The Role of Molecular Dynamics Simulations for the Study of Slow Dynamics

Abstract

A two step strategy is proposed to study dynamical properties of a physical system much slower than the time scales accessible by molecular dynamics simulations. The strategy is applied to investigate the slow dynamics of supercooled liquids.     

Numerical Calculation of the Bridge Function for Soft-Sphere Supercooled Fluids via Molecular Dynamics Simulations

Abstract

Isokinetic molecular dynamics simulations have been performed for 13,500 soft-spheres interacting through the inverse-power potential, ε([sgrave]/r)ⁿ , near and below the freezing temperature. The bridge function for the integral equation of the theory of liquids is extracted from the pair distribution function (PDF) obtained by the computer simulations for n = 6 and 12. The result is compared with that of approximate theories, i.e., the Rogers-Young (RY) approximation and a modified hypernetted-chain approximation for supercooled soft-sphere fluids (MHNCS approximation). Below the freezing temperature, the bridge function obtained by the computer simulation begins to oscillate around zero at intermediate distances where the second peak of the PDF appears. Such oscillatory behavior of the bridge function is well reproduced by the MHNCS approximation which includes correlations given by the leading elementary diagram, in remarkable contrast to that of the RY approximation. The present result suggests that the split second peak of the PDF for highly supercooled liquids is essentially dominated by the intermediate-distance-range correlation of the leading elementary diagram.     

Nonlinear optical studies of heme protein dynamics: implications for proteins as hybrid states of matter

Protein structure is fundamentally related to function. However, static structures alone are insufficient to understand how a protein works. Dynamics play an equally important role. Given that proteins are highly associated aperiodic systems, it may be expected that protein dynamics would follow glass-like dynamics. However, protein functions occur on time scales orders of magnitude faster than the time scales typically associated with glassy systems. It is becoming clear that the reaction forces driving functions do not sample entirely the large number of configurations available to a protein but are highly directed along an optimized pathway. Could there be any correlation between specific topological features in protein structures and dynamics that leads to strongly correlated atomic displacements in the dynamical response to a perturbation? This review will try to provide an answer by focusing upon recent nonlinear optical studies with the aim of directly observing functionally important protein motions over the entire dynamic range of the protein response function. The specific system chosen is photoinduced dynamics of ligand dissociation at the active site in heme proteins, with myoglobin serving as the simplest model system. The energetics and nuclear motions from the very earliest events involved in bond breaking on the femtosecond time scale all the way out to ligand escape and bimolecular rebinding on the microsecond and millisecond time scale have been mapped out. The picture that is emerging is that the system consists of strongly coupled motions from the very instant the bond breaks at the active site that cascade into low frequency collective modes specific to the protein structure. It is this coupling that imparts the ability of a protein to function on time scales more commensurate with liquids while simultaneously conserving structural integrity akin to solids.     

Formation of Transient Clusters on Nanoscopic Length Scales in a Simulated One-Component Supercooled Liquid

Dense liquids above their glass transition exhibit spatially heterogeneous dynamics in which regions within the liquid exhibit enhanced or diminished mobility relative to the average on some time scale. Substantial evidence suggests that these regions are confined to nanoscopic sizes at temperatures close to the mode coupling temperature T ^MCT, and reach well beyond the characteristic length scale over which the two-point static structure of the liquid is correlated. In this paper, we investigate the formation of clusters of mobile particles in a dynamically heterogeneous model liquid. We find that clusters are formed as a result of mobility propagation that begins from distributed locations confined within a nanoscopic local structure. This mobility is facilitated through the development of quasi-one dimensional string-like rearrangements within the nanoscopic region.     

Calculation of the Generalized Susceptibility for a Highly Supercooled Fluid Through Molecular-Dynamics Simulation

Abstract

A new method of computation of generalized susceptibility and dynamical structure factor through molecular dynamics (MD) simulation is proposed. This gives rise to a reliable and accurate result more than that calculated from a conventional method with a direct Fourier transformation. Computational results are presented for the imaginary part of the generalized susceptibility, X″ (ω), for a binary soft-sphere fluid with a super-long-time molecular dynamics (MD) simulation. Both α- and β-peaks in X″ (ω) in a supercooled fluid is shown for the first time through the present MD computation. The MD result obtained is in a good agreement with that obtained by the trapping diffusion model, which we have previously proposed for the glass transition.     

