Computational studies for spatial-temporal dynamics of cell signaling

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The main theme of this proposed work is on the mathematical and computational investigation of spatial-temporal dynamics of cell signaling, design and implementation of powerful numerical solvers to solve such models in complex and moving domains. The specificity of cellular responses to receptor stimulation is encoded by the spatial and temporal dynamics of downstream signaling networks. In recent years, it has become apparent that distinct spatial-temporal activation profiles of the same repertoire of signaling proteins result in different gene activation patterns and diverse physiological responses. In many cases, spatially localized scaffold proteins that bind and organize multiple proteins into complexes within a pathway have merged as essential factors in shaping the quantitative response behavior of a pathway. In order for a better exploration of spatially localized scaffold proteins in mitogen-activated protein kinase (MAPK) cascades, the first part of the project is to explore the roles of substrate sequestration in combination with multisite phosphorylation for the modulation of ultrasensitivity and multistabilities. For the second part of the project, guided by known experimental observations, the PI proposes to develop mathematical models to further computationally investigate how a spatially localized and moving scaffold interacts with other components in a cascade and promotes specific cellular responses with spatial-temporal dynamics, such as long-range signals, graded/binary responses, noise reduction and traveling waves. Furthermore, in order to meet the computational challenges and demands which arise from the mathematical models of above complicated biological systems, the PI will design and implement more efficient and more accurate numerical methods than are currently done for convection and reaction-diffusion coupled equations with complex and moving geometries in high-spatial dimensions. Through mathematical modeling and computational analysis, the PI hopes that this proposed work may be able to shed lights on such a fundamental question: What do localized scaffold proteins really do?Errors in cellular information processing are responsible for a variety of life-threatening or chronic diseases, such as cancer, autoimmunity and diabetes. This project seeks to provide better understanding on proper signal propagation across the cell in space and time, and such quantitative studies closely combined with experiments will deepen and advance our understanding of signal transduction inside the cell and thus may lead to design new drugs for a better treatment of above-mentioned diseases. In addition, the computational tools developed in this work will make computational exploration of complex biological systems more efficient, by reducing simulation time and at the same time producing more accurate solution through the integrated use of fast numerical solvers, front tracking method and adaptive mesh refinement.The developed mathematical and computational methods are also expected to have a broad impact on the studies of a large class of many other biological systems when interactions and transport of many bio-chemical species are involved with complex and moving geometries, and other special target applications are but not limited to protein trafficking and embryonic development. In addition, a critical ingredient for the success of this and related projects is the education and training of the next generation of mathematicians with expertise in mathematical biology and computation. Therefore this research project will provide and enhance multi-disciplinary training at the interface among mathematics, scientific computing and biology for both graduate and undergraduate students.