On Multiple Time-step Algorithms and the Ewald Sum

Abstract

We show how standard multiple time-step algorithms devised for systems with short-range potentials can be used successfully in simulations of periodic systems with long-range (Coulombic) potentials. Three strategies for incorporating the Ewald sum into a multiple time-step algorithm are considered. These are (i) evaluation of reciprocal space terms every time-step (ii) evaluating reciprocal space terms once every n time-steps and placing these terms in with the slowly varying forces and energies (iii) a modified form of the second strategy in which primary shell (close) electrostatic interactions are evaluated directly and the more distant interactions handled by the Ewald sum (once every n time-steps). Only the first and third approaches give satisfactory thermodynamic results. The third strategy is much more efficient than the first. With the third strategy substantial savings in cpu time are acheived in both the real space and, most importantly, the reciprocal space terms of the Ewald sum. This is achieved without significant loss of accuracy or stability. Overall execution time is decreased by a factor of between 2 and 3.     

Application of isotropic periodic sum method for 4-pentyl-4′-cyanobiphenyl liquid crystal

In future large-scale molecular dynamics (MD) simulations that will use parallel computing, the isotropic periodic sum (IPS) method is expected to effectively reduce the cost of interaction calculations while maintaining adequate accuracy. To assess the accuracy of this method in estimating low-charge-density polymer systems, we performed atomistic MD simulations of the bulk state of liquid crystal systems based on 4-pentyl-4′-cyanobiphenyl (5CB). In conditions of 270 K ≤ T ≤ 320 K and a normal pressure, the temperature dependence of the density, potential energy and order parameter was estimated using the IPS and Ewald sum method. The results of the IPS method and Ewald sum were consistent within the range of error. In conditions close to the phase transition point, however, the averaged values of potential energy and order parameter had a small difference. We concluded that the fundamental physical properties for the bulk state of 5CB systems are determined reasonably by using the IPS method, at least in conditions that are not close to the phase transition point.     

A determination of liquid–vapour interfacial properties for methanol using a linear-combination-based isotropic periodic sum

We performed molecular dynamics simulations of the methanol liquid–vapour interfacial systems for a wide temperature range of 200–350 K. The linear-combination-based isotropic periodic sum (LIPS) method was used for estimating Coulombic interactions of the systems. The temperature dependence of the liquid and vapour phase densities, surface thickness and surface tension using the LIPS method was almost equal to that of the Ewald sum method. The temperature dependence of the electrostatic potential profile using the LIPS method was very similar to that of the Ewald sum method. We conclude that the LIPS method provides a reasonable accuracy in determining the liquid–vapour interfacial properties of polar molecules for many temperature conditions.     

Cutoff Errors in the Ewald Summation Formulae for Point Charge Systems

Abstract

Closed formulae for both real and reciprocal space parts of cutoff errors in the Ewald summation method in cubic periodic boundary conditions are derived. Such estimates are useful in tuning parameters in molecular simulations. Errors in both the electrostatic energy and forces are considered. The estimates apply to a disordered configuration of point charges and, with some limitations, also to point-charge molecular models. The accuracy of our estimates is tested and confirmed using simulated configurations of two systems (molten salt and diethylether) under a variety of conditions.     

On the Ewald Artifacts in Computer Simulations. The Test-Case of the Octaalanine Peptide With Charged Termini

Abstract

The treatment of electrostatic interactions in molecular simulations is of fundamental importance. Ewald and related methods are being increasingly used to the detriment of cutoff schemes, which are known to produce several artifacts. A potential drawback of the Ewald method is the spatial periodicity that is imposed to the system, which could produce artifacts when applied in the simulation of liquids. In this work we analyze the octaalanine peptide with charged termini in explicit solvent, for which severe effects due to the use of Ewald sums were predicted using continuum electrostatics. Molecular Dynamics simulations for a total of 158 nanoseconds were performed in cells of different sizes. From the comparison of the results of different system sizes, no significant periodicity-induced artifacts were observed. It is argued that in current biomolecular simulations, the incomplete sampling is likely to affect the results to a larger extent than the artifacts induced by the use of Ewald sums.     

