Efficient minimization of multipole electrostatic potentials in torsion space

The development of models of macromolecular electrostatics capable of delivering improved fidelity to quantum mechanical calculations is an active field of research in computational chemistry. Most molecular force field development takes place in the context of models with full Cartesian coordinate degrees of freedom. Nevertheless, a number of macromolecular modeling programs use a reduced set of conformational variables limited to rotatable bonds. Efficient algorithms for minimizing the energies of macromolecular systems with torsional degrees of freedom have been developed with the assumption that all atom-atom interaction potentials are isotropic. We describe novel modifications to address the anisotropy of higher order multipole terms while retaining the efficiency of these approaches. In addition, we present a treatment for obtaining derivatives of atom-centered tensors with respect to torsional degrees of freedom. We apply these results to enable minimization of the Amoeba multipole electrostatics potential in a system with torsional degrees of freedom, and validate the correctness of the gradients by comparison to finite difference approximations. In the interest of enabling a complete model of electrostatics with implicit treatment of solvent-mediated effects, we also derive expressions for the derivative of solvent accessible surface area with respect to torsional degrees of freedom

Empirical Potential Function for Simplified Protein Models: Combining Contact and Local Sequence-Structure Descriptors

An effective potential function is critical for protein structure prediction and folding simulation. Simplified protein models such as those requiring only $C_\alpha$ or backbone atoms are attractive because they enable efficient search of the conformational space. We show residue specific reduced discrete state models can represent the backbone conformations of proteins with small RMSD values. However, no potential functions exist that are designed for such simplified protein models. In this study, we develop optimal potential functions by combining contact interaction descriptors and local sequence-structure descriptors. The form of the potential function is a weighted linear sum of all descriptors, and the optimal weight coefficients are obtained through optimization using both native and decoy structures. The performance of the potential function in test of discriminating native protein structures from decoys is evaluated using several benchmark decoy sets. Our potential function requiring only backbone atoms or $C_\alpha$ atoms have comparable or better performance than several residue-based potential functions that require additional coordinates of side chain centers or coordinates of all side chain atoms. By reducing the residue alphabets down to size 5 for local structure-sequence relationship, the performance of the potential function can be further improved. Our results also suggest that local sequence-structure correlation may play important role in reducing the entropic cost of protein folding.Comment: 20 pages, 5 figures, 4 tables. In press, Protein

Collective estimation of multiple bivariate density functions with application to angular-sampling-based protein loop modeling

This article develops a method for simultaneous estimation of density functions for a collection of populations of protein backbone angle pairs using a data-driven, shared basis that is constructed by bivariate spline functions defined on a triangulation of the bivariate domain. The circular nature of angular data is taken into account by imposing appropriate smoothness constraints across boundaries of the triangles. Maximum penalized likelihood is used to fit the model and an alternating blockwise Newton-type algorithm is developed for computation. A simulation study shows that the collective estimation approach is statistically more efficient than estimating the densities individually. The proposed method was used to estimate neighbor-dependent distributions of protein backbone dihedral angles (i.e., Ramachandran distributions). The estimated distributions were applied to protein loop modeling, one of the most challenging open problems in protein structure prediction, by feeding them into an angular-sampling-based loop structure prediction framework. Our estimated distributions compared favorably to the Ramachandran distributions estimated by fitting a hierarchical Dirichlet process model; and in particular, our distributions showed significant improvements on the hard cases where existing methods do not work well

Development and application of conformational methodologies: eliciting enthalpic global minima and reaction pathways

2014 Fall.The information granted by assembling the global minimum and low-enthalpy population of a chemical species or ensemble can be utilized to great effect across all fields of chemistry. With this population, otherwise impossible tasks including (but not limited to) reaction pathway characterization, protein folding, protein-ligand docking, and constructing the entropy to characterize free energy surfaces becomes a reasonable undertaking. For very small systems (single molecule with 1-3 torsions) generating the low-enthalpy population is a trivial task. However as the system grows, the task exponentially increases in difficulty. This dissertation will detail the two sides of this problem, generating the low-energy population of larger and more complex species and then utilizing those populations to garner a greater understanding of their systems. The first discussion describes a new model, Surface Editing Molecular Dynamics (SEMD), which aids in accelerating conformational searching by removing minima from the potential energy surface by adding Gaussian functions. Accompanying this new method are a multitude of new tools that can be utilized to aid in molecular dynamics simulations. The first of these tools, named CHILL, performs a projection of unproductive degrees of freedom from the molecular dynamics velocity to smooth atomic motions without artificially constraining those degrees of freedom. Another tool, Conjugate Velocity Molecular Dynamics (CVMD), rigorously generates a list of productive velocities via the biorthogonalization of local modes with a vector representation of previously explored conformational minima. In addition to these tools, a new description of distance in torsional space was developed to provide a robust means of conformational uniqueness. With each of these tools working in concert, the global minimum and associated low-enthalpy population of conformations have been obtained for various benchmark species. The second section discusses the application of conformational searching and the subsequent electronic structure calculations to characterize the reaction pathway for the ruthenium tris(2,2'-bipyridine) photocatalyzed [2+2] cycloaddition of aromatically substituted bis(enones). The APFD hybrid density functional is used along with a 6-311+g* basis and a PCM solvent model. The reaction is computed to proceed through a rate-limited formation of a cyclopentyl intermediate. Lithium tetrafluoroborate is found to facilitate initial bis(enone) reduction as well as final product distribution. In addition, aromatic substituents are found to impact both initial reduction and final product distribution

CRANKITE: a fast polypeptide backbone conformation sampler

Background: CRANKITE is a suite of programs for simulating backbone conformations of polypeptides and proteins. The core of the suite is an efficient Metropolis Monte Carlo sampler of backbone conformations in continuous three-dimensional space in atomic details. Methods: In contrast to other programs relying on local Metropolis moves in the space of dihedral angles, our sampler utilizes local crankshaft rotations of rigid peptide bonds in Cartesian space. Results: The sampler allows fast simulation and analysis of secondary structure formation and conformational changes for proteins of average length