Simulation Studies of Dynamical Heterogeneity in a Dense Two-Dimensional Dimer-Solvent System with Obstacles

A coarse-grained model of a two-dimensional colloidal suspension was designed. The model was athermal and, in addition, a lattice approximation was introduced. It consisted of solvent (monomer) molecules, dimer molecules, and immobile impenetrable obstacles that introduced additional heterogeneity into the system. Dynamic properties were determined by a Monte Carlo simulation using the dynamic lattice liquid simulation algorithm. It is shown that there is a range of obstacle concentrations in which different diffusion characteristics were observed for dimers and solvents. In the system studied, it is possible to define the ranges of concentrations of individual components (solvent, dimers, and obstacles), in which the nature of the movement of dimers and solvents is different (normal diffusion vs. subdiffusion). The ratio of diffusion coefficients of solvent molecules and dimers for short times does not depend on the concentration of obstacles, while for long times, the ratio increases but remains independent of the concentration of the dimer.

Motion of Particles in a Monolayer Induced by Coalescing of a Bubble with a Planar Air-Water Interface

The motion of particles in a monolayer induced by the coalescing of a bare bubble with a planar air-water interface was investigated in a modified Langmuir trough. Experiments were performed to understand the effect of particle hydrophobicity, subphase pH, packing density, the presence of a weak surfactant, and particle size distribution on the behavior of particle movement in the monolayer during the coalescence process. Video tracking software was used to track the particles and extract data based on the video footage. Visual inspection indicated that the coalescence of the bubble with the monolayer was a chaotic process which led the interface to oscillate to an extent that the particles underwent complete rearrangement. A simple analysis was carried out on the main forces involved in particle motion and rearrangement at the oscillating air-water interface. The motion characteristic of particles was evaluated by speed and mean-square displacement (MSD). The results showed that the butanol-treated particles had higher speed and MSD than the particles with a stronger affinity to the air-water interface. Similar results were also found at high subphase pH and low packing factor.

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.

Hopanoids Like Sterols Form Compact but Fluid Films

Hopanoids are pentacyclic molecules present in membranes from some bacteria, recently proposed as sterol surrogates in these organisms. Diplopterol is an abundant hopanoid that, similar to sterols, does not self-aggregate in lamellar structures when pure, but forms monolayers at the air-water interface. Here, we analyze the interfacial behavior of pure diplopterol and compare it with sterols from different organisms: cholesterol from mammals, ergosterol from fungi, and stigmasterol from plants. We prepared Langmuir monolayers of the compounds and studied their surface properties using different experimental approaches and molecular dynamics simulations. Our results indicate that the films formed by diplopterol, despite being compact with low mean molecular areas, high surface potentials, and high refractive index, depict shear viscosity values similar to that for fluid films. Altogether, our results reveal that hopanoids have similar interfacial behavior than that of sterols, and thus they may have the capacity of modulating bacterial membrane properties in a similar way sterols do in eukaryotes.

Fractal analysis of lateral movement in biomembranes

Lateral movement of a molecule in a biomembrane containing small compartments (0.23-μm diameter) and large ones (0.75 μm) is analyzed using a fractal description of its walk. The early time dependence of the mean square displacement varies from linear due to the contribution of ballistic motion. In small compartments, walking molecules do not have sufficient time or space to develop an asymptotic relation and the diffusion coefficient deduced from the experimental records is lower than that measured without restrictions. The model makes it possible to deduce the molecule step parameters, namely the step length and time, from data concerning confined and unrestricted diffusion coefficients. This is also possible using experimental results for sub-diffusive transport. The transition from normal to anomalous diffusion does not affect the molecule step parameters. The experimental literature data on molecular trajectories recorded at a high time resolution appear to confirm the modeled value of the mean free path length of DOPE for Brownian and anomalous diffusion. Although the step length and time give the proper values of diffusion coefficient, the DOPE speed calculated as their quotient is several orders of magnitude lower than the thermal speed. This is interpreted as a result of intermolecular interactions, as confirmed by lateral diffusion of other molecules in different membranes. The molecule step parameters are then utilized to analyze the problem of multiple visits in small compartments. The modeling of the diffusion exponent results in a smooth transition to normal diffusion on entering a large compartment, as observed in experiments.

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.

