Mathematical models of cellular movements

Mogilner0073828 三种机制——片状肌动蛋白网络的突出、细胞骨架与表面的分级粘附以及细胞骨架收缩——协同作用对于产生高效的细胞运动来说既是必要的又是充分的。 突出的实际速率和力取决于肌动蛋白单体和聚合物的局部浓度以及细胞前缘附近的大量肌动蛋白加帽、成核、聚合和粘附蛋白。 研究人员推导出偏微分方程，将所有这些蛋白质浓度的化学动力学与细胞骨架力学模型耦合起来。 这些方程通过分析求解并量化了细胞前缘突出定位的分子机制以及突出速率和力的调节。 实验表明，细胞骨架收缩的力量是肌球蛋白驱动的。 研究人员模拟了物理和角度空间中肌动蛋白丝和肌球蛋白簇的动力学，并定量描述了肌动球蛋白动态收缩机制。利用这种描述，研究人员在复杂程度不同的交互式计算机模型框架内分析了牵引、突出和分级粘附系统之间的机械化学反馈回路。 这些模型应用于鱼类角质细胞和线虫阿米巴精子的迁移。 理论结果与实验的比较阐明了细胞骨架、粘附和膜系统在细胞运动中的作用以及运动性、极化性和方向性的概念。 这些模型可以测试细胞运动的合理情况。 动物细胞的迁移是伤口愈合、形态发生和癌症现象背后的一个极其重要的过程。 当前的实验研究旨在将复杂的迁移过程分解为更容易分析的简单现象。 研究人员从理论上对这些运动现象进行建模，这将使生物学家能够定量测试现有的定性想法。 具体来说，研究人员从数学上研究了细胞力学的分子基础和自组织原理，并开发了重现观察到的细胞运动模式的计算机模型。 建模结果将为理解细胞运动提供新的跨学科水平，并提供预测重要医学和技术情况下细胞行为的新方法。

Mogilner0073828 Three mechanisms - protrusion of the lamellipodial actinnetwork, graded adhesion of the cytoskeleton to the surface, andcytoskeletal contraction - acting in concert are both necessaryand sufficient to produce highly effective cell movement. Actualrates and forces of protrusion depend on local concentrations ofactin monomers and polymers and a host of actin capping,nucleation, polymerization and adhesion proteins near the cell'sleading edge. The investigator derives partial differentialequations that couple the chemical kinetics of all these proteinconcentrations to the model of cytoskeletal mechanics. Theseequations are solved analytically and quantify molecularmechanisms of protrusion localization at the cell's leading edgeand regulation of protrusion rates and forces. Experimentssuggest that the force of the cytoskeletal contraction is myosinpowered. The investigator models the dynamics of actin filamentsand myosin clusters in physical and angular space and describesthe actomyosin dynamic contraction mechanism quantitatively.Using this description, the investigator analyzes mechanochemicalfeedback loops between systems of traction, protrusion and gradedadhesion within the frameworks of interactive computer modelsvarying in complexity. These models are applied to migration offish keratocyte and nematode amoeboid sperm. Comparison oftheoretical results with experiment clarify the roles ofcytoskeletal, adhesion and membrane systems in cellular movementsand concepts of motility, polarizability and directionality. Themodels allow testing of plausible scenarios of cell movements. Migration of animal cells is a fundamentally importantprocess underlying the phenomena of wound healing, morphogenesisand cancer. Current experimental research is aimed at dissectingthe complex processes of migration into simpler phenomena thatcan be more easily analyzed. The investigator models thesemotility phenomena theoretically, which will allow biologists totest quantitatively the existing qualitative ideas. Specifically,the investigator examines mathematically the molecular basis andthe principles of self-organization of cell mechanics anddevelops computer models that reproduce the observed patterns ofcell locomotion. Results of the modelling will provide a newinterdisciplinary level of understanding cell movements and newmethods of predicting cell behavior in important medical andtechnological situations.