M. Scott Shell

The relative entropy is fundamental to multiscale and inverse thermodynamic problems

We show that the relative entropy, S(rel) identical with Sigma(p(T)) ln(p(T)/p(M)), provides a fundamental and unifying framework for multiscale analysis and for inverse molecular-thermodynamic problems involving optimization of a model system (M) to reproduce the properties of a target one (T). We demonstrate that the relative entropy serves as a generating function for principles in variational mean-field theory and uniqueness and gives intuitive results for simple case scenarios in model development. Moreover, we suggest that the relative entropy provides a rigorous framework for multiscale simulations and offers new numerical techniques for linking models at different scales. Finally, we show that S(rel) carries physical significance by using it to quantify the deviations of a three-site model of water from simple liquids, finding that the relative entropy, a thermodynamic concept, even predicts waters kinetic anomalies.

Molecular structural order and anomalies in liquid silica

The present investigation examines the relationship between structural order, diffusivity anomalies, and density anomalies in liquid silica by means of molecular dynamics simulations. We use previously defined orientational and translational order parameters to quantify local structural order in atomic configurations. Extensive simulations are performed at different state points to measure structural order, diffusivity, and thermodynamic properties. It is found that silica shares many trends recently reported for water [J. R. Errington and P. G. Debenedetti, Nature 409, 318 (2001)]. At intermediate densities, the distribution of local orientational order is bimodal. At fixed temperature, order parameter extrema occur upon compression: a maximum in orientational order followed by a minimum in translational order. Unlike water, however, silicas translational order parameter minimum is broad, and there is no range of thermodynamic conditions where both parameters are strictly coupled. Furthermore, the temperature-density regime where both structural order parameters decrease upon isothermal compression (the structurally anomalous regime) does not encompass the region of diffusivity anomalies, as was the case for water.

A Test on Peptide Stability of AMBER Force Fields with Implicit Solvation

We used replica exchange molecular dynamics (REMD) simulations to evaluate four different AMBER force fields and three different implicit solvent models. Our aim was to determine if these physics-based models captured the correct secondary structures of two alpha-helical and two beta-peptides: the 14-mer EK helix of Baldwin and co-workers, the C-terminal helix of ribonuclease, the 16-mer C-terminal hairpin of protein G, and the trpzip2 miniprotein. The different models gave different results, but generally we found that AMBER ff96 plus the implicit solvent model of Onufriev, Bashford, and Case gave reasonable structures, and is fairly well-balanced between helix and sheet. We also observed differences in the strength of ion pairing in the solvent models, we but found that the native secondary structures were retained even when salt bridges were prevented in the conformational sampling. Overall, this work indicates that some of these all-atom physics-based force fields may be good starting points for protein folding and protein structure prediction.

An improved Monte Carlo method for direct calculation of the density of states

We present an efficient Monte Carlo algorithm for determining the density of states which is based on the statistics of transition probabilities between states. By measuring the infinite temperature transition probabilities—that is, the probabilities associated with move proposal only—we are able to extract excellent estimates of the density of states. When this estimator is used in conjunction with a Wang–Landau sampling scheme [F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001)], we quickly achieve uniform sampling of macrostates (e.g., energies) and systematically refine the calculated density of states. This approach requires only potential energy evaluations, continues to improve the statistical quality of its results as the simulation time is extended, and is applicable to both lattice and continuum systems. We test the algorithm on the Lennard-Jones liquid and demonstrate good statistical convergence properties.

A New Multiscale Algorithm and Its Application to Coarse-Grained Peptide Models for Self-Assembly

Peptide self-assembly plays a role in a number of diseases, in pharmaceutical degradation, and in emerging biomaterials. Here, we aim to develop an accurate molecular-scale picture of this process using a multiscale computational approach. Recently, Shell (Shell, M. S. J. Chem. Phys. 2008, 129, 144108-7) developed a coarse-graining methodology that is based on a thermodynamic quantity called the relative entropy, a measure of how different two molecular ensembles behave. By minimizing the relative entropy between a coarse-grained peptide system and a reference all-atom system, with respect to the coarse-grained models force field parameters, an optimized coarse-grained model can be obtained. We have reformulated this methodology using a trajectory-reweighting and perturbation strategy that enables complex coarse-grained models with at least hundreds of parameters to be optimized efficiently. This new algorithm allows for complex peptide systems to be coarse-grained into much simpler models that nonetheless recapitulate many correct features of detailed all-atom ones. In particular, we present results for a polyalanine case study, with attention to both individual peptide folding and large-scale fibril assembly.

