Reducing Spatial Stochastic Models of Membrane Receptors to Approximately Equivalent Chemical Reaction Networks through Coarse Graining

Abstract

Computational models are necessary for understanding how biological functionality emerges from a complex network of molecular interactions such as in cell signaling. Due to the complexity of biological systems, the normal scientific method of hypothesizing then testing predictions is becoming increasingly difficult. The large number of processes limits the level of modeling detail; signaling models typically adopt a non-spatial representation where each molecular process is characterized by a few parameters. However, modern microscopic imaging of receptors on cell membranes reveals an intricate structure of microdomains. Receptors, such as epidermal growth factor receptor (EGFR), vascular endothelial growth factor receptor (VEGFR), and others, tend to be grouped in the microdomains as clusters that range from a few to hundreds of biomolecules. While the origin of these clusters is not well understood, a likely explanation is the existence of microdomains with an affinity for the receptors. Using this hypothesis, we can ignore the underlying cause of the microdomains. The size and geometry of these domains can be inferred directly from microscopy; however, the relevant physical properties can only be verified through simulations. In this thesis, I propose a flexible approach to performing such simulations in a coarse grained model that is validated through solving the differential equations when possible and through equilibrium calculations when not. Due to the non-trivial nature of these cell membrane features, fully spatial models need to be used to address these issues. However, fully spatial models are computationally intense and little insight can be gained from them, because of this I propose a method to construct the well-mixed model from the spatial one. The primary issue is the difficulty of extracting the correct kinetic coefficients and that limits the predictive power of spatial models due to the inherent challenges of estimating dynamical parameters. I will use the Metropolis-Hastings Algorithm to extract these parameters from the fully spatial simulations. I use the spatial model as an intermediary step because the spatial simulations can be matched to experimental techniques that provide molecular level resolution, such as single particle tracking (SPT) data. I will then discuss issues that emerge from a baseline comparison between spatial and non-spatial simulations of a simple reversible dimerization process; the spatial simulation employed an algorithm similar to Smoldyn.