Computing the self-diffusion coefficient for TIP4P water

A molecular dynamics study was made for the TIP4P model of liquid water. Thermal dependences of water density and radial distribution functions were calculated for model verification. Different methods were used to calculate the self-diffusion coefficient, and assessed for sensitivity to molecular system size and trajectory length. The Green-Kubo formula deriving the diffusion coefficient from the velocity autocorrelation function is preferable in short MD simulations with a high sampling rate, whereas the Einstein equation for diffusion is the method of choice in long simulations. The latter approach yields more stable and reliable results, especially at very short times and for a small number of molecules, if the diffusion coefficient is estimated not from the limit ratio of mean squared displacement to time, but from the slope of the time plot of mean squared displacement.     

Simulation for diffusion behaviour of molecules in nanopattern-supported lipid bilayers based on random walk theory

In both the scientific and the technological approach, molecular manipulation with microscopic obstacles is of great importance. Recently, the application of a self-spreading lipid bilayer has attracted growing interest for its ability to transport any molecule in any desired direction. In this paper, we propose a new model, which imitates a self-spreading lipid bilayer on a substrate with metallic nanobarriers, to simulate the diffusion behaviours of molecules within it based on the random walk (RW) theory. The barriers are designed as Jones Tsai's experiments. The barrier's length, width, spacing, gap and interaction energy with molecules are investigated in this paper. The mean square displacement and diffusion coefficients (D) were calculated based on our simulation results. The results show that our simulation is consistent with the experiments. Comparing with the experimental techniques, this simulation work has improved the time- and space-resolution. Furthermore, it can simulate in rather long time-scale. Our RW models are expected to provide theoretical foundation for single molecular observation of hop diffusion in a lipid bilayer with metallic nanogates.     

Recruiting monomer for dimer formation: resolving the antagonistic mechanisms of novel immune check point inhibitors against Programmed Death Ligand-1 in cancer immunotherapy

The design of small molecule antagonists against Programmed Death Ligand-1 (PD-L1) has been the recent highlight of the immune checkpoint blockade therapy. This interventive approach has been potentiated by the development of BMS compounds; BMS-1001 and BMS-1166, which exert their therapeutic activities by inducing dimerisation of PD-L1; a molecular mechanism that has remained unclear. For the first time, we resolve the dynamical events that underlie the antagonistic mechanisms of BMS-1001 and BMS-1166 when bound to PD-L1 using an all-atom molecular dynamics (MD) simulations approach and free binding energy Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA) calculations. Time-scale dynamical findings revealed that upon binding a PD-L1 monomer, the BMS-compounds gradually facilitated the ‘inbound’ motion of another PD-L1 monomer in the same conformational phase space up till dimer formation. Moreover, the non-liganded PD-L1 monomer exhibited the highest structural flexibility and atomistic motions relative to the BMS-liganded monomer as revealed by post-MD trajectory analyses using root mean square deviation (RMSD) and root mean square fluctuations (RMSF) parameters. Trajectory investigations into ligand motions also revealed that the BMS compounds exhibited mechanistic transitions from the monomeric binding site (monomer A) where they were initially bound, to the second monomeric site (monomer B) where they were strongly bound, followed by eventual high-affinity interactions at the tunnel-like binding cleft formed upon the dimerisation of both PD-L1 monomers. These findings present a model that describes the mechanism by which the BMS compounds induce PD-L1 dimerisation and could further enhance the design of highly selective and novel monomeric recruiters of PD-L1 in cancer immunotherapy.     

Calculation of diffusion coefficient for supercritical carbon dioxide and carbon dioxide+naphthalene system by molecular dynamics simulation using EPM2 model

NVT ensemble molecular dynamics (MD) simulation has been applied to calculate the self-diffusion coefficients of carbon dioxide and the tracer diffusion coefficients of naphthalene in supercritical carbon dioxide. The simulation was carried out in the pressure range from 8 to 40 MPa. The elementary physical model proposed by Harris and Yung was adopted for carbon dioxide and some approximation models were used for naphthalene. The systems of MD simulation for carbon dioxide consist of 256 particles. One naphthalene molecule was added for carbon dioxide+naphthalene system. The system can be assumed to be an infinite dilution condition for carbon dioxide+naphthalene system and the mutual diffusion coefficients are equal to the tracer diffusion coefficients of naphthalene. The self-diffusion coefficients of carbon dioxide and the tracer diffusion coefficients of naphthalene in supercritical carbon dioxide can be calculated by mean square displacement. The calculated results of diffusion coefficients showed good agreement with the experimental data without adjustable parameters.     

Simulations of apo and holo-fatty acid binding protein: structure and dynamics of protein, ligand and internal water.

