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