Doubling the amount of the servers from 32 to 64, we got approximately a 50% improvement on throughput, while 1T8K only improved about 30% at the same range. it can solve a number of large-scale protein design problems that have not been possible with previous approaches. Let us consider an SCPD problem with BEC HCl mutable residues, in which the total energy of a rotamer sequence is defined as follows: where is the constant energy of the backbone, is the self-energy of rotamer at residue position The branch-and-bound (BnB) algorithm is a widely used search algorithm for solving various combinatorial optimization problems. This algorithm constantly divides the conformational space into several smaller subspaces (step) and then computes the bounds (including upper and lower bound) for each subspace (step). After that, those subspaces that are impossible to contain the optimal solution (in which the lower bound is larger than the known best upper bound) are safely pruned. BEC HCl To be more specific, let us consider the SCPD problem on conformational space are computed, which are denoted by if and is not part of the optimal solution, and thus can be safely eliminated. BEC HCl DEE can significantly reduce the solution space (i.e., the rotamer combinatorial space). A more powerful DEE criterion proposed by Goldstein (1994) is We extend the Goldstein DEE criterion in Equation (2), and use the extended version to further reduce the solution space by pruning infeasible conformational space. The following theorem states the criterion of our dead-end elimination-based branch pruning scheme, and its proof can be found in appendix Section 5.1. Theorem 1 (dead-end elimination-based branch pruning). (1?? residue positions have been determined. We can easily compute a simple admissible lower bound of the energy function PIK3C2B by considering the best possible rotamer assignment in each of the undetermined residues (Gainza et al., 2013), which is where is the assigned energy term for the rotamer sequence after fixing the rotamers of the first positions, and This lower bound is not tight enough though, and we provide a much tighter one using linear programming techniques here. Observing the admissible lower bound in Equation (4), if we split into two terms and , such that for all , the lower bound becomes where we leave out the constant term of the determined rotamer sequence using the convergent message passing algorithm (Globerson and Jaakkola, 2008). This type of message-passing solution to the dual of the linear programming lower bound has been used for protein design in Roberts et al. (2015). 2.2.3.?Upper bound For each conformational space in our BnB search, we apply a local search strategy to compute a relatively good solution in current conformational space and then use it to derive the upper bound. Researchers have proposed several meta-heuristic methods, such as Monte-Carlo, with simulated annealing (Kuhlman and Baker, 2000; Voigt et al., 2000) and genetic algorithms (Raha et al., 2000), to compute the BEC HCl local minimum of the protein design problem. We apply these local search methods (e.g., simulated annealing) to compute the best possible upper bound in the current conformational space. Note that these meta-heuristic methods do not provide any theoretical guarantee of finding the globally optimal solution, while our BnB algorithm can find the GMEC solution. The upper bound derived from the local minimum solution computed by these heuristic approaches may provide a tighter upper bound at the early stage of the algorithm, which can increase the fraction of pruned conformational space in our BnB search, and thus improve the efficiency of computing the globally optimal solution. 2.3.?Optimizations for the cloud infrastructure 2.3.1.?Branching as a Map function We implement cOSPREY on top of the Hadoop MapReduce framework (White, 2009). MapReduce takes a divide-and-conquer approach. During the Map step, the programmers can exploit the intrinsic independence of the input, partition the entire input into multiple.
