Mathematical Modeling of Complex Biological Systems: From Parts Lists to Understanding Systems Behavior

Article excerpt

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

Over the last decade, DNA-sequencing technologies have advanced tremendously, culminating in the deciphering of the com-plete human genome in 2001 (Landers et al. 2001; Venter et al. 2001). This achievement is a major milestone in the understanding of human biology, as the human genome provides a catalogue of all human genes and associated molecules that are required for creating a living human being. To date, however, the availability of this "parts" list specifying most human biomolecules, including DNA, proteins, and RNA, has answered only some of the questions concerning the complex phenomena of human biol-ogy, leaving many others unanswered. Moreover, the hope that with the knowledge of the human genome sequence researchers would be able to readily develop new therapies for treating human disease as yet has only partially been ful-filled. The availability of a fully sequenced human genome is a prerequisite for elucidating the origins of complex human diseases, such as cancer, obesity, Alzheimer's disease, or alcoholism but unfortunately is by no means sufficient to provide answers to all of the questions surrounding these diseases.

In the meantime, further technological advances have led to a considerable increase in the understanding of the workings of the human body under normal conditions and in various disease states. For example, transcrip-tomic1 studies are shedding light on which genes are active in a given cell at a given time, proteomic studies are discovering which proteins are present and in what amounts, and analyses of the metabolome have begun to examine which metabolic processes occur under different conditions. Most importantly, however, this work has highlighted the fact that human genes and the proteins they encode do not work in isolation but are connected at various levels in networks and pathways of varying complexity. A deeper understanding of these interactions is pivotal for understanding human diseases and developing appropriate therapeutic approaches. One crucial element in this process is the generation of mathematical models that capture the often-unexpected features of complex biological systems. The development of these models is intimately linked to the generation of experimental data using various high-throughput genomic, transcriptomic, proteomic, and metabolomic experimental strategies.

This article summarizes the challenges associated with the study of complex biological systems, the benefits of systems biology approaches, and the ways in which computational models can help consolidate and interpret the experimental data obtained using these approaches. …


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