树突状肌动蛋白网络生长的连续模型
A continuum model for the growth of dendritic actin networks
摘要：
树突状肌动蛋白网络的聚合是细胞生物学中重要的机械过程的基础，例如板状伪足的突出、神经元树突中生长锥的推进、细胞器和病原体的细胞内运输等。这些机械功能所需的力已经从肌动蛋白聚合的机械化学模型中推导出来;大多数模型都集中在单个生长的细丝上，只有少数模型通过模拟来解决细丝网络的聚合。在这里，我们提出了一个连续模型的表面生长和丝成核来描述聚合的树突状肌动蛋白网络。该模型描述了宏观应力，应变和细丝密度，而不是专注于个别细丝的增长和弹性。聚合反应的微观过程被归入动力学规律表征的长丝密度的变化和增长表面的传播。这种连续体模型可以预测不同实验中肌动蛋白网络的演化。分析的一个关键结论是，现有的法律有关力的聚合速度的单丝不能预测的反应不断增长的网络。因此，一个新的动力学规律，一致的耗散不等式，提出了捕捉不同负载条件下的树突状肌动蛋白网络的演变。该模型可以扩展到涉及机械应力和聚合动力学之间更复杂的相互作用的其他设置，例如微管、胶原蛋白丝、中间丝和碳纳米管的网络的生长。
英文摘要：
Polymerization of dendritic actin networks underlies important mechanical processes in cell biology such as the protrusion of lamellipodia, propulsion of growth cones in dendrites of neurons, intracellular transport of organelles and pathogens, among others. The forces required for these mechanical functions have been deduced from mechano-chemical models of actin polymerization; most models are focused on single growing filaments, and only a few address polymerization of filament networks through simulations. Here we propose a continuum model of surface growth and filament nucleation to describe polymerization of dendritic actin networks. The model describes growth and elasticity in terms of macroscopic stresses, strains and filament density rather than focusing on individual filaments. The microscopic processes underlying polymerization are subsumed into kinetic laws characterizing the change of filament density and the propagation of growing surfaces. This continuum model can predict the evolution of actin networks in disparate experiments. A key conclusion of the analysis is that existing laws relating force to polymerization speed of single filaments cannot predict the response of growing networks. Therefore a new kinetic law, consistent with the dissipation inequality, is proposed to capture the evolution of dendritic actin networks under different loading conditions. This model may be extended to other settings involving a more complex interplay between mechanical stresses and polymerization kinetics, such as the growth of networks of microtubules, collagen filaments, intermediate filaments and carbon nanotubes.
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