Diffusion factor calculation for TIP4P model of water

A molecular dynamics study has been undertaken for a model of liquid TIP4P water. Thermal dependencies of water density and radial distribution functions were calculated for model verification. Three methods have been used for calculation of diffusion factor thermal dependencies. Their sensitivity to molecular system size and length of used trajectory has been analyzed. It has been shown that Green-Kubo formula-based approach which associates diffusion factor with speed autocorrelation function integral is preferred in case of short MD simulations. The second approach based on Einstein equation which associates mean square displacement of molecule with time is preferred in case of long simulations. It has been also demonstrated that it is possible to modify the second approach to make it more stable and reliable. This modification is to use a slope of the graph of the mean square displacement on time as the estimation of the diffusion factor instead of the ratio of molecule mean square displacement and time.     

Single-particle tracking of oriC-GFP fluorescent spots during chromosome segregation in Escherichia coli

DNA regions close to the origin of replication were visualized by the green fluorescent protein (GFP)-Lac repressor/lac operator system. The number of oriC-GFP fluorescent spots per cell and per nucleoid in batch-cultured cells corresponded to the theoretical DNA replication pattern. A similar pattern was observed in cells growing on microscope slides used for time-lapse experiments. The trajectories of 124 oriC-GFP spots were monitored by time-lapse microscopy of 31 cells at time intervals of 1, 2, and 3 min. Spot positions were determined along the short and long axis of cells. The lengthwise movement of spots was corrected for cell elongation. The step sizes of the spots showed a Gaussian distribution with a standard deviation of approximately 110 nm. Plots of the mean square displacement versus time indicated a free diffusion regime for spot movement along the long axis of the cell, with a diffusion coefficient of 4.3+/-2.6x10(-5) microm2/s. Spot movement along the short axis showed confinement in a region of the diameter of the nucleoid ( approximately 800 nm) with an effective diffusion coefficient of 2.9+/-1.7x10(-5) microm2/s. Confidence levels for the mean square displacement analysis were obtained from numerical simulations. We conclude from the analysis that within the experimental accuracy--the limits of which are indicated and discussed--there is no evidence that spot segregation requires any other mechanism than that of cell (length) growth.     

Dynamical properties of phospholipid bilayers from computer simulation

We present the results of a 10-ns molecular dynamics simulation of a dipalmitoylphosphatidylcholine/water system. The main emphasis of the present study is on the investigation of the stability over a long time and the dynamic properties of the water/membrane system. The motion of the lipid molecules is characterized by the center of mass movement and the displacement of individual atom groups. Because of the slow movement of the headgroup atoms, their contributions to the dipole potential vary slowly and with a large amplitude. Nevertheless, the water molecules compensate the strong fluctuations and maintain an almost constant total dipole potential. From the lateral displacement of the center of masses, we calculate the lateral diffusion coefficient to be Dlat = (3 +/- 0.6) x 10(-7) cm2/s, in agreement with neutron scattering results. The rotational motion is also investigated in our simulations. The calculated value for the rotational diffusion coefficient parallel to the molecular long axis, D = (1.6 +/- 0.1) x 10(8) s-1, is in good agreement with the experiment.     

Modeling of inorganic contaminant transport in dense bentonite

To assess the safety of the waste disposal site, a knowledge of the molecular diffusion coefficient through the bentonite‐clay barrier is required. The methods commonly used to determine molecular diffusion coefficient in clay are very time consuming. Because of the large number of species involved in the radioactive waste disposal site, a model that allows diffusion coefficient to be predicted for use is desirable. Models based on free water have been proposed but are found to be inadequate for compacted bentonitic clays. A model that incorporates clay‐species‐water interaction is presented for dense bentonite. The modeling results show that the diffusion coefficient depends on the charge nature and size of the diffusing species, water chemistry, temperature, and soil structure. The predicted diffusion coefficients for some species are shown to be in excellent agreement with those measured in dense bentonite.     

