Parameterizing a Simple Potential Energy Function Appropriate for Vibrational Frequencies Using Molecular Dynamics

A Maple scheme for quickly parameterizing vibrational potential energy functions is presented. As an example, the potential energy function's parameters for the vibrational motions in H_2O_2 are obtained assuming the simplest potential energy function. This paper was originally written as a research paper, but rejected by the referees. It is therefore being edited into an ``educational'' paper for student usage.

Molecular Dynamics and the Diatomic Molecule as Harmonic Oscillator and Rigid Rotor

The HCl molecule is simulated (using Maple) in its dynamics, for both vibrational (and implied) rotational motions. A discussion of the center of mass transformations involved is part of the total presentation.

Quantum molecular dynamics and ab initio studies of the crystal structure of hydrogen and deuterium

Hydrogen isotopes play a critical role both in inertial and magnetic confinemen Nuclear Fusion. Since the preferent fuel needed for this technology is a mixture of deuterium and tritium. The study of these isotopes particularly at very low temperatures carries a technological interest in other applications. The present line promotes a deep study on the structural configuration that hydrogen and deuterium adopt at cryogenic temperatures and at high pressures. Typical conditions occurring in present Inertial Fusion target designs. Our approach is aims to determine the crystal structure characteristics, phase transitions and other parameters strongly correlated to variations of temperature and pressure.

Brownian dynamics simulations of protein folding: Access to milliseconds time scale and beyond

Protein folding occurs on a time scale ranging from milliseconds to minutes for a majority of proteins. Computer simulation of protein folding, from a random configuration to the native structure, is nontrivial owing to the large disparity between the simulation and folding time scales. As an effort to overcome this limitation, simple models with idealized protein subdomains, e.g., the diffusion–collision model of Karplus and Weaver, have gained some popularity. We present here new results for the folding of a four-helix bundle within the framework of the diffusion–collision model. Even with such simplifying assumptions, a direct application of standard Brownian dynamics methods would consume 10,000 processor-years on current supercomputers. We circumvent this difficulty by invoking a special Brownian dynamics simulation. The method features the calculation of the mean passage time of an event from the flux overpopulation method and the sampling of events that lead to productive collisions even if their probability is extremely small (because of large free-energy barriers that separate them from the higher probability events). Using these developments, we demonstrate that a coarse-grained model of the four-helix bundle can be simulated in several days on current supercomputers. Furthermore, such simulations yield folding times that are in the range of time scales observed in experiments.

A molecular level picture of the stabilization of A-DNA in mixed ethanol–water solutions

Advances in computer power, methodology, and empirical force fields now allow routine “stable” nanosecond-length molecular dynamics simulations of DNA in water. The accurate representation of environmental influences on structure remains a major, unresolved issue. In contrast to simulations of A-DNA in water (where an A-DNA to B-DNA transition is observed) and in pure ethanol (where disruption of the structure is observed), A-DNA in ≈85% ethanol solution remains in a canonical A-DNA geometry as expected. The stabilization of A-DNA by ethanol is likely due to disruption of the spine of hydration in the minor groove and the presence of ion-mediated interhelical bonds and extensive hydration across the major groove.

Molecular dynamics of MHC genesis unraveled by sequence analysis of the 1,796,938-bp HLA class I region

The intensely studied MHC has become the paradigm for understanding the architectural evolution of vertebrate multigene families. The 4-Mb human MHC (also known as the HLA complex) encodes genes critically involved in the immune response, graft rejection, and disease susceptibility. Here we report the continuous 1,796,938-bp genomic sequence of the HLA class I region, linking genes between MICB and HLA-F. A total of 127 genes or potentially coding sequences were recognized within the analyzed sequence, establishing a high gene density of one per every 14.1 kb. The identification of 758 microsatellite provides tools for high-resolution mapping of HLA class I-associated disease genes. Most importantly, we establish that the repeated duplication and subsequent diversification of a minimal building block, MIC-HCGIX-3.8–1-P5-HCGIV-HLA class I-HCGII, engendered the present-day MHC. That the currently nonessential HLA-F and MICE genes have acted as progenitors to today’s immune-competent HLA-ABC and MICA/B genes provides experimental evidence for evolution by “birth and death,” which has general relevance to our understanding of the evolutionary forces driving vertebrate multigene families.