EFFECTS OF VARIATION IN INTERCELLULAR ELECTRICAL COUPLING ON SYNAPTIC POTENTIALS IN SMOOTH MUSCLE: A COMPUTATIONAL STUDY

We have computationally explored the effect of quantitative variations in the extent of cell-to-cell electrical coupling on the synaptic potentials generated in smooth muscle. Neuronally produced spontaneous excitatory junction potentials (SEJPs) generated in a cubical “bidomain” model of syncytial tissue were simulated computationally. It was found that SEJP properties vary conspicuously as the principal parameter of interest, the cell–to–cell coupling resistance, R_i, is altered. For example, on increasing R_i, SEJP peak amplitudes at node zero (the node of generation) increase dramatically, while amplitudes at nodes 1 and 2 (which are passively depolarized) become progressively lower fractions of the amplitude of the zeroeth-node SEJP. The time to peak of the SEJPs also increases concomitantly when R_i is elevated. These observations indicate the nature of variations in synaptic potentials that would be expected under conditions of altered intercellular electrical coupling in smooth muscle. We discuss their implications in relation to the physiology of syncytial tissue, and in the context of recent experimental observations made in the presence of a putative inhibitor of cell–to–cell electrical coupling, 1-heptanol.     

Acoustic levitation: recent developments and emerging opportunities in biomaterials research

Containerless sample environments (levitation) are useful for study of nucleation, supercooling, and vitrification and for synthesis of new materials, often with non-equilibrium structures. Elimination of extrinsic nucleation by container walls extends access to supercooled and supersaturated liquids under high-purity conditions. Acoustic levitation is well suited to the study of liquids including aqueous solutions, organics, soft materials, polymers, and pharmaceuticals at around room temperature. This article briefly reviews recent developments and applications of acoustic levitation in materials R&D. Examples of experiments yielding amorphous pharmaceutical materials are presented. The implementation and results of experiments on supercooled and supersaturated liquids using an acoustic levitator at a high-energy X-ray beamline are described.     

Rheological behaviour of some antibiotic biosynthesis liquids

This paper prsents the results of teh study of rheological behaviour of antibiotic biosynthesis liquids obtained by submerged aerobic cultivation of microorganisms belonging to the actinomycete and fungi classes, in stirred tank bioreactors with turbine impellers. These liquids have a non-Newtonian behaviour which follows the power-law rhcological model with a correlation index of over 0.95. The studied liquids are pseudoplastic, and alter their rheological properties, such as consistency index, (K), flow index, (n), apparent viscosity, (η_a), maximum Newtonian viscosity (η₀), with the culture age, microrganism strain and batch conditions. Also, these liquids are time dependent, exhibiting thixotropy. The most viscous liquids are produced by Streptomyces aureofaciens and Streptomyces rimosus cultivation, while that produced by Streptomyces griseus is the least viscous. A higher pseudoplasticity appears after 30 hours culture age. Since all these biosynthesis are aerobic, a careful observation of the rhelogical behaviour dynamics is necessary to avoid the oxygen culture supply limitation and the decrease of the bioreactor performance during biosynthesis.     

A nonlinear dynamics model for simulating long range correlations of cognitive bistability

Simulation results of bistable perception due to ambiguous visual stimuli are presented which are obtained with a behavioral nonlinear dynamics model using perception–attention–memory coupling. This model provides an explanation of recent experimental results of Gao et al. (Cogn Process 7:105–112, 2006a) and it supports their speculation that the fractal character of perceptual dominance time series may be understood in terms of nonlinear and reentrant dynamics of brain processing. Percept reversals are induced by attention fatigue and noise, with an attention bias which balances the relative percept duration. Dynamical coupling of the attention bias to the perception state introduces memory effects leading to significant long range correlations of perceptual duration times as quantified by the Hurst parameter H > 0.5 (Mandelbrot, The fractal geometry of nature, 1991), in agreement with Gao et al. (Cogn Process 7:105–112, 2006a).     

