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  1. 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 ηm, and surrounded on its interior and exterior with Newtonian fluids of viscosities η−more »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∥, and its rotational resistance, ξΩ. As a result, our predictions of ξ∥ and ξΩ can be quantitatively mapped to the results on a planar membrane. In contrast, we find that the drag in perpendicular direction, ξ⊥, increases superlinearly with the filament's length, when L/R>1 and ultimately ξ⊥→∞ as L/R→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.« less
    Free, publicly-accessible full text available January 1, 2023
  2. Mechanical properties of cellular structures, including the cell cytoskeleton, are increasingly used as biomarkers for disease diagnosis and fundamental studies in cell biology. Recent experiments suggest that the cell cytoskeleton and its permeating cytosol, can be described as a poroelastic (PE) material. Biot theory is the standard model used to describe PE materials. Yet, this theory does not account for the fluid viscous stress, which can lead to inaccurate predictions of the mechanics in the dilute filamentous network of the cytoskeleton. Here, we adopt a two-phase model that extends Biot theory by including the fluid viscous stresses in the fluid'smore »momentum equation. We use generalized linear viscoelastic (VE) constitutive equations to describe the permeating fluid and the network stresses and assume a constant friction coefficient that couples the fluid and network displacement fields. As the first step in developing a computational framework for solving the resulting equations, we derive closed-form general solutions of the fluid and network displacement fields in spherical coordinates. To demonstrate the applicability of our results, we study the motion of a rigid sphere moving under a constant force inside a PE medium, composed of a linear elastic network and a Newtonian fluid. We find that the network compressibility introduces a slow relaxation of the sphere and a non-monotonic network displacements with time along the direction of the applied force. These novel features cannot be predicted if VE constitutive equation is used for the medium. We show that our results can be applied to particle-tracking microrheology to differentiate between PE and VE materials and to independently measure the permeability and VE properties of the fluid and the network phases.« less
    Free, publicly-accessible full text available October 1, 2022