Parameterization of Coulomb interaction in three-dimensional periodic systems

A simple method is proposed to calculate Coulomb interactions in three-dimensional periodic cubic systems. It is based on the parameterization of the interaction on polynomials and rational functions. The parameterized functions are compared to tabulation methods, to the Ewald calculations and cubic harmonic function fits found in the literature. Our parameterizations are computationally more efficient than, the use of tabulations at all cases and seem to be more efficient than the cubic harmonic parameterizations in the case of simultaneous potential energy and force calculations. In comparison to the Ewald method, it is feasible to use the parameterizations on small systems and on systems, where pair-wise additive short-range interactions are dominant. One also may prefer the parameterizations to the Ewald method for large systems, if limited accuracy is needed. The embedding of the method into existing molecular dynamics and Monte Carlo simulation codes is very simple. The presented investigation contains some numerical experimental data to support the correct theoretical partition of potential energy in periodic systems, as well.     

Molecular simulation of polymers with a SAFT-γ Mie approach

ABSTRACT

We review the group contribution Statistical Associating Fluid Theory with Mie interaction potentials (SAFT-γ Mie) approach for building coarse-grained models for molecular simulation of polymeric systems. In this top-down method, force field parameters for coarse-grained polymer models can be derived from thermodynamic information on constituent monomer units using the SAFT-γ Mie equation of state (EoS). This strategy can facilitate high-throughput computational screening of polymeric materials, with a corresponding states correlation expediting the force field fitting. Accurate and transferable non-bonded parameters linked to macroscopic thermodynamic data allow for calculation of properties beyond those obtainable from the EoS alone. To overcome limitations of SAFT-γ Mie regarding polymer chain stiffness and branching, hybrid top-down/bottom-up approaches have combined non-bonded parameters from SAFT-γ Mie with bond-stretching and angle-bending potentials from higher-resolution force fields. Our review critically evaluates the performance of recent SAFT-γ Mie polymer models, highlighting the strengths and weaknesses in the context of other equation of state and coarse-graining methods.     

Coarse-grained simulations of the membrane-active antimicrobial Peptide maculatin 1.1

Maculatin 1.1 (M1.1) is a membrane-active antimicrobial peptide (AMP) from an Australian tree frog that forms a kinked amphipathic α-helix in the presence of a lipid bilayer or bilayer-mimetic environment. To help elucidate its mechanism of membrane-lytic activity, we performed a total of ∼8 μs of coarse-grained molecular dynamics (CG-MD) simulations of M1.1 in the presence of zwitterionic phospholipid membranes. Several systems were simulated in which the peptide/lipid ratio was varied. At a low peptide/lipid ratio, M1.1 adopted a kinked, membrane-interfacial location, consistent with experiment. At higher peptide/lipid ratios, we observed spontaneous, cooperative membrane insertion of M1.1 peptide aggregates. The minimum size for formation of a transmembrane (TM) aggregate was just four peptides. The absence of a simple and well-defined central channel, along with the exclusion of lipid headgroups from the aggregates, suggests that a pore-like model is an unlikely explanation for the mechanism of membrane lysis by M1.1. We also performed an extended 1.25 μs simulation of the permeabilization of a complete liposome by multiple peptides. Consistent with the simpler bilayer simulations, formation of monomeric interfacial peptides and TM peptide clusters was observed. In contrast, major structural changes were observed in the vesicle membrane, implicating induced membrane curvature in the mechanism of active antimicrobial peptide lysis. This contrasted with the behavior of the nonpore-forming model peptide WALP23, which inserted into the vesicle to form extended clusters of TM α-helices with relatively little perturbation of bilayer properties.     

