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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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The potential utility of synthetic macrocycles (MCs) as drugs, particularly against low-druggability targets such as protein-protein interactions, has been widely discussed. There is little information, however, to guide the design of MCs for good target protein-binding activity or bioavailability. To address this knowledge gap, we analyze the binding modes of a representative set of MC-protein complexes. The results, combined with consideration of the physicochemical properties of approved macrocyclic drugs, allow us to propose specific guidelines for the design of synthetic MC libraries with structural and physicochemical features likely to favor strong binding to protein targets as well as good bioavailability. We additionally provide evidence that large, natural product-derived MCs can bind targets that are not druggable by conventional, drug-like compounds, supporting the notion that natural product-inspired synthetic MCs can expand the number of proteins that are druggable by synthetic small molecules.

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We report a comprehensive analysis of binding energy hot spots at the protein-protein interaction (PPI) interface between nuclear factor kappa B (NF-κB) essential modulator (NEMO) and IκB kinase subunit ß (IKKß), an interaction that is critical for NF-κB pathway signaling, using experimental alanine scanning mutagenesis and also the FTMap method for computational fragment screening. The experimental results confirm that the previously identified NEMO binding domain (NBD) region of IKKß contains the highest concentration of hot-spot residues, the strongest of which are W739, W741, and L742 (ΔΔG = 4.3, 3.5, and 3.2 kcal/mol, respectively). The region occupied by these residues defines a potentially druggable binding site on NEMO that extends for ~16 Å to additionally include the regions that bind IKKß L737 and F734. NBD residues D738 and S740 are also important for binding but do not make direct contact with NEMO, instead likely acting to stabilize the active conformation of surrounding residues. We additionally found two previously unknown hot-spot regions centered on IKKß residues L708/V709 and L719/I723. The computational approach successfully identified all three hot-spot regions on IKKß. Moreover, the method was able to accurately quantify the energetic importance of all hot-spot residues involving direct contact with NEMO. Our results provide new information to guide the discovery of small-molecule inhibitors that target the NEMO/IKKß interaction. They additionally clarify the structural and energetic complementarity between "pocket-forming" and "pocket-occupying" hot-spot residues, and further validate computational fragment mapping as a method for identifying hot spots at PPI interfaces.

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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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Binding hot spots, protein sites with high-binding affinity, can be identified using X-ray crystallography or NMR by screening libraries of small organic molecules that tend to cluster at such regions. FTMAP, a direct computational analog of the experimental screening approaches, globally samples the surface of a target protein using small organic molecules as probes, finds favorable positions, clusters the conformations and ranks the clusters on the basis of the average energy. The regions that bind several probe clusters predict the binding hot spots, in good agreement with experimental results. Small molecules discovered by fragment-based approaches to drug design also bind at the hot spot regions. To identify such molecules and their most likely bound positions, we extend the functionality of FTMAP (http://ftmap.bu.edu/param) to accept any small molecule as an additional probe. In its updated form, FTMAP identifies the hot spots based on a standard set of probes, and for each additional probe shows representative structures of nearby low energy clusters. This approach helps to predict bound poses of the user-selected molecules, detects if a compound is not likely to bind in the hot spot region, and provides input for the design of larger ligands.

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