently available, tractable decentralized research network to mathematical models of biological support their in-house which investigators from numerous systems neglect the majority of the drug discovery and disciplines (e.g., biology, genetics, molecular players in an organism. biochemistry, physics, mathematics, Moreover, all models make assump­ development programs. computer sciences, statistics, or engi­ tions about relevant time and length neering) contribute (see table, p. 58). scales. For example, the discussion One of the pioneering systems bio­ in this article focuses on modeling natives to the traditional drug discov­ logy programs is the publicly funded approaches for cellular pathways that ery and development process. German HepatoSys initiative, in neglect molecular details (e.g., the Systems biology is expected to play which more than 40 German research exact location of the molecules in the an increasingly important role in the centers cooperate in a joint program cell, or the precise three-dimensional establishment of innovative drug dis­ investigating the systems biology of structure of the proteins). It is essen­ covery strategies. Today, the industri­ the liver cell using numerous comple­ tial to keep these limitations in mind alized drug discovery process relies, to mentary approaches. The liver is an when discussing the value and validity a large degree, on highly automated organ of great medical interest with of mathematical models or when processes for screening the biological relevance to many disease areas, developing a specific model to cap­ activity of large chemical libraries in including alcohol-related diseases. ture the characteristics of a given order to identify new drug candidates. The different groups participating biological process. These screening assays enable a in HepatoSys apply a broad spectrum systematic assessment of candidate of technologies, ranging from compounds by testing their activity classical cell biological methods to Outlook: Biomedical on therapeutic targets—that is, bio­ imaging, transcriptomics, proteomics, Applications of Systems molecules that are causally involved and metabolomics; in addition, sever­ Biology and Modeling in disease outbreak or disease progres­ al groups conduct dry experiments sion (Fischer and Heyse 2005). by applying pathway modeling to Systems biology approaches have great Systematic compound screening liver cell pathways. Within the potential for enhancing the drug discov­ provides the starting point for further overall consortium, different ery and development process. Currently, chemical development to optimize the technology platforms are organized the productivity of the pharmaceutical drug-like features of the lead compound. into subgroups, or networks, which industry is lagging behind its investments Computational models of disease- focus on specific medically relevant in research and development. The out­ relevant pathways that allow for dry themes, such as liver regeneration put of new chemical entities (“NCEs,” experiments to support the assessment or detoxification processes. In a first rather than “me-too” drugs that repre­ of a candidate molecule’s safety and step, the researchers seek to recon­ sent only minor modifications of already efficacy most likely will play an increas­ struct liver-specific pathways using

Vol. 31, No. 1, 2008 57

wet and dry methods. Later, liver which is accessible to the experimen­ the different bits and pieces of informa­ metabolism and liver-specific signal­ talists as well as to the modelers. tion that are accumulating at an ever- ing and their roles in liver regenera­ Although the focus of publicly fund­ increasing pace. Just as an engineer tion and drug metabolism will be ed systems biology consortia primarily can turn a heap of metal pieces, wires, investigated. is on basic research, the results screws, and bolts into a jet plane only For HepatoSys and other systems produced will likely also be critical if he has a comprehensive blueprint, biology consortia and research cen­ for applications in the healthcare and biomedical scientists can understand the ters, it is essential that the different biotechnology sectors. workings of living organisms only if they research groups are connected via a In summary, the various systems have comprehensive models that enable central, dedicated data transfer and biology approaches developed in them to connect the often disparate exchange infrastructure to facilitate recent years provide an extraordinary pieces of information derived from the close collaboration among groups amount of new information on many experimental approaches. The Greek and disciplines. Such an infrastruc­ functions of human and other organ­ philosopher Aristotle said more than ture must include a specialized data isms relevant to research and biotech­ 2,000 years ago, “The whole is more management system that allows the nology applications. Only with the help than the sum of its parts,” and today, participating groups to deposit their of computerized modeling efforts, how­ systems biology research and model­ wet and dry data in a central location, ever, can researchers make sense of all ing efforts are helping to obtain a

Table Overview of Selected Systems Biology Consortia and Research Centers*

Consortium/Center Country Goal/Background Participants Link

HepatoSys Germany Systems biology of the German research centers www.systembiologie.de liver cell SysMap Germany Metabolism of microbial German industry and amino acid producers academic institutions Kluyver Centre Netherlands Improvement of microor­ Dutch academic www.kluyvercentre.nl ganisms for use in industrial institutions and fermentation processes industry partners BaSysBio Nine Global transcriptional 15 European research www.basysbio.eu European regulation in bacteria organizations countries SysMo Six European Dynamic molecular pro­ More than 50 www.sysmo.net countries cesses going on in working groups single-cell microorganisms Manchester United Cross-disciplinary Multidisciplinary www.mib.ac.uk Interdisciplinary Kingdom approaches to diseases research groups Biocentre such as cancer, malaria, Alzheimer’s, and cystic fibrosis Institute for Systems USA Study of biological systems Multidisciplinary www.systemsbiology.org Biology to increase understanding research groups of the immune system and other biological systems MIT Computational USA Systematic analysis of More than 10 academic www.csbi.mit.edu and Systems Biology complex biological units across the Initiative phenomena Massachusetts Institute of Technology (MIT) Kitano Symbiotic Japan Understanding of system- www.symbio.jst.go.jp Systems Project level principles of biological systems

* Links to additional groups involved in systems biology research can be found at http://www.systembiologie.de/de/links_researchgroups_international.html NOTE: Most consortia are publicly funded on a national or transnational level; some also are co-funded by industry partners.

58 Alcohol Research & Health Mathematical Modeling and Systems Biology

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