Lateral diffusion in an archipelago. The effect of mobile obstacles

Experimentally Probing the Effect of Confinement Geometry on Lipid Diffusion

The lateral mobility of molecules within the cell membrane is ultimately governed by the local environment of the membrane. Confined regions induced by membrane structures, such as protein aggregates or the actin meshwork, occur over a wide range of length scales and can impede or steer the diffusion of membrane components. However, a detailed picture of the origins and nature of these confinement effects remains elusive. Here, we prepare model lipid systems on substrates patterned with confined domains of varying geometries constructed with different materials to explore the influences of physical boundary conditions and specific molecular interactions on diffusion. We demonstrate a platform that is capable of significantly altering and steering the long-range diffusion of lipids by using simple oxide deposition approaches, enabling us to systematically explore how confinement size and shape impact diffusion over multiple length scales. While we find that a "boundary condition" description of the system captures underlying trends in some cases, we are also able to directly compare our systems to analytical models, revealing the unexpected breakdown of several approximate solutions. Our results highlight the importance of considering the length scale dependence when discussing properties such as diffusion.

Size Sensitivity of Metabolite Diffusion in Macromolecular Crowds

Metabolites play crucial roles in cellular processes, yet their diffusion in the densely packed interiors of cells remains poorly understood, compounded by conflicting reports in existing studies. Here, we employ pulsed-gradient stimulated-echo NMR and Brownian/Stokesian dynamics simulations to elucidate the behavior of nano- and subnanometer-sized tracers in crowded environments. Using Ficoll as a crowder, we observe a linear decrease in tracer diffusivity with increasing occupied volume fraction, persisting─somewhat surprisingly─up to volume fractions of 30-40%. While simulations suggest a linear correlation between diffusivity slowdown and particle size, experimental findings hint at a more intricate relationship, possibly influenced by Ficoll's porosity. Simulations and numerical calculations of tracer diffusivity in the E. coli cytoplasm show a nonlinear yet monotonic diffusion slowdown with particle size. We discuss our results in the context of nanoviscosity and discrepancies with existing studies.

Propranolol induces large-scale remodeling of lipid bilayers: tubules, patches, and holes

Herein, we report fluorescence microscopy analysis of the interaction between propranolol (PPN), a beta-adrenergic blocking agent, and planar supported lipid bilayers (SLBs), as model membranes. The results indicate that PPN can remarkably promote largescale remodeling in SLBs with various lipid compositions. It was found that PPN insertion induces the formation of long microtubules that can retract into hemispherical caps on the surface of the bilayer. These transformations are dynamic, partially reversible, and dependent upon the drug concentration. Quantitative analysis revealed a three-step model for PPN-lipid bilayer interaction, with the first step involving interfacial electrostatic adsorption, the second step centered on hydrophobic insertion, and the third step associated with membrane disruption and hole formation. By introducing cholesterol, phosphoethanolamine, phosphatidylglycerol, and phosphatidylserine lipids into the phosphocholine SLBs, it was illustrated that both the chemistry of the lipid headgroups and the packing of lipid acyl chains can substantially affect the particular steps in the interactions between PPN and lipid bilayers. Our findings may help to elucidate the possible mechanisms of PPN interaction with lipid membranes, the toxic behavior and overdosage scenarios of beta-blockers, and provide valuable information for drug development and modification.

A general expression for the statistical error in a diffusion coefficient obtained from a solid-state molecular-dynamics simulation

Analysis of the mean squared displacement of species k $$ k $$ , r k 2 $$ \left\langle {r}_k^2\right\rangle $$ , as a function of simulation time t $$ t $$ constitutes a powerful method for extracting, from a molecular-dynamics (MD) simulation, the tracer diffusion coefficient, D k * $$ {D}_k^{\ast } $$ . The statistical error in D k * $$ {D}_k^{\ast } $$ is seldom considered, and when it is done, the error is generally underestimated. In this study, we examined the statistics of r k 2 t $$ \left\langle {r}_k^2\right\rangle (t) $$ curves generated by solid-state diffusion by means of kinetic Monte Carlo sampling. Our results indicate that the statistical error in D k * $$ {D}_k^{\ast } $$ depends, in a strongly interrelated way, on the simulation time, the cell size, and the number of relevant point defects in the simulation cell. Reducing our results to one key quantity-the number of k $$ k $$ particles that have jumped at least once-we derive a closed-form expression for the relative uncertainty in D k * $$ {D}_k^{\ast } $$ . We confirm the accuracy of our expression through comparisons with self-generated MD diffusion data. With the expression, we formulate a set of simple rules that encourage the efficient use of computational resources for MD simulations.