Tracking single proteins within cells

We present experiments in which single proteins were imaged and tracked within mammalian cells. Single proteins of R-phycoerythrin (RPE) were imaged by epifluorescence microscopy in the nucleoplasm and cytoplasm at 71 frames/s. We acquired two-dimensional trajectories of proteins (corresponding to the projection of three-dimensional trajectories onto the plane of focus) for an average of 17 frames in the cytoplasm and 16 frames in the nucleus. Diffusion constants were determined from linear fits to the mean square displacement and from the mean displacement squared per frame. We find that the distribution of diffusion constants for RPE within cells is broader than the distributions obtained from RPE in a glycerol solution, from a Monte Carlo simulation, and from the theoretical distribution for simple diffusion. This suggests that on the time scales of our measurements, the motion of single RPE proteins in the cytoplasm and nucleoplasm cannot be modeled by simple diffusion with a unique diffusion constant. Our results demonstrate that it is possible to follow the motion of single proteins within cells and that the technique of single molecule tracking can be used to probe the dynamics of intracellular macromolecules.     

The dynamics of cholesterol molecules near the surface of protein farnesyltransferase - computer simulation

We have made the molecular dynamics (MD) simulations for the cluster of cholesterols localized near the protein farnesyltransferase (1FT2) at the physiological temperature T=309.75K. We have observed that the cholesterol molecules form a lodgment on the surface of protein. Several physical characteristics of the deposited cholesterol cluster have been calculated among those: the mean square displacement, diffusion coefficient, linear and angular velocity autocorrelation function and their Fourier transforms.     

Molecular dynamics simulation of water permeation through the alpha-hemolysin channel

The alpha-hemolysin (AHL) nanochannel is a non-selective channel that allows for uncontrolled transport of small molecules across membranes leading to cell death. Although it is a bacterial toxin, it has promising applications, ranging from drug delivery systems to nano-sensing devices. This study focuses on the transport of water molecules through an AHL nanochannel using molecular dynamics (MD) simulations. Our results show that AHL can quickly transport water across membranes. The first-passage time approach was used to estimate the diffusion coefficient and the mean exit time. To study the energetics of transport, the potential of mean force (PMF) of a water molecule along the AHL nanochannel was calculated. The results show that the energy barriers of water permeation across a nanopore are always positive along the channel and the values are close to thermal energy (k_BT). These findings suggest that the observed quick permeation of water is due to small energy barriers and a hydrophobic inner channel surface resulting in smaller friction. We speculate that these physical mechanisms are important in how AHL causes cell death.     

Molecular Dynamics Simulation of Substrate-Enzyme Interactions in the Active Site Channel of Superoxide Dismutase

Abstract

Molecular dynamics simulations of the diffusion of superoxide ion down the active site channel of the enzyme superoxide dismutase were performed with a parallelized version of GROMOS on the Intel iPSC/860. Our model consisted of a spherical assembly of 6968 atoms centered at a copper ion in the enzyme. Trajectory analysis revealed that the anion is directed toward the copper ion through the cooperative motions of several active site residues. Other mechanistic and structural motifs recurring through five full trajectories are examined. In addition to these qualitative results, an upper bound has been calculated for the rate constant for displacement by substrate of the water molecule that is coordinated to the copper. This required an analysis of the dynamics of crossing a free energy barrier that has been characterized in previous work. Strong frictional effects due to Coulombic interactions lead to a rather small rate constant; the transmission coefficient is less than 0.01. The mechanism of the enzyme therefore may involve diffusion of substrate up to the bound water followed by electron transfer mediated by this water, rather than displacement of the water by substrate with subsequent electron transfer.     

Subdiffraction-limit study of Kaede diffusion and spatial distribution in live Escherichia coli

Photoactivation localization microscopy (PALM) is used to study the spatial distribution and diffusion of single copies of the protein Kaede in the cytoplasm of live Escherichia coli under moderate growth conditions (67 min doubling time). The spatial distribution of Kaede is uniform within the cytoplasm. The cytoplasmic radius of 380 ± 30 nm varies little from cell to cell. Single-particle tracking using 4 ms exposure times reveals negatively curved plots of mean-square displacement versus time. A detailed comparison with Monte Carlo simulations in a spherocylindrical volume shows that the curvature can be quantitatively understood in terms of free diffusion within a confining volume. The mean diffusion coefficient across cells is <D_Kaede> = 7.3 ± 1.1 μm²·s⁻¹, consistent with a homotetrameric form of Kaede. The distribution of squared displacements along the long axis for individual Kaede molecules is consistent with homogeneous diffusion. However, for longer cells, a spatial map of one-step estimates of the diffusion coefficient along x suggests that diffusion is ∼20–40% faster within nucleoids than in the ribosome-rich region lying between nucleoid lobes at the cell mid-plane. Fluorescence recovery after photobleaching yielded <D_FRAP> = 8.3 ± 1.6 μm²·s⁻¹, in agreement with the single-particle tracking results.     

