Periodic boundary condition induced breakdown of the equipartition principle and other kinetic effects of finite sample size in classical hard-sphere molecular dynamics simulation

Distribution of energy in the ideal gas that lacks equipartition

The energy and velocity distributions of ideal gas particles were first obtained by Boltzmann and Maxwell in the second half of the nineteenth century. In the case of a finite number of particles, the particle energy distribution was obtained by Boltzmann in 1868. However, it appears that this distribution is not valid for all vessels. A round vessel is a special case due to the additional integral of motion, the conservation of the gas angular momentum. This paper is intended to fill this gap, it provides the exact distribution of particle energy for a classical non-rotating ideal gas of a finite number of colliding particles in a round vessel. This previously unknown distribution was obtained analytically from the first principles, it includes the dependence on all the particle masses. The exact mean energies of gas particles are also found to depend on the system parameters, i.e., the distribution of energy over the degrees of freedom is not uniform. Therefore, the usual ideal gas model allows for the uneven energy partitioning, which we study here both theoretically and in simple numerical experiments.

Dissociation of the Watson-Crick base pairs in vacuum and in aqueous solution: a first-principles molecular dynamics study

The damage of the DNA structure can affect the correct functioning of the cellular processes. This work investigates the required forces to dissociate the Watson-Crick (WC) base pairs AT into A and T, and GC into G and C. The WC base pairs are immersed in water under realistic conditions of temperature, volume, and density that reproduce the main characteristics of a biological system. The simulations are based on first-principles molecular dynamics combined with steering atomic forces. In addition to the force intensities, the charge transfers between the nucleic acid bases, energy variations, and temperature fluctuations in the cleavage moments are reported. With the purpose of evaluating the effects of the aqueous medium, simulations of the WC base pairs in vacuum are included. The results considering the solvated medium are consistent with the experimental measurements, and show the importance of the aqueous solution to regulate the structural modifications of the nucleic acid bases. The investigation contributes with a novel molecular model in molecular simulations, and to better understand the biological processes where the DNA compounds play an active role in life forms.Communicated by Ramaswamy H. Sarma.

A systematic review of the molecular simulation of hybrid membranes for performance enhancements and contaminant removals

Number of research on molecular simulation and design has emerged recently but there is currently a lack of review to present these studies in an organized manner to highlight the advances and feasibility. This paper aims to review the development, structural, physical properties and separation performance of hybrid membranes using molecular simulation approach. The hybrid membranes under review include ionic liquid membrane, mixed matrix membrane, and functionalized hybrid membrane for understanding of the transport mechanism of molecules through the different structures. The understanding of molecular interactions, and alteration of pore sizes and transport channels at atomistic level post incorporation of different components in hybrid membranes posing impact to the selective transport of desired molecules are also covered. Incorporation of molecular simulation of hybrid membrane in related fields such as carbon dioxide (CO₂) removal, wastewater treatment, and desalination are also reviewed. Despite the limitations of current molecular simulation methodologies, i.e., not being able to simulate the membrane operation at the actual macroscale in processing plants, it is still able to demonstrate promising results in capturing molecule behaviours of penetrants and membranes at full atomic details with acceptable separation performance accuracy. From the review, it was found that the best performing ionic liquid membrane, mixed matrix membrane and functionalized hybrid membrane can enhance the performance of pristine membrane by 4 folds, 2.9 folds and 3.3 folds, respectively. The future prospects of molecular simulation in hybrid membranes are also presented. This review could provide understanding to the current advancement of molecular simulation approach in hybrid membranes separation. This could also provide a guideline to apply molecular simulation in the related sectors.

Symmetric Molecular Dynamics

We derive a formulation of molecular dynamics that generates only symmetric configurations. We implement it for all 2D planar and 3D space groups. An atlas of 2D Lennard-Jones crystals under all planar groups is created with symmetric molecular dynamics.

Small size effects in open and closed systems: What can we learn from ideal gases about systems with interacting particles?

