Kevin Molloy

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.

Probabilistic Search and Energy Guidance for Biased Decoy Sampling in Ab Initio Protein Structure Prediction

Adequate sampling of the conformational space is a central challenge in ab initio protein structure prediction. In the absence of a template structure, a conformational search procedure guided by an energy function explores the conformational space, gathering an ensemble of low-energy decoy conformations. If the sampling is inadequate, the native structure may be missed altogether. Even if reproduced, a subsequent stage that selects a subset of decoys for further structural detail and energetic refinement may discard near-native decoys if they are high energy or insufficiently represented in the ensemble. Sampling should produce a decoy ensemble that facilitates the subsequent selection of near-native decoys. In this paper, we investigate a robotics-inspired framework that allows directly measuring the role of energy in guiding sampling. Testing demonstrates that a soft energy bias steers sampling toward a diverse decoy ensemble less prone to exploiting energetic artifacts and thus more likely to facilitate retainment of near-native conformations by selection techniques. We employ two different energy functions, the associative memory Hamiltonian with water and Rosetta. Results show that enhanced sampling provides a rigorous testing of energy functions and exposes different deficiencies in them, thus promising to guide development of more accurate representations and energy functions.

Elucidating the ensemble of functionally-relevant transitions in protein systems with a robotics- inspired method

BackgroundMany proteins tune their biological function by transitioning between different functional states, effectively acting as dynamic molecular machines. Detailed structural characterization of transition trajectories is central to understanding the relationship between protein dynamics and function. Computational approaches that build on the Molecular Dynamics framework are in principle able to model transition trajectories at great detail but also at considerable computational cost. Methods that delay consideration of dynamics and focus instead on elucidating energetically-credible conformational paths connecting two functionally-relevant structures provide a complementary approach. Effective sampling-based path planning methods originating in robotics have been recently proposed to produce conformational paths. These methods largely model short peptides or address large proteins by simplifying conformational space.MethodsWe propose a robotics-inspired method that connects two given structures of a protein by sampling conformational paths. The method focuses on small- to medium-size proteins, efficiently modeling structural deformations through the use of the molecular fragment replacement technique. In particular, the method grows a tree in conformational space rooted at the start structure, steering the tree to a goal region defined around the goal structure. We investigate various bias schemes over a progress coordinate for balance between coverage of conformational space and progress towards the goal. A geometric projection layer promotes path diversity. A reactive temperature scheme allows sampling of rare paths that cross energy barriers.Results and conclusionsExperiments are conducted on small- to medium-size proteins of length up to 214 amino acids and with multiple known functionally-relevant states, some of which are more than 13Å apart of each-other. Analysis reveals that the method effectively obtains conformational paths connecting structural states that are significantly different. A detailed analysis on the depth and breadth of the tree suggests that a soft global bias over the progress coordinate enhances sampling and results in higher path diversity. The explicit geometric projection layer that biases the exploration away from over-sampled regions further increases coverage, often improving proximity to the goal by forcing the exploration to find new paths. The reactive temperature scheme is shown effective in increasing path diversity, particularly in difficult structural transitions with known high-energy barriers.

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.

Enhancing Sampling of the Conformational Space Near the Protein Native State

A protein molecule assumes specific conformations under native conditions to fit and interact with other molecules. Due to the role that three-dimensional structure plays in protein function, significant efforts are devoted to elucidating native conformations. Many search algorithms are proposed to navigate the high-dimensional protein conformational space and its underlying energy surface in search of low-energy conformations that comprise the native state. In this work, we identify two strategies to enhance the sampling of native conformations. We show that employing an enhanced fragment library with greater structural diversity to assemble low-energy conformations allows sampling more native conformations. To efficiently handle the ensuing vast conformational space, only a representative subset of the sampled conformations are maintained and employed to further guide the search for native conformations. Our results show that these two strategies greatly enhance the sampling of the conformational space near the native state.

