From the double-stranded helix to the chiral nematic phase of B-DNA: a molecular model

B-DNA solutions of suitable concentration form left-handed chiral nematic phases (cholesterics). Such phases have also been observed in solutions of other stiff or semiflexible chiral polymers; magnitude and handedness of the cholesteric pitch are uniquely related to the molecular features. In this work we present a theoretical method and a numerical procedure which, starting from the structure of polyelectrolytes, lead to the prediction of the cholesteric pitch. Molecular expressions for the free energy of the system are obtained on the basis of steric and electrostatic interactions between polymers; the former are described in terms of excluded volume, while a mean field approximation is used for the latter. Calculations have been performed for 130 base pair fragments of B-DNA. The theoretical predictions provide an explanation for the experimental behavior, by showing the counteracting role played by shape and charge chirality of the molecule.     

Measuring coexisting densities from a two-phase molecular dynamics simulation by voronoi tessellations

A new algorithm is presented that allows for the determination of bulk liquid and vapor densities from a two-phase Molecular Dynamics (2phiMD) simulation. This new method does not use any arbitrary cutoffs for phase definitions; rather it uses single-phase simulations as a self-consistency check. The method does not use any spatial bins for generating histograms of local properties, thereby avoiding the statistical issues associated with bins. Finally, it allows one to approach very close to the critical point. The new method utilizes Voronoi tessellations to determine the molecular volume of every point at every instance in a molecular dynamics simulation. Since the molecular volume is calculated throughout the simulation, statistical parameters such as the average molecular volume and average molecular variance are easy to obtain. To define the phases, the normalized variance of the molecular volume from 1phiMD and 2phiMD is used as a self-consistency check. The new method gives new insight into the nature of the near-subcritical fluid. The critical properties from this analysis are T(c) = 1.293 and rho(c) = 0.313. Direct simulation of the two-phase system was performed up to a temperature of 1.292. The results show excellent agreement to experimental results and Gibbs Ensemble Monte Carlo for coexisting densities. We see that well below the critical temperature, some particles are neither liquid nor vapor. These interfacial particles are primarily, but not exclusively, concentrated at the bulk interface. However, as we approach the critical point, some particles are considered both liquid and vapor. These interfacial particles are distributed through the system.     

Molecular docking using shape descriptors

Molecular docking explores the binding modes of two interacting molecules. The technique is increasingly popular for studying protein-ligand interactions and for drug design. A fundamental problem problem with molecular docking is that orientation space is very large and grows combinatorially with the number of degrees of freedom of the interacting molecules. Here, we describe and evaluate algorithms that improve the efficiency and accuracy of a shape-based docking method. We use molecular organization and sampling techniques to remove the exponential time dependence on molecular size in docking calculations. The new techniques allow us to study systems that were prohibitively large for the original method. The new algorithms are tested in 10 different protein-ligand systems, including 7 systems where the ligand is itself a protein. In all cases, the new algorithms successfully reproduce the experimentally determined configurations of the ligand in the protein.     

Determination of the persistence length of an aromatic polyamide-hydrazide by small-angle x-ray diffraction

Small-angle x-ray diffraction measurements were performed upon dimethyl acetamide (DMAc) solutions of four samples of X-500, an aromatic polyamide-hydrazide. The solubility improved as the polymer molecular weight increased, the most soluble sample being in the form of a highly oriented, crystalline fiber. Molecular weights determined from the scattering curves indicate that aggregation was present in all solutions. Its extent varied with the solubility of the sample, increased with polymer concentration and, for the lowest concentrations studied, could be reduced by the addition of acetic acid. Radius of gyration values were smaller than those obtained by light scattering, probably because of insufficient resolution of the camera. The mass per unit length along the chain was found to be 18–20 Å, while the radius of gyration of the cross section was 3.5–4.8 Å. Three of the samples gave nearly the same angular intersection for the coil-and rodlike regions of the scattering curve. Two of these were whole polymers and the other a narrow fraction. The fact that essentially the same intercept was found in all three cases indicates the persistence length as measured for linear chain polymers by small-angle x-ray diffraction is independent of the heterogeneity of the sample. The intercepts, after a small correction for excluded volume effects, correspond to persistence lengths in the range 71–88 Å for DMAc solutions, which approximate those determined for dimethyl sulfoxide (DMSO) solutions by light scattering the intrinsic viscosity without correction for excluded volume, but are substantially larger than the DMSO values, corrected for excluded volume of 30–49 Å. We can offer no explanation for this difference.     

