Gene Regulation and Systems Biology 2007:1 91���110 91 REVIEW Correspondence: David S Wishart, 2-21 Athabasca Hall, University of Alberta, Edmonton, AB, Canada T6G 2E8. Tel: 780-492-0383 Fax: 780-492-1071 Email: david.wishart@ualberta.ca Computational Systems Biology in Cancer: Modeling Methods and Applications Wayne Materi2 and David S. Wishart1,2 1Departments of Biological Sciences and Computing Science, University of Alberta 2National Research Council, National Institute for Nanotechnology (NINT) Edmonton, Alberta, Canada Abstract: In recent years it has become clear that carcinogenesis is a complex process, both at the molecular and cellular levels. Understanding the origins, growth and spread of cancer, therefore requires an integrated or system-wide approach. Computational systems biology is an emerging sub-discipline in systems biology that utilizes the wealth of data from genomic, proteomic and metabolomic studies to build computer simulations of intra and intercellular processes. Several useful descriptive and predictive models of the origin, growth and spread of cancers have been developed in an effort to better understand the disease and potential therapeutic approaches. In this review we describe and assess the practical and theoretical underpinnings of commonly-used modeling approaches, including ordinary and partial differential equations, petri nets, cellular automata, agent based models and hybrid systems. A number of computer-based formalisms have been implemented to improve the accessibility of the various approaches to researchers whose primary interest lies outside of model development. We discuss several of these and describe how they have led to novel insights into tumor genesis, growth, apoptosis, vascularization and therapy. Keywords: cancer, computational systems biology, simulation, modeling, cellular automata Background Living organisms are complex systems. Nowhere is this complexity more evident than in the genesis and development of cancer. While cancer may originate from genetic and molecular changes that occur in a single cell, the subsequent proliferation, migration and interaction with other cells is crucial to its further development. In their landmark paper, Hanahan and Weinberg described six hallmarks they thought necessary for the transition from normal cells to invasive cancers (Hanahan and Weinberg, 2000). These included: 1) self-sufficiency in growth signals, 2) insensitivity to growth inhibitory signals, 3) evading apoptosis, 4) limitless replicative potential, 5) sustained angiogenesis, and 6) tissue invasion and metastasis. While genetic instability was not explicitly included in this list, it was included as an implicit enabling alteration that might start a normal cell down a mutagenic pathway leading to the acquisition of one or more of these essential characteristics. The molecules that govern the cell growth and division cycle in response to external and internal signals are numerous and interact through complex, multiply-connected pathways over a wide range of temporal and spatial scales. Tumors reflect this complexity in that they are composed of several different cell types that interact to create malignant growth (Burkert et al. 2006). Despite the widespread acceptance of this complexity, the majority of biological and biomedical studies still utilize a strictly reductionist approach, focusing on the interactions of at most a few genes or proteins in each experi- ment. Systems biology, an integrative discipline that attempts to describe and understand biology as systems of interconnected components, has arisen partly as a response to these traditional reductionist approaches. Systems biology is a young fi eld made possible by the explosion of data from genomic, transcriptomic, proteomic and metabolomic techniques developed within the last decade (Hollywood et al. 2006 Bugrim et al. 2004 Jares, 2006). Computational systems biology, which is a sub-discipline of systems biology, has developed both as a tool supporting the processing of these massive amounts of data and as a modeling discipline, building upon this ���omic��� data in order to predict biological behavior (Ideker et al. 2001a Alberghina et al. 2004). Not surprisingly, both experimental and computational systems biology approaches have provided fruitful insights into cancer. Please note that this article may not be used for commercial purposes. For further information please refer to the copyright statement at http://www.la-press.com/copyright.htm

92 Materi et al Gene Regulation and Systems Biology 2007: 1 This review provides an overview of how computational systems biology can be, and is being used to model cancer at multiple levels and scales, ranging from molecules to cells to tissues. Specifi- cally, we begin with a general description of the different computational modeling methods that can be used along with a discussion of their relative strengths and weaknesses. Following that, we describe some of the emerging formalisms, software and standards for representing biological systems. Finally, we provide a number of examples illus- trating how computational systems biology has enriched our understanding of a variety of cancer- related processes including genetic instability, tumor growth, apoptosis, angiogenesis and anti-cancer therapy. Overall it is our hope that this review