Galectin-3 Binding to α5β1 Integrin in Pore Suspended Biomembranes

Galectin-3 (Gal3) is a β-galactoside binding lectin that mediates many physiological functions, including the binding of cells to the extracellular matrix for which the glycoprotein α₅β₁ integrin is of critical importance. The mechanisms by which Gal3 interacts with membranes have not been widely explored to date due to the complexity of cell membranes and the difficulty of integrin reconstitution within model membranes. Herein, to study their interaction, Gal3 and α₅β₁ were purified, and the latter reconstituted into pore-suspended lipid bilayers comprised eggPC:eggPA. Using electrochemical impedance and fluorescence lifetime correlation spectroscopy, we found that on incubation with low nanomolar concentrations of wild-type Gal3, the membrane's admittance and fluidity, as well as integrin's lateral diffusivity, were enhanced. These effects were diminished in the following conditions: (i) absence of integrin, (ii) presence of lactose as a competitive inhibitor of glycan-Gal3 interaction, and (iii) use of a Gal3 mutant that lacked the N-terminal oligomerization domain (Gal3ΔNter). These findings indicated that WTGal3 oligomerized on α₅β₁ integrin in a glycan-dependent manner and that the N-terminal domain interacted directly with membranes in a way that is yet to be fully understood. At concentrations above 10 nM of WTGal3, membrane capacitance started to decrease and very slowly diffusing molecular species appeared, which indicated the formation of protein clusters made from WTGal3-α₅β₁ integrin assemblies. Overall, our study demonstrates the capacity of WTGal3 to oligomerize in a cargo protein-dependent manner at low nanomolar concentrations. Of note, these WTGal3 oligomers appeared to have membrane active properties that could only be revealed using our sensitive methods. At slightly higher WTGal3 concentrations, the capacity to generate lateral assemblies between cargo proteins was observed. In cells, this could lead to the construction of tubular endocytic pits according to the glycolipid-lectin (GL-Lect) hypothesis or to the formation of galectin lattices, depending on cargo glycoprotein stability at the membrane, the local Gal3 concentration, or plasma membrane intrinsic parameters. The study also demonstrates the utility of microcavity array-suspended lipid bilayers to address the biophysics of transmembrane proteins.

Ameboid cell migration through regular arrays of micropillars under confinement

Migrating cells often encounter a wide variety of topographic features-including the presence of obstacles-when navigating through crowded biological environments. Unraveling the impact of topography and crowding on the dynamics of cells is key to better understand many essential physiological processes such as the immune response. We study the impact of geometrical cues on ameboid migration of HL-60 cells differentiated into neutrophils. A microfluidic device is designed to track the cells in confining geometries between two parallel plates with distance h, in which identical micropillars are arranged in regular pillar forests with pillar spacing e. We observe that the cells are temporarily captured near pillars, with a mean contact time that is independent of h and e. By decreasing the vertical confinement h, we find that the cell velocity is not affected, while the persistence reduces; thus, cells are able to preserve their velocity when highly squeezed but lose the ability to control their direction of motion. At a given h, we show that by decreasing the pillar spacing e in the weak lateral confinement regime, the mean escape time of cells from effective local traps between neighboring pillars grows. This effect, together with the increase of cell-pillar contact frequency, leads to the reduction of diffusion constant D. By disentangling the contributions of these two effects on D in numerical simulations, we verify that the impact of cell-pillar contacts on cell diffusivity is more pronounced at smaller pillar spacing.

Protein-coated nanoparticles exhibit Lévy flights on a suspended lipid bilayer

Lateral diffusion of nano-objects on lipid membranes is a crucial process in cell biology. Recent studies indicate that nanoparticle lateral diffusion is affected by the presence of membrane proteins and deviates from Brownian motion. Gold nanoparticles (Au NPs) stabilized by short thiol ligands were dispersed near a free-standing bilayer formed in a 3D microfluidic chip. Using dark-field microscopy, the position of single NPs at the bilayer surface was tracked over time. Numerical analysis of the NP trajectories shows that NP diffusion on the bilayer surface corresponds to Brownian motion. The addition of bovine serum albumin (BSA) protein to the solution led to the formation of a protein corona on the NP surface. We found that protein-coated NPs show anomalous superdiffusion and that the distribution of their relative displacement obeys Lévy flight statistics. This superdiffusive motion is attributed to a drastic reduction in adhesive energies between the NPs and the bilayer in the presence of the protein corona. This hypothesis was confirmed by numerical simulations mimicking the random walk of a single particle near a weakly adhesive surface. These results may be generalized to other classes of nano-objects that experience adsorption-desorption behaviour with a weakly adhesive surface.