CompuCell3D Simulations Reproduce Mesenchymal Cell Migration on Flat Substrates

Mesenchymal cell crawling is a critical process in normal development, in tissue function, and in many diseases. Quantitatively predictive numerical simulations of cell crawling thus have multiple scientific, medical, and technological applications. However, we still lack a low-computational-cost approach to simulate mesenchymal three-dimensional (3D) cell crawling. Here, we develop a computationally tractable 3D model (implemented as a simulation in the CompuCell3D simulation environment) of mesenchymal cells crawling on a two-dimensional substrate. The Fürth equation, the usual characterization of mean-squared displacement (MSD) curves for migrating cells, describes a motion in which, for increasing time intervals, cell movement transitions from a ballistic to a diffusive regime. Recent experiments have shown that for very short time intervals, cells exhibit an additional fast diffusive regime. Our simulations’ MSD curves reproduce the three experimentally observed temporal regimes, with fast diffusion for short time intervals, slow diffusion for long time intervals, and intermediate time -interval-ballistic motion. The resulting parameterization of the trajectories for both experiments and simulations allows the definition of time- and length scales that translate between computational and laboratory units. Rescaling by these scales allows direct quantitative comparisons among MSD curves and between velocity autocorrelation functions from experiments and simulations. Although our simulations replicate experimentally observed spontaneous symmetry breaking, short-timescale diffusive motion, and spontaneous cell-motion reorientation, their computational cost is low, allowing their use in multiscale virtual-tissue simulations. Comparisons between experimental and simulated cell motion support the hypothesis that short-time actomyosin dynamics affects longer-time cell motility. The success of the base cell-migration simulation model suggests its future application in more complex situations, including chemotaxis, migration through complex 3D matrices, and collective cell motion.     

Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position.

We present a novel optical technique for three-dimensional tracking of single fluorescent particles using a modified epifluorescence microscope containing a weak cylindrical lens in the detection optics and a microstepper-controlled fine focus. Images of small, fluorescent particles were circular in focus but ellipsoidal above and below focus; the major axis of the ellipsoid shifted by 90 degrees in going through focus. Particle z position was determined from the image shape and orientation by applying a peak detection algorithm to image projections along the x and y axes; x, y position was determined from the centroid of the particle image. Typical spatial resolution was 12 nm along the optical axis and 5 nm in the image plane with a maximum sampling rate of 3-4 Hz. The method was applied to track fluorescent particles in artificial solutions and living cells. In a solution of viscosity 30 cP, the mean squared distance (MSD) traveled by a 264 nm diameter rhodamine-labeled bead was linear with time to 20 s. The measured diffusion coefficient, 0.0558 +/- 0.001 micron2/s (SE, n = 4), agreed with the theoretical value of 0.0556 micron2/s. Statistical variability of MSD curves for a freely diffusing bead was in quantitative agreement with Monte Carlo simulations of three-dimensional random walks. In a porous glass matrix, the MSD data was curvilinear and showed reduced bead diffusion. In cytoplasm of Swiss 3T3 fibroblasts, bead diffusion was restricted. The water permeability in individual Chinese Hamster Ovary cells was measured from the z movement of a fluorescent bead fixed at the cell surface in response osmotic gradients; water permeability was increased by > threefold in cells expressing CHIP28 water channels. The simplicity and precision of this tracking method may be useful to quantify the complex trajectories of fluorescent particles in living cells.     

Molecular dynamics study of onset of water gelation around the collagen triple helix

The onset of water gelation around a collagen-like triple helix peptide was studied at ambient temperature and pressure by performing Molecular Dynamics simulations. The radial distribution functions of the oxygen and hydrogen atoms of water are distorted below 4 A from the peptide. The distortion is accompanied by the breakdown of the tetrahedral coordination of the hydrogen-bonded network of water molecules. The water shell around the peptide consists of alternating regions of higher and lower density. In agreement with experiments we find that the first hydration shell is kinetically labile, with a residence time in the order of picoseconds for a water molecule. From the computed diffusion coefficient, a key measure of the collective dynamics, we estimate the average diffusion speed decreases by a factor of 1.5 close to the peptide compared to the liquid. Our results give new insight in gel formation and structure on a molecular level.     

