Models and computation of intracellular signaling in single and collective cell migration

许多细胞通过定向运动对刺激作出反应。例如，白色血细胞（嗜中性粒细胞）不断地向化学信号移动。细胞运动需要细胞骨架结构蛋白（主要是丝状肌动蛋白，F-肌动蛋白）的动态变化。细胞迁移调控级联反应的核心是Rho GTP酶家族（如Rac、Rho、Cdc 42），来自受体、上游效应子的刺激和下游效应子的反馈都汇集到Rho GTP酶家族中。GTP酶由GEF激活，由GAPS失活，并通过相互串扰“连接在一起”。使用数学建模，我建议调查如何动态的GTP酶的影响和规模在三个层次的生物组织：亚细胞结构（细胞边缘突起，伤口修复），细胞-细胞和细胞-基质的相互作用，和多细胞组织动力学。我的方法包括普通和偏微分方程（ODE，PDE）模型来描述时空GTdR分布和细胞行为。使用非线性动力学，分叉，近似方法和模拟，我表征的解决方案和预测行为如何依赖于生物可调参数。我还使用反应扩散方程（RDES）的抽象理论来识别可能的行为。放大到多个细胞，我将“群体”的数学适应于集体细胞动力学的微观世界。通过粘附、机械或化学信号传导、长丝状伪足等的细胞-细胞相互作用，可以描述（通过具有非局部“内核”的积分偏微分方程）。我的创新是包括影响细胞伸展/收缩性的GTdR活性，从而影响相互作用的范围和强度（内核幅度，范围）。该分析与一维和二维空间（1D，2D）的模拟相补充，可以直接与合作者的实验数据进行比较。我正在进行的和新的合作跨越亚细胞到组织尺度：（1）与W Bement（威斯康星州，细胞创伤修复）（2）与朴镇锡（Yale and USC）和Andre Levchenko（Yale），关于细胞-ECM相互作用，以及（3）与Cal Roquilley（UBC）和Arnold Hayer（麦吉尔）关于体外细胞-细胞碰撞;与Paul Kulesa（Stowers，神经嵴细胞）和Joy Richman（UBC）共同研究集体细胞迁移和形态发生。跨学科研究的HQP培训将在各个层次进行，从本科生到研究生和博士后，具有强大的EDI组件。我的主要目标是一方面将亚细胞信号与单细胞、细胞群和组织的行为联系起来，另一方面在抽象数学和具体应用之间架起桥梁。

Many cells respond to stimuli by directed motility. For example, white blood cells (neutrophils) polarize and move persistently towards chemical signals. Cell motility entails dynamic changes in structural proteins of the cytoskeleton (primarily filamentous actin, F-actin). This, in turn, is regulated by proteins that promote assembly and disassembly of the actin network or activity of molecular motors (myosin) that pull on it and reshape it. At the core of the cell-migration regulatory cascades are a family of proteins known as Rho GTPases (e.g. Rac, Rho, Cdc42) to which stimuli from receptors, upstream effectors, and feedback from downstream are funneled. GTPases are activated by GEFs, inactivated by GAPS, and "wired together" by mutual crosstalk. Using mathematical modeling, I propose to investigate how the dynamics of GTPases impacts and scale across three levels of biological organization: subcellular structures (cell edge protrusion, wound repair), cell-cell and cell-matrix interactions, and multicellular tissue dynamics. My methods include ordinary and partial differential equation (ODE, PDE) models to describe spatiotemporal GTPase distributions and cell behaviour. Using nonlinear dynamics, bifurcations, approximation methods and simulations, I characterize solutions and predict how behaviour depends on biologically tunable parameters. I also use abstract theory of reaction-diffusion equations (RDEs) to identify possible behaviour. Scaling up to multiple cells, I adapt the mathematics of "swarms" to the microworld of collective cell dynamics. Cell-cell interaction via adhesion, mechanical or chemical signaling, long filopodia, etc., can be depicted (by integro-PDEs with nonlocal "kernels"). My innovation is to include GTPase activity which affects cell spreading/contractility, and hence the range and strength of interactions (kernel magnitudes, ranges). The analysis is complemented with simulations in one and two spatial dimensions (1D, 2D), that can be directly compared to experimental data from collaborators. My ongoing and new collaborations span the subcellular to tissue scales: (1) With W Bement (Wisconsin, cell wound repair) (2) With JinSeok Park (Yale and USC) and Andre Levchenko (Yale), on cell-ECM interactions and (3) With Cal Roskelley (UBC) and Arnold Hayer (McGill) on cell-cell collisions in vitro; with Paul Kulesa (Stowers, neural crest cells) and with Joy Richman (UBC) on collective cell migration and morphogenesis. Training HQP in interdisciplinary research will take place at all levels, from undergraduates, through graduate students and post-docs, with strong EDI components. My key aims are to link subcellular signaling to the behaviour of single cells, cell groups, and tissues on one hand, and to bridge between abstract mathematics and specific applications on the other hand.