Microscopic Theory for the Diffusion of an Active Particle in a Crowded Environment

We calculate the diffusion coefficient of an active tracer in a schematic crowded environment, represented as a lattice gas of passive particles with hardcore interactions. Starting from the master equation of the problem, we put forward a closure approximation that goes beyond trivial mean field and provides the diffusion coefficient for an arbitrary density of crowders in the system. We show that our approximation is accurate for a very wide range of parameters, and that it correctly captures numerous nonequilibrium effects, which are the signature of the activity in the system. In addition to the determination of the diffusion coefficient of the tracer, our approach allows us to characterize the perturbation of the environment induced by the displacement of the active tracer. Finally, we consider the asymptotic regimes of low and high densities, in which the expression of the diffusion coefficient of the tracer becomes explicit, and which we argue to be exact.

Investigating Time-Dependent Active Motion of Janus Micromotors using Dynamic Light Scattering

Advances in fabrication methods have positioned Janus micromotors (JMs) as candidates for use as autonomous devices in applications across diverse fields, spanning drug delivery to environmental remediation. While the design of most micromotors is straightforward, the non-steady state active motion exhibited by these systems is complex and difficult to characterize. Traditionally, JM active motion is characterized using optical microscopy single particle tracking for systems confined in 2D. Dynamic light scattering (DLS) offers an alternative high-throughput method for characterizing the 3D active motion in bulk JM dispersions with additional capabilities to quantify time-dependent behavior for a broader range of JM sizes. Here, the active motion of spherical JMs is examined by DLS and it is demonstrated that the method enables decoupling of the translational and rotational diffusion. Systematic studies quantifying the time-dependent diffusive properties as a function of fuel concentration, JM concentration, and time after fuel addition are presented. The analyses presented in this work position DLS to facilitate future advances of JM systems by serving as a fast-screening characterization method for active motion.

The influence of additives on polymer matrix mobility and the glass transition

In the region near an interface, the microscopic properties of a glass forming liquid may be perturbed from their equilibrium bulk values. In this work, we probe how the interfacial effects of additive particles dispersed in a matrix can influence the local mobility of the material and its glass transition temperature, Tg. Experimental measurements and simulation results indicate that additives, such as nanoparticles, gas molecules, and oligomers, can shift the mobility and Tg of a surrounding polymer matrix (even for relatively small concentrations of additive; e.g., 5-10% by volume) relative to the pure bulk matrix, thus leading to Tg enhancement or suppression. Additives thus provide a potential route for modifying the properties of a polymer material without significantly changing its chemical composition. Here we apply the Limited Mobility (LM) model to simulate a matrix containing additive species. We show that both additive concentration, as well as the strength of its very local influence on the surrounding matrix material, will determine whether the Tg of the system is raised or lowered, relative to the pure matrix. We demonstrate that incorporation of additives into the simple LM simulation method, which has successfully described the behavior of bulk and thin film glassy solids, leads to direct connections with available experimental and simulation results for a broad range of polymer/additive systems.

Morphological deformation of Daphnia magna embryos caused by prolonged exposure to ibuprofen

The effect of chronic exposure of freshwater cladoceran Daphnia magna to low, environmentally relevant concentrations i.e 4 μgL^-1of ibuprofen (a nonsteroidal anti-inflammatory drug) in a laboratory experiment was studied. We observed the key life history traits of first and fifth generation individuals: age and size at first reproduction, number of first clutch eggs and individual growth rate. Moreover, chosen molecular/subcellular markers of experimental animals stress response such as triglyceride content, heat shock proteins (HSP) expression and DNA:RNA ratio were collected. Overall, chronic exposure to ibuprofen had no significant effect on the molecular markers nor on the life history parameters of the Daphnia. It did, however, caused lethal morphological deformities in embryos and juvenile daphnids. Depending on the clonal affiliation, exposure to a low dosage of ibuprofen over five generations resulted in the deformation of ∼3%-∼10% of the first clutch of offspring. Also, up to 90% of females carried at least one deformed embryo. This is the first time that research has revealed such an effect of ibuprofen on D. magna.