Free energy landscapes for the thermodynamic understanding of adsorption-induced deformations and structural transitions in porous materials

Soft porous crystals are flexible metal-organic frameworks that respond to physical stimuli such as temperature, pressure, and gas adsorption by large changes in their structure and unit cell volume. While they have attracted a lot of interest, molecular simulation methods that directly couple adsorption and large structural deformations in an efficient manner are still lacking. We propose here a new Monte Carlo simulation method based on non-Boltzmann sampling in (guest loading, volume) space using the Wang-Landau algorithm, and show that it can be used to fully characterize the adsorption properties and the material's response to adsorption at thermodynamic equilibrium. We showcase this new method on a simple model of the MIL-53 family of breathing materials, demonstrating its potential and contrasting it with the pitfalls of direct, Boltzmann simulations. We furthermore propose an explanation for the hysteretic nature of adsorption in terms of free energy barriers between the two metastable host phases.     

An accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems using gradient-based diffusion and tau-leaping

Stochastic simulation of reaction-diffusion systems enables the investigation of stochastic events arising from the small numbers and heterogeneous distribution of molecular species in biological cells. Stochastic variations in intracellular microdomains and in diffusional gradients play a significant part in the spatiotemporal activity and behavior of cells. Although an exact stochastic simulation that simulates every individual reaction and diffusion event gives a most accurate trajectory of the system's state over time, it can be too slow for many practical applications. We present an accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems designed to improve the speed of simulation by reducing the number of time-steps required to complete a simulation run. This method is unique in that it employs two strategies that have not been incorporated in existing spatial stochastic simulation algorithms. First, diffusive transfers between neighboring subvolumes are based on concentration gradients. This treatment necessitates sampling of only the net or observed diffusion events from higher to lower concentration gradients rather than sampling all diffusion events regardless of local concentration gradients. Second, we extend the non-negative Poisson tau-leaping method that was originally developed for speeding up nonspatial or homogeneous stochastic simulation algorithms. This method calculates each leap time in a unified step for both reaction and diffusion processes while satisfying the leap condition that the propensities do not change appreciably during the leap and ensuring that leaping does not cause molecular populations to become negative. Numerical results are presented that illustrate the improvement in simulation speed achieved by incorporating these two new strategies.     

Searching for globally optimal functional forms for interatomic potentials using genetic programming with parallel tempering

Molecular dynamics and other molecular simulation methods rely on a potential energy function, based only on the relative coordinates of the atomic nuclei. Such a function, called a force field, approximately represents the electronic structure interactions of a condensed matter system. Developing such approximate functions and fitting their parameters remains an arduous, time-consuming process, relying on expert physical intuition. To address this problem, a functional programming methodology was developed that may enable automated discovery of entirely new force-field functional forms, while simultaneously fitting parameter values. The method uses a combination of genetic programming, Metropolis Monte Carlo importance sampling and parallel tempering, to efficiently search a large space of candidate functional forms and parameters. The methodology was tested using a nontrivial problem with a well-defined globally optimal solution: a small set of atomic configurations was generated and the energy of each configuration was calculated using the Lennard-Jones pair potential. Starting with a population of random functions, our fully automated, massively parallel implementation of the method reproducibly discovered the original Lennard-Jones pair potential by searching for several hours on 100 processors, sampling only a minuscule portion of the total search space. This result indicates that, with further improvement, the method may be suitable for unsupervised development of more accurate force fields with completely new functional forms.     

