Celeste Sagui

Efficient particle-mesh Ewald based approach to fixed and induced dipolar interactions

We have implemented classical Ewald and particle-mesh Ewald (PME) based treatments of fixed and induced point dipoles into the sander molecular dynamics (MD) module of AMBER 6. During MD the induced dipoles can be propagated along with the atomic positions either by iteration to self-consistency at each time step, or by a Car–Parrinello (CP) technique using an extended Lagrangian formalism. In this paper we present the derivation of the new algorithms and compare the various options with respect to accuracy, efficiency, and effect on calculated properties of a polarizable water model. The use of PME for electrostatics of fixed charges and induced dipoles together with a CP treatment of dipole propagation in MD simulations leads to a cost overhead of only 33% above that of MD simulations using standard PME with fixed charges, allowing the study of polarizability in large macromolecular systems.

Multigrid methods for classical molecular dynamics simulations of biomolecules

We present an O(N) multigrid-based method for the efficient calculation of the long-range electrostatic forces needed for biomolecular simulations, that is suitable for implementation on massively parallel architectures. Along general lines, the method consists of: (i) a charge assignment scheme, which both interpolates and smoothly assigns the charges onto a grid; (ii) the solution of Poisson’s equation on the grid via multigrid methods; and (iii) the back interpolation of the forces and energy from the grid to the particle space. Careful approaches for the charge assignment and the force interpolation, and a Hermitian approximation of Poisson’s equation on the grid allow for the generation of the high-accuracy solutions required for high-quality molecular dynamics simulations. Parallel versions of the method scale linearly with the number of particles for a fixed number of processors, and with the number of processors, for a fixed number of particles.

Adaptively biased molecular dynamics for free energy calculations

We present an adaptively biased molecular dynamics (ABMD) method for the computation of the free energy surface of a reaction coordinate using nonequilibrium dynamics. The ABMD method belongs to the general category of umbrella sampling methods with an evolving biasing potential and is inspired by the metadynamics method. The ABMD method has several useful features, including a small number of control parameters and an O(t) numerical cost with molecular dynamics time t. The ABMD method naturally allows for extensions based on multiple walkers and replica exchange, where different replicas can have different temperatures and/or collective variables. This is beneficial not only in terms of the speed and accuracy of a calculation, but also in terms of the amount of useful information that may be obtained from a given simulation. The workings of the ABMD method are illustrated via a study of the folding of the Ace-GGPGGG-Nme peptide in a gaseous and solvated environment.

Conformations and free energy landscapes of polyproline peptides

The structure of the proline amino acid allows folded polyproline peptides to exist as both left- (PPII) and right-handed (PPI) helices. We have characterized the free energy landscapes of hexamer, nanomer, and tridecamer polyproline peptides in gas phase and implicit water as well as explicit hexane and 1-propanol for the nanomer. To enhance the sampling provided by regular molecular dynamics, we used the recently developed adaptively biased molecular dynamics method, which describes Landau free energy maps in terms of relevant collective variables. These maps, as a function of the collective variables of handedness, radius of gyration, and three others based on the peptide torsion angle ω, were used to determine the relative stability of the different structures, along with an estimate of the transition pathways connecting the different minima. Results show the existence of several metastable isomers and therefore provide a complementary view to experimental conclusions based on photo-induced electron transfer experiments with regard to the existence of stable heterogeneous subpopulations in PPII polyproline.

Surface solvation for an ion in a water cluster

We have used molecular dynamics simulations to study the structural, dynamical, and thermodynamical properties of ions in water clusters. Careful evaluations of the free energy, internal energy, and entropy are used to address controversial or unresolved issues, related to the underlying physical cause of surface solvation, and the basic assumptions that go with it. Our main conclusions are the following. (i) The main cause of surface solvation of a single ion in a water cluster is both water and ion polarization, coupled to the charge and size of the ion. Interestingly, the total energy of the ion increases near the cluster surface, while the total energy of water decreases. Also, our analysis clearly shows that the cause of surface solvation is not the size of the total water dipole (unless this is too small). (ii) The entropic contribution is the same order of magnitude as the energetic contribution, and therefore cannot be neglected for quantitative results. (iii) A pure energetic analysis can give a qualitative description of the ion position at room temperature. (iv) We have observed surface solvation of a large positive iodinelike ion in a polarizable water cluster, but not in a nonpolarizable water cluster.

Electrostatics in Biomolecular Simulations: Where Are We Now and Where Are We Heading?

