We present a technique for approximating the free energy of protein structures using Generalized Belief Propagation (GBP). The accuracy and utility of these estimates are then demonstrated in two different application domains. First, we show that the entropy component of our free energy estimates can be used to distinguish native protein structures from decoys — structures with similar internal energy to that of the native structure, but otherwise incorrect. Our method is able to correctly identify the native fold from among a set of decoys with 87.5 % accuracy over a total of 48 different immunoglobin folds. The remaining 12.5 % of native structures are ranked among the top 4 of all structures. Second, we show that our estimates of ∆∆G upon mutation for three different data sets have linear correlations between 0.64-0.69 with experimental values and statistically significant p-values. Together, these results suggests that GBP is an effective means for computing free energy in all-atom models of protein structures. GBP is also efficient, taking a few minutes to run on a typical sized protein, further suggesting that GBP may be an attractive alternative to more costly molecular dynamic simulations for some tasks.

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Abstract. Given d> 2 and a set of n grid points Q in ℜ d, we design a randomized algorithm that finds a w-wide separator, which is determined by a hyper-plane, in O(n 2 d log n) sublinear time such that Q has at most ( d + o(1))n points one either side of the hyper-plane, and at most d+1 cdwn d−1 d points within w 2 distance to the hyper-plane, where cd is a constant for fixed d. In particular, c3 = 1.209. To our best knowledge, this is the first sublinear time algorithm for finding geometric separators. Our 3D separator is applied to derive an algorithm for the protein side-chain packing problem, which improves and simplifies the previous algorithm of Xu [26]. 1

Abstract. We present an exact method for the global minimum energy conformation (GMEC) search of protein side-chains. Our method consists of a branch-and-bound (B&B) framework and a new subproblempruning scheme. The pruning scheme consists of upper/lower-bounding methods and problem-size reduction techniques. We explore a way of using the tree-reweighted max-product algorithm for computing lowerbounds of the GMEC energy. The problem-size reduction techniques are necessary when the size of the subproblem is too large to rely on more accurate yet expensive bounding methods. The experimental results show our pruning scheme is effective and our B&B method exactly solves protein sequence design cases that are very hard to solve with the dead-end elimination. 1

Abstract. High-accuracy protein structure modeling demands on accurate and very fast side chain prediction since such a procedure must be repeatedly called at each step of structure refinement. Many known side chain prediction programs, such as SCWRL and TreePack, depend on the philosophy that global information and pairwise energy function must be used to achieve high accuracy. These programs are too slow to be used in the case when side chain packing has to be used thousands of times, such as protein structure refinement and protein design. We present an unexpected study that local backbone information can determine side chain conformations accurately. LocalPack, our side chain packing program which is based on only local information, achieves equal accuracy as SCWRL and TreePack, yet runs many times faster, hence providing a key missing piece in our efforts to high-accuracy protein structure modeling. keyword: side chain prediction, local backbone features, multiclass Support Vector Machines. 1

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Abstract—Particle Swarm Optimization (PSO) is a wellknown, competitive technique for numerical optimization with real-parameter representation. This paper introduces CCPSO, a new Cooperative Particle Swarm Optimization algorithm for combinatorial problems. The cooperative strategy is achieved by splitting the candidate solution vector into components, where each component is optimized by a particle. Particles move throughout a continuous space, their movements based on the influences exerted by static particles that then get feedback based on the fitness of the candidate solution. Here, the application of this technique to side-chain packing (a proteomics optimization problem) is investigated. To verify the efficiency of the proposed CCPSO algorithm, we test our algorithm on three side-chain packing problems and compare our results with the provably optimal result. Computational results show that the proposed algorithm is very competitive, obtaining a conformation with an energy value within 1 % of the provably optimal solution in many proteins. I.

In this paper, we present several methods for computing a solution to the protein side chain packing problem, with all methods having a common solution approach of breaking the polymer into subpolymers and using maximum edge weight cliques to prune the search space for the optimal side chain packing. We characterize the graph sizes generated for each method and compare their prediction accuracies. These methods are demonstrated for computing proteins up to approximately 8000 residues. In addition, we update a result published previously.

A graphical model approach for predicting free energies of association for protein-protein

Background: Protein side-chain packing problem has remained one of the key open problems in bioinformatics. The three main components of protein side-chain prediction methods are a rotamer library, an energy function and a search algorithm. Rotamer libraries summarize the existing knowledge of the experimentally determined structures quantitatively. Depending on how much contextual information is encoded, there are backboneindependent rotamer libraries and backbone-dependent rotamer libraries. Backbone-independent libraries only encode sequential information, whereas backbone-dependent libraries encode both sequential and locally structural information. However, side-chain conformations are determined by spatially local information, rather than sequentially local information. Since in the side-chain prediction problem, the backbone structure is given, spatially local information should ideally be encoded into the rotamer libraries. Methods: In this paper, we propose a new type of backbone-dependent rotamer library, which encodes structural information of all the spatially neighboring residues. We call it protein-dependent rotamer libraries. Given any rotamer library and a protein backbone structure, we first model the protein structure as a Markov random field. Then the marginal distributions are estimated by the inference algorithms, without doing global optimization or search. The rotamers from the given library are then re-ranked and associated with the updated probabilities.