Smoluchowski dynamics of the vnd/NK‐2 homeodomain from Drosophila melanogaster: First‐order mode‐coupling approximation

This work is the first in a series devoted to applying mode coupling diffusion theory to the derivation of local dynamics properties of proteins in solution. The first‐order mode‐coupling approximation, or optimized Rouse–Zimm local dynamics (ORZLD), is applied here to derive the rotational dynamics of the bonds and compare the calculated with the experimental nmr ¹⁵N spin–lattice relaxation time behavior of the vnd/NK‐2 homeodomain from Drosophila melanogaster. The starting point for the calculations is the experimental three‐dimensional structure of the homeodomain determined by multidimensional nmr spectroscopy. The results of the computations are compared with experimentally measured ¹⁵N spin–lattice relaxation times T₁, at 34.5 and 60.8 MHz, to check the first‐order approximation. To estimate the relative importance of internal and overall rotation, both rigid and fluctuating dynamic models are examined, with fluctuations evaluated using molecular dynamics (MD) simulations. The correlation times for the fundamental bond vector time correlation function and for the second‐order bond orientational TCF are obtained as a function of the residue number for vnd/NK‐2. The stability of the corresponding local dynamics pattern for the fluctuating structure as a function of the length of the MD trajectory is presented. Diffusive dynamics, which is essentially free of model parameters even at first order in the mode‐coupling diffusion approach, confirm that local dynamics of proteins can be described in terms of rotational diffusion of a fluctuating quasi‐rigid structure. The comparison with the nmr data shows that the first‐order mode coupling diffusion approximation accounts for the correct order of magnitude of the results and of important qualitative aspects of the data sensitive to conformational changes. Indications are obtained from this study to efficiently extend the theory to higher order in the mode‐coupling expansion. These results demonstrate the promise of the mode‐coupling approach, where the local dynamics of proteins is described in terms of rotational diffusion of a fluctuating quasi‐rigid structure, to analyze nmr spin–lattice relaxation behavior. © 1999 John Wiley & Sons, Inc. Biopoly 49: 235–254, 1999     

Neuronal Spike Initiation Modulated by Extracellular Electric Fields

Based on a reduced two-compartment model, the dynamical and biophysical mechanism underlying the spike initiation of the neuron to extracellular electric fields is investigated in this paper. With stability and phase plane analysis, we first investigate in detail the dynamical properties of neuronal spike initiation induced by geometric parameter and internal coupling conductance. The geometric parameter is the ratio between soma area and total membrane area, which describes the proportion of area occupied by somatic chamber. It is found that varying it could qualitatively alter the bifurcation structures of equilibrium as well as neuronal phase portraits, which remain unchanged when varying internal coupling conductance. By analyzing the activating properties of somatic membrane currents at subthreshold potentials, we explore the relevant biophysical basis of spike initiation dynamics induced by these two parameters. It is observed that increasing geometric parameter could greatly decrease the intensity of the internal current flowing from soma to dendrite, which switches spike initiation dynamics from Hopf bifurcation to SNIC bifurcation; increasing internal coupling conductance could lead to the increase of this outward internal current, whereas the increasing range is so small that it could not qualitatively alter the spike initiation dynamics. These results highlight that neuronal geometric parameter is a crucial factor in determining the spike initiation dynamics to electric fields. The finding is useful to interpret the functional significance of neuronal biophysical properties in their encoding dynamics, which could contribute to uncovering how neuron encodes electric field signals.     

Cross-Scale Numerical Simulations Using Discrete Particle Models

Abstract

We propose a concept for a homogenous computational model in carrying out cross-scale numerical experiments on liquids. The model employs the particle paradigm and comprises three types of simulation techniques: molecular dynamics (MD), dissipative particle dynamics (DPD) and smoothed particle hydrodynamics (SPH). With respect to the definition of the collision operator, this model may work in different hierarchical spatial and time scales as: MD in the atomistic scale, DPD in the mesoscale and SPH in the macroscale. The optimal computational efficiency of the three types of cross-scale experiments are estimated in dependence on: the system size N-where N is the number of particles-and the number of processors P employed for computer simulation. For the three-hierarchical-stage, as embodied in the MD-DPD-SPH model, the efficiency is proportional to N ^8/7 but its dependence on P is different for each of the three types of cross-scale experiments. The problem of matching the different scales is discussed.     

