Diffusion in a fluid membrane with a flexible cortical cytoskeleton

Effects of Paclitaxel on Plasma Membrane Microviscosity and Lipid Composition in Cancer Cells

The cell membrane is an important regulator for the cytotoxicity of chemotherapeutic agents. However, the biochemical and biophysical effects that occur in the membrane under the action of chemotherapy drugs are not fully described. In the present study, changes in the microviscosity of membranes of living HeLa-Kyoto tumor cells were studied during chemotherapy with paclitaxel, a widely used antimicrotubule agent. To visualize the microviscosity of the membranes, fluorescence lifetime imaging microscopy (FLIM) with a BODIPY 2 fluorescent molecular rotor was used. The lipid profile of the membranes was assessed using time-of-flight secondary ion mass spectrometry ToF-SIMS. A significant, steady-state decrease in the microviscosity of membranes, both in cell monolayers and in tumor spheroids, was revealed after the treatment. Mass spectrometry showed an increase in the unsaturated fatty acid content in treated cell membranes, which may explain, at least partially, their low microviscosity. These results indicate the involvement of membrane microviscosity in the response of tumor cells to paclitaxel treatment.

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.

Nanoscale Sub-Compartmentalization of the Dendritic Spine Compartment

Compartmentalization of the membrane is essential for cells to perform highly specific tasks and spatially constrained biochemical functions in topographically defined areas. These membrane lateral heterogeneities range from nanoscopic dimensions, often involving only a few molecular constituents, to micron-sized mesoscopic domains resulting from the coalescence of nanodomains. Short-lived domains lasting for a few milliseconds coexist with more stable platforms lasting from minutes to days. This panoply of lateral domains subserves the great variety of demands of cell physiology, particularly high for those implicated in signaling. The dendritic spine, a subcellular structure of neurons at the receiving (postsynaptic) end of central nervous system excitatory synapses, exploits this compartmentalization principle. In its most frequent adult morphology, the mushroom-shaped spine harbors neurotransmitter receptors, enzymes, and scaffolding proteins tightly packed in a volume of a few femtoliters. In addition to constituting a mesoscopic lateral heterogeneity of the dendritic arborization, the dendritic spine postsynaptic membrane is further compartmentalized into spatially delimited nanodomains that execute separate functions in the synapse. This review discusses the functional relevance of compartmentalization and nanodomain organization in synaptic transmission and plasticity and exemplifies the importance of this parcelization in various neurotransmitter signaling systems operating at dendritic spines, using two fast ligand-gated ionotropic receptors, the nicotinic acetylcholine receptor and the glutamatergic receptor, and a second-messenger G-protein coupled receptor, the cannabinoid receptor, as paradigmatic examples.

Characterising the diffusion of biological nanoparticles on fluid and cross-linked membranes

Tracing the motion of macromolecules, viruses, and nanoparticles adsorbed onto cell membranes is currently the most direct way of probing the complex dynamic interactions behind vital biological processes, including cell signalling, trafficking, and viral infection. The resulting trajectories are usually consistent with some type of anomalous diffusion, but the molecular origins behind the observed anomalous behaviour are usually not obvious. Here we use coarse-grained molecular dynamics simulations to help identify the physical mechanisms that can give rise to experimentally observed trajectories of nanoscopic objects moving on biological membranes. We find that diffusion on membranes of high fluidities typically results in normal diffusion of the adsorbed nanoparticle, irrespective of the concentration of receptors, receptor clustering, or multivalent interactions between the particle and membrane receptors. Gel-like membranes on the other hand result in anomalous diffusion of the particle, which becomes more pronounced at higher receptor concentrations. This anomalous diffusion is characterised by local particle trapping in the regions of high receptor concentrations and fast hopping between such regions. The normal diffusion is recovered in the limit where the gel membrane is saturated with receptors. We conclude that hindered receptor diffusivity can be a common reason behind the observed anomalous diffusion of viruses, vesicles, and nanoparticles adsorbed on cell and model membranes. Our results enable direct comparison with experiments and offer a new route for interpreting motility experiments on cell membranes.

