Note: A pure-sampling quantum Monte Carlo algorithm with independent Metropolis.

Recently, Ospadov and Rothstein published a pure-sampling quantum Monte Carlo algorithm (PSQMC) that features an auxiliary Path Z that connects the midpoints of the current and proposed Paths X and Y, respectively. When sufficiently long, Path Z provides statistical independence of Paths X and Y. Under those conditions, the Metropolis decision used in PSQMC is done without any approximation, i.e., not requiring microscopic reversibility and without having to introduce any G(x → x'; τ) factors into its decision function. This is a unique feature that contrasts with all competing reptation algorithms in the literature. An example illustrates that dependence of Paths X and Y has adverse consequences for pure sampling.

A pure-sampling quantum Monte Carlo algorithm.

The objective of pure-sampling quantum Monte Carlo is to calculate physical properties that are independent of the importance sampling function being employed in the calculation, save for the mismatch of its nodal hypersurface with that of the exact wave function. To achieve this objective, we report a pure-sampling algorithm that combines features of forward walking methods of pure-sampling and reptation quantum Monte Carlo (RQMC). The new algorithm accurately samples properties from the mixed and pure distributions simultaneously in runs performed at a single set of time-steps, over which extrapolation to zero time-step is performed. In a detailed comparison, we found RQMC to be less efficient. It requires different sets of time-steps to accurately determine the energy and other properties, such as the dipole moment. We implement our algorithm by systematically increasing an algorithmic parameter until the properties converge to statistically equivalent values. As a proof in principle, we calculated the fixed-node energy, static α polarizability, and other one-electron expectation values for the ground-states of LiH and water molecules. These quantities are free from importance sampling bias, population control bias, time-step bias, extrapolation-model bias, and the finite-field approximation. We found excellent agreement with the accepted values for the energy and a variety of other properties for those systems.

Ground-state properties of LiH by reptation quantum Monte Carlo methods.

We apply reptation quantum Monte Carlo to calculate one- and two-electron properties for ground-state LiH, including all tensor components for static polarizabilities and hyperpolarizabilities to fourth-order in the field. The importance sampling is performed with a large (QZ4P) STO basis set single determinant, directly obtained from commercial software, without incurring the overhead of optimizing many-parameter Jastrow-type functions of the inter-electronic and internuclear distances. We present formulas for the electrical response properties free from the finite-field approximation, which can be problematic for the purposes of stochastic estimation. The α, γ, A and C polarizability values are reasonably consistent with recent determinations reported in the literature, where they exist. A sum rule is obeyed for components of the B tensor, but B(zz,zz) as well as ß(zzz) differ from what was reported in the literature.

Structure propensities in mutated polyglutamine peptides.

Polyglutamine is a naturally occurring peptide found within several proteins in neuronal cells of the brain, and its aggregation has been implicated in several neurodegenerative diseases, including Huntington's disease. The resulting aggregates have been demonstrated to possess ß-sheet structure, and experimental evidence has demonstrated that aggregation begins with a nucleus composed of a single peptide. In this paper, we computationally examined the structural tendencies of mutant polyglutamine peptides that were studied experimentally, and found to aggregate with varying efficiencies. Low-energy structures were generated for each peptide by simulated annealing molecular dynamics, and were analyzed quantitatively by various geometry-based methods. In all simulations, the carboxy-terminal end of each peptide was constrained to a ß-turn-ß-strand structure to simulate a situation in which ß-structure formation has initiated due to interaction with a seed or a growing oligomer/aggregate. Our results suggest the experimentally-observed inhibition of aggregation to be due to localized conformational restraint on the peptide backbone, which in turn confines the peptide to native coil structure, discouraging transition towards the ß-sheet structure required for aggregation.

Comparative characterization of short monomeric polyglutamine peptides by replica exchange molecular dynamics simulation.

Polyglutamine (polyQ) diseases are caused by an abnormal expansion of CAG repeats. While their detailed structure remains unclear, polyQ peptides assume beta-sheet structures when they aggregate. To investigate the conformational ensemble of short, monomeric polyQ peptides, which consist of 15 glutamine residues (Q(15)), we performed replica exchange molecular dynamics (REMD) simulations. We found that Q(15) can assume multiple configurations due to all of the residues affecting the formation of side-chain hydrogen bonds. Analysis of the free energy landscape reveals that Q(15) has a basin for random-coil structures and another for alpha-helix or beta-turn structures. To investigate properties of aggregated polyQ peptides, we performed multiple molecular dynamics (MMD) simulations for monomeric and oligomeric Q(15). MMD revealed that the formation of oligomers stabilizes the beta-turn structure by increasing the number of hydrogen bonds between the main chains.

Procrustean rotation in concert with principal component analysis of molecular dynamics trajectories: Quantifying global and local differences between conformational samples.