To Hop or not to Hop: Exceptions in the FCS Diffusion Law

Diffusion obstacles in membranes have not been directly visualized because of fast membrane dynamics and the occurrence of subresolution molecular complexes. To understand the obstacle characteristics, mobility-based methods are often used as an indirect way of assessing the membrane structure. Molecular movement in biological plasma membranes is often characterized by anomalous diffusion, but the exact underlying mechanisms are still elusive. Imaging total internal reflection fluorescence correlation spectroscopy (ITIR-FCS) is a well-established mobility-based method that provides spatially resolved diffusion coefficient maps and is combined with FCS diffusion law analysis to examine subresolution membrane organization. In recent years, although FCS diffusion law analysis has been instrumental in providing new insights into the membrane structure below the optical diffraction limit, there are certain exceptions and anomalies that require further clarification. To this end, we correlate the membrane structural features imaged by atomic force microscopy (AFM) with the dynamics measured using ITIR-FCS. We perform ITIR-FCS measurements on supported lipid bilayers (SLBs) of various lipid compositions to characterize the anomalous diffusion of lipid molecules in distinct obstacle configurations, along with the high-resolution imaging of the membrane structures with AFM. Furthermore, we validate our experimental results by performing simulations on image grids with experimentally determined obstacle configurations. This study demonstrates that FCS diffusion law analysis is a powerful tool to determine membrane heterogeneities implied from dynamics measurements. Our results corroborate the commonly accepted interpretations of imaging FCS diffusion law analysis, and we show that exceptions happen when domains reach the percolation threshold in a biphasic membrane and a network of domains behaves rather like a meshwork, resulting in hop diffusion.

Molecular transport in systems containing binding obstacles

We studied the movement of particles in crowded environments by means of extensive Monte Carlo simulations. The dynamic lattice liquid model was employed for this purpose. It is based on the cooperative movement concept and allows the study of systems at high densities. The cooperative model of molecular transport is assumed: the motion of all moving particles is highly correlated. The model is supposed to mimic lateral motion in a membrane and therefore the system is two-dimensional with moving objects and traps placed on a triangular lattice. In our study the interaction (binding) of traps with moving particles was assumed. The conditions in which subdiffusive motion appeared in the system were analysed. The influence of the strength of binding on the dynamic percolation threshold was also shown. The differences in the dynamics compared to systems with impenetrable obstacles and with systems without correlation in motion were presented and discussed. It was shown that in the case of correlated motion the influence of deep traps is similar to that of impenetrable obstacles. If the traps are shallow a recovery to normal diffusion was observed for longer time periods.

Surface reaction-diffusion kinetics on lattice at the microscopic scale

Microscopic models of reaction-diffusion processes on the cell membrane can link local spatiotemporal effects to macroscopic self-organized patterns often observed on the membrane. Simulation schemes based on the microscopic lattice method (MLM) can model these processes at the microscopic scale by tracking individual molecules, represented as hard spheres, on fine lattice voxels. Although MLM is simple to implement and is generally less computationally demanding than off-lattice approaches, its accuracy and consistency in modeling surface reactions have not been fully verified. Using the Spatiocyte scheme, we study the accuracy of MLM in diffusion-influenced surface reactions. We derive the lattice-based bimolecular association rates for two-dimensional (2D) surface-surface reaction and one-dimensional (1D) volume-surface adsorption according to the Smoluchowski-Collins-Kimball model and random walk theory. We match the time-dependent rates on lattice with off-lattice counterparts to obtain the correct expressions for MLM parameters in terms of physical constants. The expressions indicate that the voxel size needs to be at least 0.6% larger than the molecule to accurately simulate surface reactions on triangular lattice. On square lattice, the minimum voxel size should be even larger, at 5%. We also demonstrate the ability of MLM-based schemes such as Spatiocyte to simulate a reaction-diffusion model that involves all dimensions: three-dimensional (3D) diffusion in the cytoplasm, 2D diffusion on the cell membrane, and 1D cytoplasm-membrane adsorption. With the model, we examine the contribution of the 2D reaction pathway to the overall reaction rate at different reactant diffusivity, reactivity, and concentrations.

Controlling Anomalous Diffusion in Lipid Membranes

Diffusion in cell membranes is not just simple two-dimensional Brownian motion but typically depends on the timescale of the observation. The physical origins of this anomalous subdiffusion are unresolved, and model systems capable of quantitative and reproducible control of membrane diffusion have been recognized as a key experimental bottleneck. Here, we control anomalous diffusion using supported lipid bilayers containing lipids derivatized with polyethylene glycol (PEG) headgroups. Bilayers with specific excluded area fractions are formed by control of PEG lipid mole fraction. These bilayers exhibit a switch in diffusive behavior, becoming anomalous as bilayer continuity is disrupted. Using a combination of single-molecule fluorescence and interferometric imaging, we measure the anomalous behavior in this model over four orders of magnitude in time. Diffusion in these bilayers is well described by a power-law dependence of the mean-square displacement with observation time. Anomaleity in this system can be tailored by simply controlling the mole fraction of PEG lipid, producing bilayers with diffusion parameters similar to those observed for anomalous diffusion in biological membranes.