Modeling of the axon plasma membrane structure and its effects on protein diffusion

The axon plasma membrane consists of the membrane skeleton, which comprises ring-like actin filaments connected to each other by spectrin tetramers, and the lipid bilayer, which is tethered to the skeleton via, at least, ankyrin. Currently it is unknown whether this unique axon plasma membrane skeleton (APMS) sets the diffusion rules of lipids and proteins in the axon. To answer this question, we developed a coarse-grain molecular dynamics model for the axon that includes the APMS, the phospholipid bilayer, transmembrane proteins (TMPs), and integral monotopic proteins (IMPs) in both the inner and outer lipid layers. We first showed that actin rings limit the longitudinal diffusion of TMPs and the IMPs of the inner leaflet but not of the IMPs of the outer leaflet. To reconcile the experimental observations, which show restricted diffusion of IMPs of the outer leaflet, with our simulations, we conjectured the existence of actin-anchored proteins that form a fence which restricts the longitudinal diffusion of IMPs of the outer leaflet. We also showed that spectrin filaments could modify transverse diffusion of TMPs and IMPs of the inner leaflet, depending on the strength of the association between lipids and spectrin. For instance, in areas where spectrin binds to the lipid bilayer, spectrin filaments would restrict diffusion of proteins within the skeleton corrals. In contrast, in areas where spectrin and lipids are not associated, spectrin modifies the diffusion of TMPs and IMPs of the inner leaflet from normal to confined-hop diffusion. Overall, we showed that diffusion of axon plasma membrane proteins is deeply anisotropic, as longitudinal diffusion is of different type than transverse diffusion. Finally, we investigated how accumulation of TMPs affects diffusion of TMPs and IMPs of both the inner and outer leaflets by changing the density of TMPs. We showed that the APMS structure acts as a fence that restricts the diffusion of TMPs and IMPs of the inner leaflet within the membrane skeleton corrals. Our findings provide insight into how the axon skeleton acts as diffusion barrier and maintains neuronal polarity.

The axon plasma membrane skeleton consists of repeated periodic actin ring-like structures along its length connected via spectrin tetramers and anchored to the lipid bilayer at least via ankyrin. However, it is currently unclear whether this structure controls diffusion of lipids and proteins in the axon. Here, we developed a coarse-grain molecular dynamics computational model for the axon plasma membrane that comprises minimal representations for the APMS and the lipid bilayer. In a departure from current models, we found that actin rings limit diffusion of proteins only in the inner membrane leaflet. Then, we showed that actin anchored proteins likely act as “fences” confining diffusion of proteins in the outer leaflet. Our simulations, unexpectedly, also revealed that spectrin filaments could impede transverse diffusion in the inner leaflet of the axon and in some conditions modify diffusion from normal to abnormal. We predicted that diffusion of axon plasma membrane proteins is anisotropic as longitudinal diffusion is of different type than transverse (azimuthal) diffusion. We conclude that the periodic structure of the axon plays a critical role in controlling diffusion of proteins and lipids in the axon plasma membrane.

Synergistic Integration of Laboratory and Numerical Approaches in Studies of the Biomechanics of Diseased Red Blood Cells

In red blood cell (RBC) disorders, such as sickle cell disease, hereditary spherocytosis, and diabetes, alterations to the size and shape of RBCs due to either mutations of RBC proteins or changes to the extracellular environment, lead to compromised cell deformability, impaired cell stability, and increased propensity to aggregate. Numerous laboratory approaches have been implemented to elucidate the pathogenesis of RBC disorders. Concurrently, computational RBC models have been developed to simulate the dynamics of RBCs under physiological and pathological conditions. In this work, we review recent laboratory and computational studies of disordered RBCs. Distinguished from previous reviews, we emphasize how experimental techniques and computational modeling can be synergically integrated to improve the understanding of the pathophysiology of hematological disorders.

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.

Computational Biomechanics of Human Red Blood Cells in Hematological Disorders

We review recent advances in multiscale modeling of the biomechanical characteristics of red blood cells (RBCs) in hematological diseases, and their relevance to the structure and dynamics of defective RBCs. We highlight examples of successful simulations of blood disorders including malaria and other hereditary disorders, such as sickle-cell anemia, spherocytosis, and elliptocytosis.