Given the principal component analysis (PCA) of a molecular dynamics (MD) conformational trajectory for a model protein, we perform orthogonal Procrustean rotation to "best fit" the PCA squared-loading matrix to that of a target matrix computed for a related but different molecular system. The sum of squared deviations of the elements of the rotated matrix from those of the target, known as the error of fit (EOF), provides a quantitative measure of the dissimilarity between the two conformational samples. To estimate precision of the EOF, we perform bootstrap resampling of the molecular conformations within the trajectories, generating a distribution of EOF values for the system and target. The average EOF per variable is determined and visualized to ascertain where, locally, system and target sample properties differ. We illustrate this approach by analyzing MD trajectories for the wild-type and four selected mutants of the beta1 domain of protein G.

Mutation effects on structural stability of polyglutamine peptides by molecular dynamics simulation.

Huntington's disease patients commonly have glutamine (Q) repeats longer than 37 residues in the Huntingtin protein. This unusual protein will misfold and aggregate to form insoluble amyloid-like fibrils. Although the determination of polyQ structure is very important for elucidation of the aggregation mechanism, this has not yet been accomplished due to the experimental difficulties. In this study, we performed in silico mutation analysis to examine the stability of polyQ peptide on the basis of the beta-helix structure which is known as a possible model. From the results of molecular dynamics simulations for 10ns, some mutant models were found to be unstable, and their stabilities were largely dependent on the position of replaced residues. Besides, to examine the relationship between the aggregation mechanism of polyQ and the stability of the corresponding monomer, we constructed trimer models. Through the trimer studies, we confirmed that the stability of the monomer contributes significantly to that of the oligomer, and found that some mutant polyQs have the ability to inhibit polyQ aggregation. Furthermore, we estimated the free energies in solution and the conformational entropic contributions with normal mode analysis. The entropic contributions were not exhibiting remarkable differences between the models under study compared to the differences in the free energies in solution. Supposing that the stability of monomer is associated with aggregation process, the beta-helix structure has been found to be somewhat inconsistent with the experimental results in this study. Our results thus indicate the necessity for the revalidation of the beta-helix model.

Water-mediated interactions in the CRP-cAMP-DNA complex: does water mediate sequence-specific binding at the DNA primary-kink site?

The cyclic AMP receptor protein (CRP) of Escherichia coli binds preferentially to DNA sequences possessing a T:A base pair at position 6 (at which the DNA becomes kinked), but with which it does not form any direct interactions. It has been proposed that indirect readout is involved in CRP-DNA binding, in which specificity for this base pair is primarily related to sequence effects on the energetic susceptibility of the DNA to kink formation. In the current study, the possibility of contributions to indirect readout by water-mediated hydrogen bonding of CRP with the T:A base pair was investigated. A 1.0 ns molecular dynamics simulation of the CRP-cAMP-DNA complex in explicit solvent was performed, and assessed for water-mediated CRP-DNA hydrogen bonds; results were compared to several X-ray crystal structures of comparable complexes. While several water-mediated CRP-DNA hydrogen bonds were identified, none of these involved the T:A base pair at position 6. Therefore, the sequence specificity for this base pair is not likely enhanced by water-mediated hydrogen bonding with the CRP.

Molecular dynamics simulation study on the structural stabilities of polyglutamine peptides.

It is known that Huntington's disease patients commonly have glutamine (Q) repeat sequences longer than a critical length in the coding area of Huntingtin protein in their genes. As the polyglutamine (polyQ) region becomes longer than the critical length, the disease occurs and Huntingtin protein aggregates, both in vitro and in vivo, as suggested by experimental and clinical data. The determination of polyglutamine structure is thus very important for elucidation of the aggregation and disease mechanisms. Here, we perform molecular dynamics calculations on the stability of the structure based on the beta-helix structure suggested by Perutz et al. (2002) [Perutz, M.F., Finch, J.T., Berriman, J., Lesk, A., 2002. Amyloid fibers are water-filled nanotubes. Proc. Natl. Acad. Sci. USA 99, 5591]. We ensure that perfect hydrogen bonds are present between main chains of the beta-helix based on the previous studies, and perform simulations of stretches with 20, 25, 30, 37 and 40 glutamine residues (20Q, 25Q, 30Q, 37Q and 40Q) for the Perutz models with 18.5 and 20 residues per turn (one coil). Our results indicate that the structure becomes more stable with the increase of repeated number of Q, and there is a critical Q number of around 30, above which the structure of the Perutz model is kept stable. In contrast to previous studies, we started molecular dynamics simulations from conformations in which the hydrogen bonds are firmly formed between stacked main chains. This has rendered the initial beta-helix structures of polyQ much more stable for longer time, as compared to those proposed previously. Model calculations for the initial structures of polyQ dimer and tetramer have also been carried out to study a possible mechanism for aggregation.

Gamma distribution model to provide a direct assessment of the overall quality of quantum Monte Carlo-generated electron distributions.

