Diffusion of Integral Membrane Proteins in Protein-Rich Membranes

Self-diffusion is temperature independent on active membranes

Molecular transport maintains cellular structures and functions. For example, lipid and protein diffusion sculpts the dynamic shapes and structures on the cell membrane that perform essential cellular functions, such as cell signaling. Temperature variations in thermal equilibrium rapidly change molecular transport properties. The coefficient of lipid self-diffusion increases exponentially with temperature in thermal equilibrium, for example. Hence, maintaining cellular homeostasis through molecular transport is hard in thermal equilibrium in the noisy cellular environment, where temperatures can fluctuate widely due to local heat generation. In this paper, using both molecular and lattice-based modeling of membrane transport, we show that the presence of active transport originating from the cell's cytoskeleton can make the self-diffusion of the molecules on the membrane robust to temperature fluctuations. The resultant temperature-independence of self-diffusion keeps the precision of cellular signaling invariant over a broad range of ambient temperatures, allowing cells to make robust decisions. We have also found that the Kawasaki algorithm, the widely used model of lipid transport on lattices, predicts incorrect temperature dependence of lipid self-diffusion in equilibrium. We propose a new algorithm that correctly captures the equilibrium properties of lipid self-diffusion and reproduces experimental observations.

Detection and quantification of Na,K-ATPase dimers in the plasma membrane of living cells by FRET-FCS

The sodium potassium pump, Na,K-ATPase (NKA), is an integral plasma membrane protein, expressed in all eukaryotic cells. It is responsible for maintaining the transmembrane Na+ gradient and is the major determinant of the membrane potential. Self-interaction and oligomerization of NKA in cell membranes has been proposed and discussed but is still an open question. Here, we have used a combination of FRET and Fluorescence Correlation Spectroscopy, FRET-FCS, to analyze NKA in the plasma membrane of living cells. Click chemistry was used to conjugate the fluorescent labels Alexa 488 and Alexa 647 to non-canonical amino acids introduced in the NKA α1 and β1 subunits. We demonstrate that FRET-FCS can detect an order of magnitude lower concentration of green-red labeled protein pairs in a single-labeled red and green background than what is possible with cross-correlation (FCCS). We show that a significant fraction of NKA is expressed as a dimer in the plasma membrane. We also introduce a method to estimate not only the number of single and double labeled NKA, but the number of unlabeled, endogenous NKA and estimate the density of endogenous NKA at the plasma membrane to 1400 ± 800 enzymes/μm2.

Nanoporous Membranes of Densely Packed Carbon Nanotubes Formed by Lipid-Mediated Self-Assembly

Nanofiltration technology faces the competing challenges of achieving high fluid flux through uniformly narrow pores of a mechanically and chemically stable filter. Supported dense-packed 2D-crystals of single-walled carbon nanotube (CNT) porins with ∼1 nm wide pores could, in principle, meet these challenges. However, such CNT membranes cannot currently be synthesized at high pore density. Here, we use computer simulations to explore lipid-mediated self-assembly as a route toward densely packed CNT membranes, motivated by the analogy to membrane-protein 2D crystallization. In large-scale coarse-grained molecular dynamics (MD) simulations, we find that CNTs in lipid membranes readily self-assemble into large clusters. Lipids trapped between the CNTs lubricate CNT repacking upon collisions of diffusing clusters, thereby facilitating the formation of large ordered structures. Cluster diffusion follows the Saffman-Delbrück law and its generalization by Hughes, Pailthorpe, and White. On longer time scales, we expect the formation of close-packed CNT structures by depletion of the intervening shared annular lipid shell, depending on the relative strength of CNT-CNT and CNT-lipid interactions. Our simulations identify CNT length, diameter, and end functionalization as major factors for the self-assembly of CNT membranes.

Cholesterol Depletion and Membrane Deformation by MeβCD and the Resultant Enhanced T Cell Killing

Recent studies have demonstrated the crucial role of cholesterol (Chol) in regulating the mechanical properties and biological functions of cell membranes. Methyl-β-cyclodextrin (MeβCD) is commonly utilized to modulate the Chol content in cell membranes, but there remains a lack of a comprehensive understanding. In this study, using a range of different techniques, we find that the optimal ratio of MeβCD to Chol for complete removal of Chol from a phosphocholine (PC)/Chol mixed membrane with a 1:1 mol ratio is 4.5:1, while the critical MeβCD-to-Chol ratio for membrane permeation falls within the range between 1.5 and 2.4. MeβCD at elevated concentrations induces the formation of fibrils or tubes from a PC membrane. Single lipid tracking reveals that removing Chol restores the diffusion of lipid molecules in the PC/Chol membrane to levels observed in pure PC membranes. Exposure to 5 mM MeβCD for 30 min effectively eliminates Chol from various cell lines, leading to an up to 8-fold enhancement in melittin cytotoxicity over Hela cells and an up to 3.5-fold augmentation of T cell cytotoxicity against B16F10-OVA cells. This study presents a diagram that delineates the concentration- and time-dependent distribution of MeβCD-induced Chol depletion and membrane deformation, which holds significant potential for modulating the mechanical properties of cellular membranes in prospective biomedical applications.

Effects of crowding on the diffusivity of membrane adhered particles

The lateral diffusion of cell membrane inclusions, such as integral membrane proteins and bound receptors, drives critical biological processes, including the formation of complexes, cell-cell signaling, and membrane trafficking. These diffusive processes are complicated by how concentrated, or "crowded", the inclusions are, which can occupy between 30-50% of the area fraction of the membrane. In this work, we elucidate the effects of increasing concentration of model membrane inclusions in a free-standing artificial cell membrane on inclusion diffusivity and the apparent viscosity of the membrane. By multiple particle tracking of fluorescent microparticles covalently tethered to the bilayer, we show the transition from expected Brownian dynamics, which accurately measure the membrane viscosity, to subdiffusive behavior with decreased diffusion coefficient as the particle area fraction increases from 1% to around 30%, approaching physiological levels of crowding. At high crowding, the onset of non-Gaussian behavior is observed. Using hydrodynamic models relating the 2D diffusion coefficient to the viscosity of a membrane, we determine the apparent viscosity of the bilayer from the particle diffusivity and show an increase in the apparent membrane viscosity with increasing particle area fraction. However, the scaling of this increase is in contrast with the behavior of monolayer inclusion diffusion and bulk suspension rheology. These results demonstrate that physiological levels of model membrane crowding nontrivially alter the dynamics and apparent viscosity of the system, which has implications for understanding membrane protein interactions and particle-membrane transport processes.

Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories

Single-particle traces of the diffusive motion of molecules, cells, or animals are by now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics is vital in understanding the observed systems. Typically, the task is to decipher the exact type of diffusion and/or to determine the system parameters. The tools used in this endeavor are currently being revolutionized by modern machine-learning techniques. In this Perspective we provide an overview of recently introduced methods in machine-learning for diffusive time series, most notably, those successfully competing in the anomalous diffusion challenge. As such methods are often criticized for their lack of interpretability, we focus on means to include uncertainty estimates and feature-based approaches, both improving interpretability and providing concrete insight into the learning process of the machine. We expand the discussion by examining predictions on different out-of-distribution data. We also comment on expected future developments.

Transition between Different Diffusion Modes of Individual Lipids during the Membrane-Specific Action of As-CATH4 Peptides

The cell membrane permeabilization ability of immune defense antimicrobial peptides (AMPs) is widely applied in biomedicine. Although the mechanisms of peptide-membrane interactions have been widely investigated, analyses at the molecular level are still lacking. Herein, the membrane-specific action of a native AMP, As-CATH4, is investigated using a single-lipid tracking method in combination with live cell and model membrane assays conducted at different scales. The peptide-membrane interaction process is characterized by analyzing single-lipid diffusion behaviors. As-CATH4 exhibits potent antimicrobial activity through bacterial membrane permeabilization, with moderate cytotoxicity against mammalian cells. In-plane diffusion analyses of individual lipids show that the lipid molecules exhibit non-Gaussian and heterogeneous diffusion behaviors in both pristine and peptide-treated membranes, which can be decomposed into two Gaussian subgroups corresponding to normal- and slow-diffusive lipids. Assessment of the temporal evolution of these two diffusion modes of lipids reveal that the peptide action states of As-CATH4 include surface binding, transmembrane defect formation, and dynamic equilibrium. The action mechanisms of As-CATH4 at varying concentrations and against different membranes are distinguished. This work resolves the simultaneous mixed diffusion mechanisms of single lipids in biomimetic cell membranes, especially during dynamic membrane permeabilization by AMPs.

Heterogeneous biological membranes regulate protein partitioning via fluctuating diffusivity

Cell membranes phase separate into ordered L o and disordered L d domains depending on their compositions. This membrane compartmentalization is heterogeneous and regulates the localization of specific proteins related to cell signaling and trafficking. However, it is unclear how the heterogeneity of the membranes affects the diffusion and localization of proteins in L o and L d domains. Here, using Langevin dynamics simulations coupled with the phase-field (LDPF) method, we investigate several tens of milliseconds-scale diffusion and localization of proteins in heterogeneous biological membrane models showing phase separation into L o and L d domains. The diffusivity of proteins exhibits temporal fluctuations depending on the field composition. Increases in molecular concentrations and domain preference of the molecule induce subdiffusive behavior due to molecular collisions by crowding and confinement effects, respectively. Moreover, we quantitatively demonstrate that the protein partitioning into the L o domain is determined by the difference in molecular diffusivity between domains, molecular preference of domain, and molecular concentration. These results pave the way for understanding how biological reactions caused by molecular partitioning may be controlled in heterogeneous media. Moreover, the methodology proposed here is applicable not only to biological membrane systems but also to the study of diffusion and localization phenomena of molecules in various heterogeneous systems.

Implications of different membrane compartmentalization models in particle-based in silico studies

Studying membrane dynamics is important to understand the cellular response to environmental stimuli. A decisive spatial characteristic of the plasma membrane is its compartmental structure created by the actin-based membrane-skeleton (fences) and anchored transmembrane proteins (pickets). Particle-based reaction-diffusion simulation of the membrane offers a suitable temporal and spatial resolution to analyse its spatially heterogeneous and stochastic dynamics. Fences have been modelled via hop probabilities, potentials or explicit picket fences. Our study analyses the different approaches' constraints and their impact on simulation results and performance. Each of the methods comes with its own constraints; the picket fences require small timesteps, potential fences might induce a bias in diffusion in crowded systems, and probabilistic fences, in addition to carefully scaling the probability with the timesteps, induce higher computational costs for each propagation step.

Non-Gaussian Diffusion of Individual Lipids Unveils the Unique Peptide-Membrane Interaction Dynamics

The dynamics of protein (or peptide)-membrane interactions plays a central role in cellular functions; however, the underlying mechanisms remain unclear. Herein, through analyzing the diffusion of individual lipids in a bilayer membrane during the membrane actions of typical peptides (e.g., pore-forming peptide melittin and cell-penetrating peptide TAT) at varying concentrations, the spatial heterogeneity as well as temporal dynamics of lipid motions were investigated which showed close correlation with the peptide action mechanism. Specifically, the spatial heterogeneity of lipid diffusion was characterized by the non-Gaussianity of lipid trajectories, which was further decomposed into two basic diffusion modes; moreover, the temporal evolution of the Gaussian fitting parameters provided quantitative information on the varying metastable interaction states between peptides and the membrane (e.g., peptide landing, membrane insertion, and equilibrium). Generally, this work gives an insight into the correlation between single-lipid diffusion and function-realization of membrane-active peptides.