Nano- and microparticles at fluid and biological interfaces

Systems with interfaces are abundant in both technological applications and biology. While a fluid interface separates two fluids, membranes separate the inside of vesicles from the outside, the interior of biological cells from the environment, and compartmentalize cells into organelles. The physical properties of interfaces are characterized by interface tension, those of membranes are characterized by bending and stretching elasticity. Amphiphilic molecules like surfactants that are added to a system with two immiscible fluids decrease the interface tension and induce a bending rigidity. Lipid bilayer membranes of vesicles can be stretched or compressed by osmotic pressure; in biological cells, also the presence of a cytoskeleton can induce membrane tension. If the thickness of the interface or the membrane is small compared with its lateral extension, both can be described using two-dimensional mathematical surfaces embedded in three-dimensional space. We review recent work on the interaction of particles with interfaces and membranes. This can be micrometer-sized particles at interfaces that stabilise emulsions or form colloidosomes, as well as typically nanometer-sized particles at membranes, such as viruses, parasites, and engineered drug delivery systems. In both cases, we first discuss the interaction of single particles with interfaces and membranes, e.g. particles in external fields, non-spherical particles, and particles at curved interfaces, followed by interface-mediated interaction between two particles, many-particle interactions, interface and membrane curvature-induced phenomena, and applications.

Modeling of the axon membrane skeleton structure and implications for its mechanical properties

Super-resolution microscopy recently revealed that, unlike the soma and dendrites, the axon membrane skeleton is structured as a series of actin rings connected by spectrin filaments that are held under tension. Currently, the structure-function relationship of the axonal structure is unclear. Here, we used atomic force microscopy (AFM) to show that the stiffness of the axon plasma membrane is significantly higher than the stiffnesses of dendrites and somata. To examine whether the structure of the axon plasma membrane determines its overall stiffness, we introduced a coarse-grain molecular dynamics model of the axon membrane skeleton that reproduces the structure identified by super-resolution microscopy. Our proposed computational model accurately simulates the median value of the Young’s modulus of the axon plasma membrane determined by atomic force microscopy. It also predicts that because the spectrin filaments are under entropic tension, the thermal random motion of the voltage-gated sodium channels (Na_v), which are bound to ankyrin particles, a critical axonal protein, is reduced compared to the thermal motion when spectrin filaments are held at equilibrium. Lastly, our model predicts that because spectrin filaments are under tension, any axonal injuries that lacerate spectrin filaments will likely lead to a permanent disruption of the membrane skeleton due to the inability of spectrin filaments to spontaneously form their initial under-tension configuration.

Super-resolution microscopy has suggested that the actin cytoskeleton structure differ between various neuronal subcompartments. To determine the possible implication of the differing actin cytoskeleton structure, we determined the stiffness of the plasma membrane of neuronal subcompartments using atomic force microscopy (AFM). We found that axons are almost ~6 fold stiffer than the soma and ~2 fold stiffer than dendrites. By using a particle-based model for the surface membrane skeleton of the axon that comprises actin rings connected with spring filaments to represent the axonal structure, we show that regions neighboring actin rings are stiffer than areas between these rings. In these in between sub-regions, the spectrin filaments determine stiffness. Our modeling also shows that because the spectrin filaments are under tension, the thermal jitter of the actin-associated ankyrin particles, connected to the middle area of spectrin filaments, is minimal. As a result, we propose that the sodium channels bound to ankyrin particles will maintain an ordered distribution along the axon. We also predict that laceration of the spectrin filaments due to injury will cause a permanent damage to the axon since spontaneous repair of the spectrin network is not possible as spectrin filaments are under entropic tension.

Plasma Membrane is Compartmentalized by a Self-Similar Cortical Actin Meshwork

A broad range of membrane proteins display anomalous diffusion on the cell surface. Different methods provide evidence for obstructed subdiffusion and diffusion on a fractal space, but the underlying structure inducing anomalous diffusion has never been visualized because of experimental challenges. We addressed this problem by imaging the cortical actin at high resolution while simultaneously tracking individual membrane proteins in live mammalian cells. Our data confirm that actin introduces barriers leading to compartmentalization of the plasma membrane and that membrane proteins are transiently confined within actin fences. Furthermore, superresolution imaging shows that the cortical actin is organized into a self-similar meshwork. These results present a hierarchical nanoscale picture of the plasma membrane.

Exploring in vivo cholesterol-mediated interactions between activated EGF receptors in plasma membrane with single-molecule optical tracking

Background

The first step in many cellular signaling processes occurs at various types of receptors in the plasma membrane. Membrane cholesterol can alter these signaling pathways of living cells. However, the process in which the interaction of activated receptors is modulated by cholesterol remains unclear.