Our objective is to assess the accuracy of simulated quantum Monte Carlo electron distributions of atoms and molecules. Our approach is first to model the exact electron distribution by a linear combination of gamma distribution functions, with parameters chosen to exactly reproduce highly accurate literature values for a number of selected moments for the system of interest. In application to the ground-state electron distributions of helium and dihydrogen, a high level of accuracy of the model was confirmed upon comparing its predicted moments, not used in the model's parametrization, to those calculated from high-level theory. Next, we generated electron-electron and electron-nucleus distributions for dihydrogen from electron positions outputted from a variety of quantum Monte Carlo algorithms. Upon juxtaposition of the simulated distributions with the putatively exact one that we derived from the model, we quantified the error in simulated distributions. The most accurate distributions were obtained from no-compromise reptation quantum Monte Carlo, a recently developed algorithm designed to ameliorate the distributions' time-step bias. Marginally less accurate distributions were generated from fixed-node diffusion Monte Carlo with descendant counting and detailed balance.

Visualization analysis of inter-fragment interaction energies of CRP-cAMP-DNA complex based on the fragment molecular orbital method.

A visualization method for inter-fragment interaction energies (IFIEs) of biopolymers is presented on the basis of the fragment molecular orbital (FMO) method. The IFIEs appropriately illustrate the information about the interaction energies between the fragments consisting of amino acids, nucleotides and other molecules. The IFIEs are usually analyzed in a matrix form called an IFIE matrix. Analyzing the IFIE matrix, we detect important fragments for the function of biomolecular systems and quantify the strength of interaction energies based on quantum chemistry, including the effects of charge transfer, electronic polarization and dispersion force. In this study, by analyzing a protein-DNA complex, we report a visual representation of the IFIE matrix, a so-called IFIE map. We comprehensively examine what information the IFIE map contains concerning structures and stabilities of the protein-DNA complex.

Local-structural diversity and protein folding: application to all-beta off-lattice protein models.

Global measures of structural diversity within a distribution of biopolymers, such as the radius of gyration and percent native contacts, have proven useful in the analysis of simulation data for protein folding. In this paper we describe a statistical-based methodology to quantify the local structural variability of a distribution of biopolymers, applied to 46- and 69-"residue" off-lattice, three-color model proteins. Each folds into beta-barrel structures. First we perform a principal component analysis of all interbead distance variables for a large number of independent, converged Boltzmann-distributed samples of conformations collected at each of a wide range of temperatures. Next, the principal component vectors are subjected to orthogonal (varimax) rotation. The results are displayed on so-called "squared-loading" plots. These provide a quantitative measure of the contribution to the sample variance of the position of each residue relative to the others. Dominant structural elements, those having the largest structural diversity within the sampled distribution, are responsible for peaks and shoulders observed in the specific heat versus temperature curves, generated using the weighted histogram analysis method. The loading plots indicate that the local-structural diversity of these systems changes gradually with temperature through the folding transition but radically changes near the collapse transition temperature. The analysis of the structural overlap order statistic suggests that the 46-mer thermodynamic folding transition involves the native state and at least three other nearly native intermediates. In the case of the 46-mer protein model, data are generated at sufficiently low temperatures that squared-loading plots, coupled with cluster analysis, provide a local and energetic description of its glassy state.

Functionally relevant protein motions: extracting basin-specific collective coordinates from molecular dynamics trajectories.

Functionally relevant motion of proteins has been associated with a number of atoms moving in a concerted fashion along so-called "collective coordinates." We present an approach to extract collective coordinates from conformations obtained from molecular dynamics simulations. The power of this technique for differentiating local structural fluctuations between classes of conformers obtained by clustering is illustrated by analyzing nanosecond-long trajectories for the response regulator protein Spo0F of Bacillus subtilis, generated both in vacuo and using an implicit-solvent representation. Conformational clustering is performed using automated histogram filtering of the inter-C(alpha) distances. Orthogonal (varimax) rotation of the vectors obtained by principal component analysis of these interresidue distances for the members of individual clusters is key to the interpretation of collective coordinates dominating each conformational class. The rotated loadings plots isolate significant variation in interresidue distances, and these are associated with entire mobile secondary structure elements. From this we infer concerted motions of these structural elements. For the Spo0F simulations employing an implicit-solvent representation, collective coordinates obtained in this fashion are consistent with the location of the protein's known active sites and experimentally determined mobile regions.

Unbiased expectation values from diffusion quantum Monte Carlo simulations with a fixed number of walkers.

We append forward walking to a diffusion Monte Carlo algorithm which maintains a fixed number of walkers. This removes the importance sampling bias of expectation values of operators which do not commute with the Hamiltonian. We demonstrate the effectiveness of this approach by employing three importance sampling functions for the hydrogen atom ground state, two very crude. We estimate moments of the electron-nuclear distance, static polarizabilities, and high-order hyperpolarizabilites up to the fourth power in the electric field, where no use is made of the finite field approximation. The results agree with the analytical values, with a statistical error which increases substantially with decreasing overlap of the guiding function with the exact wave function.