论文标题
单细丝在流体球形膜中移动的流体动力学
Hydrodynamics of a single filament moving in a fluid spherical membrane
论文作者
论文摘要
细胞膜和其他生物界面中细胞骨架细丝和棒状蛋白的动态组织发生在许多细胞过程中。先前的建模研究考虑了单杆在流体平面膜上的动力学。我们将这些研究扩展到在球形膜上移动的单细丝在生理上相关的情况。具体来说，我们使用苗条的配方来计算在半径$ r $ $ r $和2D粘度$η_m$的膜中移动的单个长度$ l $的翻译和旋转电阻，并在其内部和外部与牛顿式的尼斯卡利亚液体包围，尼斯卡斯式粘度$η^{ - } $η^{ - } $ and $η^$和$η^$}我们首先讨论灯丝曲率最小$κ= 1/r $的情况。我们表明，球形几何形状的界限会产生流量限制效应，这些效应随着丝的长度与膜半径$ l/r $ $的增加而增加强度。这些限制流只会导致细丝沿其轴的电阻轻度增加，$ξ_ {\ Parallel} $及其旋转电阻，$ξ_Ω$。结果，我们对$ξ_\并行$和$ξ_Ω$的预测可以定量地映射到平面膜上的结果。相比之下，我们发现沿垂直方向的阻力，$ξ_\ perp $，随丝的长度而增加，当$ l/r> 1 $而最终$ξ_\ perp \ to \ infty $ AS $ l/r \ as $ l/r \到π$。接下来，我们考虑细丝曲率$κ$对其平行运动的影响，同时固定膜的半径。我们表明，随着其曲率的增加，灯丝周围的流动变得越来越不对称。这些流动不对称会在细丝上诱导净扭矩，并耦合其平行和旋转动力学。随着$ L/R $和$κ$的增加，这种耦合变得更强大。
Dynamic organization of the cytoskeletal filaments and rod-like proteins in the cell membrane and other biological interfaces occurs in many cellular processes. Previous modeling studies have considered the dynamics of a single rod on fluid planar membranes. We extend these studies to the more physiologically relevant case of a single filament moving in a spherical membrane. Specifically, we use a slender-body formulation to compute the translational and rotational resistance of a single filament of length $L$ moving in a membrane of radius $R$ and 2D viscosity $η_m$, and surrounded on its interior and exterior with Newtonian fluids of viscosities $η^{-}$ and $η^{+}$. We first discuss the case where the filament's curvature is at its minimum $κ=1/R$. We show that the boundedness of spherical geometry gives rise to flow confinement effects that increase in strength with increasing the ratio of filament's length to membrane radius $L/R$. These confinement flows only result in a mild increase in filament's resistance along its axis, $ξ_{\parallel}$, and its rotational resistance, $ξ_Ω$. As a result, our predictions of $ξ_\parallel$ and $ξ_Ω$ can be quantitatively mapped to the results on a planar membrane. In contrast, we find that the drag in perpendicular direction, $ξ_\perp$, increases superlinearly with the filament's length, when $L/R >1$ and ultimately $ξ_\perp \to \infty$ as $L/R \to π$. Next, we consider the effect of the filament's curvature, $κ$, on its parallel motion, while fixing the membrane's radius. We show that the flow around the filament becomes increasingly more asymmetric with increasing its curvature. These flow asymmetries induce a net torque on the filament, coupling its parallel and rotational dynamics. This coupling becomes stronger with increasing $L/R$ and $κ$.