Diffusional motion as a gauge of fluidity and interfacial adhesion. Supported alkylphosphonate monolayers

We report on the use of diffusion measurements to gauge the fluidity and surface binding properties of a molecular monolayer. The monolayer film consists of octadecyl-1-phosphonic acid (ODPA) and controlled amounts of a lyso-phosphatidic acid tagged with the fluorescent probe BODIPY (BLPA). The monolayer films were formed using a Langmuir-Blodgett (LB) trough and deposited onto a glass slide. Monolayer morphology was characterized during film formation using Brewster angle microscopy (BAM). Fluorescence Recovery After Photobleaching (FRAP) microscopy was used to measure translational diffusion of BLPA and Fluorescence Anisotropy Decay Imaging (FADI) was used to measure rotational diffusion of the BLPA chromophore. These results provide information on the motional freedom of the probe and, importantly, on the strength of interaction between the probe and the support. Compositional variations in the monolayer give rise to changes in constituent dynamics that reflect intermolecular interactions.

Faster Convergence of Diffusion Anisotropy Detection by Three-Step Relation of Single-Particle Trajectory

We focus on the issue of limited number of samples in the single particle tracking (SPT) when trying to extract the diffusion anisotropy that originates from the particle asymmetry. We propose a novel evaluation technique of SPT making use of the relation of the consecutive three steps. More specifically, the trend of the angle comprised of the three positions and the displacements are plotted on a scatter diagram. The particle anisotropy dependence of the shape of the scatter diagram is examined through the data from the standard numerical model of anisotropic two-dimensional Brownian motion. Comparison with the existing method reveals the faster convergence in the evaluation. In particular, our proposed method realizes the detection of diffusion anisotropy under the conditions of not only less number of data but also larger time steps. This is of practical importance not only when the abundant data is hard to achieve but also when the rotational diffusion is fast compared to the frame rate of the camera equipment, which tends to be more common for smaller particles or molecules of interest.

Simulation of diffusion in a crowded environment

We performed extensive and systematic simulation studies of two-dimensional fluid motion in a complex crowded environment. In contrast to other studies we focused on cooperative phenomena that occurred if the motion of particles takes place in a dense crowded system, which can be considered as a crude model of a cellular membrane. Our main goal was to answer the following question: how do the fluid molecules move in an environment with a complex structure, taking into account the fact that motions of fluid molecules are highly correlated. The dynamic lattice liquid (DLL) model, which can work at the highest fluid density, was employed. Within the frame of the DLL model we considered cooperative motion of fluid particles in an environment that contained static obstacles. The dynamic properties of the system as a function of the concentration of obstacles were studied. The subdiffusive motion of particles was found in the crowded system. The influence of hydrodynamics on the motion was investigated via analysis of the displacement in closed cooperative loops. The simulation and the analysis emphasize the influence of the movement correlation between moving particles and obstacles.

Stiffness of lipid monolayers with phase coexistence

The surface dilational modulus--or compressibility modulus--has been previously studied for monolayers composed of pure materials, where a jump in this modulus was related with the onset of percolation as a result of the establishment of a connected structure at the molecular level. In this work, we focused on monolayers composed of two components of low lateral miscibility. Our aim was to investigate the compressibility of mixed monolayers at pressures and compositions in the two-phase region of the phase diagram, in order to analyze the effect of the mechanical properties of each phase on the stiffness of the composite. In nine different systems with distinct molecular dipoles and charges, the stiffness of each phase and the texture at the plane of the monolayer were studied. In this way, we were able to analyze the general compressibility of two-phase lipid monolayers, regardless of the properties of their constituent parts. The results are discussed in the light of the following two hypotheses: first, the stiffness of the composite could be dominated by the stiffness of each phase as a weighted sum according to the percentage of each phase area, regardless of the distribution of the phases in the plane of the monolayer. Alternatively, the stiffness of the composite could be dominated by the mechanical properties of the continuous phase. Our results were better explained by this latter proposal, as in all the analyzed mixtures it was found that the mechanical properties of the percolating phase were the determining factors. The value of the compression modulus was closer to the value of the connected phase than to that of the dispersed phase, indicating that the bidimensional composites displayed mechanical properties that were related to the properties of each phases in a rather complex manner.

