Particle-based stochastic reaction-diffusion methods for studying T cell signaling
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Abstract
Mathematical and computational models have become an invaluable tool in understanding immune responses by aiding the formulation of new hypotheses and supplementing traditional experimental research. Over the past decade, a large body of experiments studying T cell signaling pathways have revealed that the signal transduction can be affected by stochasticity in the diffusive motion of proteins and reactive interactions between proteins. Many detailed particle-based stochastic reaction-diffusion models have been developed to properly account for such stochasticity, but there are still many unresolved issues in developing accurate and efficient numerical methods for these models, particularly when using them in realistic cellular domains with complex geometries. Moreover, the activation and deactivation of a T cell in response to antigens can be strongly affected by numerous competing signals. Such complexity poses another challenge by complicating the development of appropriate simplified models for investigating T cell signaling. To overcome these challenges, we develop both accurate and efficient numerical methods for approximating the solutions to stochastic reaction-diffusion models in complex geometries. We then apply these methods to the study of T cell signaling, and derive coarse-grained models for T cell signaling that can be understood using analytical methods. These numerical methods and simplified models should be broadly applicable to the study of a variety of models for cellular processes, involving thousands of interacting molecules in realistic cellular geometries.