Sadhu Raj Kumar, Chatterjee Sakuntala
Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India.
Phys Rev E. 2018 Mar;97(3-1):032408. doi: 10.1103/PhysRevE.97.032408.
We study the force generation by a set of parallel actin filaments growing against an elastic membrane. The elastic membrane tries to stay flat and any deformation from this flat state, either caused by thermal fluctuations or due to protrusive polymerization force exerted by the filaments, costs energy. We study two lattice models to describe the membrane dynamics. In one case, the energy cost is assumed to be proportional to the absolute magnitude of the height gradient (gradient model) and in the other case it is proportional to the square of the height gradient (Gaussian model). For the gradient model we find that the membrane velocity is a nonmonotonic function of the elastic constant μ and reaches a peak at μ=μ^{}. For μ<μ^{} the system fails to reach a steady state and the membrane energy keeps increasing with time. For the Gaussian model, the system always reaches a steady state and the membrane velocity decreases monotonically with the elastic constant ν for all nonzero values of ν. Multiple filaments give rise to protrusions at different regions of the membrane and the elasticity of the membrane induces an effective attraction between the two protrusions in the Gaussian model which causes the protrusions to merge and a single wide protrusion is present in the system. In both the models, the relative time scale between the membrane and filament dynamics plays an important role in deciding whether the shape of elasticity-velocity curve is concave or convex. Our numerical simulations agree reasonably well with our analytical calculations.
我们研究了一组平行肌动蛋白丝对抗弹性膜生长时产生的力。弹性膜试图保持平坦，任何偏离这种平坦状态的变形，无论是由热涨落引起的，还是由丝施加的突出聚合力引起的，都会消耗能量。我们研究了两种晶格模型来描述膜动力学。在一种情况下，能量消耗被假定与高度梯度的绝对值成正比（梯度模型），在另一种情况下，它与高度梯度的平方成正比（高斯模型）。对于梯度模型，我们发现膜速度是弹性常数μ的非单调函数，并且在μ = μ时达到峰值。当μ < μ时，系统无法达到稳态，膜能量随时间不断增加。对于高斯模型，对于所有非零的ν值，系统总是能达到稳态，并且膜速度随弹性常数ν单调递减。多根丝在膜的不同区域产生突出，并且在高斯模型中膜的弹性在两个突出之间诱导出有效吸引力，这导致突出合并，系统中出现单个宽突出。在这两种模型中，膜和丝动力学之间的相对时间尺度在决定弹性 - 速度曲线的形状是凹还是凸方面起着重要作用。我们的数值模拟与我们的解析计算相当吻合。