Diffusive properties of water in Artemia cysts as determined from quasi-elastic neutron scattering spectra.

Results have been obtained on the quasi-elastic spectra of neutrons scattered from pure water, a 20% agarose gel (hydration four grams H2O per gram of dry solid) and cysts of the brine shrimp Artemia for hydrations between 0.10 and 1.2 grams H2O per gram of dry solids. The spectra were interpreted using a two-component model that included contributions from the covalently bonded protons and the hydration water, and a mobile water fraction. The mobile fraction was described by a jump-diffusion correlation function for the translation motion and a simple diffusive orientational correlation function. The results for the line widths gamma (Q2) for pure water were in good agreement with previous measurements. The agarose results were consistent with NMR measurements that show a slightly reduced translational diffusion for the mobile water fraction. The Artemia results show that the translational diffusion coefficient of the mobile water fraction was greatly reduced from that of pure water. The line width was determined mainly by the rotational motion, which was also substantially reduced from the pure water value as determined from dielectric relaxation studies. The translational and rotational diffusion parameters were consistent with the NMR measurements of diffusion and relaxation. Values for the hydration fraction and the mean square thermal displacement [u2] as determined from the Q-dependence of the line areas were also obtained.     

Temporal evolution of the electron diffusion coefficient in electrolyte-filled mesoporous nanocrystalline TiO2 films

Electron transport in electrolyte-filled mesoporous TiO₂-based solar cells is described quantitatively from the perspective of the continuous-time random walk model. An analytical expression is derived for the time-dependent diffusion coefficient of electrons, which transforms at a characteristic (Fermi) time from strongly time-dependent values (dispersive transport) at short times to relatively time-independent values (nondispersive transport) at long times. At short times, the diffusion coefficient displays a power-law behavior with time. The timescale for the diffusion coefficient to reach its steady-state value is substantially longer than the Fermi time. The Fermi time and the steepness of the distribution of waiting times associated with trap sites have a strong influence on both the steady-state diffusion coefficient of electrons and on the dispersiveness of electron transport. At short timescales, ionic drag, associated with the ambipolar effect, slows electron transport through the TiO₂ matrix, whereas at steady state, transport is trap limited. Decreasing the electron density lowers the steady-state limit of the diffusion coefficient and increases the timescale over which transport is dispersive.     

A combined molecular dynamics and diffusion model of single proton conduction through gramicidin

We develop a model for proton conduction through gramicidin based on the molecular dynamics simulations of Pomès and Roux (Biophys. J. 72:A246, 1997). The transport of a single proton through the gramicidin pore is described by a potential of mean force and diffusion coefficient obtained from the molecular dynamics. In addition, the model incorporates the dynamics of a defect in the hydrogen bonding structure of pore waters without an excess proton. Proton entrance and exit were not simulated by the molecular dynamics. The single proton conduction model includes a simple representation of these processes that involves three free parameters. A reasonable value can be chosen for one of these, and the other two can be optimized to yield a good fit to the proton conductance data of, Ann. N.Y. Acad. Sci. 339:8-20) for pH > or = 1.7. A sensitivity analysis shows the significance of this fit.     

