Mathematical models of cellular movements

Mogilner0073828三种机制--片状脂膜放线网的突起、细胞骨架与表面的渐变黏附和细胞骨架收缩--协同作用对于产生高效的细胞运动是必要的，也是充分的。突起的实际速度和力取决于细胞前沿附近的因子单体和聚合物以及大量肌动蛋白封顶、成核、聚合和黏附蛋白的局部浓度。研究人员推导出了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相耦合的偏微分方程式。这些方程被解析地求解，并量化了突起在细胞前缘的定位以及突起速率和力的调节的分子机制。实验表明，细胞骨架收缩的力量是肌动的。研究人员对肌动蛋白细丝和肌球蛋白簇在物理和角度空间中的动力学进行建模，并定量描述肌动蛋白的动态收缩机制，利用这种描述，研究人员在复杂程度不同的交互计算机模型框架内分析了牵引力、突起和渐变粘连系统之间的机械力化学反馈回路。这些模型适用于鱼类角质细胞和线虫变形虫精子的迁移。理论结果与实验结果的比较，阐明了细胞骨架、黏附和膜系统在细胞运动中的作用，以及运动性、极化率和方向性的概念。Themdels允许测试细胞运动的合理场景。动物细胞的迁移是伤口愈合、形态发生和癌症等现象的一个基本的重要过程。目前的实验研究旨在将复杂的迁移过程分解成更容易分析的更简单的现象。研究人员从理论上对情感现象进行建模，这将使生物学家能够对现有的定性概念进行定量检验。具体地说，研究人员对细胞力学的分子基础和自组织原理进行了数学检验，并开发了重现观察到的细胞运动模式的计算机模型。建模的结果将为理解细胞运动提供一个新的跨学科水平，并为在重要的医疗和技术情况下预测细胞行为提供新的方法。

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.