Roughness of Transmembrane Helices Reduces Lipid Membrane Dynamics

The dynamics of cellular membranes is primarily determined by lipid species forming a bilayer. Proteins are considered mainly as effector molecules of diverse cellular processes. In addition to large assemblies of proteins, which were found to influence properties of fluid membranes, biological membranes are densely populated by small, highly mobile proteins. However, little is known about the effect of such proteins on the dynamics of membranes. Using synthetic peptides, we demonstrate that transmembrane helices interfere with the mobility of membrane components by trapping lipid acyl chains on their rough surfaces. The effect is more pronounced in the presence of cholesterol, which segregates from the rough surface of helical peptides. This may contribute to the formation or stabilization of membrane heterogeneities. Since roughness is a general property of helical transmembrane segments, our results suggest that, independent of their size or cytoskeleton linkage, integral membrane proteins affect local membrane dynamics and organization.

Urea-mediated anomalous diffusion in supported lipid bilayers

Diffusion in biological membranes is seldom simply Brownian motion; instead, the rate of diffusion is dependent on the time scale of observation and so is often described as anomalous. In order to help better understand this phenomenon, model systems are needed where the anomalous diffusion of the lipid bilayer can be tuned and quantified. We recently demonstrated one such model by controlling the excluded area fraction in supported lipid bilayers (SLBs) through the incorporation of lipids derivatized with polyethylene glycol. Here, we extend this work, using urea to induce anomalous diffusion in SLBs. By tuning incubation time and urea concentration, we produce bilayers that exhibit anomalous behaviour on the same scale as that observed in biological membranes.

Fluctuations of random walks in critical random environments

Percolation networks have been widely used in the description of porous media but are now found to be relevant to understand the motion of particles in cellular membranes or the nucleus of biological cells. Random walks on the infinite cluster at criticality of a percolation network are asymptotically ergodic. On any finite size cluster of the network stationarity is reached at finite times, depending on the cluster's size. Despite of this we here demonstrate by combination of analytical calculations and simulations that at criticality the disorder and cluster size average of the ensemble of clusters leads to a non-vanishing variance of the time averaged mean squared displacement, regardless of the measurement time. Fluctuations of this relevant experimental quantity due to the disorder average of such ensembles are thus persistent and non-negligible. The relevance of our results for single particle tracking analysis in complex and biological systems is discussed.

Crossover from picosecond collective to single particle dynamics defines the mechanism of lateral lipid diffusion

It has been widely accepted that the thermally excited motions of the molecules in a cell membrane is the prerequisite for a cell to carry its biological functions. On the other hand, the detailed mapping of the ultrafast picosecond single-molecule and the collective lipid dynamics in a cell membrane remains rather elusive. Here, we report all-atom molecular dynamics simulations of a 1,2-dipalmitoyl-sn-glycero-3-phosphocholine bilayer over a wide range of temperature. We elucidate a molecular mechanism underlying the lateral lipid diffusion in a cell membrane across the gel, rippled, and liquid phases using an analysis of the longitudinal and transverse current correlation spectra, the velocity auto-correlation functions, and the molecules mean square displacements. The molecular mechanism is based on the anomalous ultrafast vibrational properties of lipid molecules at the viscous-to-elastic crossover. The macroscopic lipid diffusion coefficients predicted by the proposed diffusion model are in a good agreement with experimentally observed values. Furthermore, we unveil the role of water confined at the water-lipid interface in triggering collective vibrations in a lipid bilayer.

Actin filaments partition primary cilia membranes into distinct fluid corrals

Lee et al. examine the dynamics of membrane proteins within the ciliary membrane using quantum dots and 2P Super FRAP. They show that ciliary membrane proteins diffuse rapidly within highly fluid local membrane domains delimited by actin filaments.