Single molecule observations of desorption-mediated diffusion at the solid-liquid interface

By directly observing molecular trajectories on a chemically heterogeneous surface, we have identified two distinct modes of diffusion involving (1) displacements within isolated surface islands (crawling mode), and (2) displacements where a molecule desorbs from an island, diffuses through the adjacent liquid phase, and readsorbs on another island (flying mode). The diffusion coefficients corresponding to these two modes differ by an order of magnitude, and both modes are also observed on chemically homogeneous surfaces. Comparison with previous results suggested that desorption-mediated diffusion is the primary transport mechanism in self-assembled monolayer formation.

Rheological properties of a two phase lipid monolayer at the air/water interface: effect of the composition of the mixture

Many biologically relevant monolayers show coexistence of discrete domains of a long-range ordered condensed phase dispersed in a continuous, disordered, liquid-expanded phase. In this work, we determined the viscous and elastic components of the compressibility modulus and the shear viscosity of monolayers exhibiting phase coexistence with the aim at elucidating the contribution of each phase to the observed monolayer mechanical properties. To this purpose, mixed monolayers with different proportions of distearoylphosphatidylcholine (DSPC) and dimyristoylphosphatidylcholine (DMPC) were prepared and their rheological properties were analyzed. The relationship between the phase diagram of the mixture at 10 mN m(-1) and the rheological properties was studied. We found that the monolayer shear viscosity is highly dependent on the presence of domains and on the domain density. In turn, the monolayer compressibility is only influenced by the presence of domains for high domain densities. For monolayers that look homogeneous on the micrometer scale (DSPC amount lower that 23 mol %), all the analyzed rheological properties remain similar to those observed for pure DMPC monolayers, indicating that in this proportion range the DSPC molecules contribute as DMPC to the surface rheology in spite of having hydrocarbon chains four carbons longer.

A hidden Markov model for single particle tracks quantifies dynamic interactions between LFA-1 and the actin cytoskeleton

The extraction of hidden information from complex trajectories is a continuing problem in single-particle and single-molecule experiments. Particle trajectories are the result of multiple phenomena, and new methods for revealing changes in molecular processes are needed. We have developed a practical technique that is capable of identifying multiple states of diffusion within experimental trajectories. We model single particle tracks for a membrane-associated protein interacting with a homogeneously distributed binding partner and show that, with certain simplifying assumptions, particle trajectories can be regarded as the outcome of a two-state hidden Markov model. Using simulated trajectories, we demonstrate that this model can be used to identify the key biophysical parameters for such a system, namely the diffusion coefficients of the underlying states, and the rates of transition between them. We use a stochastic optimization scheme to compute maximum likelihood estimates of these parameters. We have applied this analysis to single-particle trajectories of the integrin receptor lymphocyte function-associated antigen-1 (LFA-1) on live T cells. Our analysis reveals that the diffusion of LFA-1 is indeed approximately two-state, and is characterized by large changes in cytoskeletal interactions upon cellular activation.

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.

Attractive membrane domains control lateral diffusion

Lipid membranes play a fundamental role in vital cellular functions such as signal transduction. Many of these processes rely on lateral diffusion within the membrane, generally a complex fluid containing ordered microdomains. However, little attention has been paid to the alterations in transport dynamics of a diffusing species caused by long-range interactions with membrane domains. In this paper, we address the effect of such interactions on diffusive transport by studying lateral diffusion in a phase-separated Langmuir phospholipid monolayer via single-particle tracking. We find that attractive dipole-dipole interactions between condensed phase domains and diffusing probe beads lead to transient confinement at the phase boundaries, causing a transition from two- to one-dimensional diffusion. Using Brownian dynamics simulations, the long-term diffusion constant for such a system is found to have a sensitive, Boltzmann-like, dependence on the interaction strength. In addition, this interaction strength is shown to be a strong function of the ratio of domain to particle size. As similar interactions are expected in biological membranes, the modulation of diffusive transport dynamics by varying interaction strength and/or domain size may offer cells selective spatial and temporal control over signaling processes.

Diffusion of nanoparticles in monolayers is modulated by domain size

Langmuir monolayers are often used as simple models for biological membranes. The possibility to change their composition and phase state in a very controlled manner as well as access to a large observation area makes them a versatile tool for the investigation of membrane-related interactions. Inspired by experiments in our group, we investigate the interaction of single, partially charged nanoparticles with lipid microdomains by Monte Carlo simulations. Condensed domains in inhomogeneous Langmuir monolayers exhibit an electric dipole field interacting attractively with the nanoparticle's dipole moment. With increasing domain size, the resulting electric field changes from single dipole to semi-infinite domain characteristics, significantly influencing the motion of the particle. Small immobile domains (R = 1 microm) confine the movement of the tracer to the boundary of the domain whereas for large domains (R > or = 10 microm) its motion is only temporarily hindered. This suggests a powerful mechanism for controlling diffusive transport in lipid membranes.

