Brian S. Olson

Guiding the Search for Native-like Protein Conformations with an Ab-initio Tree-based Exploration

In this paper we propose a robotics-inspired method to enhance sampling of native-like conformations when employing only aminoacid sequence information for a protein at hand. Computing such conformations, essential to associating structural and functional information with gene sequences, is challenging due to the high-dimensionality and the rugged energy surface of the protein conformational space. The contribution of this paper is a novel two-layered method to enhance the sampling of geometrically distinct low-energy conformations at a coarse-grained level of detail. The method grows a tree in conformational space reconciling two goals: (i) guiding the tree towards lower energies; and (ii) not oversampling geometrically similar conformations. Discretizations of the energy surface and a low-dimensional projection space are employed to select more often for expansion low-energy conformations in under-explored regions of the conformational space. The tree is expanded with low-energy conformations through a Metropolis Monte Carlo framework that uses a move set of physical fragment configurations. Testing on sequences of eight small-to-medium structurally diverse proteins shows that the method rapidly samples native-like conformations in a few hours on a single CPU. Analysis shows that computed conformations are good candidates for further detailed energetic refinements by larger studies in protein engineering and design.

Evolutionary-inspired probabilistic search for enhancing sampling of local minima in the protein energy surface

BackgroundDespite computational challenges, elucidating conformations that a protein system assumes under physiologic conditions for the purpose of biological activity is a central problem in computational structural biology. While these conformations are associated with low energies in the energy surface that underlies the protein conformational space, few existing conformational search algorithms focus on explicitly sampling low-energy local minima in the protein energy surface.MethodsThis work proposes a novel probabilistic search framework, PLOW, that explicitly samples low-energy local minima in the protein energy surface. The framework combines algorithmic ingredients from evolutionary computation and computational structural biology to effectively explore the subspace of local minima. A greedy local search maps a conformation sampled in conformational space to a nearby local minimum. A perturbation move jumps out of a local minimum to obtain a new starting conformation for the greedy local search. The process repeats in an iterative fashion, resulting in a trajectory-based exploration of the subspace of local minima.Results and conclusionsThe analysis of PLOWs performance shows that, by navigating only the subspace of local minima, PLOW is able to sample conformations near a proteins native structure, either more effectively or as well as state-of-the-art methods that focus on reproducing the native structure for a protein system. Analysis of the actual subspace of local minima shows that PLOW samples this subspace more effectively that a naive sampling approach. Additional theoretical analysis reveals that the perturbation function employed by PLOW is key to its ability to sample a diverse set of low-energy conformations. This analysis also suggests directions for further research and novel applications for the proposed framework.

In search of the protein native state with a probabilistic sampling approach.

The three-dimensional structure of a protein is a key determinant of its biological function. Given the cost and time required to acquire this structure through experimental means, computational models are necessary to complement wet-lab efforts. Many computational techniques exist for navigating the high-dimensional protein conformational search space, which is explored for low-energy conformations that comprise a proteins native states. This work proposes two strategies to enhance the sampling of conformations near the native state. An enhanced fragment library with greater structural diversity is used to expand the search space in the context of fragment-based assembly. To manage the increased complexity of the search space, only a representative subset of the sampled conformations is retained to further guide the search towards the native state. Our results make the case that these two strategies greatly enhance the sampling of the conformational space near the native state. A detailed comparative analysis shows that our approach performs as well as state-of-the-art ab initio structure prediction protocols.

Off-lattice protein structure prediction with homologous crossover

Ab-initio structure prediction refers to the problem of using only knowledge of the sequence of amino acids in a protein molecule to find spatial arrangements, or conformations, of the amino-acid chain capturing the protein in its biologically-active or native state. This problem is a central challenge in computational biology. It can be posed as an optimization problem, but current top ab-initio protocols employ Monte Carlo sampling rather than evolutionary algorithms (EAs) for conformational search. This paper presents a hybrid EA that incorporates successful strategies used in state-of-the-art ab-initio protocols. Comparison to a top Monte-Carlo-based sampling method shows that the domain-specific enhancements make the proposed hybrid EA competitive. A detailed analysis on the role of crossover operators and a novel implementation of homologous 1-point crossover shows that the use of crossover with mutation is more effective than mutation alone in navigating the protein energy surface.