Extracting, quantifying, and comparing dynamical and biomechanical properties of living matter through single particle tracking

A panoply of new tools for tracking single particles and molecules has led to an explosion of experimental data, leading to novel insights into physical properties of living matter governing cellular development and function, health and disease. In this Perspective, we present tools to investigate the dynamics and mechanics of living systems from the molecular to cellular scale via single-particle techniques. In particular, we focus on methods to measure, interpret, and analyse complex data sets that are associated with forces, materials properties, transport, and emergent organisation phenomena within biological and soft-matter systems. Current approaches, challenges, and existing solutions in the associated fields are outlined in order to support the growing community of researchers at the interface of physics and the life sciences. Each section focuses not only on the general physical principles and the potential for understanding living matter, but also on details of practical data extraction and analysis, discussing limitations, interpretation, and comparison across different experimental realisations and theoretical frameworks. Particularly relevant results are introduced as examples. While this Perspective describes living matter from a physical perspective, highlighting experimental and theoretical physics techniques relevant for such systems, it is also meant to serve as a solid starting point for researchers in the life sciences interested in the implementation of biophysical methods.

First-passage times in conical varying-width channels biased by a transverse gravitational force: Comparison of analytical and numerical results

We study the crossing time statistic of diffusing point particles between the two ends of expanding and narrowing two-dimensional conical channels under a transverse external gravitational field. The theoretical expression for the mean first-passage time for such a system is derived under the assumption that the axial diffusion in a two-dimensional channel of smoothly varying geometry can be approximately described as a one-dimensional diffusion in an entropic potential with position-dependent effective diffusivity in terms of the modified Fick-Jacobs equation. We analyze the channel crossing dynamics in terms of the mean first-passage time, combining our analytical results with extensive two-dimensional Brownian dynamics simulations, allowing us to find the range of applicability of the one-dimensional approximation. We find that the effective particle diffusivity decreases with increasing amplitude of the external potential. Remarkably, the mean first-passage time for crossing the channel is shown to assume a minimum at finite values of the potential amplitude.

Heterogeneous Nanostructures Cause Anomalous Diffusion in Lipid Monolayers

The diffusion and mobility in biomembranes are crucial for various cell functions; however, the mechanisms involved in such processes remain ambiguous due to the complex membrane structures. Herein, we investigate how the heterogeneous nanostructures cause anomalous diffusion in dipalmitoylphosphatidylcholine (DPPC) monolayers. By identifying the existence of condensed nanodomains and clarifying their impact, our findings renew the understanding of the hydrodynamic description and the statistical feature of the diffusion in the monolayers. We find a universal characteristic of the multistage mean square displacement (MSD) with an intermediate crossover, signifying two membrane viscosities at different scales: the short-time scale describes the local fluidity and is independent of the nominal DPPC density, and the long-time scale represents the global continuous phase taking into account nanodomains and increases with DPPC density. The constant short-time viscosity reflects a dynamic equilibrium between the continuous fluid phase and the condensed nanodomains in the molecular scale. Notably, we observe an "anomalous yet Brownian" phenomenon exhibiting an unusual double-peaked displacement probability distribution (DPD), which is attributed to the net dipolar repulsive force from the heterogeneous nanodomains around the microdomains. The findings provide physical insights into the transport of membrane inclusions that underpin various biological functions and drug deliveries.

NEU1 and NEU3 enzymes alter CD22 organization on B cells

The B cell membrane expresses sialic-acid-binding immunoglobulin-like lectins, also called Siglecs, that are important for modulating immune response. Siglecs have interactions with sialoglycoproteins found on the same membrane (cis-ligands) that result in homotypic and heterotypic receptor clusters. The regulation and organization of these clusters, and their effect on cell activation, is not clearly understood. We investigated the role of human neuraminidase enzymes NEU1 and NEU3 on the clustering of CD22 on B cells using confocal microscopy. We observed that native NEU1 and NEU3 activity influence the cluster size of CD22. Using single-particle tracking, we observed that NEU3 activity increased the lateral mobility of CD22, which was in contrast to the effect of exogenous bacterial NEU enzymes. Moreover, we show that native NEU1 and NEU3 activity influenced cellular Ca²⁺ levels, supporting a role for these enzymes in regulating B cell activation. Our results establish a role for native NEU activity in modulating CD22 organization and function on B cells.

Seipin transmembrane segments critically function in triglyceride nucleation and lipid droplet budding from the membrane

Lipid droplets (LDs) are organelles formed in the endoplasmic reticulum (ER) to store triacylglycerol (TG) and sterol esters. The ER protein seipin is key for LD biogenesis. Seipin forms a cage-like structure, with each seipin monomer containing a conserved hydrophobic helix and two transmembrane (TM) segments. How the different parts of seipin function in TG nucleation and LD budding is poorly understood. Here, we utilized molecular dynamics simulations of human seipin, along with cell-based experiments, to study seipin’s functions in protein–lipid interactions, lipid diffusion, and LD maturation. An all-atom simulation indicates that seipin TM segment residues and hydrophobic helices residues located in the phospholipid tail region of the bilayer attract TG. Simulating larger, growing LDs with coarse-grained models, we find that the seipin TM segments form a constricted neck structure to facilitate conversion of a flat oil lens into a budding LD. Using cell experiments and simulations, we also show that conserved, positively charged residues at the end of seipin’s TM segments affect LD maturation. We propose a model in which seipin TM segments critically function in TG nucleation and LD growth.