以消散场成像和单微粒跟踪技术揭示GLUT4囊泡和分泌囊泡的不同动态过程

葡萄糖转运子蛋白4(glucose transporter 4,GLUT4)在维持体内葡萄糖动态平衡的过程中起着至关重要的作用。GLUT4贮存囊泡(GLUT4 storage vesicle,GSV)和神经内分泌细胞中的分泌囊泡含有许多相同的蛋白。研究证明这些蛋白调节了分泌囊泡的胞内转运过程,但是GLUT4囊泡和分泌囊泡是否具有相同的胞内动态过程还未阐明。文章以3T3-L1纤维原细胞中的GSV和神经内分泌细胞PC12细胞中的分泌囊泡:致密核心大囊泡(large dense core vesicle,LDCV)为研究对象,使用消散场显微成像技术和单微粒跟踪技术直观观察了活体细胞内单个GSV和LDCV的三维运动轨迹。通过以适当方程拟合单个囊泡的均方位移曲线,发现两种囊泡都具有三种运动模式。定量分析显示作自由扩散运动和方向性扩散运动的GSV数量明显多于LDCV。对比GSV和LDCV的三维扩散系数,发现GSV的扩散系数中值为7.2×10-4μm2/s,而LDCV的扩散系数中值仅为1.94×10-4μm2/s。这一结果说明GSV的活动性远大于LDCV,提示GSV的胞内转运过程涉及不同的分子机制。     

Hydrogen bond analysis of confined water in mesoporous silica using the reactive force field

ABSTRACT

The structural and dynamical properties of water confined in nanoporous silica with a pore diameter of 2.7?nm were investigated by performing large-scale molecular dynamics simulations using the reactive force field. The radial distribution function and diffusion coefficient of water were calculated, and the values at the centre of the pore agreed well with experimental values for real water. In addition, the pore was divided into thin coaxial layers, and the average number of hydrogen bonds, hydrogen bond lifetime and hydrogen bond strength were calculated as a function of the radial distance from the pore central axis. The analysis showed that hydrogen bonds involving silanol (Si–OH) have a longer lifetime, although the average number of hydrogen bonds per atom does not change from that at the pore centre. The longer lifetime, as well as smaller diffusion coefficient, of these hydrogen bonds is attributed to their greater strength.     

Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells

Macromolecular crowding dramatically affects cellular processes such as protein folding and assembly, regulation of metabolic pathways, and condensation of DNA. Despite increased attention, we still lack a definition for how crowded a heterogeneous environment is at the molecular scale and how this manifests in basic physical phenomena like diffusion. Here, we show by means of fluorescence correlation spectroscopy and computer simulations that crowding manifests itself through the emergence of anomalous subdiffusion of cytoplasmic macromolecules. In other words, the mean square displacement of a protein will grow less than linear in time and the degree of this anomality depends on the size and conformation of the traced particle and on the total protein concentration of the solution. We therefore propose that the anomality of the diffusion can be used as a quantifiable measure for the crowdedness of the cytoplasm at the molecular scale.     

Evolution of linkage disequilibrium of the founders in exponentially growing populations

Evolution of linkage disequilibrium of the founders in exponentially growing populations was studied using a time-inhomogeneous It? process model. The model is an extension of the diffusion approximation of the Wright-Fisher model. As a measure of linkage disequilibrium, the squared standard linkage deviation, which is defined by a ratio of the moments, was considered. A system of ordinary differential equations that these moments obey was obtained. This system can be solved numerically. By simulations, it was shown that the squared standard linkage deviation gives a good approximation of the expectation of the squared correlation coefficient of gamete frequencies. In addition, a perturbative solution was obtained when the growth rate is not large. By using the perturbation, an asymptotic formula for the squared standard linkage deviation after a large number of generations was obtained. According to the formula, the squared standard linkage deviation tends to be 1/(4Nc), where N is the current size of the population and c is the recombination fraction between two loci. It is dependent on neither the initial effective size, the growth rate, nor the mutation rate. In exponentially growing populations, linkage disequilibrium will be asymptotically the same as that in a constant size population, the effective size of which is the current effective size.     

Interactions between lignin and urea researched by molecular simulation

Molecular simulations of interactions between urea molecules and lignin polymer have been carried out with the aim of understanding the mechanism of urea slow-release behaviours in lignin–urea materials. It has been found, by docking technology and natural bond orbital analysis, that H-bonds and π-electronic conjugation effect are the main driving forces to keep urea molecules adsorbed on the lignin. In the NPT (isothermal–isobaric ensemble) simulations, mean-squared displacement results show that water molecules can promote the urea molecules gradually away from the lignin. Furthermore, in NVT (canonical ensemble) molecular dynamic simulations, results on diffusion constants of urea molecules in lignin–urea system show that diffusion constant of urea molecules in a urea–water–lignin system increases with an increase in the water content. Conclusions gained from two different kinds of simulation are in agreement with each other and are consistent with the experimental observations.