Abstract In this review, we discuss current methods and developments in the treatment of electrostatic interactions in biomolecular and soft matter simulations. We review the current ‘work horses’, namely, Ewald summation based methods such the Particle-Mesh Ewald, and others, and also newer real-space methods such as multigrid methods, and local algorithms for Coulombs law. We also pay attention to boundary conditions. Although periodic boundary conditions are used most commonly, it is often desirable to have systems that are confined or have boundaries. Finally, we briefly describe some current and available software for the computation of electrostatics in biomolecular and soft matter simulations.

Reaction path ensemble of the B–Z-DNA transition: a comprehensive atomistic study

Since its discovery in 1979, left-handed Z-DNA has evolved from an in vitro curiosity to a challenging DNA structure with crucial roles in gene expression, regulation and recombination. A fundamental question that has puzzled researchers for decades is how the transition from B-DNA, the prevalent right-handed form of DNA, to Z-DNA is accomplished. Due to the complexity of the B–Z-DNA transition, experimental and computational studies have resulted in several different, apparently contradictory models. Here, we use molecular dynamics simulations coupled with state-of-the-art enhanced sampling techniques operating through non-conventional reaction coordinates, to investigate the B–Z-DNA transition at the atomic level. Our results show a complex free energy landscape, where several phenomena such as over-stretching, unpeeling, base pair extrusion and base pair flipping are observed resulting in interconversions between different DNA conformations such as B-DNA, Z-DNA and S-DNA. In particular, different minimum free energy paths allow for the coexistence of different mechanisms (such as zipper and stretch–collapse mechanisms) that previously had been proposed as independent, disconnected models. We find that the B–Z-DNA transition—in absence of other molecular partners—can encompass more than one mechanism of comparable free energy, and is therefore better described in terms of a reaction path ensemble.

Conformational free energies of methyl-α-L-iduronic and methyl-β-D-glucuronic acids in water

We present a simulation protocol that allows for efficient sampling of the degrees of freedom of a solute in explicit solvent. The protocol involves using a nonequilibrium umbrella sampling method, in this case, the recently developed adaptively biased molecular dynamics method, to compute an approximate free energy for the slow modes of the solute in explicit solvent. This approximate free energy is then used to set up a Hamiltonian replica exchange scheme that samples both from biased and unbiased distributions. The final accurate free energy is recovered via the weighted histogram analysis technique applied to all the replicas, and equilibrium properties of the solute are computed from the unbiased trajectory. We illustrate the approach by applying it to the study of the puckering landscapes of the methyl glycosides of alpha-L-iduronic acid and its C5 epimer beta-D-glucuronic acid in water. Big savings in computational resources are gained in comparison to the standard parallel tempering method.

A Statistical Analysis of the PPII Propensity of Amino Acid Guests in Proline-Rich Peptides

There has been considerable debate about the intrinsic PPII propensity of amino-acid residues in denatured polypeptides. Experimentally, the propensity scale is based on the behavior of guest amino-acid residues placed in the middle of polyproline hosts. We have used classical molecular dynamics simulations, with state-of-the-art force fields to carry out a comprehensive analysis of the conformational equilibria of the proline-based host oligopeptides with single guests. The tracked structural characteristics include the PPII content, the cis/trans isomerization of the prolyl bonds, the puckering of the pyrrolidine rings of the proline residues, and the secondary structural motifs. We find no evidence for an intrinsic PPII propensity in any of the guest amino acids other than proline. Instead, the PPII content as derived from experiments may be explained in terms of: 1), a local correlation between the dihedral angles of the guest amino acid and the proline residue immediately preceding it; and 2), a nonlocal correlation between the cis/trans states of the peptide bonds. In terms of the latter, we find that the presence of a guest (other than proline, tyrosine, or tryptophan) increases the trans content of most of the prolyl bonds, which results in an effective increase of the peptide PPII content. With respect to the local dihedral correlations, we find that these are well described in terms of the so-called odds-ratio statistic. Expressed in terms of free energy language, the PPII content based on the odds-ratio of the relevant residues correlate well with the experimentally measured PPII content.

Ab initio calculation of electrostatic multipoles with Wannier functions for large-scale biomolecular simulations

It has long been known that accurate electrostatics is a key issue for improving current force fields for large-scale biomolecular simulations. Typically, this calls for an improved and more accurate description of the molecular electrostatic potential, which eliminates the artifacts associated with current point charge-based descriptions. In turn, this involves the partitioning of the extended molecular charge distribution, so that charges and multipole moments can be assigned to different atoms. As an alternate to current approaches, we have investigated a charge partitioning scheme that is based on the maximally localized Wannier functions. This has the advantage of partitioning the charge, and placing it around the molecule in a chemically meaningful manner. Moreover, higher order multipoles may all be calculated without any undue numerical difficulties. Tests on isolated molecules and water dimers, show that the molecular electrostatic potentials generated by such a Wannier-function based approach are in excellent agreement with the density functional-based calculations.