Two molecular dynamics simulations of 5 ns each have been carried out for rat intestinal fatty acid binding protein, in apo-form and with bound palmitate. The fatty acid and a number of water molecules are encapsulated in a large interior cavity of the barrel-shaped protein. The simulations are compared to experimental data and analyzed in terms of root mean square deviations, atomic B-factors, secondary structure elements, hydrogen bond patterns, and distance constraints derived from nuclear Overhauser experiments. Excellent agreement is found between simulated and experimental solution structures of holo-FABP, but a number of differences are observed for the apo-form. The ligand in holo-FABP shows considerable displacement after about 1.5 ns and displays significant configurational entropy. A novel computational approach has been employed to identify internal water and to capture exchange pathways. Orifices in the portal and gap regions of the protein, discussed in the experimental literature, have been confirmed as major openings for solvent exchange between the internal cavity and bulk water. A third opening on the opposite side of the barrel experiences significant exchange but it does not provide a pathway for further passage to the central cavity. Internal water is characterized in terms of density distributions, interaction energies, mobility, protein contact times, and water molecule coordination. A number of differences are observed between the apo and holo-forms and related to differences in the protein structure. Solvent inside apo-FABP, for example, shows characteristics of a water droplet, while solvent in holo-FABP benefits from interactions with the ligand headgroup and slightly stronger interactions with protein residues.     

The X-ray absorption spectroscopy Debye-Waller factors of an iron compound and of met-myoglobin as a function of temperature

Protein dynamics can be characterized by the mean square displacements of the individual atoms of a molecule. This concept is extended to X-ray absorption spectroscopy (XAS) of proteins where the physical information in the Debye-Waller factor is in general neglected. In a first step, a procedure for the investigation of the temperature dependence of XAS spectra has been developed for a small iron compound. Subsequently, experiments have been performed on met-myoglobin. It is shown that the mean square displacements of XAS are smaller than those obtained by M?ssbauer spectroscopy and far smaller than crystallographic mean square displacements. This behavior is explained by the different sensitivity of the methods. XAS measures a relative mean square displacement between the absorbing and backscattering atoms only. A comparison with mean square displacements calculated from normal modes shows that static displacements contribute significantly. It becomes obvious that the atoms of the active center show a high correlation of their motions.     

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.     

Random-walk models of cell dispersal included in mechanobiological simulations of tissue differentiation

Computational models have shown that biophysical stimuli can be correlated with observed patterns of tissue differentiation, and simulations have been performed that predict the time course of tissue differentiation in, for example, long bone fracture healing. Some simulations have used a diffusion model to simulate the migration and proliferation of cells with the differentiating tissue. However, despite the convenience of the diffusion model, diffusion is not the mechanism of cell dispersal: cells disperse by crawling or proliferation, or are transported in a moving fluid. In this paper, a random-walk model (i.e., a stochastic model), with and without a preferred direction, is studied as an approach to simulate cell proliferation/migration in differentiating tissues and it is compared with the diffusion model. A simulation of tissue differentiation of gap tissue in a two-dimensional model of a bone/implant interface was performed to demonstrate the differences between diffusion vs. random walk with a preferred direction. Results of diffusion and random-walk models are similar with respect to the change in the stiffness of the gap tissue but rather different results are obtained regarding tissue patterning in the differentiating tissues; the diffusion approach predicted continuous patterns of tissue differentiation whereas the random-walk model showed a more discontinuous pattern-histological results are not available that can unequivocally establish which is most similar to experimental observation. Comparing isotropic to anisotropic random walk (preferred direction of proliferation and cell migration), a more rapid reduction of the relative displacement between implant and bone is predicted. In conclusion, we have shown how random-walk models of cell dispersal and proliferation can be implemented, and shown where differences between them exist. Further study of the random-walk model is warranted, given the importance of cell seeding and cell dispersal/proliferation in many mechanobiological problems.     

Molecular Dynamics Simulation of WSK-3, a Computationally Designed, Water-Soluble Variant of the Integral Membrane Protein KcsA

Poor solubility and low expression levels often make membrane proteins difficult to study. An alternative to the use of detergents to solubilize these aggregation-prone proteins is the partial redesign of the sequence so as to confer water solubility. Recently, computationally assisted membrane protein solubilization (CAMPS) has been reported, where exposed hydrophobic residues on a protein's surface are computationally redesigned. Herein, the structure and fluctuations of a designed, water-soluble variant of KcsA (WSK-3) were studied using molecular dynamics simulations. The root mean square deviation of the protein from its starting structure, where the backbone coordinates are those of KcsA, was 1.8 angstroms. The structure of salt bridges involved in structural specificity and solubility were examined. The preferred configuration of ions and water in the selectivity filter of WSK-3 was consistent with the reported preferences for KcsA. The structure of the selectivity filter was maintained, which is consistent with WSK-3 having an affinity for agitoxin2 comparable to that of wild-type KcsA. In contrast to KcsA, the central cavity's side chains were observed to reorient, allowing water diffusion through the side of the cavity wall. These simulations provide an atomistic analysis of the CAMPS strategy and its implications for further investigations of membrane proteins.     

