Computational studies for spatial-temporal dynamics of cell signaling

这项拟议工作的主要主题是对细胞信号的时空动力学进行数学和计算研究，设计和实现强大的数值求解器来求解复杂和移动区域中的此类模型。细胞对受体刺激的反应的特异性是由下游信号网络的空间和时间动态编码的。近年来，同一组信号蛋白的不同时空激活模式导致不同的基因激活模式和不同的生理反应已变得十分明显。在许多情况下，空间定位的支架蛋白结合并将多个蛋白质组织成一个途径内的复合体，已经作为塑造途径定量反应行为的基本因素而合并。为了更好地探索丝裂原活化蛋白激酶(MAPK)级联中空间定位的支架蛋白，本项目的第一部分是探索底物隔离和多位点磷酸化在调节超敏感性和多稳定性中的作用。对于该项目的第二部分，在已知实验观察的指导下，PI建议开发数学模型，以进一步计算研究空间定位和移动的支架如何与级联中的其他组件相互作用，并通过时空动力学促进特定的细胞响应，如远程信号、分级/二进制响应、降噪和行波。此外，为了满足上述复杂生物系统数学模型所带来的计算挑战和要求，PI将设计和实现比目前在高空间维上具有复杂和运动几何形状的对流和反应扩散耦合方程的更有效和更精确的数值方法。通过数学建模和计算分析，PI希望这项拟议的工作可能能够阐明这样一个基本问题：定位的支架蛋白到底做了什么？细胞信息处理中的错误导致了各种威胁生命或慢性疾病，如癌症、自身免疫和糖尿病。该项目旨在更好地了解细胞内信号在空间和时间上的正确传播，这种定量研究与实验紧密结合将深化和推进我们对细胞内信号转导的理解，从而可能导致设计新的药物来更好地治疗上述疾病。此外，本工作开发的计算工具将通过综合使用快速数值求解器、前沿跟踪方法和自适应网格加密来减少模拟时间，同时产生更准确的解，从而使复杂生物系统的计算探索更加高效。所开发的数学和计算方法也有望对许多其他生物系统的研究产生广泛的影响，当许多生物化学物种的相互作用和运输涉及复杂和运动的几何形状，以及其他特殊的目标应用，但不限于蛋白质运输和胚胎发育。此外，这一项目和相关项目成功的一个关键因素是教育和培训下一代具有数学生物学和计算专业知识的数学家。因此，本研究项目将为研究生和本科生提供和加强数学、科学计算和生物之间的多学科交叉培训。

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.