Characterizing Energy Landscapes of Peptides Using a Combination of Stochastic Algorithms

Obtaining accurate representations of energy landscapes of biomolecules such as proteins and peptides is central to the study of their physicochemical properties and biological functions. Peptides are particularly interesting, as they exploit structural flexibility to modulate their biological function. Despite their small size, peptide modeling remains challenging due to the complexity of the energy landscape of such highly-flexible dynamic systems. Currently, only stochastic sampling-based methods can efficiently explore the conformational space of a peptide. In this paper, we suggest to combine two such methods to obtain a full characterization of energy landscapes of small yet flexible peptides. First, we propose a simplified version of the classical Basin Hopping algorithm to reveal low-energy regions in the landscape, and thus to identify the corresponding meta-stable structural states of a peptide. Then, we present several variants of a robotics-inspired algorithm, the Transition-based Rapidly-exploring Random Tree, to quickly determine transition path ensembles, as well as transition probabilities between meta-stable states. We demonstrate this combined approach on met-enkephalin.

GUIDING PROBABILISTIC SEARCH OF THE PROTEIN CONFORMATIONAL SPACE WITH STRUCTURAL PROFILES

The roughness of the protein energy surface poses a significant challenge to search algorithms that seek to obtain a structural characterization of the native state. Recent research seeks to bias search toward near-native conformations through one-dimensional structural profiles of the protein native state. Here we investigate the effectiveness of such profiles in a structure prediction setting for proteins of various sizes and folds. We pursue two directions. We first investigate the contribution of structural profiles in comparison to or in conjunction with physics-based energy functions in providing an effective energy bias. We conduct this investigation in the context of Metropolis Monte Carlo with fragment-based assembly. Second, we explore the effectiveness of structural profiles in providing projection coordinates through which to organize the conformational space. We do so in the context of a robotics-inspired search framework proposed in our lab that employs projections of the conformational space to guide search. Our findings indicate that structural profiles are most effective in obtaining physically realistic near-native conformations when employed in conjunction with physics-based energy functions. Our findings also show that these profiles are very effective when employed instead as projection coordinates to guide probabilistic search toward undersampled regions of the conformational space.

A stochastic roadmap method to model protein structural transitions

Evidence is emerging that the role of protein structure in disease needs to be rethought. Sequence mutations in proteins are often found to affect the rate at which a protein switches between structures. Modeling structural transitions in wildtype and variant proteins is central to understanding the molecular basis of disease. This paper investigates an efficient algorithmic realization of the stochastic roadmap simulation framework to model structural transitions in wildtype and variants of proteins implicated in human disorders. Our results indicate that the algorithm is able to extract useful information on the impact of mutations on protein structure and function.

A Survey of Computational Methods for Protein Function Prediction

Rapid advances in high-throughout genome sequencing technologies have resulted in millions of protein-encoding gene sequences with no functional characterization. Automated protein function annotation or prediction is a prime problem for computational methods to tackle in the post-genomic era of big molecular data. While recent community-driven experiments demonstrate that the accuracy of function prediction methods has significantly improved, challenges remain. The latter are related to the different sources of data exploited to predict function, as well as different choices in representing and integrating heterogeneous data. Current methods predict function from a protein’s sequence, often in the context of evolutionary relationships, from a protein’s three-dimensional structure or specific patterns in the structure, from neighbors in a protein–protein interaction network, from microarray data, or a combination of these different types of data. Here we review these methods and the state of protein function prediction, emphasizing recent algorithmic developments, remaining challenges, and prospects for future research.

Interleaving Global and Local Search for Protein Motion Computation

We propose a novel robotics-inspired algorithm to compute physically-realistic motions connecting thermodynamically-stable and semi-stable structural states in protein molecules. Protein motion computation is a challenging problem due to the high-dimensionality of the search space involved and ruggedness of the potential energy surface underlying the space. To handle the multiple local minima issue, we propose a novel algorithm that is not based on the traditional Molecular Dynamics or Monte Carlo frameworks but instead adapts ideas from robot motion planning. In particular, the algorithm balances computational resources between a global search aimed at obtaining a global view of the network of protein conformations and their connectivity and a detailed local search focused on realizing such connections with physically-realistic models. We present here promising results on a variety of proteins and demonstrate the general utility of the algorithm and its capability to improve the state of the art without employing system-specific insight.