Kinetics analysis methods for approximate folding landscapes

Fast and flexible coarse-grained prediction of protein folding routes using ensemble modeling and evolutionary sequence variation

MOTIVATION

Protein folding is a dynamic process through which polypeptide chains reach their native 3D structures. Although the importance of this mechanism is widely acknowledged, very few high-throughput computational methods have been developed to study it.

RESULTS

In this paper, we report a computational platform named P3Fold that combines statistical and evolutionary information for predicting and analyzing protein folding routes. P3Fold uses coarse-grained modeling and efficient combinatorial schemes to predict residue contacts and evaluate the folding routes of a protein sequence within minutes or hours. To facilitate access to this technology, we devise graphical representations and implement an interactive web interface that allows end-users to leverage P3Fold predictions. Finally, we use P3Fold to conduct large and short scale experiments on the human proteome that reveal the broad conservation and variations of structural intermediates within protein families.

AVAILABILITY AND IMPLEMENTATION

A Web server of P3Fold is freely available at http://csb.cs.mcgill.ca/P3Fold.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Structure-Guided Protein Transition Modeling with a Probabilistic Roadmap Algorithm

Proteins are macromolecules in perpetual motion, switching between structural states to modulate their function. A detailed characterization of the precise yet complex relationship between protein structure, dynamics, and function requires elucidating transitions between functionally-relevant states. Doing so challenges both wet and dry laboratories, as protein dynamics involves disparate temporal scales. In this paper, we present a novel, sampling-based algorithm to compute transition paths. The algorithm exploits two main ideas. First, it leverages known structures to initialize its search and define a reduced conformation space for rapid sampling. This is key to address the insufficient sampling issue suffered by sampling-based algorithms. Second, the algorithm embeds samples in a nearest-neighbor graph where transition paths can be efficiently computed via queries. The algorithm adapts the probabilistic roadmap framework that is popular in robot motion planning. In addition to efficiently computing lowest-cost paths between any given structures, the algorithm allows investigating hypotheses regarding the order of experimentally-known structures in a transition event. This novel contribution is likely to open up new venues of research. Detailed analysis is presented on multiple-basin proteins of relevance to human disease. Multiscaling and the AMBER ff14SB force field are used to obtain energetically-credible paths at atomistic detail.

A General, Adaptive, Roadmap-Based Algorithm for Protein Motion Computation

Precious information on protein function can be extracted from a detailed characterization of protein equilibrium dynamics. This remains elusive in wet and dry laboratories, as function-modulating transitions of a protein between functionally-relevant, thermodynamically-stable and meta-stable structural states often span disparate time scales. In this paper we propose a novel, robotics-inspired algorithm that circumvents time-scale challenges by drawing analogies between protein motion and robot motion. The algorithm adapts the popular roadmap-based framework in robot motion computation to handle the more complex protein conformation space and its underlying rugged energy surface. Given known structures representing stable and meta-stable states of a protein, the algorithm yields a time- and energy-prioritized list of transition paths between the structures, with each path represented as a series of conformations. 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. Promising results are presented on a variety of proteins that demonstrate the general utility of the algorithm and its capability to improve the state of the art without employing system-specific insight.

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.

SIMS: a hybrid method for rapid conformational analysis

Proteins are at the root of many biological functions, often performing complex tasks as the result of large changes in their structure. Describing the exact details of these conformational changes, however, remains a central challenge for computational biology due the enormous computational requirements of the problem. This has engendered the development of a rich variety of useful methods designed to answer specific questions at different levels of spatial, temporal, and energetic resolution. These methods fall largely into two classes: physically accurate, but computationally demanding methods and fast, approximate methods. We introduce here a new hybrid modeling tool, the Structured Intuitive Move Selector (sims), designed to bridge the divide between these two classes, while allowing the benefits of both to be seamlessly integrated into a single framework. This is achieved by applying a modern motion planning algorithm, borrowed from the field of robotics, in tandem with a well-established protein modeling library. sims can combine precise energy calculations with approximate or specialized conformational sampling routines to produce rapid, yet accurate, analysis of the large-scale conformational variability of protein systems. Several key advancements are shown, including the abstract use of generically defined moves (conformational sampling methods) and an expansive probabilistic conformational exploration. We present three example problems that sims is applied to and demonstrate a rapid solution for each. These include the automatic determination of “active” residues for the hinge-based system Cyanovirin-N, exploring conformational changes involving long-range coordinated motion between non-sequential residues in Ribose-Binding Protein, and the rapid discovery of a transient conformational state of Maltose-Binding Protein, previously only determined by Molecular Dynamics. For all cases we provide energetic validations using well-established energy fields, demonstrating this framework as a fast and accurate tool for the analysis of a wide range of protein flexibility problems.

Residue Level Three-dimensional Workspace Maps for Conformational Trajectory Planning of Proteins

The function of a protein macromolecule often requires conformational transitions between two native conformations. Understanding these transitions is essential to the understanding of how proteins function, as well as to the ability to design and manipulate protein-based nanomechanical systems. In this paper we propose a set of 3D Cartesian workspace maps for exploring protein pathways. These 3D maps are constructed in the Euclidean space for triads of chain segments of protein molecules that have been shown to have a high probability of occurrence in naturally observed proteins based on data obtained from more than 38,600 proteins from the Protein Data Bank (PDB). We show that the proposed 3D propensity maps are more effective navigation tools than the propensity maps constructed in the angle space. We argue that the main reason for this improved efficiency is the fact that, although there is a one-to-one mapping between the 2D dihedral angle maps and the 3D Cartesian maps, the propensity distributions are significantly different in the two spaces. Hence, the 3D maps allow the pathway planning to be performed directly in the 3D Euclidean space based on propensities computed in the same space, which is where protein molecules change their conformations.

Simulating RNA folding kinetics on approximated energy landscapes

We present a general computational approach to simulate RNA folding kinetics that can be used to extract population kinetics, folding rates and the formation of particular substructures that might be intermediates in the folding process. Simulating RNA folding kinetics can provide unique insight into RNA whose functions are dictated by folding kinetics and not always by nucleotide sequence or the structure of the lowest free-energy state. The method first builds an approximate map (or model) of the folding energy landscape from which the population kinetics are analyzed by solving the master equation on the map. We present results obtained using an analysis technique, map-based Monte Carlo simulation, which stochastically extracts folding pathways from the map. Our method compares favorably with other computational methods that begin with a comprehensive free-energy landscape, illustrating that the smaller, approximate map captures the major features of the complete energy landscape. As a result, our method scales to larger RNAs. For example, here we validate kinetics of RNA of more than 200 nucleotides. Our method accurately computes the kinetics-based functional rates of wild-type and mutant ColE1 RNAII and MS2 phage RNAs showing excellent agreement with experiment.