Viscosity of supercooled aqueous glycerol solutions, validity of the Stokes-Einstein relationship, and implications for cryopreservation

The viscosity of supercooled glycerol aqueous solutions, with glycerol mass fractions between 0.70 and 0.90, have been determined to confirm that the Avramov-Milchev equation describes very well the temperature dependence of the viscosity of the binary mixtures including the supercooled regime. On the contrary, it is shown that the free volume model of viscosity, with the parameters proposed in a recent work (He, Fowler, Toner, J. Appl. Phys. 100 (2006) 074702), overestimates the viscosity of the glycerol-rich mixtures at low temperatures by several orders of magnitude. Moreover, the free volume model for the water diffusion leads to predictions of the Stokes-Einstein product, which are incompatible with the experimental findings. We conclude that the use of these free volume models, with parameters obtained by fitting experimental data far from the supercooled and glassy regions, lead to incorrect predictions of the deterioration rates of biomolecules, overestimating their life times in these cryopreservation media.     

Mode‐coupling Smoluchowski dynamics of a double‐stranded DNA oligomer

The local dynamics of a double‐stranded DNA d(TpCpGpCpG)₂ is obtained to second order in the mode‐coupling expansion of the Smoluchowski diffusion theory. The time correlation functions of bond variables are derived and the ¹³C‐nmr spin–lattice relaxation times T₁ of different ¹³C along the chains are calculated and compared to experimental data from the literature at three frequencies. The DNA is considered as a fluctuating three‐dimensional structure undergoing rotational diffusion. The fluctuations are evaluated using molecular dynamics simulations, with the ensemble averages approximated by time averages along a trajectory of length 1 ns. Any technique for sampling the configurational space can be used as an alternative. For a fluctuating three‐dimensional (3D) structure using the three first‐order vector modes of lower rates, higher order basis sets of second‐rank tensor are built to give the required mode coupling dynamics. Second‐ and even first‐order theories are found to be in close agreement with the experimental results, especially at high frequency, where the differences in T₁ for ¹³C in the base pairs, sugar, and backbone are well described. These atomistic calculations are of general application for studying, on a molecular basis, the local dynamics of fluctuating 3D structures such as double‐helix DNA fragments, proteins, and protein–DNA complexes. © 1999 John Wiley & Sons, Inc. Biopoly 50: 613–629, 1999     

Fundamental considerations in the effect of molecular weight on the glass transition of the gelatin/cosolute system

Four molecular fractions of gelatin produced by alkaline hydrolysis of collagen were investigated in the presence of cosolute to record the mechanical properties of the glass transition in high-solid preparations. Dynamic oscillatory and stress relaxation moduli in shear were recorded from 40°C to temperatures as low as -60°C. The small-deformation behavior of these linear polymers was separated by the method of reduced variables into a basic function of time alone and a basic function of temperature alone. The former allowed the reduction of isothermal runs into a master curve covering 17 orders of magnitude in the time domain. The latter follows the passage from the rubbery plateau through the glass transition region to the glassy state seen in the variation of shift factor, a(T) , as a function of temperature. The mechanical glass transition temperature (T(g) ) is pinpointed at the operational threshold of the free volume theory and the predictions of the reaction rate theory. Additional insights into molecular dynamics are obtained via the coupling model of cooperativity, which introduces the concept of coupling constant or interaction strength of local segmental motions that govern structural relaxation at the vicinity of T(g) . The molecular weight of the four gelatin fractions appears to have a profound effect on the transition temperature or coupling constant of vitrified matrices, as does the protein chemistry in relation to that of amorphous synthetic polymers or gelling polysaccharides.     

Ephaptic coupling of cardiac cells through the junctional electric potential

Cardiac cells are electrically coupled through gap junction channels, which allow ionic current to spread intercellularly from one cell to the next. In addition, it is possible that cardiac cells are coupled through the electric potential in the junctional cleft space between neighboring cells. We develop and analyze a mathematical model of two cells coupled through a common junctional cleft potential. Consistent with more detailed models, we find that the coupling mechanism is highly parameter dependent. Analysis of our model reveals that there are two time scales involved, and the dynamics of the slow subsystem provide new mathematical insight into how the coupling mechanism works. We find that there are two distinct types of propagation failure and we are able to characterize parameter space into regions of propagation success and the two different types of propagation failure.     

