A search algorithm for fixed-composition protein design

We present a computational protein design algorithm for finding low-energy sequences of fixed amino acid composition. The search algorithms used in protein design typically do not restrict amino acid composition. However, the random energy model of Shakhnovich suggests that the use of fixed-composition sequences may circumvent defects in the modeling of the denatured state. Our algorithm, FC_FASTER, links fixed-composition versions of Monte Carlo and the FASTER algorithm. As proof of principle, FC_FASTER was tested on an experimentally validated, full-sequence design of the beta1 domain of protein G. For the wild-type composition, FC_FASTER found a lower energy sequence than the experimentally validated sequence. Also, for a different composition, FC_FASTER found the hypothetical lowest-energy sequence in 14 out of 32 trials.     

Dramatic performance enhancements for the FASTER optimization algorithm

FASTER is a combinatorial optimization algorithm useful for finding low-energy side-chain configurations in side-chain placement and protein design calculations. We present two simple enhancements to FASTER that together improve the computational efficiency of these calculations by as much as two orders of magnitude with no loss of accuracy. Our results highlight the importance of choosing appropriate initial configurations, and show that efficiency can be improved by stringently limiting the number of positions that are allowed to relax in response to a perturbation. The changes we describe improve the quality of solutions found for large-scale designs, and allow them to be found in hours rather than days. The improved FASTER algorithm finds low-energy solutions more efficiently than common optimization schemes based on the dead-end elimination theorem and Monte Carlo. These advances have prompted investigations into new methods for force field parameterization and multiple state design.     

Dead-end elimination for multistate protein design

Multistate protein design is the task of predicting the amino acid sequence that is best suited to selectively and stably fold to one state out of a set of competing structures. Computationally, it entails solving a challenging optimization problem. Therefore, notwithstanding the increased interest in multistate design, the only implementations reported are based on either genetic algorithms or Monte Carlo methods. The dead-end elimination (DEE) theorem cannot be readily transfered to multistate design problems despite its successful application to single-state protein design. In this article we propose a variant of the standard DEE, called type-dependent DEE. Our method reduces the size of the conformational space of the multistate design problem, while provably preserving the minimal energy conformational assignment for any choice of amino acid sequence. Type-dependent DEE can therefore be used as a preprocessing step in any computational multistate design scheme. We demonstrate the applicability of type-dependent DEE on a set of multistate design problems and discuss its strength and limitations.     

An object-oriented library for computational protein design

Recent advances in computational protein design have established it as a viable technique for the rational generation of stable protein sequences, novel protein folds, and even enzymatic activity. We present a new and object-oriented library of code, written specifically for protein design applications in C(++), called EGAD Library. The modular fashion in which this library is written allows developers to tailor various energy functions and minimizers for a specific purpose. It also allows for the generation of novel protein design applications with a minimal amount of code investment. It is our hope that this will permit labs that have not considered protein design to apply it to their own systems, thereby increasing its potential as a tool in biology. We also present various uses of EGAD Library: in the development of Interaction Viewer, a PyMOL plug-in for viewing interactions between protein residues; in the repacking of protein cores; and in the prediction of protein-protein complex stabilities.     

SIMONA 1.0: An efficient and versatile framework for stochastic simulations of molecular and nanoscale systems

Molecular simulation methods have increasingly contributed to our understanding of molecular and nanoscale systems. However, the family of Monte Carlo techniques has taken a backseat to molecular dynamics based methods, which is also reflected in the number of available simulation packages. Here, we report the development of a generic, versatile simulation package for stochastic simulations and demonstrate its application to protein conformational change, protein–protein association, small-molecule protein docking, and simulation of the growth of nanoscale clusters of organic molecules. Simulation of molecular and nanoscale systems (SIMONA) is easy to use for standard simulations via a graphical user interface and highly parallel both via MPI and the use of graphical processors. It is also extendable to many additional simulations types. Being freely available to academic users, we hope it will enable a large community of researchers in the life- and materials-sciences to use and extend SIMONA in the future. SIMONA is available for download under http://int.kit.edu/nanosim/simona . © 2012 Wiley Periodicals, Inc.     

Field-programmable gate arrays and quantum Monte Carlo: Power efficient coprocessing for scalable high-performance computing

Massively parallel architectures offer the potential to significantly accelerate an application relative to their serial counterparts. However, not all applications exhibit an adequate level of data and/or task parallelism to exploit such platforms. Furthermore, the power consumption associated with these forms of computation renders “scaling out” for exascale levels of performance incompatible with modern sustainable energy policies. In this work, we investigate the potential for field-programmable gate arrays (FPGAs) to feature in future exascale platforms, and their capacity to improve performance per unit power measurements for the purposes of scientific computing. We have focused our efforts on variational Monte Carlo, and report on the benefits of coprocessing with a FPGA relative to a purely multicore system.     