Simulation of receptor triggering by kinetic segregation shows role of oligomers and close-contacts

The activation of T cells, key players of the immune system, involves local evacuation of phosphatase CD45 from a region of the T cell's surface, segregating it from the T cell receptor. What drives this evacuation? In the presence of antigen, what ensures evacuation happens in the subsecond timescales necessary to initiate signaling? In the absence of antigen, what mechanisms ensure that evacuation does not happen spontaneously, which could cause signaling errors? Phenomena known to influence spatial organization of CD45 or similar surface molecules include diffusive motion in the lipid bilayer, oligomerization reactions, and mechanical compression against a nearby surface, such as that of the cell presenting the antigen. Computer simulations can investigate hypothesized spatiotemporal mechanisms of T cell signaling. The challenge to computational studies of evacuation is that the base process, spontaneous evacuation by simple diffusion, is in the extreme rare event limit, meaning direct stochastic simulation is unfeasible. Here, we combine particle-based spatial stochastic simulation with the weighted ensemble method for rare events to compute the mean first passage time for cell surface availability by surface reorganization of CD45. We confirm mathematical estimates that, at physiological concentrations, spontaneous evacuation is extremely rare, roughly 300 years. We find that dimerization decreases the time required for evacuation. A weak bimolecular interaction (dissociation constant estimate 460 μM) is sufficient for an order of magnitude reduction of spontaneous evacuation times, and oligomerization to hexamers reduces times to below 1 s. This introduces a mechanism whereby externally induced CD45 oligomerization could significantly modify T cell function. For large regions of close contact, such as those induced by large microvilli, molecular size and compressibility imply a nonzero reentry probability of 60%, decreasing evacuation times. Simulations show that these reduced evacuation times are still unrealistically long (even with a fourfold variation centered around previous estimates of parameters), suggesting that a yet-to-be-described mechanism, besides compressional exclusion at a close contact, drives evacuation.

Assembly and Analysis of Cell-Scale Membrane Envelopes

The march toward exascale computing will enable routine molecular simulation of larger and more complex systems, for example, simulation of entire viral particles, on the scale of approximately billions of atoms─a simulation size commensurate with a small bacterial cell. Anticipating the future hardware capabilities that will enable this type of research and paralleling advances in experimental structural biology, efforts are currently underway to develop software tools, procedures, and workflows for constructing cell-scale structures. Herein, we describe our efforts in developing and implementing an efficient and robust workflow for construction of cell-scale membrane envelopes and embedding membrane proteins into them. A new approach for construction of massive membrane structures that are stable during the simulations is built on implementing a subtractive assembly technique coupled with the development of a structure concatenation tool (fastmerge), which eliminates overlapping elements based on volumetric criteria rather than adding successive molecules to the simulation system. Using this approach, we have constructed two "protocells" consisting of MARTINI coarse-grained beads to represent cellular membranes, one the size of a cellular organelle and another the size of a small bacterial cell. The membrane envelopes constructed here remain whole during the molecular dynamics simulations performed and exhibit water flux only through specific proteins, demonstrating the success of our methodology in creating tight cell-like membrane compartments. Extended simulations of these cell-scale structures highlight the propensity for nonspecific interactions between adjacent membrane proteins leading to the formation of protein microclusters on the cell surface, an insight uniquely enabled by the scale of the simulations. We anticipate that the experiences and best practices presented here will form the basis for the next generation of cell-scale models, which will begin to address the addition of soluble proteins, nucleic acids, and small molecules essential to the function of a cell.

The interplay between membrane topology and mechanical forces in regulating T cell receptor activity

T cells are critically important for host defense against infections. T cell activation is specific because signal initiation requires T cell receptor (TCR) recognition of foreign antigen peptides presented by major histocompatibility complexes (pMHC) on antigen presenting cells (APCs). Recent advances reveal that the TCR acts as a mechanoreceptor, but it remains unclear how pMHC/TCR engagement generates mechanical forces that are converted to intracellular signals. Here we propose a TCR Bending Mechanosignal (TBM) model, in which local bending of the T cell membrane on the nanometer scale allows sustained contact of relatively small pMHC/TCR complexes interspersed among large surface receptors and adhesion molecules on the opposing surfaces of T cells and APCs. Localized T cell membrane bending is suggested to increase accessibility of TCR signaling domains to phosphorylation, facilitate selective recognition of agonists that form catch bonds, and reduce noise signals associated with slip bonds.

Subdiffusive-Brownian crossover in membrane proteins: a generalized Langevin equation-based approach

In this work, we propose a generalized Langevin equation-based model to describe the lateral diffusion of a protein in a lipid bilayer. The memory kernel is represented in terms of a viscous (instantaneous) and an elastic (noninstantaneous) component modeled through a Dirac δ function and a three-parameter Mittag-Leffler type function, respectively. By imposing a specific relationship between the parameters of the three-parameter Mittag-Leffler function, the different dynamical regimes-namely ballistic, subdiffusive, and Brownian, as well as the crossover from one regime to another-are retrieved. Within this approach, the transition time from the ballistic to the subdiffusive regime and the spectrum of relaxation times underlying the transition from the subdiffusive to the Brownian regime are given. The reliability of the model is tested by comparing the mean-square displacement derived in the framework of this model and the mean-square displacement of a protein diffusing in a membrane calculated through molecular dynamics simulations.

Optimizing purification of the peripheral membrane protein FAM92A1 fused to a modified spidroin tag

Cryo-electron microscopy has revolutionized structural biology. In particular structures of proteins at the membrane interface have been a major contribution of cryoEM. Yet, visualization and characterization of peripheral membrane proteins remains challenging; mostly because there is no unified purification strategy for these proteins. FAM92A1 is a novel peripheral membrane protein that binds to the mitochondrial inner membrane. There, FAM92A1 dimers bind to the membrane and play an essential role in regulating the mitochondrial ultrastructure. Curiously, FAM92A1 has also an important function in ciliogenesis. FAM92A1 is part of the membrane bending Bin1/Amphiphsyin/RVS (BAR) domain protein family. Currently, there is no structure of FAM92A1, mostly because FAM92A1 is unstable and insoluble at high concentrations, like many BAR domain proteins. Yet, pure and concentrated protein is a necessity for screening to generate samples suitable for structure determination. Here, we present an optimized purification and expression strategy for dimeric FAM92A1. To our knowledge, we are the first to use the spidroin tag NT* to successfully purify a peripheral membrane protein. Our results show that NT* not only increases solubility but stabilizes FAM92A1 as a dimer. FAM92A1 fused to NT* is active because it is able to efficiently bend membranes. Taken together, our strategy indicates that this is a possible avenue to express and purify other challenging BAR domain proteins.