Small systems have higher surface area-to-volume ratios than macroscopic systems. The thermodynamics of small systems therefore deviates from the description of classical thermodynamics. One consequence of this is that properties of small systems can be dependent on the system's ensemble. By comparing the properties in grand canonical (open) and canonical (closed) systems, we investigate how a small number of particles can induce an ensemble dependence. Emphasis is placed on the insight that can be gained by investigating ideal gases. The ensemble equivalence of small ideal gas systems is investigated by deriving the properties analytically, while the ensemble equivalence of small systems with particles interacting via the Lennard-Jones or the Weeks-Chandler-Andersen potential is investigated through Monte Carlo simulations. For all the investigated small systems, we find clear differences between the properties in open and closed systems. For systems with interacting particles, the difference between the pressure contribution to the internal energy, and the difference between the chemical potential contribution to the internal energy, are both increasing with the number density. The difference in chemical potential is, with the exception of the density dependence, qualitatively described by the analytic formula derived for an ideal gas system. The difference in pressure, however, is not captured by the ideal gas model. For the difference between the properties in the open and closed systems, the response of increasing the particles' excluded volume is similar to the response of increasing the repulsive forces on the system walls. This indicates that the magnitude of the difference between the properties in open and closed systems is related to the restricted movement of the particles in the system. The work presented in this paper gives insight into the mechanisms behind ensemble in-equivalence in small systems, and illustrates how a simple statistical mechanical model, such as the ideal gas, can be a useful tool in these investigations.

Anomalous Effects of Velocity Rescaling Algorithms: The Flying Ice Cube Effect Revisited

The flying ice cube effect is a molecular dynamics simulation artifact in which the use of velocity rescaling thermostats sometimes causes violation of the equipartition theorem, affecting both structural and dynamic properties. The reason for this artifact and the conditions under which it occurs have not been fully understood. Since the flying ice cube effect was first demonstrated, a new velocity rescaling algorithm (the CSVR thermostat) has been developed and become popular without its effects on the equipartition theorem being truly known. Meanwhile, the use of simple velocity rescaling and Berendsen (weak coupling) thermostat algorithms has not abated but has actually continued to grow. Here, we have calculated the partitioning of the kinetic energy between translational, rotational, and vibrational modes in simulations of diatomic molecules to explicitly determine whether the equipartition theorem is violated under different thermostats and while rescaling velocities to different kinetic energy distributions. We have found that the underlying cause of the flying ice cube effect is a violation of balance leading to systematic redistributions of kinetic energy under simple velocity rescaling and the Berendsen thermostat. When velocities are instead rescaled to the canonical ensemble's kinetic energy distribution, as is done with the CSVR thermostat, the equipartition theorem is not violated, and we show that the CSVR thermostat satisfies detailed balance. The critical necessity for molecular dynamics practitioners to abandon the use of popular yet incorrect velocity rescaling algorithms is underscored with an example demonstrating that the main result of a highly cited study is entirely due to artifacts resulting from the study's use of the Berendsen thermostat.

Synthesis and anti-tumor activity of EF24 analogues as IKKβ inhibitors

EF24 is an IKKβ inhibitor (IC₅₀: 72 μM) containing various anti-tumor activities. In this study, a series of EF24 analogs targeting IKKβ were designed and synthesized. Several IKKβ inhibitors with better activities than EF24 were screened out and B3 showed best IKKβ inhibitory (IC₅₀: 6.6 μM). Molecular docking and dynamic simulation experiments further confirmed this inhibitory effect. B3 obviously suppressed the viability of Hela229, A549, SGC-7901 and MGC-803 cells. Then, in SGC-7901 and MGC-803 cells, B3 blocked the NF-κB signal pathway by inhibiting IKKβ phosphorylation, and followed arrested the cell cycle at G2/M phase by suppressing the Cyclin B1 and Cdc2 p34 expression, induced the cell apoptosis by down-regulating Bcl-2 protein and up-regulating cleaved-caspase3. Moreover, B3 significantly reduced tumor growth and suppressed the IKKβ-NF-κB signal pathway in SGC-7901 xenograft model. In total, this study present a potential IKKβ inhibitor as anti-tumor precursor.

Nonzero Ideal Gas Contribution to the Surface Tension of Water

Surface tension, the tendency of fluid interfaces to behave elastically and minimize their surface, is routinely calculated as the difference between the lateral and normal components of the pressure or, invoking isotropy in momentum space, of the virial tensor. Here we show that the anisotropy of the kinetic energy tensor close to a liquid-vapor interface can be responsible for a large part of its surface tension (about 15% for water, independent from temperature).