will provide an improved understanding of modeling issues and thereby assist the reader in selecting an appropriate method for their own research. Approaches to Computational Systems Modeling To be truly useful to a biologist or physician, computational modeling should: 1) produce useful predictions or extrapolations that match experi- mental results 2) permit data to be generated that is beyond present-day experimental capabilities 3) allow experiments to be performed in silico to save time or cost 4) yield non-intuitive insights into how a system or process works 5) identify missing components, processes or functions in a system 6) allow complex processes to be better understood or visualized and 7) facilitate the consolidation of quantitative data about a given system or process. Simulations encompass many different spatial and temporal scales, ranging from nanometers to meters and nanoseconds to days (Fig. 1). Processes that occur over very small dimensions (nm) or short time periods (ms) are often referred to as ���fine grain��� models, while processes occuring over longer time periods (s) or larger (mm or cm) dimen- sions are called ���coarse grain��� models. A funda- mental challenge to computational systems biology is to develop models and modeling tools that can deal with this wide range of granularity. In this review we will describe some of the newer or more innovative modeling techniques that are being developed to permit both temporal and spatio- temporal modeling over this wide range of scales, including: 1) systems of ordinary differential equations (ODEs), partial differential equations (PDEs) and related techniques, 2) Petri nets, 3) cellular automata (CA), dynamic cellular automata (DCA) and agent-based models (ABMs) and 4) hybrid approaches. Figure 1 presents an overview of scaling issues in modeling cancer and indicates which approaches are particularly well- suited to dealing with each area. Building models of complex biological processes is an iterative process that requires considerable attention to detail. The network topology or struc- ture of a model may arise through literature surveys or directly by computational analysis of high- throughput data (Wang et al. 2007���[Epub ahead of print]). In many instances such analyses may reveal novel regulatory or signal transduction interactions whose kinetics and stoichiometry is unknown (Janes et al. 2005 Kumar et al. 2007). Quantitatively accurate modeling requires explicit values for many variables including molecular concentrations, cellular distribution of molecules, reactions rates, diffusion rates, transport rates and degradation rates. While many of these can be estimated from the literature or various online databases, a number of parameters often remain unknown at the start of any simulation. As a result, many modeling processes require that one provide estimates for key parameters. Usually ���best guess��� fi rst order estimates can be used and then fi ne-tuned using a well-understood instance of the model as a comparison. Parameters are iteratively adjusted on subsequent simulations until the model accu- rately reflects the known test case (Ideker et al. 2001a Kunkel et al. 2004 Ideker et al. 2006). This period of validation is always required where any unknown parameters exist. However, a detailed discussion of network discovery and the model refinement/validation process is beyond the scope of this review. Computational modeling using differential equations Biological systems are essentially multicomponent chemical reactors and thus can be represented as systems of chemical reactions. This view permits mathematical analysis using powerful techniques developed from chemistry. Many standard biochem- istry texts provide thorough derivations of ordinary differential equations (ODEs) for both simple and complex reactions. In fact, ODE based modeling is the most common simulation approach in computational

93 Computational systems biology in cancer Gene Regulation and Systems Biology 2007: 1 systems biology, reflecting both its rigor and adapt- ability (Kitano, 2002 De Jong, 2002). Simple ODEs may have exact solutions. However, most complex ODEs do not have exact solutions and must be solved numerically. Based on methods fi rst derived by Newton and Gauss, numerical integrators utilize linear approximations of smooth curves over small time intervals to compute subsequent values of reactant concentra- tions. Improving the accuracy of these linear esti- mates may require using smaller time intervals, leading to computationally intense processes that Figure 1. Issues of scale in modeling cancer. From whole organism to tumor tissue to individual cells to the molecules of replication and metabolism, modeling tumors spans about nine orders of spatio-temporal magnitude. Shown above are some of the modeling issues which need to be addressed at each level of simulation. Each text box includes the relevant spatio-temporal scale and modeling issues encountered at that level. Appropriate modeling approaches to address each issue are shown in brackets. Building hierarchical systems of inter-related models is still a primary challenge to modern researchers. ODE ��� Ordinary differential equation system, PDE ��� Partial differential equation system, DCA ��� Dynamic cellular automaton, PN ��� Petri net system, ABM ��� Agent based model.