Adaptation of a fast Fourier transform-based docking algorithm for protein design

Designing proteins with novel protein/protein binding properties can be achieved by combining the tools that have been developed independently for protein docking and protein design. We describe here the sequence-independent generation of protein dimer orientations by protein docking for use as scaffolds in protein sequence design algorithms. To dock monomers into sequence-independent dimer conformations, we use a reduced representation in which the side chains are approximated by spheres with atomic radii derived from known C2 symmetry-related homodimers. The interfaces of C2-related homodimers are usually more hydrophobic and protein core-like than the interfaces of heterodimers; we parameterize the radii for docking against this feature to capture and recreate the spatial characteristics of a hydrophobic interface. A fast Fourier transform-based geometric recognition algorithm is used for docking the reduced representation protein models. The resulting docking algorithm successfully predicted the wild-type homodimer orientations in 65 out of 121 dimer test cases. The success rate increases to approximately 70% for the subset of molecules with large surface area burial in the interface relative to their chain length. Forty-five of the predictions exhibited less than 1 A C(alpha) RMSD compared to the native X-ray structures. The reduced protein representation therefore appears to be a reasonable approximation and can be used to position protein backbones in plausible orientations for homodimer design.     

基于瞬发伽马谱学的元素重建算法

质子治疗中的瞬发伽马射线是质子和靶标之间核反应的产物,瞬发伽马射线的特征能量和强度可以用来确定靶中元素的种类和数量,在之前的实验中已经证明,无论反应截面多么复杂,一旦确定了被照射元素和入射质子的能量,元素浓度与伽马射线光子数之间就存在一定的线性关系。然而,这种线性关系很难应用于医学成像,而且氢的非线性行为迄今尚未研究。本文将这种线性关系推广到包括氢等非线性情况的混合元素材料,并提出了一种通用的数学形式,即基于瞬发伽马谱学的重建算法 (PGSRA)。PGSRA的基本假设是样品材料的PGS与元素的每摩尔伽马射线有某种关系。对于碳和氧,这种关系是线性的,而对于氢,这种关系是非线性的。由于2.23 MeV的伽马线来源于中子吸收辐射,我们仔细研究了氢非线性行为。利用蒙特卡罗模拟验证了碳、氧和氢的不同组合,如PMMA、戊二醇和乙醇二醇的线性和非线性关系。在这项工作中开发的PGSRA可能是PGS和医学成像之间的第一座桥梁。     

Improving the Wang-Landau algorithm for polymers and proteins

The 1/t Wang-Landau algorithm is tested on simple models of polymers and proteins. It is found that this method resolves the problem of the saturation of the error present in the original algorithm for lattice polymers. However, for lattice proteins, which have a rough energy landscape with an unknown energy minimum, it is found that the density of states does not converge in all runs. A new variant of the Wang-Landau algorithm that appears to solve this problem is described and tested. In the new variant, the optimum modification factor is calculated in the same straightforward way throughout the simulation. There is only one free parameter for which a value of unity appears to give near optimal convergence for all run lengths for lattice homopolymers when pull moves are used. For lattice proteins, a much smaller value of the parameter is needed to ensure rapid convergence of the density of states for energies discovered late in the simulation, which unfortunately results in poor convergence early on in the run.     

Monte Carlo studies of a novel X-ray tube anode design

When energetic electrons are incident on high atomic number absorbers, a substantial fraction is back-scattered. This phenomenon is responsible for several undesirable effects in X-ray tubes, in particular a reduction in the X-ray output. The extent of this shortfall has been estimated by using Monte Carlo simulation to start electrons at increasing depth inside the anode, the results indicating that an output enhancement of nearly 50% could be achieved in principle if the electrons wasted in back-scatter events could be trapped inside a tungsten anode. To test this idea a further set of simulations were done for a novel anode geometry. Results showed that X-ray tube efficiencies might be substantially enhanced by this approach.     

An improved pairwise decomposable finite-difference Poisson-Boltzmann method for computational protein design

Our goal is to develop accurate electrostatic models that can be implemented in current computational protein design protocols. To this end, we improve upon a previously reported pairwise decomposable, finite difference Poisson-Boltzmann (FDPB) model for protein design (Marshall et al., Protein Sci 2005, 14, 1293). The improvement involves placing generic sidechains at positions with unknown amino acid identity and explicitly capturing two-body perturbations to the dielectric environment. We compare the original and improved FDPB methods to standard FDPB calculations in which the dielectric environment is completely determined by protein atoms. The generic sidechain approach yields a two to threefold increase in accuracy per residue or residue pair over the original pairwise FDPB implementation, with no additional computational cost. Distance dependent dielectric and solvent-exclusion models were also compared with standard FDPB energies. The accuracy of the new pairwise FDPB method is shown to be superior to these models, even after reparameterization of the solvent-exclusion model.     

