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The Virtual Cell Paradigm Proceedings of the 2006 Winter Simulation Conference L. F. Perrone, F. P. Wieland, J. Liu, B. G. Lawson, D. M. Nicol, and R. M. Fujimoto, eds. THINK SIMULATION – THINK EXPERIMENT: THE VIRTUAL CELL PARADIGM Ion I. Moraru James C. Schaff Leslie M. Loew Dept. of Cell Biology University of Connecticut Health Center Farmington, CT 06030-3505, U.S.A. ABSTRACT gene knockouts, drug targeting). Perhaps more useful, how- ever, is when the model is unable to predict the observed bi- The Virtual Cell modeling and simulation framework is the ology, implying that the elements of the model are either in- product of interdisciplinary research in biology that applies correct or incomplete. Analysis of such faulty models can the diverse strengths and experiences of individuals from directly motivate the discovery, via new experiments, of engineering, the physical sciences, the biological sciences, previously unknown critical biochemical or structural fea- and mathematics. A key feature is the separation of layers tures required for the cellular process under investigation. (core technologies and abstractions) representing biologi- However, the difficulties associated with the formula- cal models, physical mechanisms, geometry, mathematical tion of mathematical models and the generation of simula- models and numerical methods. This reduces software tions from them has impeded the adoption of this disci- complexity, allowing independent development and verifi- plined and quantitative approach to research in traditional cation, but most importantly it clarifies the impact of mod- cell biology, as well as slowed down the process of realiz- eling decisions, assumptions, and approximations. The re- ing the ultimate potential of the new, large scale, “omic” sult is a physically consistent, mathematically rigorous, datasets, keeping the rapidly growing area of systems biol- spatial modeling and simulation framework for cell biol- ogy at a level of mostly qualitative, top-down approaches ogy. The Virtual Cell has a rich, interactive user interface (Moraru and Loew 2005). Because biologists rarely have which connects to remote services providing scalable ac- sufficient training in the mathematics and physics required cess to a modeling database and a large dedicated cluster to build quantitative models, modeling has been largely the for shared computation and storage. In addition to new purview of theoreticians who have the appropriate training modeling capabilities, future developments will emphasize but little experience in the laboratory. With the notable ex- data and tool interoperability, extensibility, and experimen- ception of areas with rich traditions of biophysical research tally oriented model analysis tools. (such as cardiac and neuronal electrophysiology), this dis- connection to the laboratory has limited the impact of 1 INTRODUCTION mathematical modeling in cell biology and, in some quar- ters, has even given modeling a poor reputation. The accelerating progress in cataloguing the critical molecu- lar and structural elements responsible for cell function has 2 ABSTRACTING BIOLOGY FROM led to the hope that cell biological processes can be analyzed SIMULATION and understood in terms of the interactions of these compo- nents. Besides the obvious need for the acquisition and or- The Virtual Cell project (<http://vcell.org/>) ganization of quantitative data on these interactions, another aims to address the above problems by providing a compu- critical prerequisite for such analyses is the effective synthe- tational modeling framework that is accessible to cell bi- sis of this data by constructing models that can then predict ologists. It does this by abstracting and automating the the overall behavior of the biological system. If the model mathematical and physical operations involved in con- correctly predicts the biological endpoint, one can hypothe- structing models and generating simulations from them. It size that the elements within the model are sufficient, and was originally developed to specifically target the need for often one can discern which of these elements are the most building and solving spatial models of intracellular phe- critical. This can then be tested by further experiments de- nomena, and it has since grown into a large platform that is signed to specifically perturb or remove these elements (e.g., being continuously enhanced with new features (Slep- 1-4244-0501-7/06/$20.00 ©2006 IEEE 1713 Moraru, Schaff, and Loew chenko et al. 2003). The current layered, modular design of the Virtual Cell was motivated by several factors: manag- ing complexity, facilitating model reuse, providing bio- logically and mathematically oriented tools, and building a distributed architecture. One of the innovative features in the design of the Vir- tual Cell is the introduction of three distinct layers of ab- stractions in the modeling process, which are following a paradigm similar to hypothesis-driven experimental stud- ies. Figure 1 schematizes the way in which the modeling process is structured within the Virtual Cell. This hierar- chical layered structure starts with the system Physiology – essentially the mechanistic hypothesis to be investigated. It includes the description of the molecular species and hy- pothesized interactions localized to cellular structures. Cellular structures need only be specified as the topologi- cal arrangement of membranes and membrane bounded Figure 1: Decomposing the Modeling Process in the Vir- compartments. Interactions can be biochemical reactions tual Cell BioModel Workspace defined either within volumetric compartments of the cell or in membranes; molecular fluxes across membranes; and Finally, as shown in Figure 1, several simulations can electrical currents. Additionally, the Physiology captures be spawned off of a given Application. That is, the mathe- the biochemical and biophysical properties of these inter- matics can be solved with multiple choices of numerical actions as rate laws for reactions and fluxes rate (that can solver, time step, mesh size for spatial simulations, time be determined as an explicit function of the local environ- duration and overrides of the default initial conditions or ment, e.g., concentrations, surface densities, membrane po- parameter values to permit parameter scans. A local sensi- tential, and of one or more kinetic parameters, e.g., kon and tivity analysis service is also available at the simulation koff). Mass action and Michaelis-Menten rate laws are level to aid in parameter estimation and to determine which available automatically, and arbitrary user-defined general features of the model are most critical in determining its kinetic expressions can also be used. Membrane transport overall behavior. A parameter estimation tool can fit non- kinetics can be specified with expressions for molecular spatial models to time series experimental data. A particu- flux or, for ions, the electric current. The transport kinetics lar simulation specification is, in turn, sufficient to describe can be described in terms of standard electrophysiological the software requirements for numerically calculating solu- formulas (e.g., Goldman-Hodgkin-Katz permeability or tions and the Virtual Cell thus automatically generates the Nernst conductance) or as user defined molecular flux or appropriate C++ code to produce simulation results. current. Such a decomposition of modeling concepts makes The Physiology can then have several Applications – possible the effective reuse of the model in multiple con- essentially the “virtual experiment” environment, the set of texts. To allow a single quantitative mechanistic hypothe- conditions under which one or more simulations will be sis to be validated under multiple experimental conditions performed. A particular Application would specify a spe- at different scales and using different physical approxima- cific geometry (e.g., size and shape of a cell), the boundary tions, the abstract physiological modeling concept is util- conditions, default initial concentrations and parameter ized. For example, a receptor binding reaction localized to values, and whether any of the reactions are sufficiently a membrane can have many different mathematical forms fast to permit a pseudo-steady state approximation. Also at while the quantitative mechanistic description is un- the Application level, individual reactions can be disabled changed. Its form depends on whether the membrane is as an aid in determining the proper initial conditions for a mapped to a spatially resolved surface, or mapped volu- prestimulus stable state. An Application of a Physiology is metrically as a distributed surface for an unresolved organ- sufficient to completely describe the governing mathemat- elle, or as non-spatial representation in a compartmental ics of the model and the mathematical representation of the model. The mathematical form also depends on additional system is automatically generated at this point by the soft- modeling assumptions, such as whether the reaction is ware (stored in a proprietary, but quite intuitive, mathe- “knocked out” or considered to be “fast” (pseudo-steady matical description language, VCMDL, that can be viewed state approximation). by the user). The Virtual Cell is designed to maintain a We will now use a study of calcium dynamics in a separation between this mathematical description, gener- neuronal cell (Fink et al. 1999, Fink et al. 2000) as a con- ated either via a BioModel or a MathModel, and the details crete illustration
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