In this paper we extend a recently introduced rigid body minimization algorithm, defined on manifolds, to the problem of minimizing the energy of interacting flexible molecules. The goal is to integrate moving the ligand in six dimensional rotational/translational space with internal rotations around rotatable bonds within the two molecules. We show that adding rotational degrees of freedom to the rigid moves of the ligand results in an overall optimization search space that is a manifold to which our manifold optimization approach can be extended. The effectiveness of the method is shown for three different docking problems of increasing complexity. First we minimize the energy of fragment-size ligands with a single rotatable bond as part of a protein mapping method developed for the identification of binding hot spots. Second, we consider energy minimization for docking a flexible ligand to a rigid protein receptor, an approach frequently used in existing methods. In the third problem we account for flexibility in both the ligand and the receptor. Results show that minimization using the manifold optimization algorithm is substantially more efficient than minimization using a traditional all-atom optimization algorithm while producing solutions of comparable quality. In addition to the specific problems considered, the method is general enough to be used in a large class of applications such as docking multidomain proteins with flexible hinges. The code is available under open source license (at http://cluspro.bu.edu/Code/Code_Rigtree.tar), and with minimal effort can be incorporated into any molecular modeling package.

We propose a novel stochastic global optimization algorithm with applications to the refinement stage of protein docking prediction methods. Our approach can process conformations sampled from multiple clusters, each roughly corresponding to a different binding energy funnel. These clusters are obtained using a density-based clustering method. In each cluster, we identify a smooth “permissive” subspace which avoids high-energy barriers and then underestimate the binding energy function using general convex polynomials in this subspace. We use the underestimator to bias sampling towards its global minimum. Sampling and subspace underestimation are repeated several times and the conformations sampled at the last iteration form a refined ensemble. We report computational results on a comprehensive benchmark of 224 protein complexes, establishing that our refined ensemble significantly improves the quality of the conformations of the original set given to the algorithm. We also devise a method to enhance the ensemble from which near-native models are selected.

The fast Fourier transform (FFT) sampling algorithm has been used with success in application to protein-protein docking and for protein mapping, the latter docking a variety of small organic molecules for the identification of binding hot spots on the target protein. Here we explore the local rather than global usage of the FFT sampling approach in docking applications. If the global FFT based search yields a near-native cluster of docked structures for a protein complex, then focused resampling of the cluster generally leads to a substantial increase in the number of conformations close to the native structure. In protein mapping, focused resampling of the selected hot spot regions generally reveals further hot spots that, while not as strong as the primary hot spots, also contribute to ligand binding. The detection of additional ligand binding regions is shown by the improved overlap between hot spots and bound ligands.

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Background: Systemic inflammation has been implicated in the pathobiology of HFpEF. We examined the association of upstream mediators of inflammation as ascertained by fatty-acid derived eicosanoid and eicosanoid-related metabolites with HFpEF status and exercise manifestations of HFpEF. Methods: We studied 510 participants with chronic dyspnea and preserved LVEF who underwent invasive cardiopulmonary exercise testing (CPET). We examined the association of 890 eicosanoid and eicosanoid-related metabolites ascertained using mass spectrometry with HFpEF status (defined as abnormal rest or exercise PCWP) using multivariable logistic regression (FDR q-value <0.1 deemed significant). In secondary analyses, we examined eicosanoid profiles of specific exercise traits, including cardiac vs extra-cardiac organ reserve using principal component analysis. To corroborate findings, significant metabolites were tested against incident HF in 5192 MESA participants. Results: Among 510 participants (mean age 56±16 years, 63% women), 257 had physiologic evidence of HFpEF. We found 70 eicosanoid and eicosanoid-related metabolites were associated with HFpEF status including 17 named and 53 putative eicosanoids and eicosanoid-related metabolites. Specific prostaglandin (15R-PGF2a and 11ß-dhk-PGF2a) and linoleic acid derivatives (12,13 EpOME) were associated with greater odds of HFpEF, whereas epoxide (8(9)-EpETE), docosanoid (13,14-DiHDPA), and oxylipin (12-OPDA) derivatives were associated with lower odds of HFpEF(P<0.008 for all). Eicosanoid profiles showed heterogeneous associations across cardiac vs extra-cardiac contributors to exercise intolerance. In the MESA sample, we found that 18 eicosanoids and eicosanoid-related metabolites were associated with the development of future heart failure (P<0.05 for all). Conclusions: We found 70 pro- and anti-inflammatory eicosanoid and eicosanoid-related metabolites that were associated with physiologic HFpEF, including prostaglandin, linoleic acid, and epoxide derivatives. Among these, 18 were associated with future development of heart failure in the community. Further, eicosanoid profiles highlighted contributions to exercise intolerance. Specific eicosanoid and eicosanoid-related metabolites may contribute to the pathogenesis of HFpEF and may serve as potential therapeutic targets for intervention.