Single-particle tracking of membrane protein diffusion in a potential: simulation, detection, and application to confined diffusion of CFTR Cl- channels

Confined diffusion of membrane receptors and lipids can result from intramembrane barriers, skeletal interactions, rafts, and other phenomena. We simulated single-particle diffusion in two dimensions in an arbitrary potential, V(r), based on summation of random and potential gradient-driven motions. Algorithms were applied and verified for detection of potential-driven diffusion, and for determination of V(r) from radial particle density distributions, taking into account experimental uncertainties in particle position and finite trajectory recording. Single-particle tracking (SPT) analysis of the diffusion of cystic fibrosis transmembrane conductance regulator (CFTR) Cl(-) channels in mammalian cells revealed confined diffusion with diffusion coefficient approximately 0.004 microm(2)/s. SPT data fitted closely to a springlike attractive potential, V(r) = kr(2), but not to other V(r) forms such as hard-wall or viscoelastic-like potentials. The "spring constant", k, determined from SPT data was 2.6 +/- 0.8 pN/microm, and not altered significantly by modulation of skeletal protein architecture by jasplakinolide. However, k was reduced by a low concentration of latrunculin, supporting the involvement of actin in the springlike tethering of CFTR. Confined diffusion of membrane proteins is likely a general phenomenon suitable for noninvasive V(r) analysis of force-producing mechanisms. Our data provide the first measurement of actin elasticity, to the best of our knowledge, that does not involve application of an external force.

Accurate particle position measurement from images

The moment method is an image analysis technique for subpixel estimation of particle positions. The total error in the calculated particle position includes effects of pixel locking and random noise in each pixel. Pixel locking, also known as peak locking, is an artifact where calculated particle positions are concentrated at certain locations relative to pixel edges. We report simulations to gain an understanding of the sources of error and their dependence on parameters the experimenter can control. We suggest an algorithm, and we find optimal parameters an experimenter can use to minimize total error and pixel locking. For a dusty plasma experiment, we find that a subpixel accuracy of 0.017 pixel or better can be attained. These results are also useful for improving particle position measurement and particle tracking velocimetry using video microscopy in fields including colloids, biology, and fluid mechanics.

A biological interpretation of transient anomalous subdiffusion. I. Qualitative model

Anomalous subdiffusion has been reported for two-dimensional diffusion in the plasma membrane and three-dimensional diffusion in the nucleus and cytoplasm. If a particle diffuses in a suitable infinite hierarchy of binding sites, diffusion is well known to be anomalous at all times. But if the hierarchy is finite, diffusion is anomalous at short times and normal at long times. For a prescribed set of binding sites, Monte Carlo calculations yield the anomalous diffusion exponent and the average time over which diffusion is anomalous. If even a single binding site is present, there is a very short, almost artifactual, period of anomalous subdiffusion, but a hierarchy of binding sites extends the anomalous regime considerably. As is well known, an essential requirement for anomalous subdiffusion due to binding is that the diffusing particle cannot be in thermal equilibrium with the binding sites; an equilibrated particle diffuses normally at all times. Anomalous subdiffusion due to barriers, however, still occurs at thermal equilibrium, and anomalous subdiffusion due to a combination of binding sites and barriers is reduced but not eliminated on equilibration. This physical model is translated directly into a plausible biological model testable by single-particle tracking.

Lateral diffusion and percolation in membranes

An algorithm based on Voronoi tessellation and percolation theory is presented to study the diffusion of model membrane components (solutes) in the plasma membrane. The membrane is modeled as a two-dimensional space with integral membrane proteins as static obstacles. The Voronoi diagram consists of vertices, which are equidistant from three matrix obstacles, joined by edges. An edge between two vertices is said to be connected if solute particles can pass directly between the two regions. The percolation threshold, pc, determined using this passage criterion is pc approximately equal to 0.53. This is smaller than if the connectivity of edges were assigned randomly, in which case the percolation threshold pr=2/3, where p is the fraction of connected edges. Molecular dynamics simulations show that diffusion is determined by percolation of clusters of edges.