Molecular dynamics simulation of human interleukin-4: comparison with NMR data and effect of pH,counterions and force field on tertiary structure stability

The human protein interleukin-4 (IL-4) has been simulated at two different pH values 2 and 6, with different amounts of counterions present in the aqueous solution, and with two different force-field parameter sets using molecular dynamics simulation with the aim of validation of force field and simulation set-up by comparison to experimental nuclear magnetic resonance data, such as proton–proton nuclear Overhauser effect (NOE) distance bounds, ³ J(HN,HC_α) coupling constants and backbone N–H order parameters. Thirteen simulations varying in the length from 3 to 7 ns are compared.

At pH 6 both force-field parameter sets used do largely reproduce the NOE's and order parameters, the GROMOS 45A3 set slightly better than the GROMOS 53A6 set. ³ J values predicted from the simulation agree less well with experimental values. At pH 2 the protein unfolds, unless counterions are explicitly present in the system, but even then the agreement with experiment is worse than at pH 6. When simulating a highly charged protein, such as IL-4 at pH 2, the inclusion of counterions in the simulation seems mandatory.     

Temperature‐dependent developmental model of Neoseiulus californicus (McGregor) (Acari,Phytoseiidae)

The developmental time and survival of immature stages of Neoseiulus californicus were studied at nine constant temperatures (12, 16, 24, 24, 28 32, 36, 38 and 40°C), 60–70% RH, and a photoperiod of 16 : 8 (L : D) h. The total mortality of immature N. californicus was lowest at 24°C (4.5%) and highest at 38°C (15.2%). The total developmental time decreased with increasing temperature between 12°C (18.38 days) and 32°C (2.98 days), and increased beyond 32°C. The relationship between the developmental rate and temperature was fitted by five nonlinear developmental rate models (Logan 6, Lactin 1, 2 and Briere 1, 2). The nonlinear shape of temperature development was best described by the Lactin 1 model (r² = 0.98). The developmental variation of each stage was well described by the three‐parameter Weibull distribution model (r² = 0.91–0.93). The temperature‐dependent developmental models of N. californicus developed in this study could be used to determine optimal temperature conditions for its mass rearing, to predict its seasonal population dynamics in fruit tree orchards or greenhouse crops, or to develop a population dynamics model of N. californicus.     

Mode coupling points to functionally important residues in myosin II

Relevance of mode coupling to energy/information transfer during protein function, particularly in the context of allosteric interactions is widely accepted. However, existing evidence in favor of this hypothesis comes essentially from model systems. We here report a novel formal analysis of the near‐native dynamics of myosin II, which allows us to explore the impact of the interaction between possibly non‐Gaussian vibrational modes on fluctutational dynamics. We show that an information‐theoretic measure based on mode coupling alone yields a ranking of residues with a statistically significant bias favoring the functionally critical locations identified by experiments on myosin II. Proteins 2014; 82:1777–1786. © 2014 Wiley Periodicals, Inc.     

A novel method to predict the glass transition of 70% glycerol aqueous solution

Vitrification has been used to successfully cryopreserve cells and tissues for over 60 years. Glass transition temperature (T _g) of the vitrification is a critical parameter, which has been investigated experimentally. In this study, an isothermal–isobaric molecular simulation (NPT-MD) is proposed to investigate the glass transition and T _g of such vitrification solution. The cohesive energy density, solubility parameter (δ) and bulk modulus of the solution during the process of the glass transition are investigated as well. The results indicate that these properties as functions of temperature can give a definite inflexion; thus, these properties can be used to predict T _g more accurately than the heat capacity (C _p ), density (ρ), volume (V) and radial distribution function (rdf). At the same time, the predicted values of T _g agree well with the experimental results. Therefore, molecular dynamics simulation is a potential method for investigating the glass transition and T _g of the vitrification solutions.