The problem of finding the most probable (MAP) configuration in graphical models comes up in a wide range of applications. In a general graphical model this problem is NP hard, but various approximate algorithms have been developed. Linear programming (LP) relaxations are a standard method in computer science for approximating combinatorial problems and have been used for finding the most probable assignment in small graphical models. However, applying this powerful method to real-world problems is extremely challenging due to the large numbers of variables and constraints in the linear program. Tree-Reweighted Belief Propagation is a promising recent algorithm for solving LP relaxations, but little is known about its running time on large problems. In this paper we compare tree-reweighted belief propagation (TRBP) and powerful generalpurpose LP solvers (CPLEX) on relaxations of real-world graphical models from the fields of computer vision and computational biology. We find that TRBP almost always finds the solution significantly faster than all the solvers in CPLEX and more importantly, TRBP can be applied to large scale problems for which the solvers in CPLEX cannot be applied. Using TRBP we can find the MAP configurations in a matter of minutes for a large range of real world problems. 1.

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Introduction Approaches to protein structure prediction are based on the thermodynamic hypothesis, which postulates that the native state of a protein is the state of lowest free energy under physiological conditions. Normally, this state corresponds to the lowest basin of the effective energy surface. The term `effective energy' or `potential of mean force' refers to the free energy of the system (protein plus solvent) for a fixed protein conformation; that is, it consists of the intramolecular energy of the protein plus the solvation free energy [1,2]. Although the vibrational entropy of the folded state is large [3], it is approximately equal to that of a single unfolded conformer [4,5]. The large stabilizing entropy of the unfolded `state' arises from the multitude of conformers of similar energy that contributes to it. It has been suggested that the native state is surrounded by an ensemble of similar conformations [6]. This appears to be true for a protein like a-lactalbumin, wh

The ultimate goal of protein design is the creation of novel proteins that perform specified tasks. A necessary requirement for meeting this goal is the ability to identify sequences that fold

ABSTRACT Protein–small molecule docking algorithms provide a means to model the struc-ture of protein–small molecule complexes in struc-tural detail and play an important role in drug development. In recent years the necessity of sim-ulating protein side-chain flexibility for an accu-rate prediction of the protein–small molecule inter-faces has become apparent, and an increasing number of docking algorithms probe different ap-proaches to include protein flexibility. Here we de-scribe a new method for docking small molecules into protein binding sites employing a Monte Carlo minimization procedure in which the rigid body position and orientation of the small mole-cule and the protein side-chain conformations are optimized simultaneously. The energy function comprises van der Waals (VDW) interactions, an implicit solvation model, an explicit orientation hydrogen bonding potential, and an electrostatics model. In an evaluation of the scoring function the computed energy correlated with experimen-tal small molecule binding energy with a correla-tion coefficient of 0.63 across a diverse set of 229 protein – small molecule complexes. The docking method produced lowest energy models with a root mean square deviation (RMSD) smaller than 2 A ̊ in 71 out of 100 protein–small molecule crystal structure complexes (self-docking). In cross-docking calculations in which both protein side-chain and small molecule internal degrees of freedom were varied the lowest energy predictions had RMSDs less than 2 A ̊ in 14 of 20 test cases. Proteins

ABSTRACT A major limitation of current comparative modeling methods is the accuracy with which regions that are structurally divergent from homologues of known structure can be modeled. Because structural differences between homologous proteins are responsible for variations in protein function and specificity, the ability to model these differences has important functional consequences. Although existing methods can provide reasonably accurate models of short loop regions, modeling longer structurally divergent regions is an unsolved problem. Here we describe a method based on the de novo structure prediction algorithm, Rosetta, for predicting conformations of structurally divergent regions in comparative models.

Side-chain prediction is an important subproblem of the general protein folding problem. Despite much progress in side-chain prediction, performance is far from satisfactory. As an example, the ROSETTA protocol that uses simulated annealing to select the minimum energy conformations, correctly predicts the first two side-chain angles for approximately 72 % of the buried residues in a standard data set. Is further improvement more likely to come from better search methods, or from better energy functions? Given that exact minimization of the energy is NP hard, it is difficult to get a systematic answer to this question. In this paper, we present a novel search method and a novel method for learning energy functions from training data that are both based on Tree Reweighted Belief Propagation (TRBP). We find that TRBP can find the global optimum of the ROSETTA energy function in a few minutes of computation for approximately 85 % of the proteins in a standard benchmark set. TRBP can also effectively bound the partition function which enables using the Conditional Random Fields (CRF) framework for learning. Interestingly, finding the global minimum does not significantly improve side-chain prediction for

Protein–DNA interactions are crucial for many biological processes. Attempts to model these interactions have generally taken the form of amino acid–base recognition codes or purely sequence-based profile methods, which depend on the availability of extensive sequence and structural information for specific structural families, neglect side-chain conformational variability, and lack generality beyond the structural family used to train the model. Here, we take advantage of recent advances in rotamer-based protein design and the large number of structurally characterized protein–DNA complexes to develop and parameterize a simple physical model for protein–DNA interactions. The model shows considerable promise for redesigning amino acids at protein–DNA interfaces, as design calculations recover the amino acid residue identities and conformations at these interfaces with accuracies comparable to sequence recovery in globular proteins. The model shows promise also for predicting DNA-binding specificity for fixed protein sequences: native DNA sequences are selected correctly from pools of competing DNA substrates; however, incorporation of backbone movement will likely be required to improve performance in homology modeling applications. Interestingly, optimization of zinc finger protein amino acid sequences for high-affinity binding to specific DNA sequences results in proteins with little or no predicted specificity, suggesting that naturally occurring DNA-binding proteins are optimized for specificity rather than affinity. When combined with algorithms that optimize specificity directly, the simple computational model developed here should be useful for the engineering of proteins with novel DNA-binding specificities.

ABSTRACT We present a simple and effective algorithm RDOCK for refining unbound predictions generated by a rigid-body docking algorithm ZDOCK, which has been developed earlier by our group. The main component of RDOCK is a three-stage energy minimization scheme, followed by the evaluation of electrostatic and desolvation ener-gies. Ionic side chains are kept neutral in the first two stages of minimization, and reverted to their full charge states in the last stage of brief minimiza-tion. Without side chain conformational search or filtering/clustering of resulting structures, RDOCK represents the simplest approach toward refining unbound docking predictions. Despite its simplic-ity, RDOCK makes substantial improvement upon the top predictions by ZDOCK with all three scoring functions and the improvement is observed across all three categories of test cases in a large bench-mark of 49 non-redundant unbound test cases. RDOCK makes the most powerful combination with ZDOCK2.1,whichuses pairwise shape complementa-rity as the scoring function. Collectively, they rank a near-native structure as the number-one predic-tion for 18 test cases (37 % of the benchmark), and within the top 4 predictions for 24 test cases (49 % of the benchmark). To various degrees, funnel-like energy landscapes are observed for these 24 test cases. To the best of our knowledge, this is the first report of binding funnels starting from global searches for a broad range of test cases. These results are particularly exciting, given that we have not used any biological information that is specific to individual test cases and the whole process is entirely automated. Among three categories of test cases, the best results are seen for enzyme/inhibitor, with a near-native structure ranked as the number-one prediction for 48 % test cases, and within the top 10 predictions for 78 % test cases. RDOCK is freely available to academic users at