Methods

In this study, we measured single-molecule optical trajectories of epidermal growth factor receptors moving in the plasma membranes of two cancerous cell lines and one normal endothelial cell line. A stochastic model was developed and applied to identify critical information from single-molecule trajectories.

Results

We discovered that unliganded epidermal growth factor receptors may reside nearby cholesterol-riched regions of the plasma membrane and can move into these lipid domains when subjected to ligand binding. The amount of membrane cholesterol considerably affects the stability of correlated motion of activated epidermal growth factor receptors.

Conclusions

Our results provide single-molecule evidence of membrane cholesterol in regulating signaling receptors. Because the three cell lines used for this study are quite diverse, our results may be useful to shed light on the mechanism of cholesterol-mediated interaction between activated receptors in live cells.

Modeling of band-3 protein diffusion in the normal and defective red blood cell membrane

We employ a two-component red blood cell (RBC) membrane model to simulate lateral diffusion of band-3 proteins in the normal RBC and in the RBC with defective membrane proteins. The defects reduce the connectivity between the lipid bilayer and the membrane skeleton (vertical connectivity), or the connectivity of the membrane skeleton itself (horizontal connectivity), and are associated with the blood disorders of hereditary spherocytosis (HS) and hereditary elliptocytosis (HE) respectively. Initially, we demonstrate that the cytoskeleton limits band-3 lateral mobility by measuring the band-3 macroscopic diffusion coefficients in the normal RBC membrane and in a lipid bilayer without the cytoskeleton. Then, we study band-3 diffusion in the defective RBC membrane and quantify the relation between band-3 diffusion coefficients and percentage of protein defects in HE RBCs. In addition, we illustrate that at low spectrin network connectivity (horizontal connectivity) band-3 subdiffusion can be approximated as anomalous diffusion, while at high horizontal connectivity band-3 diffusion is characterized as confined diffusion. Our simulations show that the band-3 anomalous diffusion exponent depends on the percentage of protein defects in the membrane cytoskeleton. We also confirm that the introduction of attraction between the lipid bilayer and the spectrin network reduces band-3 diffusion, but we show that this reduction is lower than predicted by the percolation theory. Furthermore, we predict that the attractive force between the spectrin filament and the lipid bilayer is at least 20 times smaller than the binding forces at band-3 and glycophorin C, the two major membrane binding sites. Finally, we explore diffusion of band-3 particles in the RBC membrane with defects related to vertical connectivity. We demonstrate that in this case band-3 diffusion can be approximated as confined diffusion for all attraction levels between the spectrin network and the lipid bilayer. By comparing the diffusion coefficients measured in horizontal vs. vertical defects, we conclude that band-3 mobility is primarily controlled by the horizontal connectivity.

Erythrocyte membrane model with explicit description of the lipid bilayer and the spectrin network

The membrane of the red blood cell (RBC) consists of spectrin tetramers connected at actin junctional complexes, forming a two-dimensional (2D) sixfold triangular network anchored to the lipid bilayer. Better understanding of the erythrocyte mechanics in hereditary blood disorders such as spherocytosis, elliptocytosis, and especially, sickle cell disease requires the development of a detailed membrane model. In this study, we introduce a mesoscale implicit-solvent coarse-grained molecular dynamics (CGMD) model of the erythrocyte membrane that explicitly describes the phospholipid bilayer and the cytoskeleton, by extending a previously developed two-component RBC membrane model. We show that the proposed model represents RBC membrane with the appropriate bending stiffness and shear modulus. The timescale and self-consistency of the model are established by comparing our results with experimentally measured viscosity and thermal fluctuations of the RBC membrane. Furthermore, we measure the pressure exerted by the cytoskeleton on the lipid bilayer. We find that defects at the anchoring points of the cytoskeleton to the lipid bilayer (as in spherocytes) cause a reduction in the pressure compared with an intact membrane, whereas defects in the dimer-dimer association of a spectrin filament (as in elliptocytes) cause an even larger decrease in the pressure. We conjecture that this finding may explain why the experimentally measured diffusion coefficients of band-3 proteins are higher in elliptocytes than in spherocytes, and higher than in normal RBCs. Finally, we study the effects that possible attractive forces between the spectrin filaments and the lipid bilayer have on the pressure applied on the lipid bilayer by the filaments. We discover that the attractive forces cause an increase in the pressure as they diminish the effect of membrane protein defects. As this finding contradicts with experimental results, we conclude that the attractive forces are moderate and do not impose a complete attachment of the filaments to the lipid bilayer.