Development of an optimized activatable MMP-14 targeted SPECT imaging probe

Matrix metalloproteinase-14 (MT1-MMP or MMP-14) is a membrane-associated protease implicated in a variety of tissue remodeling processes and a molecular hallmark of select metastatic cancers. The ability to detect MMP-14 in vivo would be useful in studying its role in pathologic processes and may potentially serve as a guide for the development of targeted molecular therapies. Four MMP-14 specific probes containing a positively charged cell penetrating peptide (CPP) d-arginine octamer (r(8)) linked with a MMP-14 peptide substrate and attenuating sequences with glutamate (8e, 4e) or glutamate-glycine (4eg and 4egg) repeating units were modeled using an AMBER force field method. The probe with 4egg attenuating sequence exhibited the highest CPP/attenuator interaction, predicting minimized cellular uptake until cleaved. The in vitro MMP-14-mediated cleavage studies using the human recombinant MMP-14 catalytic domain revealed an enhanced cleavage rate that directly correlated with the linearity of the embedded peptide substrate sequence. Successful cleavage and uptake of a technetium-99m labeled version of the optimal probe was demonstrated in MMP-14 transfected human breast cancer cells. Two-fold reduction of cellular uptake was found in the presence of a broad spectrum MMP inhibitor. The combination of computational chemistry, parallel synthesis and biochemical screening, therefore, shows promise as a set of tools for developing new radiolabeled probes that are sensitive to protease activity.

Blind test of physics-based prediction of protein structures

We report here a multiprotein blind test of a computer method to predict native protein structures based solely on an all-atom physics-based force field. We use the AMBER 96 potential function with an implicit (GB/SA) model of solvation, combined with replica-exchange molecular-dynamics simulations. Coarse conformational sampling is performed using the zipping and assembly method (ZAM), an approach that is designed to mimic the putative physical routes of protein folding. ZAM was applied to the folding of six proteins, from 76 to 112 monomers in length, in CASP7, a community-wide blind test of protein structure prediction. Because these predictions have about the same level of accuracy as typical bioinformatics methods, and do not utilize information from databases of known native structures, this work opens up the possibility of predicting the structures of membrane proteins, synthetic peptides, or other foldable polymers, for which there is little prior knowledge of native structures. This approach may also be useful for predicting physical protein folding routes, non-native conformations, and other physical properties from amino acid sequences.

Energy landscapes, ideal glasses, and their equation of state

Using the inherent structure formalism originally proposed by Stillinger and Weber [Phys. Rev. A 25, 978 (1982)], we generalize the thermodynamics of an energy landscape that has an ideal glass transition and derive the consequences for its equation of state. In doing so, we identify a separation of configurational and vibrational contributions to the pressure that corresponds with simulation studies performed in the inherent structure formalism. We develop an elementary model of landscapes appropriate for simple liquids that is based on the scaling properties of the soft-sphere potential complemented with a mean-field attraction. The resulting equation of state provides an accurate representation of simulation data for the Lennard-Jones fluid, suggesting the usefulness of a landscape-based formulation of supercooled liquid thermodynamics. Finally, we consider the implications of both the general theory and the model with respect to the so-called Sastry density and the ideal glass transition. Our analysis...

The impact of resolution upon entropy and information in coarse-grained models.

By eliminating unnecessary degrees of freedom, coarse-grained (CG) models tremendously facilitate numerical calculations and theoretical analyses of complex phenomena. However, their success critically depends upon the representation of the system and the effective potential that governs the CG degrees of freedom. This work investigates the relationship between the CG representation and the many-body potential of mean force (PMF), W, which is the appropriate effective potential for a CG model that exactly preserves the structural and thermodynamic properties of a given high resolution model. In particular, we investigate the entropic component of the PMF and its dependence upon the CG resolution. This entropic component, SW, is a configuration-dependent relative entropy that determines the temperature dependence of W. As a direct consequence of eliminating high resolution details from the CG model, the coarsening process transfers configurational entropy and information from the configuration space into SW. In order to further investigate these general results, we consider the popular Gaussian Network Model (GNM) for protein conformational fluctuations. We analytically derive the exact PMF for the GNM as a function of the CG representation. In the case of the GNM, -TSW is a positive, configuration-independent term that depends upon the temperature, the complexity of the protein interaction network, and the details of the CG representation. This entropic term demonstrates similar behavior for seven model proteins and also suggests, in each case, that certain resolutions provide a more efficient description of protein fluctuations. These results may provide general insight into the role of resolution for determining the information content, thermodynamic properties, and transferability of CG models. Ultimately, they may lead to a rigorous and systematic framework for optimizing the representation of CG models.

Predicting peptide structures in native proteins from physical simulations of fragments.

It has long been proposed that much of the information encoding how a protein folds is contained locally in the peptide chain. Here we present a large-scale simulation study designed to examine the extent to which conformations of peptide fragments in water predict native conformations in proteins. We perform replica exchange molecular dynamics (REMD) simulations of 872 8-mer, 12-mer, and 16-mer peptide fragments from 13 proteins using the AMBER 96 force field and the OBC implicit solvent model. To analyze the simulations, we compute various contact-based metrics, such as contact probability, and then apply Bayesian classifier methods to infer which metastable contacts are likely to be native vs. non-native. We find that a simple measure, the observed contact probability, is largely more predictive of a peptides native structure in the protein than combinations of metrics or multi-body components. Our best classification model is a logistic regression model that can achieve up to 63% correct classifications for 8-mers, 71% for 12-mers, and 76% for 16-mers. We validate these results on fragments of a protein outside our training set. We conclude that local structure provides information to solve some but not all of the conformational search problem. These results help improve our understanding of folding mechanisms, and have implications for improving physics-based conformational sampling and structure prediction using all-atom molecular simulations.