Physical properties of primary cilia membranes in living cells were examined using two independent, high-spatiotemporal-resolution approaches: fast tracking of single quantum dot–labeled G protein–coupled receptors and a novel two-photon super-resolution fluorescence recovery after photobleaching of protein ensemble. Both approaches demonstrated the cilium membrane to be partitioned into corralled domains spanning 274 ± 20 nm, within which the receptors are transiently confined for 0.71 ± 0.09 s. The mean membrane diffusion coefficient within the corrals, D_m1 = 2.9 ± 0.41 µm²/s, showed that the ciliary membranes were among the most fluid encountered. At longer times, the apparent membrane diffusion coefficient, D_m2 = 0.23 ± 0.05 µm²/s, showed that corral boundaries impeded receptor diffusion 13-fold. Mathematical simulations predict the probability of G protein–coupled receptors crossing corral boundaries to be 1 in 472. Remarkably, latrunculin A, cytochalasin D, and jasplakinolide treatments altered the corral permeability. Ciliary membranes are thus partitioned into highly fluid membrane nanodomains that are delimited by filamentous actin.

Scaling relationships for translational diffusion constants applied to membrane domain dissolution and growth

We compare the way that relationships for diffusion constants scale with the size of diffusing membrane domains and the geometry of their environments. Then, we review our experimental work on the dynamics of dissolution/growth of membrane domains in crowding induced mixing, phase separation, and Ostwald ripening in a highly confined environment. Overall, the scaling relationships applied to diffusion constants obtained by fits to our dynamic data indicate that dissolution and growth is influenced by the diffusion of clusters or small domains of lipids, in addition to kinetic processes and geometrical constraints.

Numerical calculation on a two-step subdiffusion behavior of lateral protein movement in plasma membranes

A two-step subdiffusion behavior of lateral movement of transmembrane proteins in plasma membranes has been observed by using single-molecule experiments. A nested double-compartment model where large compartments are divided into several smaller ones has been proposed in order to explain this observation. These compartments are considered to be delimited by membrane-skeleton "fences" and membrane-protein "pickets" bound to the fences. We perform numerical simulations of a master equation using a simple two-dimensional lattice model to investigate the heterogeneous diffusion dynamics behavior of transmembrane proteins within plasma membranes. We show that the experimentally observed two-step subdiffusion process can be described using fence and picket models combined with decreased local diffusivity of transmembrane proteins in the vicinity of the pickets. This allows us to explain the two-step subdiffusion behavior without explicitly introducing nested double compartments.

Smoldyn: particle-based simulation with rule-based modeling, improved molecular interaction and a library interface

Motivation

Smoldyn is a spatial and stochastic biochemical simulator. It treats each molecule of interest as an individual particle in continuous space, simulating molecular diffusion, molecule-membrane interactions and chemical reactions, all with good accuracy. This article presents several new features.

Results

Smoldyn now supports two types of rule-based modeling. These are a wildcard method, which is very convenient, and the BioNetGen package with extensions for spatial simulation, which is better for complicated models. Smoldyn also includes new algorithms for simulating the diffusion of surface-bound molecules and molecules with excluded volume. Both are exact in the limit of short time steps and reasonably good with longer steps. In addition, Smoldyn supports single-molecule tracking simulations. Finally, the Smoldyn source code can be accessed through a C/C ++ language library interface.

Availability and Implementation

Smoldyn software, documentation, code, and examples are at http://www.smoldyn.org .

Contact

steven.s.andrews@gmail.com.

Diffusion of Integral Membrane Proteins in Protein-Rich Membranes

The lateral diffusion of embedded proteins along lipid membranes in protein-poor conditions has been successfully described in terms of the Saffman-Delbrück (SD) model, which predicts that the protein diffusion coefficient D is weakly dependent on its radius R as D ∝ ln(1/R). However, instead of being protein-poor, native cell membranes are extremely crowded with proteins. On the basis of extensive molecular simulations, we here demonstrate that protein crowding of the membrane at physiological levels leads to deviations from the SD relation and to the emergence of a stronger Stokes-like dependence D ∝ 1/R. We propose that this 1/R law mainly arises due to geometrical factors: smaller proteins are able to avoid confinement effects much better than their larger counterparts. The results highlight that the lateral dynamics in the crowded setting found in native membranes is radically different from protein-poor conditions and plays a significant role in formation of functional multiprotein complexes.

Effects of soft interactions and bound mobility on diffusion in crowded environments: a model of sticky and slippery obstacles

Crowded environments modify the diffusion of macromolecules, generally slowing their movement and inducing transient anomalous subdiffusion. The presence of obstacles also modifies the kinetics and equilibrium behavior of tracers. While previous theoretical studies of particle diffusion have typically assumed either impenetrable obstacles or binding interactions that immobilize the particle, in many cellular contexts bound particles remain mobile. Examples include membrane proteins or lipids with some entry and diffusion within lipid domains and proteins that can enter into membraneless organelles or compartments such as the nucleolus. Using a lattice model, we studied the diffusive movement of tracer particles which bind to soft obstacles, allowing tracers and obstacles to occupy the same lattice site. For sticky obstacles, bound tracer particles are immobile, while for slippery obstacles, bound tracers can hop without penalty to adjacent obstacles. In both models, binding significantly alters tracer motion. The type and degree of motion while bound is a key determinant of the tracer mobility: slippery obstacles can allow nearly unhindered diffusion, even at high obstacle filling fraction. To mimic compartmentalization in a cell, we examined how obstacle size and a range of bound diffusion coefficients affect tracer dynamics. The behavior of the model is similar in two and three spatial dimensions. Our work has implications for protein movement and interactions within cells.

