An official website of the United States government
Abstract We investigate the effect of steric and hydrodynamic interactions (HI) on quiescent diffusion and flow‐driven transport of finite‐sized nanoparticles through periodic 2D (two‐dimensional) and 3D (three‐dimensional) nanopost arrays using Stokesian dynamics simulations. We find that steric and HI hinder particle diffusivity under quiescent conditions and enhance longitudinal dispersion under flow. Moreover, the presence of HI leads to a power‐law increase in the longitudinal dispersion coefficient with Pe due to spatial variations in the fluid velocity. Lastly, our simulations reveal that longitudinal particle dispersion coefficients behave similarly in 2D and 3D when HI are included.
more »
« less
The combined hydrodynamic and thermodynamic effects of immobilized proteins on the diffusion of mobile transmembrane proteins
The plasma membranes of cells are thin viscous sheets in which some transmembrane proteins have two-dimensional mobility and some are immobilized. Previous studies have shown that immobile proteins retard the short-time diffusivity of mobile particles through hydrodynamic interactions and that steric effects of immobile proteins reduce the long-time diffusivity in a model that neglects hydrodynamic interactions. We present a rigorous derivation of the long-time diffusivity of a single mobile protein interacting hydrodynamically and thermodynamically with an array of immobile proteins subject to periodic boundary conditions. This method is based on a finite element method (FEM) solution of the probability density of the mobile protein diffusing with a position-dependent mobility determined through a multipole solution of Stokes equations. The simulated long-time diffusivity in square arrays decreases as the spacing in the array approaches the particle size in a manner consistent with a lubrication analysis. In random arrays, steric effects lead to a percolation threshold volume fraction above which long-time diffusion is arrested. The FEM/multipole approach is used to compute the long-time diffusivity far away from this threshold. An approximate analysis of mobile protein diffusion through a network of pores connected by bonds with resistances determined by the FEM/multipole calculations is then used to explore higher immobile area fractions and to evaluate the finite simulation cell size scaling behaviour of diffusion near the percolation threshold. Surprisingly, the ratio of the long-time diffusivity to the spatially averaged short-time diffusivity in these two-dimensional fixed arrays is higher in the presence of hydrodynamic interactions than in their absence. Finally, the implications of this work are discussed, including the possibility of using the methods developed here to investigate more complex diffusive phenomena observed in cell membranes.
more »
« less
- Award ID(s):
- 1803156
- PAR ID:
- 10162407
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 877
- ISSN:
- 0022-1120
- Page Range / eLocation ID:
- 648 to 681
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be attributed to interactions between proteins and membranes. These interactions include protein diffusion and formation of aggregates due to protein–protein interactions in the plane of the membrane. Recently, we developed a model that couples the in-plane flow of lipids and diffusion of proteins with the out-of-plane bending of the membrane. Building on this work, here, we focus on the role of explicit aggregation of proteins on the surface of the membrane in the presence of membrane bending and diffusion. We develop a comprehensive framework that includes lipid flow, membrane bending, the entropy of protein distribution, along with an explicit aggregation potential and derive the governing equations for the coupled system. We compare this framework to the Cahn–Hillard formalism to predict the regimes in which the proteins form patterns on the membrane. We demonstrate the utility of this model using numerical simulations to predict how aggregation and diffusion, when coupled with curvature generation, can alter the landscape of membrane–protein interactions.more » « less
-
The features that stabilize the structures of membrane proteins remain poorly understood. Polar interactions contribute modestly, and the hydrophobic effect contributes little to the energetics of apolar side-chain packing in membranes. Disruption of steric packing can destabilize the native folds of membrane proteins, but is packing alone sufficient to drive folding in lipids? If so, then membrane proteins stabilized by this feature should be readily designed and structurally characterized—yet this has not been achieved. Through simulation of the natural protein phospholamban and redesign of variants, we define a steric packing code underlying its assembly. Synthetic membrane proteins designed using this code and stabilized entirely by apolar side chains conform to the intended fold. Although highly stable, the steric complementarity required for their folding is surprisingly stringent. Structural informatics shows that the designed packing motif recurs across the proteome, emphasizing a prominent role for precise apolar packing in membrane protein folding, stabilization, and evolution.more » « less
-
Recent single-molecule measurements [Schoch et al., Proc. Natl. Acad. Sci. U. S. A. 118, e2113202118 (2021)] have observed dynamic lipid–lipid correlations in membranes with submicrometer spatial resolution and submillisecond temporal resolution. While short from an instrumentation standpoint, these length and time scales remain long compared to microscopic molecular motions. Theoretical expressions are derived to infer experimentally measurable correlations from the two-body diffusion matrix appropriate for membrane-bound bodies coupled by hydrodynamic interactions. The temporal (and associated spatial) averaging resulting from finite acquisition times has the effect of washing out correlations as compared to naive predictions (i.e., the bare elements of the diffusion matrix), which would be expected to hold for instantaneous measurements. The theoretical predictions are shown to be in excellent agreement with Brownian dynamics simulations of experimental measurements. Numerical results suggest that the experimental measurement of membrane protein diffusion, in complement to lipid diffusion measurements, might help to resolve the experimental ambiguities encountered for certain black lipid membranes.more » « less
-
null (Ed.)Autonomous active, elastic filaments that interact with each other to achieve cooperation and synchrony underlie many critical functions in biology. The mechanisms underlying this collective response and the essential ingredients for stable synchronization remain a mystery. Inspired by how these biological entities integrate elasticity with molecular motor activity to generate sustained oscillations, a number of synthetic active filament systems have been developed that mimic oscillations of these biological active filaments. Here, we describe the collective dynamics and stable spatiotemporal patterns that emerge in such biomimetic multi-filament arrays, under conditions where steric interactions may impact or dominate the collective dynamics. To focus on the role of steric interactions, we study the system using Brownian dynamics, without considering long-ranged hydrodynamic interactions. The simulations treat each filament as a connected chain of self-propelling colloids. We demonstrate that short-range steric inter-filament interactions and filament roughness are sufficient – even in the absence of inter-filament hydrodynamic interactions – to generate a rich variety of collective spatiotemporal oscillatory, traveling and static patterns. We first analyze the collective dynamics of two- and three-filament clusters and identify parameter ranges in which steric interactions lead to synchronized oscillations and strongly occluded states. Generalizing these results to large one-dimensional arrays, we find rich emergent behaviors, including traveling metachronal waves, and modulated wavetrains that are controlled by the interplay between the array geometry, filament activity, and filament elasticity. Interestingly, the existence of metachronal waves is non-monotonic with respect to the inter-filament spacing. We also find that the degree of filament roughness significantly affects the dynamics – specifically, filament roughness generates a locking-mechanism that transforms traveling wave patterns into statically stuck and jammed configurations. Taken together, simulations suggest that short-ranged steric inter-filament interactions could combine with complementary hydrodynamic interactions to control the development and regulation of oscillatory collective patterns. Furthermore, roughness and steric interactions may be critical to the development of jammed spatially periodic states; a spatiotemporal feature not observed in purely hydrodynamically interacting systems.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2019.592
