Mathematical models of cellular movements

三种机制——板足肌动蛋白网络的突出，细胞骨架与表面的分级粘附和细胞骨架收缩——协同作用是产生高效细胞运动的必要和充分的。实际的突出率和力取决于局部的肌动蛋白单体和聚合物的浓度，以及细胞边缘附近的肌动蛋白盖帽、成核、聚合和粘附蛋白的宿主。研究者推导出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结合的偏微分方程。这些方程是解析解决和量化分子机制的突出定位在细胞的前缘和调节突出率和力。实验表明，细胞骨架收缩的力量是肌球蛋白驱动的。研究者模拟了肌动蛋白丝和肌凝蛋白簇在物理空间和角度空间的动力学，并定量描述了肌动蛋白的动态收缩机制。利用这一描述，研究者在复杂程度不同的交互式计算机模型框架内分析了牵引、突出和分级粘连系统之间的机械化学反馈回路。这些模型应用于鱼类角化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系统、粘附系统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。这些模型允许对细胞运动的合理场景进行测试。动物细胞的迁移是伤口愈合、形态发生和癌症发生的重要过程。目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。研究者对这些动力现象进行了理论建模，这将允许生物学家对现有的定性观点进行定量测试。具体来说，研究者在数学上研究了细胞力学的分子基础和自组织原理，并开发了再现观察到的细胞运动模式的计算机模型。建模的结果将提供一个新的跨学科水平的理解细胞运动和预测细胞行为在重要的医疗和技术情况的新方法。

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.