Vesiculation of healthy and defective red blood cells

Vesiculation of mature red blood cells (RBCs) contributes to removal of defective patches of the erythrocyte membrane. In blood disorders, which are related to defects in proteins of the RBC membrane, vesiculation of the plasma membrane is intensified. Several hypotheses have been proposed to explain RBC vesiculation but the exact underlying mechanisms and what determines the sizes of the vesicles are still not completely understood. In this work, we apply a two-component coarse-grained molecular dynamics RBC membrane model to study how RBC vesiculation is controlled by the membrane spontaneous curvature and by lateral compression of the membrane. Our simulation results show that the formation of small homogeneous vesicles with a diameter less than 40 nm can be attributed to a large spontaneous curvature of membrane domains. On the other hand, compression on the membrane can cause the formation of vesicles with heterogeneous composition and with sizes comparable with the size of the cytoskeleton corral. When spontaneous curvature and lateral compression are simultaneously considered, the compression on the membrane tends to facilitate formation of vesicles originating from curved membrane domains. We also simulate vesiculation of RBCs with membrane defects connected to hereditary elliptocytosis (HE) and to hereditary spherocytosis (HS). When the vertical connectivity between the lipid bilayer and the membrane skeleton is elevated, as in normal RBCs, multiple vesicles are shed from the compressed membrane with diameters similar to the cytoskeleton corral size. In HS RBCs, where the connectivity between the lipid bilayer and the cytoskeleton is reduced, larger-size vesicles are released under the same compression ratio as in normal RBCs. Lastly, we find that vesicles released from HE RBCs can contain cytoskeletal filaments due to fragmentation of the membrane skeleton while vesicles released from the HS RBCs are depleted of cytoskeletal filaments.

Interplay of cytoskeletal activity and lipid phase stability in dynamic protein recruitment and clustering

Recent experiments have revealed that some membrane proteins aggregate to form clusters. This type of process has been proven to be dynamic and to be actively maintained by external kinetics. Additionally, this dynamic recruiting is cholesterol- and actin-dependent, suggesting that raft organization and cytoskeleton rearrangement play a crucial role. In the present study, we propose a simple model that provides a general framework to describe the dynamical behavior of lipid-protein assemblies. Our results suggest that lipid-mediated interactions and cytoskeleton-anchored proteins contribute to the modulation of such behavior. In particular, we find a resonant condition between the membrane protein and cytoskeleton dynamics that results in the invariance of the ratio of clustered proteins that is found in in vivo experimental observations.

Differential effects of G- and F-actin on the plasma membrane calcium pump activity

We have previously shown that plasma membrane calcium ATPase (PMCA) pump activity is affected by the membrane protein concentration (Vanagas et al., Biochim Biophys Acta 1768:1641-1644, 2007). The results of this study provided evidence for the involvement of the actin cytoskeleton. In this study, we explored the relationship between the polymerization state of actin and its effects on purified PMCA activity. Our results show that PMCA associates with the actin cytoskeleton and this interaction causes a modulation of the catalytic activity involving the phosphorylated intermediate of the pump. The state of actin polymerization determines whether it acts as an activator or an inhibitor of the pump: G-actin and/or short oligomers activate the pump, while F-actin inhibits it. The effects of actin on PMCA are the consequence of direct interaction as demonstrated by immunoblotting and cosedimentation experiments. Taken together, these findings suggest that interactions with actin play a dynamic role in the regulation of PMCA-mediated Ca(2+) extrusion through the membrane. Our results provide further evidence of the activation-inhibition phenomenon as a property of many cytoskeleton-associated membrane proteins where the cytoskeleton is no longer restricted to a mechanical function but is dynamically involved in modulating the activity of integral proteins with which it interacts.