Coarse-grained simulations of the salt dependence of the radius of gyration of polyelectrolytes as models for biomolecules in aqueous solution

The salt dependent radius of gyration of a polyelectrolyte in aqueous solution is calculated in an environment where the polyelectrolyte is surrounded by a permeable membrane that exchanges only solvent particles with the bulk. We obtain additionally the scaling exponent of the gyration radius as a function of the polymerization degree, and find that the polyelectrolyte retains a stretched conformation during the condensation and re-expansion process, indicating that these effects are of an electrostatic nature. The solvent quality is also shown to affect the polyelectrolyte conformation, especially for the poor solvent case. These results are obtained using a hybridized Monte Carlo technique with the coarse-grained, dissipative particle dynamics method with fluctuating number of solvent particles. The full range of the electrostatic interactions is included in the simulations, using the Ewald sum method, and the counterions and solvent molecules are included explicitly. In the complex systems mentioned above, the electrostatic interactions and the solvent quality play a key role in understanding phenomena that do not occur in uncharged systems. Our results are compared and validated with the behavior of some biomolecules under similar environments.     

Effect of Calcium ion on synaptotagmin-like protein during pre-fusion of vesicle for exocytosis in blood-brain barrier

BackgroundCalcium signaling and membrane fusion play key roles in exocytosis of drug-containing vesicles through the blood-brain barrier (BBB). Identifying the role of synaptotagmin-like protein4-a (Slp4-a) in the presence of Ca²⁺ ions, at the pre-fusion stage of a vesicle with the basolateral membrane of endothelial cell, can reveal brain drug transportation across BBB.MethodsWe utilized molecular dynamics (MD) simulations with a coarse-grained PACE force field to investigate the behaviors of Slp4-a with vesicular and endothelial membranes at the pre-fusion stage of exocytosis since all-atom MD simulation or experiments are more time-consuming and expensive to capture these behaviors.ResultsThe Slp4-a pulls lipid membranes (vesicular and endothelial) into close proximity and disorganizes lipid arrangement at contact points, which are predictors for initiation of fusion. Our MD results also indicate that Slp4-a needs Ca²⁺ to bind with weakly-charged POPE lipids (phosphatidylethanolamine).ConclusionsSlp4-a is an important trigger for membrane fusion in BBB exocytosis. It binds to lipid membranes at multiple binding sites and triggers membrane disruption for fusion in calcium-dependent case.General significanceUnderstanding the prefusion process of the vesicle will help to design better drug delivery mechanisms to the brain through formidable BBB.     

Multiscale modeling of lipids and lipid bilayers

A multiscale modeling approach is applied for simulations of lipids and lipid assemblies on mesoscale. First, molecular dynamics simulation of initially disordered system of lipid molecules in water within all-atomic model was carried out. On the next stage, structural data obtained from the molecular dynamics (MD) simulation were used to build a coarse-grained (ten sites) lipid model, with effective interaction potentials computed by the inverse Monte Carlo method. Finally, several simulations of the coarse-grained model on longer length- and time-scale were performed, both within Monte Carlo and molecular dynamics simulations: a periodical sample of lipid molecules ordered in bilayer, a free sheet of such bilayer without periodic boundary conditions, formation of vesicle from a plain membrane, process of self-assembly of lipids randomly dispersed in volume. It was shown that the coarse-grained model, developed exclusively from all-atomic simulation data, reproduces well all the basic features of lipids in water solution.     

Teaching an old dog new tricks: A lipid membrane-based electric immunosensor for real-time probing of the spike S1 protein subunit from SARS-CoV-2

Fast, cheap, and easy to implement point-of-care testing for various pathogens constituted a game changer in past years due to its potential for early disease diagnosis. Herein, we report on the proof-of-concept of a simple method enabling in vitro detection of a structural spike protein subunit from the SARS-CoV-2 (S₁) in aqueous samples. At the core of this discovery lies the well-known paradigm of monitoring the capacitive current across a reconstituted zwitterionic lipid membrane subjected to a periodic transmembrane potential, followed by the real-time spectral analysis enabling the extraction of the second harmonic of the capacitive current. Subsequent changes in the amplitude of this harmonic recorded during lipid membrane–S₁ interactions were correlated with alterations induced in the inner membrane potential profile by the S₁ protein subunit adsorption, and were shown to be augmented by ionic strength, the presence of a specific monoclonal antibody designed against the S₁ subunit and the angiotensin-converting enzyme 2 (ACE2) protein receptor, and uninhibited by the presence of other human serum proteins.     

