David L. Beveridge

Free Energy Simulationsa

Monte Carlo or molecular dynamics simulations involve the numerical determinations of the statistical thermodynamics and related structural, energetic and (in the case of molecular dynamics) dynamic properties of an atomic or molecular assembly on a high-speed digital computer. Applications to molecular systems range from the study of the motions of atoms or groups of atoms of a molecule or macromolecule under the influence of intramolecular energy functions to the exploration of the structure and energetics of condensed fluid phases such as liquid water and aqueous solutions based on intermolecular potentials. The quantities determined in a typical Monte Carlo or molecular dynamics simulation include the average or mean configurational energy (thermodynamic excess internal energy), various spatial distribution functions for equilibrium systems, and time-correlation functions for dynamical systems, along with detailed structural and energetic analyses thereof. Diverse problems in structural and reaction chemistry of molecules in solution, such as solvation potentials, solvent effects on conformational stability and the effect of solvent on chemical reaction kinetics and mechanism via activated complex theory also require a particular knowledge of the configurational free energy, which in principle follows directly from the statistical thermodynamic partition function for the system. Considerations on free energy in molecular simulations take a distinctly different form for intramolecular and intermolecular degrees of freedom. For the intramolecular case, the problem involves vibrational and librational modes of motion on the intramolecular energy surface. We will discuss briefly a t the end of this paper the harmonic and quasiharmonic approximation used to compute vibrational contributions to the free energy, but we will restrict the focus herein to the intermolecular case, where the particles of the system undergo diffusional motion and a harmonic or quasiharmonic treatment breaks down. These considerations apply also in the case of a flexible molecule, where conformational transitions are effectively an intramolecular “diffusional mode.” Conventional Monte Carlo and molecular dynamics procedures for diffusional modes, although firmly grounded in Boltzmann statistical mechanics and dynamics, do not proceed via the direct determination of a partition function because of well-known

A 5-NANOSECOND MOLECULAR DYNAMICS TRAJECTORY FOR B-DNA : ANALYSIS OF STRUCTURE, MOTIONS, AND SOLVATION

We report the results of four new molecular dynamics (MD) simulations on the DNA duplex of sequence d(CGCGAATTCGCG)2, including explicit consideration of solvent water, and a sufficient number of Na+ counterions to provide electroneutrality to the system. Our simulations are configured particularly to characterize the latest MD models of DNA, and to provide a basis for examining the sensitivity of MD results to the treatment of boundary conditions, electrostatics, initial placement of solvent, and run lengths. The trajectories employ the AMBER 4.1 force field. The simulations use particle mesh Ewald summation for boundary conditions, and range in length from 500 ps to 5.0 ns. Analysis of the results is carried out by means of time series for conformationalm, helicoidal parameters, newly developed indices of DNA axis bending, and groove widths. The results support a dynamically stable model of B-DNA for d(CGCGAATTCGCG)2 over the entire length of the trajectory. The MD results are compared with corresponding crystallographic and NMR studies on the d(CGCGAATTCGCG)2 duplex, and placed in the context of observed behavior of B-DNA by comparisons with the complete crystallographic data base of B-form structures. The calculated distributions of mobile solvent molecules, both water and counterions, are displayed. The calculated solvent structure of the primary solvation shell is compared with the location of ordered solvent positions in the corresponding crystal structure. The results indicate that ordered solvent positions in crystals are roughly twice as structured as bulk water. Detailed analysis of the solvent dynamics reveals evidence of the incorporation of ions in the primary solvation of the minor groove B-form DNA. The idea of localized complexation of otherwise mobile counterions in electronegative pockets in the grooves of DNA helices introduces an additional source of sequence-dependent effects on local conformational, helicoidal, and morphological structure, and may have important implications for understanding the functional energetics and specificity of the interactions of DNA and RNA with regulatory proteins, pharmaceutical agents, and other ligands.

A systematic molecular dynamics study of nearest-neighbor effects on base pair and base pair step conformations and fluctuations in B-DNA

It is well recognized that base sequence exerts a significant influence on the properties of DNA and plays a significant role in protein–DNA interactions vital for cellular processes. Understanding and predicting base sequence effects requires an extensive structural and dynamic dataset which is currently unavailable from experiment. A consortium of laboratories was consequently formed to obtain this information using molecular simulations. This article describes results providing information not only on all 10 unique base pair steps, but also on all possible nearest-neighbor effects on these steps. These results are derived from simulations of 50–100 ns on 39 different DNA oligomers in explicit solvent and using a physiological salt concentration. We demonstrate that the simulations are converged in terms of helical and backbone parameters. The results show that nearest-neighbor effects on base pair steps are very significant, implying that dinucleotide models are insufficient for predicting sequence-dependent behavior. Flanking base sequences can notably lead to base pair step parameters in dynamic equilibrium between two conformational sub-states. Although this study only provides limited data on next-nearest-neighbor effects, we suggest that such effects should be analyzed before attempting to predict the sequence-dependent behavior of DNA.