Yeast chorismate mutase in the R state: Simulations of the active site

The isomerization of chorismate to prephenate by chorismate mutase in the biosynthetic pathway that forms Tyr and Phe involves C5—O (ether) bond cleavage and C1—C9 bond formation in a Claisen rearrangement. Development of negative charge on the ether oxygen, stabilized by Lys-168 and Glu-246, is inferred from the structure of a complex with a transition state analogue (TSA) and from the pH-rate profile of the enzyme and the E246Q mutant. These studies imply a protonated Glu-246 well above pH 7. Here, several 500-ps molecular dynamics simulations test the stability of enzyme–TSA complexes by using a solvated system with stochastic boundary conditions. The simulated systems are (i) protonated Glu-246 (stable), (ii) deprotonated Glu-246 (unstable), (iii) deprotonated Glu-246 plus one H2O between Glu-246 and the ether oxygen (unstable), (iv) the E246Q mutant (stable), and (v) addition of OH− between protonated Glu-246 and the ether oxygen. In (v), a local conformational change of Lys-168 displaced the OH− into the solvent region, suggesting a possible rate-determining step that precedes the catalytic step. In a 500-ps simulation of the enzyme complexed with the reactant chorismate or the product prephenate, no water molecule remained near the oxygen of the ligand. Calculations using the linearized Poisson–Boltzmann equation show that the effective pKa of Glu-246 is shifted from 5.8 to 8.1 as the negative charge on the ether oxygen of the TSA is changed from −0.56 electron to −0.9 electron. Altogether, these results support retention of a proton on Glu-246 to high pH and the absence of a water molecule in the catalytic steps.

Molecular dynamics of a grid-mounted molecular dipolar rotor in a rotating electric field

Classical molecular dynamics is applied to the rotation of a dipolar molecular rotor mounted on a square grid and driven by rotating electric field E(ν) at T ≃ 150 K. The rotor is a complex of Re with two substituted o-phenanthrolines, one positively and one negatively charged, attached to an axial position of Rh\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{2}^{4+}}}\end{equation*}\end{document} in a [2]staffanedicarboxylate grid through 2-(3-cyanobicyclo[1.1.1]pent-1-yl)malonic dialdehyde. Four regimes are characterized by a, the average lag per turn: (i) synchronous (a < 1/e) at E(ν) = |E(ν)| > Ec(ν) [Ec(ν) is the critical field strength], (ii) asynchronous (1/e < a < 1) at Ec(ν) > E(ν) > Ebo(ν) > kT/μ, [Ebo(ν) is the break-off field strength], (iii) random driven (a ≃ 1) at Ebo(ν) > E(ν) > kT/μ, and (iv) random thermal (a ≃ 1) at kT/μ > E(ν). A fifth regime, (v) strongly hindered, W > kT, Eμ, (W is the rotational barrier), has not been examined. We find Ebo(ν)/kVcm−1 ≃ (kT/μ)/kVcm−1 + 0.13(ν/GHz)1.9 and Ec(ν)/kVcm−1 ≃ (2.3kT/μ)/kVcm−1 + 0.87(ν/GHz)1.6. For ν > 40 GHz, the rotor behaves as a macroscopic body with a friction constant proportional to frequency, η/eVps ≃ 1.14 ν/THz, and for ν < 20 GHz, it exhibits a uniquely molecular behavior.

Quantification of the hydrophobic interaction by simulations of the aggregation of small hydrophobic solutes in water

The hydrophobic interaction, the tendency for nonpolar molecules to aggregate in solution, is a major driving force in biology. In a direct approach to the physical basis of the hydrophobic effect, nanosecond molecular dynamics simulations were performed on increasing numbers of hydrocarbon solute molecules in water-filled boxes of different sizes. The intermittent formation of solute clusters gives a free energy that is proportional to the loss in exposed molecular surface area with a constant of proportionality of 45 ± 6 cal/mol⋅Å2. The molecular surface area is the envelope of the solute cluster that is impenetrable by solvent and is somewhat smaller than the more traditional solvent-accessible surface area, which is the area transcribed by the radius of a solvent molecule rolled over the surface of the cluster. When we apply a factor relating molecular surface area to solvent-accessible surface area, we obtain 24 cal/mol⋅Å2. Ours is the first direct calculation, to our knowledge, of the hydrophobic interaction from molecular dynamics simulations; the excellent qualitative and quantitative agreement with experiment proves that simple van der Waals interactions and atomic point-charge electrostatics account for the most important driving force in biology.

Ultrafast detection and control of molecular dynamics

Many elementary chemical and physical processes such as the breaking of a chemical bond or the vibrational motion of atoms within a molecule take place on a femtosecond (fs = 10−15 s) or picosecond (ps = 10−12 s) time scale. It is now possible to monitor these events as a function of time with temporal resolution well below 100 fs. This capability is based on the pump-probe technique where one optical pulse triggers a reaction and a second delayed optical pulse probes the changes that ensue. To illustrate this capability, the dynamics of ligand motion within a protein are presented. Moving beyond casual observation of a reaction to active control of its outcome requires additional experimental and theoretical effort. To illustrate the concept of control, the effect of optical pulse duration on the vibrational dynamics of a tri-atomic molecule are discussed. The experimental and theoretical resources currently available are poised to make the dream of reaction control a reality for certain molecular systems.