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.     

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.     

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.     

Molecular Dynamics Simulation of Limiting Conductance for Li + Ion in Supercritical Water using Polarizable Models

We report results of molecular dynamics simulations of the limiting conductance of Li + ion in ambient water and in supercritical water using polarizable models for water and Li + . The limiting conductances of Li + in ambient water calculated from mean square displacement (MSD) using four points transferable intermolecular potential model (TIP4P), extended simple point charge model (SPC/E), and revised polarizable model 1 (RPOL1) are larger than the experimental value. The behavior of the limiting conductance of Li + in supercritical water using the RPOL models results in good agreement with experimental results for the limiting conductance of LiCl. The agreement of the RPOL1 model with the experimental results is much better than the RPOL2 model in the higher-density regime, whereas that of the RPOL2 model is much better than the RPOL1 model in the lower-density regime. Using the RPOL models (in contrast to the SPC/E model), the number of hydration water molecules around Li + is the dominating contributor to the limiting conductance in the higher-density regime. In agreement with the SPC/E model, the interaction strength between Li + and the hydration water molecules is a non-factor in the lower-density region since the potential energy per hydration water molecule decreases with decreasing water density at the lowest water densities.     

Mean field stochastic boundary molecular dynamics simulation of a phospholipid in a membrane

Computer simulations of phospholipid membranes have been carried out by using a combined approach of molecular and stochastic dynamics and a mean field based on the Marcelja model. First, the single-chain mean field simulations of Pastor et al. [(1988) J. Chem. Phys. 89, 1112-1127] were extended to a complete dipalmitoylphosphatidylcholine molecule; a 102-ns Langevin dynamics simulation is presented and compared with experiment. Subsequently, a hexagonally packed seven-lipid array was simulated with Langevin dynamics and a mean field at the boundary and with molecular dynamics (and no mean field) in the center. This hybrid method, mean field stochastic boundary molecular dynamics, reduces bias introduced by the mean field and eliminates the need for periodic boundary conditions. As a result, simulations extending to tens of nanoseconds may be carried out by using a relatively small number of molecules to model the membrane environment. Preliminary results of a 20-ns simulation are reported here. A wide range of motions, including overall reorientation with a nanosecond decay time, is observed in both simulations, and good agreement with NMR, IR, and neutron diffraction data is found.     

Structural and dynamic roles of permanent water molecules in ligand molecular recognition by chicken liver bile acid binding protein

Chicken liver bile acid binding protein (cL-BABP) crystallizes with water molecules in its binding site. To obtain insights on the role of internal water, we performed two 100 ns molecular dynamics (MD) simulations in explicit solvent for cL-BABP, as apo form and as a complex with two molecules of cholic acid, and analyzed in detail the dynamics properties of all water molecules. The diffusion coefficients of the more persistent internal water molecules are significantly different from the bulk, but similar between the two protein forms. A different number of molecules and a different organization are observed for apo- and holo-cL-BABP. Most water molecules identified in the binding site of the apo-crystal diffuse to the bulk during the simulation. In contrast, almost all the internal waters of the holo-crystal maintain the same interactions with internal sidechains and ligands, which suggests they have a relevant role in protein-ligand molecular recognition. Only in the presence of these water molecules we were able to reproduce, by a classical molecular docking approach, the structure of the complex cL-BABP::cholic acid with a low ligand root mean square deviation (RMSD) with respect to its reference positioning. Literature data reported a conserved pattern of hydrogen bonds between a single water molecule and three amino acid residues of the binding site in a series of crystallized FABP. In cL-BABP, the interactions between this conserved water molecule and the three residues are present in the crystal of both apo- and holo-cL-BABP but are lost immediately after the start of molecular dynamics. Copyright (c) 2008 John Wiley & Sons, Ltd.     

Orientational exchange approach to fluorescence anisotropy decay.