Monte Carlo studies of the structure of dilute aqueous sclutions of Li+, Na+, K+, F−, and Cl−

Monte Carlo–Metropolis statistical thermodynamic computer simulations are reported for dilute aqueous solutions of Li+, Na+, K+, F−, and Cl−. The calculations are carried out on systems consisting of one ion and 215 water molecules at 25 °C and experimental densities. The condensed phase environment is modeled using periodic boundary conditions. The configurational energies are developed under the assumption of pairwise additivity by means of potential functions representative of nonempirical quantum mechanical calculations of the ion–water and water–water energies. The internal energies, radial distribution functions, and related thermodynamic properties are calculated for each system. The structure of the local solution environment around each dissolved ion is analyzed in terms of quasicomponent distribution functions. The results are compared with analogous calculations on a smaller system to estimate the effect of long‐range forces in the ion–water potential function on the calculated results.

Nucleic acids: theory and computer simulation, Y2K.

Molecular dynamics simulations on DNA and RNA that include solvent are now being performed under realistic environmental conditions of water activity and salt. Improvements to force-fields and treatments of long-range interactions have significantly increased the reliability of simulations. New studies of sequence effects, axis bending, solvation and conformational transitions have appeared.

Theoretical studies of hydrogen bonding in liquid water and dilute aqueous solutions

Monte Carlo computer simulations of liquid water and dilute aqueous solutions are analyzed in terms of the nature and extent of intermolecular hydrogen bonding. A geometric definition of the hydrogen bond is used. Calculations on liquid water at 25 °C, 37 °C, and 50 °C, were carried out based on the quantum mechanical MCY potential of Matsuoka, Clementi, and Yoshimine and at 10 °C based on the empirical ST2 potential. The effect of a dissolved solute on aqueous hydrogen bonding was studied for dilute aqueous solutions of Li+, Na+, K+, F−, Cl−, and CH4. The nature of the hydrogen bonding was characterized with quasicomponent distribution functions defined as a function of the intermolecular coordinates relevant to hydrogen bonding. The extent of the hydrogen bonding is described using a network analysis approach developed by Geiger, Stillinger, and Rahman. The results on the quasicomponent distribution functions show that the average hydrogen bond angle deviates with 10 °–25 ° from a linear form, quite ind...

Analysis of local helix bending in crystal structures of DNA oligonucleotides and DNA-protein complexes

Sequence-dependent bending of the helical axes in 112 oligonucleotide duplex crystal structures resident in the Nucleic Acid Database have been analyzed and compared with the use of bending dials, a computer graphics tool. Our analysis includes structures of both A and B forms of DNA and considers both uncomplexed forms of the double helix as well as those bound to drugs and proteins. The patterns in bending preferences in the crystal structures are analyzed by base pair steps, and emerging trends are noted. Analysis of the 66 B-form structures in the Nucleic Acid Database indicates that uniform trends within all pyrimidine-purine and purine-pyrimidine steps are not necessarily observed but are found particularly at CG and GC steps of dodecamers. The results support the idea that AA steps are relatively straight and that larger roll bends occur at or near the junctions of these A-tracts with their flanking sequences. The data on 16 available crystal structures of protein-DNA complexes indicate that the majority of the DNA bends induced via protein binding are sharp localized kinks. The analysis of the 30 available A-form DNA structures indicates that these structures are also bent and show a definitive preference for bending into the deep major groove over the shallow minor groove.

A modification of the generalized Born theory for improved estimates of solvation energies and pK shifts

We present herein an appraisal on the performance of the generalized Born (GB) model in estimating the solvation energies of small molecules and pKa shifts of dicarboxylic acids. The quality of the solvation energy results obtained with the GB model was exceedingly good as already reported in the literature but the pKa shift estimates fell short of expectations. Analysis of the problem on a simple prototype system revealed that with the GB model, the estimates of the two components, viz. the shielding and the self-energy terms, to be somewhat in error. These errors compensate each other in the calculation of solvation energies but affect the intramolecular interaction energies and hence pK shifts differently. We examine here the feasibility of introducing modifications to the GB model for a simultaneous evaluation of both solvation and intramolecular interaction energies.

Convergence characteristics of Monte Carlo–Metropolis computer simulations on liquid water

Very long (∼5000 K) Monte Carlo computer simulations are reported for liquid water described in terms of the analytical potential functions of Matsuoka, Clementi, and Yoshimine and Rahman and Stillinger’s empirical ST2 potential. The convergence characteristics of both realizations are fully developed in terms of internal energy, heat capacity molecular distribution functions, and structural indices. A hierarchy in the calculated properties emerges with respect to the degree of computational effort required to obtain reproducible results. Mean energy and radial distribution functions are the most accessible quantities. Fluctuation properties such as heat capacity require roughly twice as many configurations to stabilize as simple orientational averaged quantities. The structural changes over the equilibrated segments of the realization were examined in terms of quasicomponent distribution functions and found to be small in chemical terms.

μABC: a systematic microsecond molecular dynamics study of tetranucleotide sequence effects in B-DNA.

We present the results of microsecond molecular dynamics simulations carried out by the ABC group of laboratories on a set of B-DNA oligomers containing the 136 distinct tetranucleotide base sequences. We demonstrate that the resulting trajectories have extensively sampled the conformational space accessible to B-DNA at room temperature. We confirm that base sequence effects depend strongly not only on the specific base pair step, but also on the specific base pairs that flank each step. Beyond sequence effects on average helical parameters and conformational fluctuations, we also identify tetranucleotide sequences that oscillate between several distinct conformational substates. By analyzing the conformation of the phosphodiester backbones, it is possible to understand for which sequences these substates will arise, and what impact they will have on specific helical parameters.