Abstract:
A recently developed statistical mechanical Quasi-Chemical Theory (QCT) has led to significant insights into solvation phenomena for both hydrophilic and hydrophobic solutes. The QCT exactly partitions solvation free energies into three components: 1) inner-shell chemical, 2) outer-shell packing, and 3) outer-shell long-ranged contributions. In this paper, we discuss efficient methods for computing each of the three parts of the free energy. A Bayesian estimation approach is developed to compute the inner-shell chemical and outer-shell packing contributions. We derive upper and lower bounds on the outer-shell long-ranged portion of the free energy by expressing this component in two equivalent ways. Local, high energy contacts between solute and solvent are eliminated by spatial conditioning in this free energy piece, leading to near-Gaussian distributions of solute-solvent interactions energies. Thus, the average of the two mean-field bounds yields an accurate and efficient free energy estimate. Aqueous solvation free energy results are presented for several solutes, including methane, perfluoromethane, water, and the sodium and chloride ions. The results demonstrate the accuracy and efficiency of the methods. The approach should prove useful in computing solvation free energies in inhomogeneous, restricted environments.

Abstract:
Quasi-chemical theory is utilized to analyze the roles of solute polarization and size in determining the structure and thermodynamics of bulk anion hydration for the Hofmeister series Cl$^-$, Br$^-$, and I$^-$. Excellent agreement with experiment is obtained for whole salt hydration free energies using the polarizable AMOEBA force field. The quasi-chemical approach exactly partitions the solvation free energy into inner-shell, outer-shell packing, and outer-shell long-ranged contributions by means of a hard-sphere condition. Small conditioning radii, even well inside the first maximum of the ion-water(oxygen) radial distribution function, result in Gaussian behavior for the long-ranged contribution that dominates the ion hydration free energy. The spatial partitioning allows for a mean-field treatment of the long-ranged contribution, leading to a natural division into first-order electrostatic, induction, and van der Waals terms. The induction piece exhibits the strongest ion polarizability dependence, while the larger-magnitude first-order electrostatic piece yields an opposing but weaker polarizability dependence. In addition, a structural analysis is performed to examine the solvation anisotropy around the anions. As opposed to the hydration free energies, the solvation anisotropy depends more on ion polarizability than on ion size: increased polarizability leads to increased anisotropy. The water dipole moments near the ion are similar in magnitude to bulk water, while the ion dipole moments are found to be significantly larger than those observed in quantum mechanical studies. Possible impacts of the observed over-polarization of the ions on simulated anion surface segregation are discussed.

Abstract:
We generalize Kontsevich's construction of L-infinity derivations of polyvector fields from the affine space to an arbitrary smooth algebraic variety. More precisely, we construct a map (in the homotopy category) from Kontsevich's graph complex to the deformation complex of the sheaf of polyvector fields on a smooth algebraic variety. We show that the action of Deligne-Drinfeld elements of the Grothendieck-Teichmueller Lie algebra on the cohomology of the sheaf of polyvector fields coincides with the action of odd components of the Chern character. Using this result, we deduce that the A-hat genus in the Calaque-Van den Bergh formula arXiv:0708.2725 for the isomorphism between harmonic and Hochschild structures can be replaced by a generalized A-hat genus.

Abstract:
The extension of the classical Bayesian penalized spline method to inference on vector-valued functions is considered, with an emphasis on characterizing the suitability of the method for general application.We show that the standard quadratic penalty is exactly analogous to the energy of a stretched string, with the penalty parameter corresponding to its tension. This physical analogy motivates a discussion of resolution independence, which we define as the convergence of a computational function estimate to arbitrary accuracy with increasing resolution.The multidimensional context makes direct application of standard procedures for choosing the penalty parameter difficult, and a new method is proposed and compared to the established generalized cross-validation (GCV) and Akaike information criterion (AIC) functions.Our Bayesian method for choosing this parameter is derived by introducing a scal e independence criterion to ensure that simultaneously scaling the function samples and their variances does not significantly change the posterior parameter distribution. Due to the possibility of an exact polynomial fit, numerical issues prevent the use of this prior, and a solution is presented based on adding a st ring zero-point energy. This makes more complicated approaches recently propose d in the literature unnecessary, and eliminates the requirement for sensitivity analysis when the function deviates from the above mentioned polynomial. An important class of problems which can be analyzed by this method are stochastic numerical integrators, which are considered as an example problem. This work represents the first extension of penalized spline methods to inference on multidimensional numerical integrators reported in the literature. Several numerical calculations illustrate the above points and address practical application issues.