Excluded volume effects in on- and off-lattice reaction-diffusion models

Mathematical models are important tools to study the excluded volume effects on reaction-diffusion systems, which are known to play an important role inside living cells. Detailed microscopic simulations with off-lattice Brownian dynamics become computationally expensive in crowded environments. In this study, the authors therefore investigate to which extent on-lattice approximations, the so-called cellular automata models, can be used to simulate reactions and diffusion in the presence of crowding molecules. They show that the diffusion is most severely slowed down in the off-lattice model, since randomly distributed obstacles effectively exclude more volume than those ordered on an artificial grid. Crowded reaction rates can be both increased and decreased by the grid structure and it proves important to model the molecules with realistic sizes when excluded volume is taken into account. The grid artefacts increase with increasing crowder density and they conclude that the computationally more efficient on-lattice simulations are accurate approximations only for low crowder densities.

Gradient-driven diffusion and pattern formation in crowded mixtures

Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion affects microstructure, which in turn affects diffusivity; a key question is how this complex coupling controls both transport and pattern formation. To examine these mechanisms, we study a two-dimensional multicomponent lattice gas model, where "tracer" molecules diffuse between a source and a sink separated by a solution of sticky "crowder" molecules that cluster to form dynamically evolving obstacles. In the high-temperature limit, crowders and tracers are miscible, and transport may be predicted analytically. At intermediate temperatures, crowders phase separate into clusters that drift toward the tracer sink. As a result, steady-state tracer diffusivity depends nonmonotonically on both temperature and crowder density, and we observe a variety of complex microstructures. In the low-temperature limit, crowders rapidly aggregate to form obstacles that are kinetically arrested; if crowder density is near the percolation threshold, resulting tracer diffusivity shows scaling behavior with the same scaling exponent as the random resistor network model. Though highly idealized, this simple model reveals fundamental mechanisms governing coupled gradient-driven diffusion, phase separation, and microstructural evolution in crowded mixtures.

Effect of benzocaine and propranolol on phospholipid-based bilayers

Drug/bilayer interactions are fundamental in determining the action mechanism of active ingredients. Neutron techniques represent unique tools for having a clear comprehension of such interactions.

There Is No Simple Model of the Plasma Membrane Organization

Ever since technologies enabled the characterization of eukaryotic plasma membranes, heterogeneities in the distributions of its constituents were observed. Over the years this led to the proposal of various models describing the plasma membrane organization such as lipid shells, picket-and-fences, lipid rafts, or protein islands, as addressed in numerous publications and reviews. Instead of emphasizing on one model we in this review give a brief overview over current models and highlight how current experimental work in one or the other way do not support the existence of a single overarching model. Instead, we highlight the vast variety of membrane properties and components, their influences and impacts. We believe that highlighting such controversial discoveries will stimulate unbiased research on plasma membrane organization and functionality, leading to a better understanding of this essential cellular structure.

N-glycosylation enables high lateral mobility of GPI-anchored proteins at a molecular crowding threshold

The protein density in biological membranes can be extraordinarily high, but the impact of molecular crowding on the diffusion of membrane proteins has not been studied systematically in a natural system. The diversity of the membrane proteome of most cells may preclude systematic studies. African trypanosomes, however, feature a uniform surface coat that is dominated by a single type of variant surface glycoprotein (VSG). Here we study the density-dependence of the diffusion of different glycosylphosphatidylinositol-anchored VSG-types on living cells and in artificial membranes. Our results suggest that a specific molecular crowding threshold (MCT) limits diffusion and hence affects protein function. Obstacles in the form of heterologous proteins compromise the diffusion coefficient and the MCT. The trypanosome VSG-coat operates very close to its MCT. Importantly, our experiments show that N-linked glycans act as molecular insulators that reduce retarding intermolecular interactions allowing membrane proteins to function correctly even when densely packed.

