Motion of objects embedded in lipid bilayer membranes: Advection and effective viscosity

Dynamic framework for large-scale modeling of membranes and peripheral proteins

In this chapter, we present a novel computational framework to study the dynamic behavior of extensive membrane systems, potentially in interaction with peripheral proteins, as an alternative to conventional simulation methods. The framework effectively describes the complex dynamics in protein-membrane systems in a mesoscopic particle-based setup. Furthermore, leveraging the hydrodynamic coupling between the membrane and its surrounding solvent, the coarse-grained model grounds its dynamics in macroscopic kinetic properties such as viscosity and diffusion coefficients, marrying the advantages of continuum- and particle-based approaches. We introduce the theoretical background and the parameter-space optimization method in a step-by-step fashion, present the hydrodynamic coupling method in detail, and demonstrate the application of the model at each stage through illuminating examples. We believe this modeling framework to hold great potential for simulating membrane and protein systems at biological spatiotemporal scales, and offer substantial flexibility for further development and parametrization.

Dynamic correlations in lipid bilayer membranes over finite time intervals

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.

A vesicle microrheometer for high-throughput viscosity measurements of lipid and polymer membranes

Viscosity is a key property of cell membranes that controls mobility of embedded proteins and membrane remodeling. Measuring it is challenging because existing approaches involve complex experimental designs and/or models, and the applicability of some methods is limited to specific systems and membrane compositions. As a result there is scarcity of systematic data, and the reported values for membrane viscosity vary by orders of magnitude for the same system. Here, we show how viscosity of membranes can be easily obtained from the transient deformation of giant unilamellar vesicles. The approach enables a noninvasive, probe-independent, and high-throughput measurement of the viscosity of membranes made of lipids or polymers with a wide range of compositions and phase state. Using this novel method, we have collected a significant amount of data that provides insights into the relation between membrane viscosity, composition, and structure.

Active gels, heavy tails, and the cytoskeleton

The eukaryotic cell's cytoskeleton is a prototypical example of an active material: objects embedded within it are driven by molecular motors acting on the cytoskeleton, leading to anomalous diffusive behavior. Experiments tracking the behavior of cell-attached objects have observed anomalous diffusion with a distribution of displacements that is non-Gaussian, with heavy tails. This has been attributed to "cytoquakes" or other spatially extended collective effects. We show, using simulations and analytical theory, that a simple continuum active gel model driven by fluctuating force dipoles naturally creates heavy power-law tails in cytoskeletal displacements. We predict that this power law exponent should depend on the geometry and dimensionality of where force dipoles are distributed through the cell; we find qualitatively different results for force dipoles in a 3D cytoskeleton and a quasi-two-dimensional cortex. We then discuss potential applications of this model both in cells and in synthetic active gels.

Hydrodynamic coupling for particle-based solvent-free membrane models

The great challenge with biological membrane systems is the wide range of scales involved, from nanometers and picoseconds for individual lipids to the micrometers and beyond millisecond for cellular signaling processes. While solvent-free coarse-grained membrane models are convenient for large-scale simulations and promising to provide insight into slow processes involving membranes, these models usually have unrealistic kinetics. One major obstacle is the lack of an equally convenient way of introducing hydrodynamic coupling without significantly increasing the computational cost of the model. To address this, we introduce a framework based on anisotropic Langevin dynamics, for which major in-plane and out-of-plane hydrodynamic effects are modeled via friction and diffusion tensors from analytical or semi-analytical solutions to Stokes hydrodynamic equations. Using this framework, in conjunction with our recently developed membrane model, we obtain accurate dispersion relations for planar membrane patches, both free-standing and in the vicinity of a wall. We briefly discuss how non-equilibrium dynamics is affected by hydrodynamic interactions. We also measure the surface viscosity of the model membrane and discuss the affecting dissipative mechanisms.