Abstract:
A theoretical study of the structural and electronic properties of the chloride ion and water molecules in the first hydration shell is presented. The calculations are performed on an ensemble of configurations obtained from molecular dynamics simulations of a single chloride ion in bulk water. The simulations utilize the polarizable AMOEBA force field for trajectory generation, and MP2-level calculations are performed to examine the electronic structure properties of the ions and surrounding waters in the external field of more distant waters. The ChelpG method is employed to explore the effective charges and dipoles on the chloride ions and first-shell waters. The Quantum Theory of Atoms in Molecules (QTAIM) is further utilized to examine charge transfer from the anion to surrounding water molecules. From the QTAIM analysis, 0.2 elementary charges are transferred from the ion to the first-shell water molecules. The default AMOEBA model overestimates the average dipole moment magnitude of the ion compared with the estimated quantum mechanical value. The average magnitude of the dipole moment of the water molecules in the first shell treated at the MP2 level, with the more distant waters handled with an AMOEBA effective charge model, is 2.67 D. This value is close to the AMOEBA result for first-shell waters (2.72 D) and is slightly reduced from the bulk AMOEBA value (2.78 D). The magnitude of the dipole moment of the water molecules in the first solvation shell is most strongly affected by the local water-water interactions and hydrogen bonds with the second solvation shell, rather than by interactions with the ion.

Abstract:
The original ideas of Cooper and Dryden, that allosteric signalling can be induced between distant binding sites on proteins without any change in mean structural conformation, has proved to be a remarkably prescient insight into the rich structure of protein dynamics. It represents an alternative to the celebrated Monod-Wyman-Changeux mechanism and proposes that modulation of the amplitude of thermal fluctuations around a mean structure, rather than shifts in the structure itself, give rise to allostery in ligand binding. In a complementary approach to experiments on real proteins, here we take a theoretical route to identify the necessary structural components of this mechanism. By reviewing and extending an approach that moves from very coarse-grained to more detailed models, we show that, a fundamental requirement for a body supporting fluctuation-induced allostery is a strongly inhomogeneous elastic modulus. This requirement is reflected in many real proteins, where a good approximation of the elastic structure maps strongly coherent domains onto rigid blocks connected by more flexible interface regions.

Abstract:
The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added subsequently to that original work, to explore the consequences of the purely statistical point of view. We show how standard methods in the equilibrium theory could have been derived simply from a description of the available problem information. In addition, our presentation leads to novel insights into questions associated with symmetry and non-equilibrium statistical mechanics. Two surprising consequences to be explored in further work are that (in)distinguishability factors are automatically predicted from the problem formulation and that a quantity related to the thermodynamic entropy production is found by considering information loss in non-equilibrium processes. Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complexity by successively adding information to create progressively more complex descriptions of a physical system. Our result is that such statistical mechanical descriptions can be used to create transparent, computable, experimentally-relevant models that may be informed by more detailed atomistic simulations. We also derive a theory for the kinetic behavior of this system, identifying the nonequilibrium `process' free energy functional. The Gibbs relation for this functional is a fluctuation-dissipation theorem applicable arbitrarily far from equilibrium, that captures the effect of non-local and time-dependent behavior from transient driving forces. Based on this work, it is clear that statistical mechanics is a general tool for constructing the relationships between constraints on system information.