Multi-Objective Stochastic Search for Sampling Local Minima in the Protein Energy Surface

We present an evolutionary stochastic search algorithm to obtain a discrete representation of the protein energy surface in terms of an ensemble of conformations representing local minima. This objective is of primary importance in protein structure modeling, whether the goal is to obtain a broad view of potentially different structural states thermodynamically available to a protein system or to predict a single representative structure of a unique functional native state. In this paper, we focus on the latter setting, and show how approaches from evolutionary computation for effective stochastic search and multi-objective analysis can be combined to result in protein conformational search algorithms with high exploration capability. From a broad computational perspective, the contributions of this paper are on how to balance global and local search of some high-dimensional search space and how to guide the search in the presence of a noisy, inaccurate scoring function. From an application point of view, the contributions are demonstrated in the domain of template-free protein structure prediction on the primary subtask of sampling diverse low-energy decoy conformations of an amino-acid sequence. Comparison with the approach used for decoy sampling in the popular Rosetta protocol on 20 diverse protein sequences shows that the evolutionary algorithm proposed in this paper is able to access lower-energy regions with similar or better proximity to the known native structure.

Efficient basin hopping in the protein energy surface

The vast and rugged protein energy surface can be effectively represented in terms of local minima. The basin-hopping framework, where a structural perturbation is followed by an energy minimization, is particularly suited to obtaining this coarse-grained representation. Basin hopping is effective for small systems both in locating lower-energy minima and obtaining conformations near the native structure. The efficiency decreases for large systems. Our recent work improves efficiency on large systems through molecular fragment replacement. In this paper, we conduct a detailed investigation of two components in basin hopping, perturbation and minimization, and how they work in concert to affect the sampling of near-native local minima. We show that controlling the magnitude of perturbation jumps is related to the ability to effectively steer the exploration towards conformations near the protein native state. In minimization, we show that a simple greedy search is just as effective as Metropolis Monte Carlo-based minimization. Finally, we show that an evolutionary-inspired approach based on the Pareto front is particularly effective in reducing the ensemble of sampled local minima and obtains a simpler representation of the probed energy surface.

Rapid sampling of local minima in protein energy surface and effective reduction through a multi-objective filter

BackgroundMany problems in protein modeling require obtaining a discrete representation of the protein conformational space as an ensemble of conformations. In ab-initio structure prediction, in particular, where the goal is to predict the native structure of a protein chain given its amino-acid sequence, the ensemble needs to satisfy energetic constraints. Given the thermodynamic hypothesis, an effective ensemble contains low-energy conformations which are similar to the native structure. The high-dimensionality of the conformational space and the ruggedness of the underlying energy surface currently make it very difficult to obtain such an ensemble. Recent studies have proposed that Basin Hopping is a promising probabilistic search framework to obtain a discrete representation of the protein energy surface in terms of local minima. Basin Hopping performs a series of structural perturbations followed by energy minimizations with the goal of hopping between nearby energy minima. This approach has been shown to be effective in obtaining conformations near the native structure for small systems. Recent work by us has extended this framework to larger systems through employment of the molecular fragment replacement technique, resulting in rapid sampling of large ensembles.MethodsThis paper investigates the algorithmic components in Basin Hopping to both understand and control their effect on the sampling of near-native minima. Realizing that such an ensemble is reduced before further refinement in full ab-initio protocols, we take an additional step and analyze the quality of the ensemble retained by ensemble reduction techniques. We propose a novel multi-objective technique based on the Pareto front to filter the ensemble of sampled local minima.Results and conclusionsWe show that controlling the magnitude of the perturbation allows directly controlling the distance between consecutively-sampled local minima and, in turn, steering the exploration towards conformations near the native structure. For the minimization step, we show that the addition of Metropolis Monte Carlo-based minimization is no more effective than a simple greedy search. Finally, we show that the size of the ensemble of sampled local minima can be effectively and efficiently reduced by a multi-objective filter to obtain a simpler representation of the probed energy surface.

