Translational diffusion coefficients of membrane protein aggregates in free and supported lipid membranes

TL;DR

This work investigates how hydrodynamic interactions govern the diffusion of membrane protein aggregates on free and supported lipid membranes. By applying Kirkwood-Riseman theory, the authors compute instantaneous diffusion coefficients and introduce hydrodynamic radii that map multi-particle mobility to effective single-particle mobility, revealing data collapse across various aggregate geometries. They further develop a random-interior, outline-based approximation that estimates diffusivity from an aggregate's outline when precise interior particle positions are unavailable. The findings offer a practical framework for analyzing membrane organization and signaling, and highlight avenues to extend the model to include membrane deformations, finite thickness, and lipid composition effects.

Abstract

There is increasing evidence that numerous membrane proteins can assemble into aggregates that modulate their function and affect many cellular processes such as signal transduction and endocytosis. Here, we present a theoretical description of the instantaneous translational diffusion coefficients of transmembrane protein aggregates on free and supported lipid membranes using Kirkwood-Riseman theory. We find that hydrodynamic interactions within protein aggregates must be accounted for, as neglecting them yields several times lower diffusion coefficients. By deriving hydrodynamic radii for free and supported lipid membranes, we identify effective length scales that accurately characterize aggregate diffusivities in the presence of hydrodynamic interactions. These findings motivate the approximation of an aggregate by its outline and a random particle distribution inside it. We show that this approach provides a practical method to accurately determine aggregate diffusion coefficients when the particle locations cannot be resolved. The results presented in this article have immediate implications for the formation and function of membrane protein aggregates.

Figures (6)

• Figure 1: Setups for single particle diffusion (a) and the diffusion of a protein aggregate (b), here drawn as crosslinked, a distance $h$ away from a rigid substrate. We apply KR theory to the aggregate types in (c), where each realization of a self-avoiding random walk (SAW), diffusion-limited aggregation (DLA), diffusion-limited cluster aggregation (DLCA) has $400$ particles and the lattice animal (LA) has $400$ edges (not shown).
• Figure 2: Normalized diffusion coefficients for diffusion-limited aggregation (DLA) with a varying number of particles $N$ at different wall distances $h$. Each marker corresponds to a separate realization of DLA (see Sec. \ref{['app:simDeets']} for simulation details). We find that the diffusion coefficients decay more rapidly with decreasing distances to the wall. Comparison to the case without hydrodynamic interactions between the particles (black full line, $\bm{T}_{ij} = \bm0$) shows a difference of up to two orders of magnitude in the diffusion coefficients, illustrating the importance of accounting for hydrodynamic interactions.
• Figure 3: Diffusion coefficients for each realization of all aggregation types plotted against the radius of gyration defined in Eq. \ref{['eq:Rgdef']} for the SD case in (a) and for the ES case with $h=20~\mathrm{nm}$ and $h=2~\mathrm{nm}$ in (b). In the SD case, $R_\mathrm{g}$ groups the data well with a relatively small spread in the data. However, replacing the particle radius by $R_\mathrm{g}$ in Eq. \ref{['eq:DSD']} ($D_\mathrm{SD}$) yields a poor approximation for large aggregates. In contrast, the fit by Petrov and Schwille petrov2008translational of HPW theory ($D_\mathrm{HPW}$), valid for large particles, provides a good approximation of the data. In the ES case, we observe a significant spread in the data and substituting $R_\mathrm{g}$ in Eq. \ref{['eq:DES']} ($D_\mathrm{ES}$) does not approximate the results well.
• Figure 4: Diffusion coefficients plotted against the hydrodynamic radius for the SD case in (a) and for the small and large radius expansion of the ES case in (b) and (c), respectively. In all cases, we find that the data collapse well onto single curves. The lines in (a)--(c) correspond to the left-hand sides of Eqs. \ref{['eq:RHSD_def']}, \ref{['eq:RHESs']} and \ref{['eq:RHESl']}. Subfigure (d) shows the mean and standard deviation of the errors corresponding to these curves, binned by $R_\mathrm{H}^\mathrm{SD}$ and $R_\mathrm{H}^\mathrm{ES,l}$ across all aggregate types. While the error remains generally below $20\%$ for the SD case, it becomes exceedingly large for large aggregate in the ES case. Note that the legend in (b) also applies to (c).
• Figure 5: Outlines used to approximate an aggregate (blue circles). The buffer (left) describes all points that are within a radius of the original geometry (purple area). Alternatively, we can describe the aggregate by its convex hull (red dashed line) and a buffer around it (purple area).