Abstract:
Humans vary in their susceptibility to human immunodeficiency virus type 1 (HIV-1) acquisition and in the level of HIV-1 replication following infection [1,2]. Virus phenotype, the magnitude of cytotoxic T lymphocyte response, major histocompatability complex (MHC) class I haplotype, and chemokine receptor polymorphisms have all been shown to contribute to this variability [3-5]. Recent studies suggest that further undefined host factors are also contributing to the level of virus control in the HIV-1-infected individual [6].Some of the undefined host factors contributing to HIV-1 containment may be responsible for the variable ability of cells to be infected by and sustain replication of these viruses. It has been shown that permissiveness for HIV-1 varies substantially between isolated primary cells Permissiveness, the ability of cells to be infected and sustain the replication of HIV-1, also varies substantially between isolated primary cells of individuals [7]. It has been shown that the permissiveness of isolated primary rhesus monkey lymphocytes for SIV infection correlates with in vivo viral set point [8].The variability in permissiveness observed in rhesus monkey PBMC for SIV replication can be shaped by dominant and nondominant mechanisms: through the altered expression of required host factors and/or virus restricting molecules [9]. The ability of a cell to become infected by HIV/SIV requires cellular expression of diverse proteins and HIV/SIV replication can be repressed by the cellular expression of a number of restriction factors including TRIM5α and APOBEC3G [10,11]. While the restriction factor TRIM5α appears to be under positive selection and is highly polymorphic in a given species, there is little evidence that this genetic variability has functional consequences [12-15].We set out to identify genetic mechanisms underlying the variable susceptibility to lentivirus replication in a primate species through an analysis of the differential rhesus monke

Abstract:
The cytoplasmic TRIM5α proteins of certain mammalian lineages efficiently recognize the incoming capsids of particular retroviruses and potently restrict infection in a species-specific manner. Successful retroviruses have evolved capsids that are less efficiently recognized by the TRIM5α proteins of the natural hosts. To address whether TRIM5α contributes to the outcome of retroviral infection in a susceptible host species, we investigated the impact of TRIM5 polymorphisms in rhesus monkeys on the course of a simian immunodeficiency virus (SIV) infection. Full-length TRIM5α cDNAs were derived from each of 79 outbred monkeys and sequenced. Associations were explored between the expression of particular TRIM5 alleles and both the permissiveness of cells to SIV infection in vitro and clinical sequelae of SIV infection in vivo. Natural variation in the TRIM5α B30.2(SPRY) domain influenced the efficiency of SIVmac capsid binding and the in vitro susceptibility of cells from the monkeys to SIVmac infection. We also show the importance in vivo of the interaction of SIVmac with different allelic forms of TRIM5, demonstrating that particular alleles are associated with as much as 1.3 median log difference in set-point viral loads in SIVmac-infected rhesus monkeys. Moreover, these allelic forms of TRIM5 were associated with the extent of loss of central memory (CM) CD4+ T cells and the rate of progression to AIDS in the infected monkeys. These findings demonstrate a central role for TRIM5α in limiting the replication of an immunodeficiency virus infection in a primate host.

Abstract:
The functional activity of superantigens is based on capacity of these microbial proteins to bind to both the β-chain of the T cell receptor (TcR) and the major histocompatibility complex (MHC) class II dimer. We have previously shown that a subset of the bacterial superantigens also binds to a membrane protein, designated p85, which is expressed by renal epithelial cells. This binding activity is a property of SEB, SEC1, 2 and 3, but not SEA, SED, SEE or TSST. The crystal structure of the tri-molecular complex of the superantigen staphylococcal enterotoxin B (SEB) with both the TcR and class II has previously been reported. However, the relative contributions of regions of the superantigen to the overall functional activity of this superantigen remain undefined. In an effort to better define the molecular basis for the interaction of SEB with the TcR β-chain, we report studies here which show the comparative contributions of amino- and carboxy-terminal regions in the superantigen activity of SEB. Recombinant fusion proteins composed of bacterial maltose-binding protein linked to either full-length or truncated toxins in which the 81 N-terminal, or 19 or 34 C-terminal amino acids were deleted, were generated for these studies. This approach provides a determination of the relative strength of the functional activity of the various regions of the superantigen protein.