Fluctuations in Hertz chains at equilibrium

We examine the long-term behavior of nonintegrable, energy-conserved, one-dimensional systems of macroscopic grains interacting via a contact-only generalized Hertz potential and held between stationary walls. Such systems can be set up to have no phononic background excitation and represent examples of a sonic vacuum. Existing dynamical studies showed the absence of energy equipartitioning in such systems, hence their long-term dynamics was described as quasiequilibrium. Here we show that these systems do in fact reach thermal equilibrium at sufficiently long times, as indicated by the calculated heat capacity. As a by-product, we show how fluctuations of system quantities, and thus the distribution functions, are influenced by the Hertz potential. In particular, the variance of the system's kinetic energy probability density function is reduced by a factor related to the contact potential.

Memory effects in nanoparticle dynamics and transport

In this work, we use the generalized Langevin equation (GLE) to characterize and understand memory effects in nanoparticle dynamics and transport. Using the GLE formulation, we compute the memory function and investigate its scaling with the mass, shape, and size of the nanoparticle. It is observed that changing the mass of the nanoparticle leads to a rescaling of the memory function with the reduced mass of the system. Further, we show that for different mass nanoparticles it is the initial value of the memory function and not its relaxation time that determines the "memory" or "memoryless" dynamics. The size and the shape of the nanoparticle are found to influence both the functional-form and the initial value of the memory function. For a fixed mass nanoparticle, increasing its size enhances the memory effects. Using GLE simulations we also investigate and highlight the role of memory in nanoparticle dynamics and transport.

Saturated palmitic acid induces myocardial inflammatory injuries through direct binding to TLR4 accessory protein MD2

Obesity increases the risk for a number of diseases including cardiovascular diseases and type 2 diabetes. Excess saturated fatty acids (SFAs) in obesity play a significant role in cardiovascular diseases by activating innate immunity responses. However, the mechanisms by which SFAs activate the innate immune system are not fully known. Here we report that palmitic acid (PA), the most abundant circulating SFA, induces myocardial inflammatory injury through the Toll-like receptor 4 (TLR4) accessory protein MD2 in mouse and cell culture experimental models. Md2 knockout mice are protected against PA- and high-fat diet-induced myocardial injury. Studies of cell surface binding, cell-free protein–protein interactions and molecular docking simulations indicate that PA directly binds to MD2, supporting a mechanism by which PA activates TLR4 and downstream inflammatory responses. We conclude that PA is a crucial contributor to obesity-associated myocardial injury, which is likely regulated via its direct binding to MD2.

The free fatty acid-mediated inflammatory activities are regulated through TLR4. Here the authors show that palmitic acid binds to MD2, initiating complex formation with TLR4, recruitment of MyD88, and subsequent activation of pro-inflammatory molecules, and that MD2 blockade protects against diet-induced cardiac dysfunction.

Velocity and energy distributions in microcanonical ensembles of hard spheres

In a microcanonical ensemble (constant NVE, hard reflecting walls) and in a molecular dynamics ensemble (constant NVEPG, periodic boundary conditions) with a number N of smooth elastic hard spheres in a d-dimensional volume V having a total energy E, a total momentum P, and an overall center of mass position G, the individual velocity components, velocity moduli, and energies have transformed beta distributions with different arguments and shape parameters depending on d, N, E, the boundary conditions, and possible symmetries in the initial conditions. This can be shown marginalizing the joint distribution of individual energies, which is a symmetric Dirichlet distribution. In the thermodynamic limit the beta distributions converge to gamma distributions with different arguments and shape or scale parameters, corresponding respectively to the Gaussian, i.e., Maxwell-Boltzmann, Maxwell, and Boltzmann or Boltzmann-Gibbs distribution. These analytical results agree with molecular dynamics and Monte Carlo simulations with different numbers of hard disks or spheres and hard reflecting walls or periodic boundary conditions. The agreement is perfect with our Monte Carlo algorithm, which acts only on velocities independently of positions with the collision versor sampled uniformly on a unit half sphere in d dimensions, while slight deviations appear with our molecular dynamics simulations for the smallest values of N.