Membrane lateral structure: the influence of immobilized particles on domain size

In experiments on model membranes, formation of large domains of different lipid composition is readily observed. However, no such phase separation is observed in the membranes of intact cells. Instead, small transient inhomogeneities called lipid rafts are expected in these systems. One of the numerous attempts to explain small domains refers to the coupling of the membrane to its surroundings, which leads to the immobilization of some of the membrane molecules. These immobilized molecules then act as static obstacles for the remaining mobile ones. We present detailed Molecular Dynamics simulations demonstrating that this can indeed account for small domains. This confirms previous Monte Carlo studies based on simplified models. Furthermore, by directly comparing domain structures obtained using Molecular Dynamics to Monte Carlo simulations of the Ising model, we demonstrate that domain formation in the presence of obstacles is remarkably insensitive to the details of the molecular interactions.

Non-Gaussianity in single-particle tracking: use of kurtosis to learn the characteristics of a cage-type potential

Nonlinear interaction of membrane proteins with cytoskeleton and membrane leads to non-Gaussian structure of their displacement probability distribution. We propose a statistical analysis technique for learning the characteristics of the nonlinear potential from the time dependence of the cumulants of the displacement distribution. The efficiency of the approach is demonstrated on the analysis of the kurtosis of the displacement distribution of the particle traveling on a membrane in a cage-type potential. Results of numerical simulations are supported by analytical predictions. We show that the approach allows robust identification of some characteristics of the potential for the much lower temporal resolution compared with the mean-square displacement analysis and we demonstrate robustness to experimental errors in determining the particle positions.

Clustered diffusion of integrins

We discuss the diffusion of clusters of integrins (and other similar membrane proteins) on a cell membrane with a cortical cytoskeleton. We argue that protein clusters--in contrast with normal oligomers, which are forced to pass through cytoskeletal barriers all at once--should be treated essentially as many-legged random walkers that can pass through a cytoskeletal barrier by putting one leg at a time through the fence. We present the mathematics that should describe the phenomenon, which result in a two-parameter model of diffusion that should apply to any cluster size. We also perform and discuss numerical simulations of the effect in the erythrocyte model system.

Plasmodesmata viewed as specialised membrane adhesion sites

A significant amount of work has been expended to identify the elusive components of plasmodesmata (PD) to help understand their structure, as well as how proteins are targeted to them. This review focuses on the role that lipid membranes may play in defining PD both structurally and as subcellular targeting addresses. Parallels are drawn to findings in other areas of research which focus on the lateral segregation of membrane domains and the generation of three-dimensional organellar shapes from flat lipid bilayers. We conclude that consideration of the protein-lipid interactions in cell biological studies of PD components and PD-targeted proteins may yield new insights into some of the many open questions regarding these unique structures.

Spatial structure and diffusive dynamics from single-particle trajectories using spline analysis

Single-particle tracking of biomolecular probes has provided a wealth of information about intracellular trafficking and the dynamics of proteins and lipids in the cell membrane. Conventional mean-square displacement (MSD) analysis of single-particle trajectories often assumes that probes are moving in a uniform environment. However, the observed two-dimensional motion of probe particles is influenced by the local three-dimensional geometry of the cell membrane and intracellular structures, which are rarely flat at the submicron scale. This complex geometry can lead to spatially confined trajectories that are difficult to analyze and interpret using conventional two-dimensional MSD analysis. Here we present two methods to analyze spatially confined trajectories: spline-curve dynamics analysis, which extends conventional MSD analysis to measure diffusive motion in confined trajectories; and spline-curve spatial analysis, which measures spatial structures smaller than the limits of optical resolution. We show, using simulated random walks and experimental trajectories of quantum dot probes, that differences in measured two-dimensional diffusion coefficients do not always reflect differences in underlying diffusive dynamics, but can instead be due to differences in confinement geometries of cellular structures.

Computer simulations of protein diffusion in compartmentalized cell membranes

The diffusion of proteins in the cell membrane is investigated using computer simulations of a two-dimensional model. The membrane is assumed to be divided into compartments, with adjacent compartments separated by a barrier of stationary obstacles. Each compartment contains traps represented by stationary attractive disks. Depending on their size, these traps are intended to model either smaller compartments or binding sites. The simulations are intended to model the double-compartment model, which has been used to interpret single molecule experiments in normal rat kidney cells, where five regimes of transport are observed. The simulations show, however, that five regimes are observed only when there is a large separation between the sizes of the traps and large compartments, casting doubt on the double compartment model for the membrane. The diffusive behavior is sensitive to the concentration and size of traps and the strength of the barrier between compartments suggesting that the diffusion of proteins can be effectively used to characterize the structure of the membrane.