A sparse algorithm for the evaluation of the local energy in quantum Monte Carlo

A new algorithm is presented for the sparse representation and evaluation of Slater determinants in the quantum Monte Carlo (QMC) method. The approach, combined with the use of localized orbitals in a Slater-type orbital basis set, significantly extends the size molecule that can be treated with the QMC method. Application of the algorithm to systems containing up to 390 electrons confirms that the cost of evaluating the Slater determinant scales linearly with system size.     

Preprocessing of rotamers for protein design calculations

We have developed a process that significantly reduces the number of rotamers in computational protein design calculations. This process, which we call Vegas, results in dramatic computational performance increases when used with algorithms based on the dead-end elimination (DEE) theorem. Vegas estimates the energy of each rotamer at each position by fixing each rotamer in turn and utilizing various search algorithms to optimize the remaining positions. Algorithms used for this context specific optimization can include Monte Carlo, self-consistent mean field, and the evaluation of an expression that generates a lower bound energy for the fixed rotamer. Rotamers with energies above a user-defined cutoff value are eliminated. We found that using Vegas to preprocess rotamers significantly reduced the calculation time of subsequent DEE-based algorithms while retaining the global minimum energy conformation. For a full boundary design of a 51 amino acid fragment of engrailed homeodomain, the total calculation time was reduced by 12-fold.     

Gradient gravitational search: An efficient metaheuristic algorithm for global optimization

The adaptation of novel techniques developed in the field of computational chemistry to solve the concerned problems for large and flexible molecules is taking the center stage with regard to efficient algorithm, computational cost and accuracy. In this article, the gradient‐based gravitational search (GGS) algorithm, using analytical gradients for a fast minimization to the next local minimum has been reported. Its efficiency as metaheuristic approach has also been compared with Gradient Tabu Search and others like: Gravitational Search, Cuckoo Search, and Back Tracking Search algorithms for global optimization. Moreover, the GGS approach has also been applied to computational chemistry problems for finding the minimal value potential energy of two‐dimensional and three‐dimensional off‐lattice protein models. The simulation results reveal the relative stability and physical accuracy of protein models with efficient computational cost. © 2015 Wiley Periodicals, Inc.     

An efficient molecular docking using conformational space annealing

Molecular docking falls into the general category of global optimization problems because its main purpose is to find the most stable complex consisting of a receptor and its ligand. Conformational space annealing (CSA), a powerful global optimization method, is incorporated with the Tinker molecular modeling package to perform molecular docking simulations of six receptor-ligand complexes (3PTB, 1ULB, 2CPP, 1STP, 3CPA, and 1PPH) from the Protein Data Bank. In parallel, Monte Carlo with the minimization (MCM) method is also incorporated into the Tinker package for comparison. The energy function, consisting of electrostatic interactions, van der Waals interactions, and torsional energy terms, is calculated using the AMBER94 all-atom empirical force field. Rigid docking simulations for all six complexes and flexible docking simulations for three complexes (1STP, 3CPA, and 1PPH) are carried out using the CSA and the MCM methods. The simulation results show that the docking procedures using the CSA method generally find the most stable complexes as well as the native-like complexes more efficiently and accurately than those using the MCM, demonstrating that CSA is a promising search method for molecular docking problems.     

An optimized initialization algorithm to ensure accuracy in quantum Monte Carlo calculations

Quantum Monte Carlo (QMC) calculations require the generation of random electronic configurations with respect to a desired probability density, usually the square of the magnitude of the wavefunction. In most cases, the Metropolis algorithm is used to generate a sequence of configurations in a Markov chain. This method has an inherent equilibration phase, during which the configurations are not representative of the desired density and must be discarded. If statistics are gathered before the walkers have equilibrated, contamination by nonequilibrated configurations can greatly reduce the accuracy of the results. Because separate Markov chains must be equilibrated for the walkers on each processor, the use of a long equilibration phase has a profoundly detrimental effect on the efficiency of large parallel calculations. The stratified atomic walker initialization (STRAW) shortens the equilibration phase of QMC calculations by generating statistically independent electronic configurations in regions of high probability density. This ensures the accuracy of calculations by avoiding contamination by nonequilibrated configurations. Shortening the length of the equilibration phase also results in significant improvements in the efficiency of parallel calculations, which reduces the total computational run time. For example, using STRAW rather than a standard initialization method in 512 processor calculations reduces the amount of time needed to calculate the energy expectation value of a trial function for a molecule of the energetic material RDX to within 0.01 au by 33%.     

Comparison of predicted native structures of Met-enkephalin based on various accessible-surface-area solvent models

We examine the variation and similarity of the native structures predicted from various accessible-surface-area solvent models for peptide Met-enkephalin. Both ECEPP/2 and ECEPP/3 force fields have been used in conjunction with ten different sets of accessible-surface-area parameterization. The native structures were determined by an implementation of the basin hopping Monte Carlo technique. The results suggest that the implicit solvent models examined in this study should be employed in computer simulations with extreme caution. In addition, the effect of fixing or not fixing the peptide angles omega has been examined. We conclude that fixing omega generally gives rise to a poor prediction.