Molecular Dynamics Simulation Study of DNA Triplex Formed by Mixed Sequences in Solution

Abstract

The unrestrained molecular dynamics simulation of the triple helical DNA with mix sequences d(GACTGGTGAC)?d(CTGACCACTG)*d (GACTGGTGAC), using the particle mesh Ewald sum, is presented here. The Ewald summation method effectively eliminates the usual “cut-off” of the long—range interactions and allowed us to evaluate the full effect of the electrostatic forces. The AMBER5.0 force field has been used during the simulation in solvent. The MD results support a dynamically stable model of DNA triplex over the entire length of the trajectory. The duplex structure assumes the conformation, which is very close to B-DNA. In mixed sequences the purine bases occurs in both strand of DNA duplex. The bases of third strand do not favor the Hoogsteen or/and reverse Hoogsteen type of Hydrogen bonding but they form hydrogen bonds with the bases of both the strand of DNA duplex. The orientation of the third strand is parallel to one of the strand of duplex and all nucleotides (C, A, G & T) show isomorphic behavior with respect to the DNA duplex. The conformation of all the three strands is almost same except few exceptions. Due to interaction of third strand the conformational change in the duplex structure and a finite amount of displacement in the W-C base pairs have been observed. The conformational variation of the back bone torsion angles and helicoidal parameters, groove widths have been discussed. The sequence—dependent effects on local conformation, helicoidal and morphological structure, width of the grooves of DNA helix may have important implication for understanding the functional energetics and specificity of interactions of DNA and its triplexes with proteins, pharmaceutical agents and other legends.     

Self-assembly and interactions of short antimicrobial cationic lipopeptides with membrane lipids: ITC,FTIR and molecular dynamics studies

In this work, the self-organization and the behavior of the surfactant-like peptides in the presence of biological membrane models were studied. The studies were focused on synthetic palmitic acid-containing lipopeptides, C₁₆–KK–NH₂ (I), C₁₆–KGK–NH₂ (II) and C₁₆–KKKK–NH₂ (III). The self-assembly was explored by molecular dynamics simulations using a coarse-grained force field. The critical micellar concentration was estimated by the surface tension measurements. The thermodynamics of the peptides binding to the anionic and zwitterionic lipids were established using isothermal titration calorimetry (ITC). The influence of the peptides on the lipid acyl chain ordering was determined using FTIR spectroscopy. The compounds studied show surface-active properties with a distinct CMC over the millimolar range. An increase in the steric and electrostatic repulsion between polar head groups shifts the CMC toward higher values and reduces the aggregation number. An analysis of the peptide–membrane binding revealed a unique interplay between the initial electrostatic and the subsequent hydrophobic interactions enabling the lipopeptides to interact with the lipid bilayer. In the case of C₁₆–KKKK–NH₂ (III), compensation of the electrostatic and hydrophobic interactions upon binding to the anionic membrane has been suggested and consequently no overall binding effects were noticed in ITC thermograms and FTIR spectra.     

Theoretical Models of Chronotherapy: I. Periodic Perturbations in Oscillating Chemical Reactions

Dynamics resulting from periodic perturbations in oscillating chemical reaction, as theoretical models of chronotherapy techniques are studied. Replication reactions and fluctuations take place in these models giving rise to new species with autocatalitic properties. Oscillating chemical reaction models due to Hanusse (H) with three intermediaries and Bourceanu (E₁, E₂, E₃ ) with four, five and six intermediaries, respectively, are taken for this study and are manipulated numerically using a Gear algorithm. The bifurcation diagrams are obtained applying non-linear dynamic techniques, such as, power spectrum, stroboscopic method, Lyapunov exponents and correlation dimension D 2. The dynamics of Hanusse and Bourceanu perturbed models are very similar. The main dynamic behaviours observed after perturbation are quasiperiodicity, entrainment, some Arnold tongues and situations without chemical meaning. Chaos is not observed. This study contributes to understand theoretical and practical aspects of the chronotherapy techniques.     

