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Fast Fourier transform (FFT) based approaches have been successful in application to modeling of relatively rigid protein-protein complexes. Recently, we have been able to adapt the FFT methodology to treatment of flexible protein-peptide interactions. Here, we report our latest attempt to expand the capabilities of the FFT approach to treatment of flexible protein-ligand interactions in application to the D3R PL-2016-1 challenge. Based on the D3R assessment, our FFT approach in conjunction with Monte Carlo minimization off-grid refinement was among the top performing methods in the challenge. The potential advantage of our method is its ability to globally sample the protein-ligand interaction landscape, which will be explored in further applications.

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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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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.

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We study the impact of optimizing the side-chain positions in the interface region between two proteins during the process of binding. Mathematically, the problem is similar to side-chain prediction, which has been extensively explored in the process of protein structure prediction. The protein-protein docking application, however, has a number of characteristics that necessitate different algorithmic and implementation choices. In this work, we implement a distributed approximate algorithm that can be implemented on multiprocessor architectures and enables a trade-off between accuracy and running speed. We report computational results on benchmarks of enzyme-inhibitor and other types of complexes, establishing that the side-chain flexibility our algorithm introduces substantially improves the performance of docking protocols. Furthermore, we establish that the inclusion of unbound side-chain conformers in the side-chain positioning problem is critical in these performance improvements. The code is available to the community under open source license.

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In this paper we consider the problem of minimization of a cost function that depends on the location and poses of one or more rigid bodies, or bodies that consist of rigid parts hinged together. We present a unified setting for formulating this problem as an optimization on an appropriately defined manifold for which efficient manifold optimizations can be developed. This setting is based on a Lie group representation of the rigid movements of a body that is different from what is commonly used for this purpose. We illustrate this approach by using the steepest descent algorithm on the manifold of the search space and specify conditions for its convergence.

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Our work is motivated by energy minimization of biological macromolecules, an essential step in computational docking. By allowing some ligand flexibility, we generalize a recently introduced novel representation of rigid body minimization as an optimization on the [Formula: see text] manifold, rather than on the commonly used Special Euclidean group SE(3). We show that the resulting flexible docking can also be formulated as an optimization on a Lie group that is the direct product of simpler Lie groups for which geodesics and exponential maps can be easily obtained. Our computational results for a local optimization algorithm developed based on this formulation show that it is about an order of magnitude faster than the state-of-the-art local minimization algorithms for computational protein-small molecule docking.

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BACKGROUND: Zoonotic cutaneous leishmaniasis (ZCL) due to Leishmania major is increasing in many parts of Iran. This disease originally is a disease found in gerbils. Leishmania parasites are transmitted by sandflies that live and breed in gerbil burrows. Nested PCR amplified Leishmania ITS1-5.8S rRNA gene in both main reservoir host "Rhombomys opimus" and in the "Phlebotomus papatasi" main vector of ZCL, in Iran. Population differentiation and seasonal variation of sandflies were analyzed at a microgeographical level in order to identify any isolation by distance, habitat or seasons. METHODS: Populations of sandflies were sampled from the edges of villages in Natanz, Isfahan province, Iran, using the Centers for Disease Control traps and sticky papers. Individual sandflies were identified based on external and internal morphological characters. Nested PCR protocols were used to amplify Leishmania ITS1-5.8S rRNA gene, which were shown to be species-specific via DNA sequence. RESULTS: A total of 4500 sandflies were collected and identified. P. papatasi, Phlebotomus sergenti and Phlebotomus jacusieli from genus Phlebotomus and Sergentomyia sintoni and Sergentomyia clydei from genus Sergentomyia were identified in this region. P. papatasi was the most abundant sandfly in the collections. Ten out of 549 female P. papatasi and four out of 19 R. opimus were found to be infected with L. major. CONCLUSION: Seasonal activity of sandflies starts in June and ends in November. Abundance of P. papatasi was in September. Finding and molecular typing of L. major in P. papatasi and R. opimus confirmed the main vector and reservoir in this region.

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Our work is motivated by energy minimization in the space of rigid affine transformations of macromolecules, an essential step in computational protein-protein docking. We introduce a novel representation of rigid body motion that leads to a natural formulation of the energy minimization problem as an optimization on the [Formula: see text] manifold, rather than the commonly used SE(3). The new representation avoids the complications associated with optimization on the SE(3) manifold and provides additional flexibilities for optimization not available in that formulation. The approach is applicable to general rigid body minimization problems. Our computational results for a local optimization algorithm developed based on the new approach show that it is about an order of magnitude faster than a state of art local minimization algorithms for computational protein-protein docking.

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Virtually all docking methods include some local continuous minimization of an energy/scoring function in order to remove steric clashes and obtain more reliable energy values. In this paper, we describe an efficient rigid-body optimization algorithm that, compared to the most widely used algorithms, converges approximately an order of magnitude faster to conformations with equal or slightly lower energy. The space of rigid body transformations is a nonlinear manifold, namely, a space which locally resembles a Euclidean space. We use a canonical parametrization of the manifold, called the exponential parametrization, to map the Euclidean tangent space of the manifold onto the manifold itself. Thus, we locally transform the rigid body optimization to an optimization over a Euclidean space where basic optimization algorithms are applicable. Compared to commonly used methods, this formulation substantially reduces the dimension of the search space. As a result, it requires far fewer costly function and gradient evaluations and leads to a more efficient algorithm. We have selected the LBFGS quasi-Newton method for local optimization since it uses only gradient information to obtain second order information about the energy function and avoids the far more costly direct Hessian evaluations. Two applications, one in protein-protein docking, and the other in protein-small molecular interactions, as part of macromolecular docking protocols are presented. The code is available to the community under open source license, and with minimal effort can be incorporated into any molecular modeling package.