Cell patterning by secretion-induced plasma membrane flows

Cells self-organize using reaction-diffusion and fluid-flow principles. Whether bulk membrane flows contribute to cell patterning has not been established. Here, using mathematical modeling, optogenetics, and synthetic probes, we show that polarized exocytosis causes lateral membrane flows away from regions of membrane insertion. Plasma membrane–associated proteins with sufficiently low diffusion and/or detachment rates couple to the flows and deplete from areas of exocytosis. In rod-shaped fission yeast cells, zones of Cdc42 GTPase activity driving polarized exocytosis are limited by GTPase activating proteins (GAPs). We show that membrane flows pattern the GAP Rga4 distribution and that coupling of a synthetic GAP to membrane flows is sufficient to establish the rod shape. Thus, membrane flows induced by Cdc42-dependent exocytosis form a negative feedback restricting the zone of Cdc42 activity.

Rapid statistical discrimination of fluorescence images of T cell receptors on immobilizing surfaces with different coating conditions

The spatial organization of T cell receptors (TCRs) correlates with membrane-associated signal amplification, dispersion, and regulation during T cell activation. Despite its potential clinical importance, quantitative analysis of the spatial arrangement of TCRs from standard fluorescence images remains difficult. Here, we report Statistical Classification Analyses of Membrane Protein Images or SCAMPI as a technique capable of analyzing the spatial arrangement of TCRs on the plasma membrane of T cells. We leveraged medical image analysis techniques that utilize pixel-based values. We transformed grayscale pixel values from fluorescence images of TCRs into estimated model parameters of partial differential equations. The estimated model parameters enabled an accurate classification using linear discrimination techniques, including Fisher Linear Discriminant (FLD) and Logistic Regression (LR). In a proof-of-principle study, we modeled and discriminated images of fluorescently tagged TCRs from Jurkat T cells on uncoated cover glass surfaces (Null) or coated cover glass surfaces with either positively charged poly-L-lysine (PLL) or TCR cross-linking anti-CD3 antibodies (OKT3). Using 80 training images and 20 test images per class, our statistical technique achieved 85% discrimination accuracy for both OKT3 versus PLL and OKT3 versus Null conditions. The run time of image data download, model construction, and image discrimination was 21.89 s on a laptop computer, comprised of 20.43 s for image data download, 1.30 s on the FLD-SCAMPI analysis, and 0.16 s on the LR-SCAMPI analysis. SCAMPI represents an alternative approach to morphology-based qualifications for discriminating complex patterns of membrane proteins conditioned on a small sample size and fast runtime. The technique paves pathways to characterize various physiological and pathological conditions using the spatial organization of TCRs from patient T cells.

Anisotropic diffusion of membrane proteins at experimental timescales

Single-particle tracking (SPT) experiments of lipids and membrane proteins provide a wealth of information about the properties of biomembranes. Careful analysis of SPT trajectories can reveal deviations from ideal Brownian behavior. Among others, this includes confinement effects and anomalous diffusion, which are manifestations of both the nanoscale structure of the underlying membrane and the structure of the diffuser. With the rapid increase in temporal and spatial resolution of experimental methods, a new aspect of the motion of the particle, namely, anisotropic diffusion, might become relevant. This aspect that so far received only little attention is the anisotropy of the diffusive motion and may soon provide an additional proxy to the structure and topology of biomembranes. Unfortunately, the theoretical framework for detecting and interpreting anisotropy effects is currently scattered and incomplete. Here, we provide a computational method to evaluate the degree of anisotropy directly from molecular dynamics simulations and also point out a way to compare the obtained results with those available from SPT experiments. In order to probe the effects of anisotropic diffusion, we performed coarse-grained molecular dynamics simulations of peripheral and integral membrane proteins in flat and curved bilayers. In agreement with the theoretical basis, our computational results indicate that anisotropy can persist up to the rotational relaxation time [τ=(2D_r)^-1], after which isotropic diffusion is observed. Moreover, the underlying topology of the membrane bilayer can couple with the geometry of the particle, thus extending the spatiotemporal domain over which this type of motion can be detected.