Self-assembly of mixtures of a dendrimer and lipids: effects of hydrophobicity and electrostatics

Self-assemblies of mixtures of a G7 dendrimer and dimyristoylphosphatidylcholine (DMPC) lipids were simulated using the coarse-grained force fields. A single G7 dendrimer, which consists of either a hydrophilic or a hydrophobic interior, was simulated with the randomly distributed zwitterionic DMPC or anionic lipids. For the dendrimer with hydrophilic interior, its mixture with anionic lipids self-assembles to the dendrimer-encasing liposome, but the one with zwitterionic lipids does not. The liposome diameter agrees with experiment, which is smaller than the typical liposome without dendrimer. This indicates that the strong electrostatic interactions between dendrimer terminals and lipid phosphates induce high curvature of the bilayer, leading to such a small liposome. For the dendrimer with hydrophobic interior, lipids penetrate the dendrimer interior because of the hydrophobic interactions between the dendrimer interior and lipid tails, leading to the dendrimer–lipid micelle with increased dendrimer size. These simulation findings agree qualitatively with the experimentally proposed liposome and micelle models, and indicate that these proposed conformations of the dendrimer–lipid complexes are significantly modulated by dendrimer hydrophobicity and lipid charge.     

A computational avenue towards understanding and design of zwitterionic anti-biofouling materials

ABSTRACT

This review introduces a computational avenue towards understanding and design of zwitterionic anti-biofouling materials. Biofouling means nonspecific adsorption of proteins, cells, and bacteria on materials and devices. It can sabotage materials functions and bring detrimental effects on the biological systems. Various anti-biofouling materials have been developed and zwitterionic materials emerge as promising candidates recently. The design and understanding of zwitterionic anti-biofouling materials rely on the answers of three fundamental questions: (a) what molecular properties govern the anti-biofouling performance of materials, (b) what is the structure–property-anti-biofouling relationship for materials, and (c) how to identify anti-biofouling materials based on the revealed mechanisms? This paper discussed the efforts of answering the three questions using molecular simulations. We first discuss the simulations that revealed the importance of hydration in the anti-biofouling performance of materials and why this mechanism leads to the discovery of zwitterionic anti-biofouling materials, then the simulations that investigated structure-properties-performance relationships of zwitterionic anti-biofouling materials, and the development of computational approaches that can identify zwitterionic anti-biofouling molecules. Finally, we discuss the opportunities in understanding and design of anti-biofouling biomaterials using computer simulations.     

Ewald Summation in the Molecular Dynamics Simulation of Large Ionic Systems

Abstract

The accuracy and efficiency of the direct Ewald summation are discussed in terms of the size of a Molecular Dynamics (MD) ionic system and the ranges of the r-space and q-space summations. The dependence of the convergence parameter α on the size of the system and on the choice of cut-off radius for the short-range potential is given. The possibility of neglecting the q-space term for large ionic systems is discussed in terms of the accuracy and efficiency of the simulation.     

Interactions of the fatty acid-binding protein ReP1-NCXSQ with lipid membranes. Influence of the membrane electric field on binding and orientation

The regulatory protein of the squid nerve sodium calcium exchanger (ReP1-NCXSQ) is a 15 kDa soluble, intracellular protein that regulates the activity of the Na⁺/Ca ²⁺ exchanger in the squid axon. It is a member of the cellular retinoic acid-binding proteins family and the fatty acid-binding proteins superfamily. It is composed of ten beta strands defining an inner cavity and a domain of two short alpha helix segments. In this work, we studied the binding and orientation of ReP1-NCXSQ in anionic and zwitterionic lipid membranes using molecular dynamics (MD) simulations. Binding to lipid membranes was also measured by filtration binding assay. ReP1-NCXSQ acquired an orientation in the anionic membranes with the positive end of the macrodipole pointing to the lipid membrane. Potential of mean force calculations, in agreement with experimental measurements, showed that the binding to the anionic interfaces in low ionic strength was stronger than the binding to anionic interfaces in high ionic strength or to zwitterionic membranes. The results of MD showed that the electrostatic binding can be mediated not only by defined patches or domains of basic residues but also by a global asymmetric distribution of charges. A combination of dipole–electric field interaction and local interactions determined the orientation of ReP1-NCXSQ in the interface.