Brownian Dynamics, Molecular Dynamics, and Monte Carlo modeling of colloidal systems

This paper serves as an introductory review of Brownian Dynamics (BD), Molecular Dynamics (MD), and Monte Carlo (MC) modeling techniques. These three simulation methods have proven to be exceptional investigative solutions for probing discrete molecular, ionic, and colloidal motions at their basic microscopic levels. The review offers a general study of the classical theories and algorithms that are foundational to Brownian Dynamics, Molecular Dynamics, and Monte Carlo simulations. Important topics of interest include fundamental theories that govern Brownian motion, the Langevin equation, the Verlet algorithm, and the Metropolis method. Brownian Dynamics demonstrates advantages over Molecular Dynamics as pertaining to the issue of time-scale separation. Monte Carlo methods exhibit strengths in terms of ease of implementation. Hybrid techniques that combine these methods and draw from these efficacies are also presented. With their rigorous microscopic approach, Brownian Dynamics, Molecular Dynamics, and Monte Carlo methods prove to be especially viable modeling methods for problems with challenging complexities such as high-level particle concentration and multiple particle interactions. These methods hold promising potential for effective modeling of transport in colloidal systems.     

New approach to free energy of solvation applying continuum models to molecular dynamics simulation

A new approach to the calculation of the free energy of solvation from trajectories obtained by molecular dynamics simulation is presented. The free energy of solvation is computed as the sum of three contributions originated at the cavitation of the solute by the solvent, the solute-solvent nonpolar (repulsion and dispersion) interactions, and the electrostatic solvation of the solute. The electrostatic term is calculated based on ideas developed for the broadly used continuum models, the cavitational contribution from the excluded volume by the Claverie-Pierotti model, and the Van der Waals term directly from the molecular dynamics simulation. The proposed model is tested for diluted aqueous solutions of simple molecules containing a variety of chemically important functions: methanol, methylamine, water, methanethiol, and dichloromethane. These solutions were treated by molecular dynamics simulations using SPC/E water and the OPLS force field for the organic molecules. Obtained free energies of solvation are in very good agreement with experimental data.     

The gel route to transition metal oxides

The so-called “sol-gel” process offers new approaches to the synthesis of transition metal oxides. Based on inorganic polymerization from molecular precursors, it leads to highly condensed species or colloids. These colloids are actually two-phase systems in which small oxide particles are dispersed in a liquid medium. A very large interface separates both phases and interfacial phenomena, at the oxide-water interface, lead to new features in the physics and chemistry of transition metal oxides. Ordered aggregation of oxide particles may occur, giving rise to colloidal crystals or anisotropic tactoids in which the mean distance between particles can be of about 0, 1 μm. This distance can be decreased leading to ordered solid aggregates. Transition metal oxide gels exhibit the physical properties of both phases, i.e., electronic properties arising from electron hopping through the mixed valence oxide network and ionic properties arising from proton diffusion through the liquid phase. Electronic and ionic properties appear to be strongly related through the very large interface. Large coatings can be easily deposited from colloidal solutions and transition metal oxide gels should be very useful for making microionic devices.     

Helix formation in linear achiral dendronized polymers: a computer simulation study

We present a molecular simulation study of the structure of linear dendronized polymers. We use excluded volume interactions in the context of a generic coarse grained molecular model whose geometrical parameters are tuned to represent a poly(paraphenylene) backbone with benzyl ether, Frechet-type dendrons. We apply Monte Carlo sampling in order to investigate the formation of packing-induced chiral structures along the polymer backbone of these chemically achiral systems. We find that helical structures can be formed, usually with defects consisting of domains with reversed helical handedness. Clear signs of helical arrangements of the dendrons begin to appear for dendritic generation g=4, while for g=5 these arrangements dominate and perfect helices can be observed as equilibrium structures obtained from certain types of starting configurations.     