Pore Forming Protein Induced Biomembrane Reorganization and Dynamics: A Focused Review

Pore forming proteins are a broad class of pathogenic proteins secreted by organisms as virulence factors due to their ability to form pores on the target cell membrane. Bacterial pore forming toxins (PFTs) belong to a subclass of pore forming proteins widely implicated in bacterial infections. Although the action of PFTs on target cells have been widely investigated, the underlying membrane response of lipids during membrane binding and pore formation has received less attention. With the advent of superresolution microscopy as well as the ability to carry out molecular dynamics (MD) simulations of the large protein membrane assemblies, novel microscopic insights on the pore forming mechanism have emerged over the last decade. In this review, we focus primarily on results collated in our laboratory which probe dynamic lipid reorganization induced in the plasma membrane during various stages of pore formation by two archetypal bacterial PFTs, cytolysin A (ClyA), an α-toxin and listeriolysin O (LLO), a β-toxin. The extent of lipid perturbation is dependent on both the secondary structure of the membrane inserted motifs of pore complex as well as the topological variations of the pore complex. Using confocal and superresolution stimulated emission depletion (STED) fluorescence correlation spectroscopy (FCS) and MD simulations, lipid diffusion, cholesterol reorganization and deviations from Brownian diffusion are correlated with the oligomeric state of the membrane bound protein as well as the underlying membrane composition. Deviations from free diffusion are typically observed at length scales below ∼130 nm to reveal the presence of local dynamical heterogeneities that emerge at the nanoscale-driven in part by preferential protein binding to cholesterol and domains present in the lipid membrane. Interrogating the lipid dynamics at the nanoscale allows us further differentiate between binding and pore formation of β- and α-PFTs to specific domains in the membrane. The molecular insights gained from the intricate coupling that occurs between proteins and membrane lipids and receptors during pore formation are expected to improve our understanding of the virulent action of PFTs.

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.

Bacterial protein listeriolysin O induces nonmonotonic dynamics because of lipid ejection and crowding

Membrane-bound protein complexes involving pore forming toxins (PFTs) released by virulent bacteria are known to form transmembrane pores leading to host cell lysis. Developing alternative strategies against PFT mediated bacterial virulence factors requires an understanding of the cellular membrane response. However, membrane disruption and related lipid reorganization events during attack by PFTs remain largely unexplored. We report counterintuitive and nonmonotonic variations in lipid diffusion, measured using confocal fluorescence correlation spectroscopy, due to interplay of lipid ejection and crowding by membrane-bound oligomers of a prototypical cholesterol-dependent cytolysin, listeriolysin O (LLO). The observed dynamical crossover is correlated with concentration dependent transitions of LLO oligomeric state populations from rings to arc-like pore complexes, predicted using a proposed two-state free area-based diffusion model. At low PFT concentrations, a hitherto unexplored regime of increased lipid diffusivity is attributed to lipid ejection events because of a preponderance of ring-like pore states. At higher protein concentrations in which membrane-inserted arc-like pores dominate, lipid ejection is less efficient and the ensuing crowding results in a lowering of lipid diffusion. These variations in lipid dynamics are corroborated by macroscopic rheological response measurements of PFT bound vesicles. Our study correlates PFT oligomeric state transitions, membrane remodeling, and mechanical property variations, providing unique insights into the pore forming mechanisms of cholesterol-dependent cytolysins.

Universal Relation between Instantaneous Diffusivity and Radius of Gyration of Proteins in Aqueous Solution

Protein conformational fluctuations are highly complex and exhibit long-term correlations. Here, molecular dynamics simulations of small proteins demonstrate that these conformational fluctuations directly affect the protein's instantaneous diffusivity D_{I}. We find that the radius of gyration R_{g} of the proteins exhibits 1/f fluctuations that are synchronous with the fluctuations of D_{I}. Our analysis demonstrates the validity of the local Stokes-Einstein-type relation D_{I}∝1/(R_{g}+R_{0}), where R_{0}∼0.3  nm is assumed to be a hydration layer around the protein. From the analysis of different protein types with both strong and weak conformational fluctuations, the validity of the Stokes-Einstein-type relation appears to be a general property.

Persistent collective motion of a dispersing membrane domain

We study the Brownian motion of an assembly of mobile inclusions embedded in a fluid membrane. The motion includes the dispersal of the assembly, accompanied by the diffusion of its center of mass. Usually, the former process is much faster than the latter because the diffusion coefficient of the center of mass is inversely proportional to the number of particles. However, in the case of membrane inclusions, we find that the two processes occur on the same timescale, thus significantly prolonging the lifetime of the assembly as a collectively moving object. This effect is caused by the quasi-two-dimensional membrane flows, which couple the motions of even the most remote inclusions in the assembly. The same correlations also cause the diffusion coefficient of the center of mass to decay slowly with time, resulting in weak subdiffusion. We confirm our analytical results by Brownian dynamics simulations with flow-mediated correlations. The effect reported here should have implications for the stability of nanoscale membrane heterogeneities.

Binding Revisited-Avidity in Cellular Function and Signaling

When characterizing biomolecular interactions, avidity, is an umbrella term used to describe the accumulated strength of multiple specific and unspecific interactions between two or more interaction partners. In contrast to the affinity, which is often sufficient to describe monovalent interactions in solution and where the binding strength can be accurately determined by considering only the relationship between the microscopic association and dissociation rates, the avidity is a phenomenological macroscopic parameter linked to several microscopic events. Avidity also covers potential effects of reduced dimensionality and/or hindered diffusion observed at or near surfaces e.g., at the cell membrane. Avidity is often used to describe the discrepancy or the "extra on top" when cellular interactions display binding that are several orders of magnitude stronger than those estimated in vitro. Here we review the principles and theoretical frameworks governing avidity in biological systems and the methods for predicting and simulating avidity. While the avidity and effects thereof are well-understood for extracellular biomolecular interactions, we present here examples of, and discuss how, avidity and the underlying kinetics influences intracellular signaling processes.