Simulation of Molecular Transport in Systems Containing Mobile Obstacles

In this paper, we investigate the movement of molecules in crowded environments with obstacles undergoing Brownian motion by means of extensive Monte Carlo simulations. Our investigations were performed using the dynamic lattice liquid model, which was based on the cooperative movement concept and allowed to mimic systems at high densities where the motion of all elements (obstacles as well as moving particles) were highly correlated. The crowded environments are modeled on a two-dimensional triangular lattice containing obstacles (particles whose mobility was significantly reduced) moving by a Brownian motion. The subdiffusive motion of both elements in the system was analyzed. It was shown that the percolation transition does not exist in such systems in spite of the cooperative character of the particles' motion. The reduction of the obstacle mobility leads to the longer caging of liquid particles by mobile obstacles.

Heterogeneous surfaces to repel proteins

The nonspecific adsorption of proteins is usually undesirable on solid surfaces as it induces adverse responses, such as platelet adhesion on medical devices, negative signals of biosensors and contamination blockage of filtration membranes. Thus, an important scheme in material science is to design and fabricate protein-repulsive surfaces. Early approaches in this field focused on homogeneous surfaces comprised of single type functionality. Yet, recent researches have demonstrated that surfaces with heterogeneities (chemistry and topography) show promising performance against protein adsorption. In this review, we will summarize the recent achievements and discuss the new perspectives in the research of developing and characterizing heterogeneous surfaces to repel proteins. The protein repulsion mechanisms of different heterogeneous surfaces will also be discussed in details, followed by the perspective and challenge of this emerging field.

Effects of protein crowding on membrane systems

Cellular membranes are typically decorated with a plethora of embedded and adsorbed macromolecules, e.g. proteins, that participate in numerous vital processes. With typical surface densities of 30,000 proteins per μm(2) cellular membranes are indeed crowded places that leave only few nanometers of private space for individual proteins. Here, we review recent advances in our understanding of protein crowding in membrane systems. We first give a brief overview on state-of-the-art approaches in experiment and simulation that are frequently used to study crowded membranes. After that, we review how crowding can affect diffusive transport of proteins and lipids in membrane systems. Next, we discuss lipid and protein sorting in crowded membrane systems, including effects like protein cluster formation, phase segregation, and lipid droplet formation. Subsequently, we highlight recent progress in uncovering crowding-induced conformational changes of membranes, e.g. membrane budding and vesicle formation. Finally, we give a short outlook on potential future developments in the field of crowded membrane systems. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Measurements of rhodopsin diffusion within signaling membrane microcompartments in live photoreceptors

High-resolution multiphoton imaging of live cells has become an invaluable method to study protein dynamics in highly compartmentalized subcellular environments. Here we describe procedures that we recently developed to quantify rhodopsin mobility within and between retinal rod photoreceptor light signaling microcompartments, the disc membrane lobules, using multiphoton fluorescence relaxation after photoconversion.

A Lattice-Boltzmann scheme for the simulation of diffusion in intracellular crowded systems

Background

The intracellular environment is a complex and crowded medium where the diffusion of proteins, metabolites and other molecules can be decreased. One of the most popular methodologies for the simulation of diffusion in crowding systems is the Monte Carlo algorithm (MC) which tracks the movement of each particle. This can, however, be computationally expensive for a system comprising a large number of molecules. On the other hand, the Lattice Boltzmann Method (LBM) tracks the movement of collections of molecules, which represents significant savings in computational time. Nevertheless in the classical manifestation of such scheme the crowding conditions are neglected.

Methods

In this paper we use Scaled Particle Theory (SPT) to approximate the probability to find free space for the displacement of hard-disk molecules and in this way to incorporate the crowding effect to the LBM. This new methodology which couples SPT and LBM is validated using a kinetic Monte Carlo (kMC) algorithm, which is used here as our "computational experiment".

Results

The results indicate that LBM over-predicts the diffusion in 2D crowded systems, while the proposed coupled SPT-LBM predicts the same behaviour as the kinetic Monte Carlo (kMC) algorithm but with a significantly reduced computational effort. Despite the fact that small deviations between the two methods were observed, in part due to the mesoscopic and microscopic nature of each method, respectively, the agreement was satisfactory both from a qualitative and a quantitative point of view.

Conclusions

A crowding-adaptation to LBM has been developed using SPT, allowing fast simulations of diffusion-systems of different size hard-disk molecules in two-dimensional space. This methodology takes into account crowding conditions; not only the space fraction occupied by the crowder molecules but also the influence of the size of the crowder which can affect the displacement of molecules across the lattice system.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-015-0769-8) contains supplementary material, which is available to authorized users.

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