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The drag of a filament moving in a supported spherical bilayer

Published online by Cambridge University Press:  10 January 2024

Wenzheng Shi Open the ORCID record for Wenzheng Shi [Opens in a new window] ,
Moslem Moradi Open the ORCID record for Moslem Moradi [Opens in a new window]  and
Ehssan Nazockdast Open the ORCID record for Ehssan Nazockdast [Opens in a new window]
Wenzheng Shi
Affiliation:
Department of Applied Physical Sciences, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
Moslem Moradi
Affiliation:
Department of Applied Physical Sciences, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
Ehssan Nazockdast*
Affiliation:
Department of Applied Physical Sciences, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
*
†Email address for correspondence: ehssan@email.unc.edu
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Abstract

Many of the cell membrane's vital functions are achieved by the self-organization of the proteins and biopolymers embedded in it. The protein dynamics is in part determined by its drag. A large number of these proteins can polymerize to form filaments. In vitro studies of protein–membrane interactions often involve using rigid beads coated with lipid bilayers, as a model for the cell membrane. Motivated by this, we use slender-body theory to compute the translational and rotational resistance of a single filamentous protein embedded in the outer layer of a supported bilayer membrane and surrounded on the exterior by a Newtonian fluid. We first consider the regime where the two layers are strongly coupled through their inter-leaflet friction. We find that the drag along the parallel direction grows linearly with the filament's length and quadratically with the length for the perpendicular and rotational drag coefficients. These findings are explained using scaling arguments and by analysing the velocity fields around the moving filament. We then present and discuss the qualitative differences between the drag of a filament moving in a freely suspended bilayer and a supported membrane as a function of the membrane's inter-leaflet friction. Finally, we briefly discuss how these findings can be used in experiments to determine membrane rheology. In summary, we present a formulation that allows computation of the effects of membrane properties (its curvature, viscosity and inter-leaflet friction), and the exterior and interior three-dimensional fluids’ depth and viscosity on the drag of a rod-like/filamentous protein, all in a unified theoretical framework.

JFM classification

Biological Fluid Dynamics: Membranes Low-Reynolds-number flows: Slender-body theory Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 979 , 25 January 2024 , A6
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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