Diffusion on Membrane Domes, Tubes, and Pearling Structures

Diffusion is a fundamental mechanism for protein distribution in cell membranes. These membranes often exhibit complex shapes, which range from shallow domes to elongated tubular or pearl-like structures. Shape complexity of the membrane influences the diffusive spreading of proteins and molecules. Despite the importance membrane geometry plays in these diffusive processes, it is challenging to establish the dependence between diffusion and membrane morphology. We solve the diffusion equation numerically on various static curved shapes representative for experimentally observed membrane shapes. Our results show that membrane necks become diffusion barriers. We determine the diffusive half-time, i.e., the time that is required to reduce the amount of protein in the budded region by one half, and find a quadratic relation between the diffusive half-time and the averaged mean curvature of the membrane shape, which we rationalize by a scaling law. Our findings thus help estimate the characteristic diffusive timescale based on the simple measure of membrane mean curvature.

Large-scale simulation of biomembranes incorporating realistic kinetics into coarse-grained models

Biomembranes are two-dimensional assemblies of phospholipids that are only a few nanometres thick, but form micrometre-sized structures vital to cellular function. Explicit molecular modelling of biologically relevant membrane systems is computationally expensive due to the large number of solvent particles and slow membrane kinetics. Coarse-grained solvent-free membrane models offer efficient sampling but sacrifice realistic kinetics, thereby limiting the ability to predict pathways and mechanisms of membrane processes. Here, we present a framework for integrating coarse-grained membrane models with continuum-based hydrodynamics. This framework facilitates efficient simulation of large biomembrane systems with large timesteps, while achieving realistic equilibrium and non-equilibrium kinetics. It helps to bridge between the nanometer/nanosecond spatiotemporal resolutions of coarse-grained models and biologically relevant time- and lengthscales. As a demonstration, we investigate fluctuations of red blood cells, with varying cytoplasmic viscosities, in 150-milliseconds-long trajectories, and compare kinetic properties against single-cell experimental observations.

Diffusive transport of nanoscale objects through cell membranes: a computational perspective

Diffusion is an essential and fundamental means of transport of substances on cell membranes, and the dynamics of biomembranes plays a crucial role in the regulation of numerous cellular processes. The understanding of the complex mechanisms and the nature of particle diffusion have a bearing on establishing guidelines for the design of efficient transport materials and unique therapeutic approaches. Herein, this review article highlights the most recent advances in investigating diffusion dynamics of nanoscale objects on biological membranes, focusing on the approaches of tailored computer simulations and theoretical analysis. Due to the presence of the complicated and heterogeneous environment on native cell membranes, the diffusive transport behaviors of nanoparticles exhibit unique and variable characteristics. The general aspects and basic theories of normal diffusion and anomalous diffusion have been introduced. In addition, the influence of a series of external and internal factors on the diffusion behaviors is discussed, including particle size, membrane curvature, particle-membrane interactions or particle-inclusion, and the crowding degree of membranes. Finally, we seek to identify open problems in the existing experimental, simulation, and theoretical research studies, and to propose challenges for future development.

Rotational Diffusion of Membrane Proteins in Crowded Membranes

Membrane proteins travel along cellular membranes and reorient themselves to form functional oligomers and protein-lipid complexes. Following the Saffman-Delbrück model, protein radius sets the rate of this diffusive motion. However, it is unclear how this model, derived for ideal and dilute membranes, performs under crowded conditions of cellular membranes. Here, we study the rotational motion of membrane proteins using molecular dynamics simulations of coarse-grained membranes and 2-dimensional Lennard-Jones fluids with varying levels of crowding. We find that the Saffman-Delbrück model captures the size-dependency of rotational diffusion under dilute conditions where protein-protein interactions are negligible, whereas stronger scaling laws arise under crowding. Together with our recent work on lateral diffusion, our results reshape the description of protein dynamics in native membrane environments: The translational and rotational motions of proteins with small transmembrane domains are rapid, whereas larger proteins or protein complexes display substantially slower dynamics.

Statistical Tests for Force Inference in Heterogeneous Environments

We devise a method to detect and estimate forces in a heterogeneous environment based on experimentally recorded stochastic trajectories. In particular, we focus on systems modeled by the heterogeneous overdamped Langevin equation. Here, the observed drift includes a "spurious” force term when the diffusivity varies in space. We show how Bayesian inference can be leveraged to reliably infer forces by taking into account such spurious forces of unknown amplitude as well as experimental sources of error. The method is based on marginalizing the force posterior over all possible spurious force contributions. The approach is combined with a Bayes factor statistical test for the presence of forces. The performance of our method is investigated analytically, numerically and tested on experimental data sets. The main results are obtained in a closed form allowing for direct exploration of their properties and fast computation. The method is incorporated into TRamWAy, an open-source software platform for automated analysis of biomolecule trajectories.

Unraveling Dynamic Transitions in Time-Resolved Biomolecular Motions by A Dressed Diffusion Model

Recent experimental data reveal the complexity of diffusion dynamics beyond the scope of classical Brownian dynamics. The particles exhibit diverse diffusive motions from the anomalous toward classical diffusion over a wide range of temporal scales. Here a dressed diffusion model is developed to account for non-Brownian phenomena. By coupling the particle dynamics with a local field, the dressed diffusion model generalizes the Langevin equation through coupled damping kernels and generates the salient feature of time-dependent diffusion dynamics reported in the experimental measurements of biomolecules. The dressed diffusion model provides one quantitative aspect for future endeavors in this rapid-growing field.