Molecular insight into conformational transmission of human P-glycoprotein

P-glycoprotein (P-gp), a kind of ATP-binding cassette transporter, can export candidates through a channel at the two transmembrane domains (TMDs) across the cell membranes using the energy released from ATP hydrolysis at the two nucleotide-binding domains (NBDs). Considerable evidence has indicated that human P-gp undergoes large-scale conformational changes to export a wide variety of anti-cancer drugs out of the cancer cells. However, molecular mechanism of the conformational transmission of human P-gp from the NBDs to the TMDs is still unclear. Herein, targeted molecular dynamics simulations were performed to explore the atomic detail of the conformational transmission of human P-gp. It is confirmed that the conformational transition from the inward- to outward-facing is initiated by the movement of the NBDs. It is found that the two NBDs move both on the two directions (x and y). The movement on the x direction leads to the closure of the NBDs, while the movement on the y direction adjusts the conformations of the NBDs to form the correct ATP binding pockets. Six key segments (KSs) protruding from the TMDs to interact with the NBDs are identified. The relative movement of the KSs along the y axis driven by the NBDs can be transmitted through α-helices to the rest of the TMDs, rendering the TMDs to open towards periplasm in the outward-facing conformation. Twenty eight key residue pairs are identified to participate in the interaction network that contributes to the conformational transmission from the NBDs to the TMDs of human P-gp. In addition, 9 key residues in each NBD are also identified. The studies have thus provided clear insight into the conformational transmission from the NBDs to the TMDs in human P-gp.

Modelling and enhanced molecular dynamics to steer structure-based drug discovery

The ever-increasing gap between the availabilities of the genome sequences and the crystal structures of proteins remains one of the significant challenges to the modern drug discovery efforts. The knowledge of structure-dynamics-functionalities of proteins is important in order to understand several key aspects of structure-based drug discovery, such as drug-protein interactions, drug binding and unbinding mechanisms and protein-protein interactions. This review presents a brief overview on the different state of the art computational approaches that are applied for protein structure modelling and molecular dynamics simulations of biological systems. We give an essence of how different enhanced sampling molecular dynamics approaches, together with regular molecular dynamics methods, assist in steering the structure based drug discovery processes.

Perturbation method to calculate the density of states

Monte Carlo switching moves ("perturbations") are defined between two or more classical Hamiltonians sharing a common ground-state energy. The ratio of the density of states (DOS) of one system to that of another is related to the ensemble averages of the microcanonical acceptance probabilities of switching between these Hamiltonians, analogously to the case of Bennett's acceptance ratio method for the canonical ensemble [C. H. Bennett, J. Comput. Phys. 22, 245 (1976)]. Thus, if the DOS of one of the systems is known, one obtains those of the others and, hence, the partition functions. As a simple test case, the vapor pressure of an anharmonic Einstein crystal is computed, using the harmonic Einstein crystal as the reference system in one dimension; an auxiliary calculation is also performed in three dimensions. As a further example of the algorithm, the energy dependence of the ratio of the DOS of the square-well and hard-sphere tetradecamers is determined, from which the temperature dependence of the constant-volume heat capacity of the square-well system is calculated and compared with canonical Metropolis Monte Carlo estimates. For these cases and reference systems, the perturbation calculations exhibit a higher degree of convergence per Monte Carlo cycle than Wang-Landau (WL) sampling, although for the one-dimensional oscillator the WL sampling is ultimately more efficient for long runs. Last, we calculate the vapor pressure of liquid gold using an empirical Sutton-Chen many-body potential and the ideal gas as the reference state. Although this proves the general applicability of the method, by its inherent perturbation approach the algorithm is suitable for those particular cases where the properties of a related system are well known.

Temperature dependence of the heat diffusivity of proteins

In a combined experimental-theoretical study, we investigated the transport of vibrational energy from the surrounding solvent into the interior of a heme protein, the sperm whale myoglobin double mutant L29W-S108L, and its dependence on temperature from 20 to 70 K. The hindered libration of a CO molecule that is not covalently bound to any part of the protein but is trapped in one of its binding pockets (the Xe4 pocket) was used as the local thermometer. Energy was deposited into the solvent by IR excitation. Experimentally, the energy transfer rate increased from (30 ps)(-1) at 20 K to (8 ps)(-1) at 70 K. This temperature trend is opposite to what is expected, assuming that the mechanism of heat transport is similar to that in glasses. In order to elucidate the mechanism and its temperature dependence, nonequilibrium molecular dynamics (MD) simulations were performed, which, however, predicted an essentially temperature-independent rate of vibrational energy flow. We tentatively conclude that the MD potentials overestimate the coupling between the protein and the CO molecule, which appears to be the rate-limiting step in the real system at low temperatures. Assuming that this coupling is anharmonic in nature, the observed temperature trend can readily be explained.