Thermodynamics and kinetics of bubble nucleation: Simulation methodology

The simulation of homogeneous liquid to vapor nucleation is investigated using three rare-event algorithms, boxed molecular dynamics, hybrid umbrella sampling Monte Carlo, and forward flux sampling. Using novel implementations of these methods for efficient use in the isothermal-isobaric ensemble, the free energy barrier to nucleation and the kinetic rate are obtained for a Lennard-Jones fluid at stretched and at superheated conditions. From the free energy surface mapped as a function of two order parameters, the global density and largest bubble volume, we find that the free energy barrier height is larger when projected over bubble volume. Using a regression analysis of forward flux sampling results, we show that bubble volume is a more ideal reaction coordinate than global density to quantify the progression of the metastable liquid toward the stable vapor phase and the intervening free energy barrier. Contrary to the assumptions of theoretical approaches, we find that the bubble takes on cohesive non-spherical shapes with irregular and (sometimes highly) undulating surfaces. Overall, the resulting free energy barriers and rates agree well between the methods, providing a set of complementary algorithms useful for studies of different types of nucleation events.     

Simulated tempering based on global balance or detailed balance conditions: Suwa–Todo,heat bath,and Metropolis algorithms

Simulated tempering (ST) is a useful method to enhance sampling of molecular simulations. When ST is used, the Metropolis algorithm, which satisfies the detailed balance condition, is usually applied to calculate the transition probability. Recently, an alternative method that satisfies the global balance condition instead of the detailed balance condition has been proposed by Suwa and Todo. In this study, ST method with the Suwa–Todo algorithm is proposed. Molecular dynamics simulations with ST are performed with three algorithms (the Metropolis, heat bath, and Suwa–Todo algorithms) to calculate the transition probability. Among the three algorithms, the Suwa–Todo algorithm yields the highest acceptance ratio and the shortest autocorrelation time. These suggest that sampling by a ST simulation with the Suwa–Todo algorithm is most efficient. In addition, because the acceptance ratio of the Suwa–Todo algorithm is higher than that of the Metropolis algorithm, the number of temperature states can be reduced by 25% for the Suwa–Todo algorithm when compared with the Metropolis algorithm. © 2015 Wiley Periodicals, Inc.     

Molecular beacons: a novel DNA probe for nucleic acid and protein studies

A new concept has been introduced for molecular beacon DNA molecules. Molecular beacons are a new class of oligonucleotides that can report the presence of specific nucleic acids in both homogeneous solutions and at the liquid-solid interface. They emit an intense fluorescent signal only when hybridized to their target DNA or RNA molecules. Biotinylated molecular beacons have been designed and used for the development of ultrasensitive DNA sensors and for DNA molecular interaction studies at a solid-liquid interface. Molecular beacons have also been used to study protein-DNA interactions. They have provided a variety of exciting opportunities in DNA/RNA/protein studies.     

Replica exchange and expanded ensemble simulations as Gibbs sampling: simple improvements for enhanced mixing

The widespread popularity of replica exchange and expanded ensemble algorithms for simulating complex molecular systems in chemistry and biophysics has generated much interest in discovering new ways to enhance the phase space mixing of these protocols in order to improve sampling of uncorrelated configurations. Here, we demonstrate how both of these classes of algorithms can be considered as special cases of Gibbs sampling within a Markov chain Monte Carlo framework. Gibbs sampling is a well-studied scheme in the field of statistical inference in which different random variables are alternately updated from conditional distributions. While the update of the conformational degrees of freedom by Metropolis Monte Carlo or molecular dynamics unavoidably generates correlated samples, we show how judicious updating of the thermodynamic state indices--corresponding to thermodynamic parameters such as temperature or alchemical coupling variables--can substantially increase mixing while still sampling from the desired distributions. We show how state update methods in common use can lead to suboptimal mixing, and present some simple, inexpensive alternatives that can increase mixing of the overall Markov chain, reducing simulation times necessary to obtain estimates of the desired precision. These improved schemes are demonstrated for several common applications, including an alchemical expanded ensemble simulation, parallel tempering, and multidimensional replica exchange umbrella sampling.     