Fluorescence depolarization is a powerful technique in resolving dynamics of molecular systems. Data obtained in fluorescence depolarization experiments are highly complex. Mathematical models for analyzing data from depolarization due to rotational motion have been largely based on the rotational diffusion equation. These results have been verified by Monte Carlo simulations. It has been implicitly stated that a 90 degrees jump model between predefined orientations such as presented by G. Weber (1971. J. Chem. Phys. 55:2399-2411) should, for the specific case of fluorescence depolarization, give the same answer as the diffusion equation. Since the highly symmetric cases considered by G. Weber gave the same result as the diffusion equation, it has been desirable to use this method in cases where depolarization arises from both discrete processes and rotational diffusion. We have derived, in a compartmental formalism, the general result for excitation and emission dipoles not necessarily coincident with any of the principal rotational axes of the fluorophore from this exchange model, and have found it to be different from that of the diffusion equation approach. We have also verified this difference with a Monte Carlo simulation of our exchange model. This derivation allows us to define the limits of validity of the 90 degrees exchanges to model rotational diffusion. Also, for systems where movements may be jumps between a few preferred orientations, the actual physical mechanism of depolarization may not be accurately represented by continuous diffusion. The compartmental formalism developed here can be used to easily combine rotational motions with discrete position jumps or other level kinetics.(ABSTRACT TRUNCATED AT 250 WORDS)     

Temperature dependence of protein dynamics: computer simulation analysis of neutron scattering properties

The temperature dependence of the internal dynamics of an isolated protein, bovine pancreatic trypsin inhibitor, is examined using normal mode analysis and molecular dynamics (MD) simulation. It is found that the protein exhibits marked anharmonic dynamics at temperatures of approximately 100-120 K, as evidenced by departure of the MD-derived average mean square displacement from that of the harmonic model. This activation of anharmonic dynamics is at lower temperatures than previously detected in proteins and is found in the absence of solvent molecules. The simulation data are also used to investigate neutron scattering properties. The effects are determined of instrumental energy resolution and of approximations commonly used to extract mean square displacement data from elastic scattering experiments. Both the presence of a distribution of mean square displacements in the protein and the use of the Gaussian approximation to the dynamic structure factor lead to quantified underestimation of the mean square displacement obtained.     

Three-dimensional model of a substrate-bound SARS chymotrypsin-like cysteine proteinase predicted by multiple molecular dynamics simulations: catalytic efficiency regulated by substrate binding

Severe acute respiratory syndrome (SARS) is a contagious and deadly disease caused by a new coronavirus. The protein sequence of the chymotrypsin-like cysteine proteinase (CCP) responsible for SARS viral replication has been identified as a target for developing anti-SARS drugs. Here, I report the ATVRLQ(p1)A(p1')-bound CCP 3D model predicted by 420 different molecular dynamics simulations (2.0 ns for each simulation with a 1.0-fs time step). This theoretical model was released at the Protein Data Bank (PDB; code: 1P76) before the release of the first X-ray structure of CCP (PDB code: 1Q2W). In contrast to the catalytic dyad observed in X-ray structures of CCP and other coronavirus cysteine proteinases, a catalytic triad comprising Asp187, His41, and Cys145 is found in the theoretical model of the substrate-bound CCP. The simulations of the CCP complex suggest that substrate binding leads to the displacement of a water molecule entrapped by Asp187 and His41, thus converting the dyad to a more efficient catalytic triad. The CCP complex structure has an expanded active-site pocket that is useful for anti-SARS drug design. In addition, this work demonstrates that multiple molecular dynamics simulations are effective in correcting errors that result from low-sequence-identity homology modeling.     

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.     

Structure and dynamics of the dilauroylphosphatidylethanolamine lipid bilayer.

A 200-ps molecular dynamics (MD) simulation trajectory of a model dilauroylphosphatidylethanolamine (DLPE) bilayer in water at 315 K has been generated. Segmental order parameters, electron density profiles, and water pair distribution functions have been calculated. Comparison to experiment is made where possible. The dynamics of the system has been studied by analyzing the velocity autocorrelation functions (VAF) of both water and lipid atoms. Furthermore, the diffusive properties of water have been analyzed by computing the mean square displacement (MSD) and orientational correlation function (OCF) of water in two regions around the bilayer. The calculated order parameters show a behavior similar to the liquid crystalline phase of other bilayers, but the region around C1-C3 does not show the expected behavior. The electron density profile shows features that are characteristic of the liquid crystalline phase. The radial distribution functions suggest ordering of water near the charged head groups, which results in about 15 water molecules solvating each lipid molecule. We find from the VAF, MSD, and OCF calculation that the water molecules near the head groups of the lipid bilayer move more slowly than those further away. The VAF of the hydrocarbon chains have features of low-frequency motions that are probably cooperative nature in addition to the high-frequency motions associated with bond angle and torsional motions.