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.

中文翻译：

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树突肌动蛋白网络生长的连续模型

树突肌动蛋白网络的聚合是细胞生物学中重要机械过程的基础，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是从肌动蛋白聚合的机械化学模型中推导出来的。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解决了细丝网络的聚合。在这里，我们提出了一个表面生长和细丝成核的连续模型来描述树突肌动蛋白网络的聚合。该模型根据宏观应力、应变和细丝密度来描述生长和弹性，而不是关注单个细丝。聚合背后的微观过程被归入表征长丝密度变化和生长表面传播的动力学定律中。这种连续模型可以预测不同实验中肌动蛋白网络的演变。分析的一个关键结论是，现有的将力与单丝聚合速度相关的定律无法预测增长网络的响应。因此，提出了一种与耗散不等式一致的新动力学定律来捕捉不同负载条件下树突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相互作用的其他设置，例如微管、胶原丝、中间丝和碳纳米管网络的生长。