Increased Confinement and Polydispersity of STIM1 and Orai1 after Ca2+ Store Depletion

STIM1 (a Ca²⁺ sensor in the endoplasmic reticulum (ER) membrane) and Orai1 (a pore-forming subunit of the Ca²⁺-release-activated calcium channel in the plasma membrane) diffuse in the ER membrane and plasma membrane, respectively. Upon depletion of Ca²⁺ stores in the ER, STIM1 translocates to the ER-plasma membrane junction and binds Orai1 to trigger store-operated Ca²⁺ entry. However, the motion of STIM1 and Orai1 during this process and its roles to Ca²⁺ entry is poorly understood. Here, we report real-time tracking of single STIM1 and Orai1 particles in the ER membrane and plasma membrane in living cells before and after Ca²⁺ store depletion. We found that the motion of single STIM1 and Orai1 particles exhibits anomalous diffusion both before and after store depletion, and their mobility-measured by the radius of gyration of the trajectories, mean-square displacement, and generalized diffusion coefficient-decreases drastically after store depletion. We also found that the measured displacement distribution is non-Gaussian, and the non-Gaussian parameter drastically increases after store depletion. Detailed analyses and simulations revealed that single STIM1 and Orai1 particles are confined in the compartmentalized membrane both before and after store depletion, and the changes in the motion after store depletion are explained by increased confinement and polydispersity of STIM1-Orai1 complexes formed at the ER-plasma membrane junctions. Further simulations showed that this increase in the confinement and polydispersity after store depletion localizes a rapid increase of Ca²⁺ influx, which can facilitate the rapid activation of local Ca²⁺ signaling pathways and the efficient replenishing of Ca²⁺ store in the ER in store-operated Ca²⁺ entry.

Clustering and dynamics of crowded proteins near membranes and their influence on membrane bending

Atomistic molecular dynamics simulations of concentrated protein solutions in the presence of a phospholipid bilayer are presented to gain insights into the dynamics and interactions at the cytosol-membrane interface. The main finding is that proteins that are not known to specifically interact with membranes are preferentially excluded from the membrane, leaving a depletion zone near the membrane surface. As a consequence, effective protein concentrations increase, leading to increased protein contacts and clustering, whereas protein diffusion becomes faster near the membrane for proteins that do occasionally enter the depletion zone. Since protein-membrane contacts are infrequent and short-lived in this study, the structure of the lipid bilayer remains largely unaffected by the crowded protein solution, but when proteins do contact lipid head groups, small but statistically significant local membrane curvature is induced, on average.

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

An interfacial regularized Stokeslet scheme is presented to predict the motion of solid bodies (e.g., proteins or gel-phase domains) embedded within flowing lipid bilayer membranes. The approach provides a numerical route to calculate velocities and angular velocities in complex flow fields that are not amenable to simple Faxén-like approximations. Additionally, when applied to shearing motions, the calculations yield predictions for the effective surface viscosity of dilute rigid-body-laden membranes. In the case of cylindrical proteins, effective viscosity calculations are compared to two prior analytical predictions from the literature. Effective viscosity predictions for a dilute suspension of rod-shaped objects in the membrane are also presented.

Fine tuning of the photosystem II major antenna mobility within the thylakoid membrane of higher plants

Depending on the amount of light, the photosystem II (PSII) antennae or Light Harvesting Complexes (LHCII) switch between two states within the thylakoid membranes of higher plants, i.e., a light-harvesting and a photoprotective mode. This switch is co-regulated by a pH gradient (ΔpH) across the membrane and the interaction with the PSII subunit S (PsbS) that is proposed to induce LHCII aggregation. Herein we employ all-atom and coarse-grained molecular simulations of the major LHCII trimer at low and excess ΔpH, as well as in complexation with PsbS within a native thylakoid membrane model. Our results demonstrate the aggregation potential of LHCII and, consistent with the experimental literature, reveal the role of PsbS at atomic resolution. PsbS alters the LHCII-thylakoid lipid interactions and restores the LHCII mobility that is lost in the transition to photoprotective conditions (low lumenal pH). In agreement with this finding, diffusion of the integral membrane protein LHCII is dependent on both, electrostatic interactions and hydrophobic mismatch, while it does not obey the Saffman-Delbrück diffusion model.

Computational Modeling of Realistic Cell Membranes

Cell membranes contain a large variety of lipid types and are crowded with proteins, endowing them with the plasticity needed to fulfill their key roles in cell functioning. The compositional complexity of cellular membranes gives rise to a heterogeneous lateral organization, which is still poorly understood. Computational models, in particular molecular dynamics simulations and related techniques, have provided important insight into the organizational principles of cell membranes over the past decades. Now, we are witnessing a transition from simulations of simpler membrane models to multicomponent systems, culminating in realistic models of an increasing variety of cell types and organelles. Here, we review the state of the art in the field of realistic membrane simulations and discuss the current limitations and challenges ahead.

Multiscale Simulations of Biological Membranes: The Challenge To Understand Biological Phenomena in a Living Substance

Biological membranes are tricky to investigate. They are complex in terms of molecular composition and structure, functional over a wide range of time scales, and characterized by nonequilibrium conditions. Because of all of these features, simulations are a great technique to study biomembrane behavior. A significant part of the functional processes in biological membranes takes place at the molecular level; thus computer simulations are the method of choice to explore how their properties emerge from specific molecular features and how the interplay among the numerous molecules gives rise to function over spatial and time scales larger than the molecular ones. In this review, we focus on this broad theme. We discuss the current state-of-the-art of biomembrane simulations that, until now, have largely focused on a rather narrow picture of the complexity of the membranes. Given this, we also discuss the challenges that we should unravel in the foreseeable future. Numerous features such as the actin-cytoskeleton network, the glycocalyx network, and nonequilibrium transport under ATP-driven conditions have so far received very little attention; however, the potential of simulations to solve them would be exceptionally high. A major milestone for this research would be that one day we could say that computer simulations genuinely research biological membranes, not just lipid bilayers.

The Devil Is in the Details: What Do We Really Track in Single-Particle Tracking Experiments of Diffusion in Biological Membranes?