Studying functional dynamics in bio-molecules using accelerated molecular dynamics

Many biologically important processes such as enzyme catalysis, signal transduction, ligand binding and allosteric regulation occur on the micro- to millisecond time-scale. Despite the sustained and rapid increase in available computational power and the development of efficient simulation algorithms, molecular dynamics (MD) simulations of proteins and bio-machines are generally limited to time-scales of tens to hundreds of nano-seconds. In this perspective article we present a comprehensive review of Accelerated Molecular Dynamics (AMD), an extended biased potential molecular dynamics approach that allows for the efficient study of bio-molecular systems up to time-scales several orders of magnitude greater than those accessible using standard classical MD methods, whilst still maintaining a fully atomistic representation of the system. Compared to many other approaches, AMD affords efficient enhanced conformational space sampling without any a priori understanding of the underlying free energy surface, nor does it require the specific prior definition of a reaction coordinate or a set of collective variables. Successful applications of the AMD method, including the study of slow time-scale functional dynamics in folded proteins and the conformational behavior of natively unstructured proteins are discussed and an outline of the different variants and extensions to the standard AMD approach is presented.     

Vibrational spectra of anhydrous and monohydrated caffeine and theophylline molecules and crystals

Density functional theory and classical molecular dynamics simulations are used to investigate the vibrational spectra of caffeine and theophylline anhydrous and monohydrate molecules and those of their crystalline anhydrous and monohydrated states, with emphasis in the terahertz region of the spectra. To better understand the influence of water in the monohydrate crystal spectra, we analyze the vibrational spectra of water monomer, dimer, tetramer, and pentamer, and also those of liquid water at two different temperatures. In small water clusters, we observe the progressive addition of translational and librational modes to the terahertz region of the spectra. The water spectra predicted by rigid and flexible water models is examined with classical molecular dynamics, and the respective peaks, especially in the terahertz region, are compared with those found in the small clusters. Similar analysis done for caffeine and theophylline monohydrate molecules using density functional theory clearly shows the presence of water modes in the librational states and in the water stretching region. Molecular dynamics of caffeine and theophylline anhydrous and monohydrate crystals reveal the influence of vibrations from the molecule-molecule (caffeine or theophylline) crystal stacks and those from the water-molecule interactions found in the monohydrate molecules and new modes from molecule-molecule, water-molecule, and water-water hydrogen bonding interactions arising from collective effects in the crystal structure. Findings illustrate challenges of terahertz technology for the detection of specific substances in condensed phases.     

Improvements and new capabilities for the multiple Knudsen cell device used in high-temperature mass spectrometry

The thermodynamic properties of condensed phases, i.e. the activities of components, can be determined from partial pressures measured by the Knudsen cell mass spectrometric method. Improvements in accuracy and yield of this method are obtained with the use of twin cells, an idea proposed in the 1960s. The multiple cell method was perfected in 1977 in our laboratory. Changes to molecular beam sampling and furnace assemblies were required to make the multiple Knudsen cell technique work properly. This paper summarizes these prerequisites, and presents a new device and the associated method of measurements, as well as the necessary tests performed with a silver sample in each cell.     

N.M.R. investigations and the molecular field theory of nematic mixtures

N.M.R. measurements have shown that the mixture E5 can be described by a single order parameter. Based on molecular field theory the nematic-isotropic transition and the temperature dependence of the order parameter in the nematic phase are considered for a binary mixture of nematogens. Guided by the results of the N.M.R. measurements the binary mixture is treated as an effective medium characterized by a single order parameter. Soft attractive forces are taken into account as well as the excluded volume. The coexistence of nematic and isotropic phases in the phase transition region is discussed in detail.