The Roles of Space and Stochasticity in Computational Simulations of Cellular Biochemistry: Quantitative Analysis and Qualitative Insights

Abstract

Most of the fascinating phenomena studied in cell biology emerge from interactions among highly organized multi-molecular structures and rapidly propagating molecular signals embedded into complex and frequently dynamic cellular morphologies. For the exploration of such systems, computational simulation has proved to be an invaluable tool, and many researchers in this field have developed sophisticated computational models for application to specific cell biological questions. However it is often difficult to reconcile conflicting computational results that use different simulation approaches (for example partial differential equations versus particle-based stochastic methods) to describe the same phenomenon. Moreover, the details of the computational implementation of any particular algorithm may give rise to quantitatively or even qualitatively different results for the same set of starting assumptions and parameters. In an effort to address this issue systematically, we have defined a series of computational test cases ranging from very simple (bimolecular binding in solution) to moderately complex (spatial and temporal oscillations generated by proteins binding to membranes) that represent building blocks for comprehensive three-dimensional models of cellular function. Having used two or more distinct computational approaches to solve each of these test cases with consistent parameter sets, we generally find modest but measurable differences in the solutions of the same problem, and a few cases where significant deviations arise. We discuss the strengths and limitations of commonly used computational approaches for exploring cell biological questions and provide a framework for decision-making by researchers wishing to develop new models for cell biology. As computational power and speed continue to increase at a remarkable rate, the dream of a fully comprehensive computational model of a living cell may be drawing closer to reality, but our analysis demonstrates that it will be crucial to evaluate the accuracy of such models critically and systematically.