Basin hopping as a general and versatile optimization framework for the characterization of biological macromolecules

Since its introduction, the basin hopping (BH) framework has proven useful for hard nonlinear optimization problems with multiple variables and modalities. Applications span a wide range, from packing problems in geometry to characterization of molecular states in statistical physics. BH is seeing a reemergence in computational structural biology due to its ability to obtain a coarse-grained representation of the protein energy surface in terms of local minima. In this paper, we show that the BH framework is general and versatile, allowing to address problems related to the characterization of protein structure, assembly, and motion due to its fundamental ability to sample minima in a high-dimensional variable space. We show how specific implementations of the main components in BH yield algorithmic realizations that attain state-of-the-art results in the context of ab initio protein structure prediction and rigid protein-protein docking. We also show that BH can map intermediate minima related with motions connecting diverse stable functionally relevant states in a protein molecule, thus serving as a first step towards the characterization of transition trajectories connecting these states.

Populating Local Minima in the Protein Conformational Space

Protein Modeling conceptualizes the protein energy landscape as a funnel with the native structure at the low-energy minimum. Current protein structure prediction algorithms seek the global minimum by searching for low-energy conformations in the hope that some of these reside in local minima near the native structure. The search techniques employed, however, fail to explicitly model these local minima. This work proposes a memetic algorithm which combines methods from evolutionary computation with cutting-edge structure prediction protocols. The Protein Local Optima Walk (PLOW) algorithm proposed here explores the space of local minima by explicitly projecting each move in the conformation space to a nearby local minimum. This allows PLOW to jump over local energy barriers and more effectively sample near-native conformations. Analysis across a broad range of proteins shows that PLOW outperforms an MMC-based method and compares favorably against other published abini to structure prediction algorithms.

A population-based evolutionary search approach to the multiple minima problem in de novo protein structure prediction

BackgroundElucidating the native structure of a protein molecule from its sequence of amino acids, a problem known as de novo structure prediction, is a long standing challenge in computational structural biology. Difficulties in silico arise due to the high dimensionality of the protein conformational space and the ruggedness of the associated energy surface. The issue of multiple minima is a particularly troublesome hallmark of energy surfaces probed with current energy functions. In contrast to the true energy surface, these surfaces are weakly-funneled and rich in comparably deep minima populated by non-native structures. For this reason, many algorithms seek to be inclusive and obtain a broad view of the low-energy regions through an ensemble of low-energy (decoy) conformations. Conformational diversity in this ensemble is key to increasing the likelihood that the native structure has been captured.MethodsWe propose an evolutionary search approach to address the multiple-minima problem in decoy sampling for de novo structure prediction. Two population-based evolutionary search algorithms are presented that follow the basic approach of treating conformations as individuals in an evolving population. Coarse graining and molecular fragment replacement are used to efficiently obtain protein-like child conformations from parents. Potential energy is used both to bias parent selection and determine which subset of parents and children will be retained in the evolving population. The effect on the decoy ensemble of sampling minima directly is measured by additionally mapping a conformation to its nearest local minimum before considering it for retainment. The resulting memetic algorithm thus evolves not just a population of conformations but a population of local minima.Results and conclusionsResults show that both algorithms are effective in terms of sampling conformations in proximity of the known native structure. The additional minimization is shown to be key to enhancing sampling capability and obtaining a diverse ensemble of decoy conformations, circumventing premature convergence to sub-optimal regions in the conformational space, and approaching the native structure with proximity that is comparable to state-of-the-art decoy sampling methods. The results are shown to be robust and valid when using two representative state-of-the-art coarse-grained energy functions.