Single-particle tracking (SPT) is an experimental technique that allows one to follow the dynamics of individual molecules in biological membranes with unprecedented precision. Given the importance of lipid and membrane protein diffusion in the formation of nanoscale functional complexes, it is critical to understand what exactly is measured in SPT experiments. To clarify this issue, we employed nanoscale computer simulations designed to match SPT experiments that exploit streptavidin-functionalized Au nanoparticles (AuNPs). The results show that lipid labeling interferes critically with the diffusion process; thus, the diffusion measured in SPT is a far more complex process than what has been assumed. It turns out that the influence of AuNP-based labels on the dynamics of probe lipids includes not only the AuNP-induced viscous drag that is the more significant the larger the NP but, more importantly, also the effects related to the interactions of the streptavidin linker with membrane lipids. Due to these effects, the probe lipid moves in a concerted manner as a complex with the linker protein and numerous unlabeled lipids, which can slow down the motion of the probe by almost an order of magnitude. Furthermore, our simulations show that nonlinker streptavidin tetramers on the AuNP surface are able to interact with the membrane lipids, which could potentially lead to multivalent labeling of the NPs by the probe lipids. Our results further demonstrate that in the submicrosecond time domain the motion of the probe lipid is uncorrelated with the motion of the AuNP, showing that there is a 1 μs limit for the temporal resolution of the SPT technique. However, this limit for the temporal resolution depends on the nanoparticle size and increases rapidly with growing AuNPs. Overall, the results provide a molecular-scale framework to accurately interpret SPT data and to design protocols that minimize label-induced artifacts.

Influenza A M2 Channel Clustering at High Protein/Lipid Ratios: Viral Budding Implications

Protein dynamics in crowded environments is important for understanding protein functions in vivo and is especially relevant for membrane proteins because of the roles of protein-protein interactions in membrane protein functions and their regulation. Here, using solid-state NMR spectroscopy in combination with coarse-grained molecular dynamics simulations, we report that the rotational correlation time for the transmembrane domain of the influenza A M2 proton channel in lipid bilayers increases dramatically at an elevated protein/lipid ratio. This increase is attributable to persistent protein-protein interactions, thus revealing for the first time, to the best of our knowledge, extensive cluster formation of the M2 tetrameric channel. Such clustering appears to have direct biological relevance during budding of the nascent influenza virus, which does not use the endosomal sorting complexes required for transport machinery. Indeed, initial coarse-grained molecular dynamics simulations of the longer M2 construct known as the conductance domain suggest clustering-induced membrane curvature formation.

Microdomain formation is a general property of bacterial membrane proteins and induces heterogeneity of diffusion patterns

Background

Proteins within the cytoplasmic membrane display distinct localization patterns and arrangements. While multiple models exist describing the dynamics of membrane proteins, to date, there have been few systematic studies, particularly in bacteria, to evaluate how protein size, number of transmembrane domains, and temperature affect their diffusion, and if conserved localization patterns exist.

Results

We have used fluorescence microscopy, single-molecule tracking (SMT), and computer-aided visualization methods to obtain a better understanding of the three-dimensional organization of bacterial membrane proteins, using the model bacterium Bacillus subtilis. First, we carried out a systematic study of the localization of over 200 B. subtilis membrane proteins, tagged with monomeric mVenus-YFP at their original gene locus. Their subcellular localization could be discriminated in polar, septal, patchy, and punctate patterns. Almost 20% of membrane proteins specifically localized to the cell poles, and a vast majority of all proteins localized in distinct structures, which we term microdomains. Dynamics were analyzed for selected membrane proteins, using SMT. Diffusion coefficients of the analyzed transmembrane proteins did not correlate with protein molecular weight, but correlated inversely with the number of transmembrane helices, i.e., transmembrane radius. We observed that temperature can strongly influence diffusion on the membrane, in that upon growth temperature upshift, diffusion coefficients of membrane proteins increased and still correlated inversely to the number of transmembrane domains, following the Saffman–Delbrück relation.

Conclusions

The vast majority of membrane proteins localized to distinct multimeric assemblies. Diffusion of membrane proteins can be suitably described by discriminating diffusion coefficients into two protein populations, one mobile and one immobile, the latter likely constituting microdomains. Our results show there is high heterogeneity and yet structural order in the cell membrane, and provide a roadmap for our understanding of membrane organization in prokaryotes.

Electronic supplementary material

The online version of this article (10.1186/s12915-018-0561-0) contains supplementary material, which is available to authorized users.

From Dynamics to Membrane Organization: Experimental Breakthroughs Occasion a "Modeling Manifesto"

New experimental techniques, especially in the context of observing molecular dynamics, reveal the plasma membrane to be heterogeneous and "scale rich," from nanometers to microns and from microseconds to seconds. This is critical information, which shows that scale-dependent transport governs the molecular encounters that underlie cellular signaling. The data are rich and reaffirm the importance of the cortical cytoskeleton, protein aggregates, and lipidomic complexity on the statistics of molecular encounters. Moreover, the data demand simulation approaches with a particular set of features, hence the "manifesto." Together with the experimental data, simulations that satisfy these requirements hold the promise of a deeper understanding of membrane spatiotemporal organization. Several experimental breakthroughs in measuring molecular membrane dynamics are reviewed, the constraints that they place on simulations are discussed, and the status of simulation approaches that aim to meet them are detailed.

Hydrodynamics of Diffusion in Lipid Membrane Simulations

By performing molecular dynamics simulations with up to 132 million coarse-grained particles in half-micron sized boxes, we show that hydrodynamics quantitatively explains the finite-size effects on diffusion of lipids, proteins, and carbon nanotubes in membranes. The resulting Oseen correction allows us to extract infinite-system diffusion coefficients and membrane surface viscosities from membrane simulations despite the logarithmic divergence of apparent diffusivities with increasing box width. The hydrodynamic theory of diffusion applies also to membranes with asymmetric leaflets and embedded proteins, and to a complex plasma-membrane mimetic.

Communication between the leaflets of asymmetric membranes revealed from coarse-grain molecular dynamics simulations

We use coarse-grain molecular simulations to investigate the structural and dynamics differences between an asymmetric and a symmetrical membrane, both containing beta barrel transmembrane proteins. We find in where the dynamics of the two leaflets differ greatly, the slowest leaflet dominates the structural effects and importance of protein-lipid interactions.