Thermodynamic parameters for the helix-coil transition of oligopeptides: molecular dynamics simulation with the peptide growth method.

The helix-coil transition equilibrium of polypeptides in aqueous solution was studied by molecular dynamics simulation. The peptide growth simulation method was introduced to generate dynamic models of polypeptide chains in a statistical (random) coil or an alpha-helical conformation. The key element of this method is to build up a polypeptide chain during the course of a molecular transformation simulation, successively adding whole amino acid residues to the chain in a predefined conformation state (e.g., alpha-helical or statistical coil). Thus, oligopeptides of the same length and composition, but having different conformations, can be incrementally grown from a common precursor, and their relative conformational free energies can be calculated as the difference between the free energies for growing the individual peptides. This affords a straightforward calculation of the Zimm-Bragg sigma and s parameters for helix initiation and helix growth. The calculated sigma and s parameters for the polyalanine alpha-helix are in reasonable agreement with the experimental measurements. The peptide growth simulation method is an effective way to study quantitatively the thermodynamics of local protein folding.

Molecular dynamics simulation of organic-inorganic nanocomposites: Layering behavior and interlayer structure of organoclays

Isothermal-isobaric (NPT) molecular dynamics simulation has been performed to investigate the layering behavior and structure of nanoconfined quaternary alkylammoniums in organoclays. This work is focused on systems consisting of two clay layers and a number of alkylammoniums, and involves the use of modified Dreiding force field. The simulated basal spacings of organoclays agree satisfactorily with the experimental results in the literature. The atomic density profiles in the direction normal to the clay surface indicate that the alkyl chains within the interlayer space of montmorillonite exhibit an obvious layering behavior. The headgroups of long alkyl chains are distributed within two layers close to the clay surface, whereas the distributions of methyl and methylene groups are strongly dependent on the alkyl chain length and clay layer charge. Monolayer, bilayer, and pseudo-trilayer structures are found in organoclays modified with single long alkyl chains, which are identical to the structural models based on the measured basal spacings. A pseudo-quadrilayer structure, for the first time to our knowledge, is also identified in organoclays with double long alkyl chains. In the mixture structure of paraffin-type and multilayer, alkyl chains do not lie flat within a single layer but interlace, and also jump to the next layer in pseudo-trilayer as well as next nearest layer in pseudo-quadrilayer.

Tractable molecular theory of transport of Lennard-Jones fluids in nanopores

We present here a tractable theory of transport of simple fluids in cylindrical nanopores, which is applicable over a wide range of densities and pore sizes. In the Henry law low-density region the theory considers the trajectories of molecules oscillating between diffuse wall collisions, while at higher densities beyond this region the contribution from viscous flow becomes significant and is included through our recent approach utilizing a local average density model. The model is validated by means of equilibrium as well nonequilibrium molecular dynamics simulations of supercritical methane transport in cylindrical silica pores over a wide range of temperature, density, and pore size. The model for the Henry law region is exact and found to yield an excellent match with simulations at all conditions, including the single-file region of very small pore size where it is shown to provide the density-independent collective transport coefficient. It is also shown that in the absence of dispersive interactions the model reduces to the classical Knudsen result, but in the presence of such interactions the latter model drastically overpredicts the transport coefficient. For larger micropores beyond the single-file region the transport coefficient is reduced at high density because of intermolecular interactions and hindrance to particle crossings leading to a large decrease in surface slip that is not well represented by the model. However, for mesopores the transport coefficient increases monotonically with density, over the range studied, and is very well predicted by the theory, though at very high density the contribution from surface slip is slightly overpredicted. It is also seen that the concept of activated diffusion, commonly associated with diffusion in small pores, is fundamentally invalid for smooth pores, and the apparent activation energy is not simply related to the minimum pore potential or the adsorption energy as generally assumed. (C) 2004 American Institute of Physics.

Modeling molecular transport in slit pores

We examine the transport of methane in microporous carbon by performing equilibrium and nonequilibrium molecular dynamics simulations over a range of pore sizes, densities, and temperatures. We interpret these simulation results using two models of the transport process. At low densities, we consider a molecular flow model, in which intermolecular interactions are neglected, and find excellent agreement between transport diffusion coefficients determined from simulation, and those predicted by the model. Simulation results indicate that the model can be applied up to fluid densities of the order to 0.1-1 nm(-3). Above these densities, we consider a slip flow model, combining hydrodynamic theory with a slip condition at the solid-fluid interface. As the diffusion coefficient at low densities can be accurately determined by the molecular flow model, we also consider a model where the slip condition is supplied by the molecular flow model. We find that both density-dependent models provide a useful means of estimating the transport coefficient that compares well with simulation. (C) 2004 American Institute of Physics.