GPU-Accelerated Exploration of Biomolecular Energy Landscapes

Investigation into the effect of phenylalanine gating on anaerobic haem breakdown using the energy landscape approach

We have recently demonstrated a novel anaerobic NADH-dependent haem breakdown reaction, which is carried out by a range of haemoproteins. The Yersinia enterocolitica protein, HemS, is the focus of further research presented in the current paper. Using conventional experimental methods, bioinformatics, and energy landscape theory (ELT), we provide new insight into the mechanism of the novel breakdown process. Of particular interest is the behavior of a double phenylalanine gate, which opens and closes according to the relative situations of haem and NADH within the protein pocket. This behavior suggests that the double phe-gate fulfills a regulatory role within the pocket, controlling the access of NADH to haem. Additionally, stopped-flow spectroscopy results provide kinetic comparisons between the wild-type and the selected mutants. We also present a fully resolved crystal structure for the F104AF199A HemS monomer, including its extensive loop, the first such structure to be completely resolved for HemS or any of its close homologues. The energy landscapes approach provided key information regarding the gating strategy employed by HemS, compensating for current limitations with conventional biophysical and molecular dynamics approaches. We propose that ELT become more widely used in the field, particularly in the investigation of the dynamics and interactions of weak-binding ligands, and for gating features, within protein cavities.

Combining experiment and energy landscapes to explore anaerobic heme breakdown in multifunctional hemoproteins

To survive, many pathogens extract heme from their host organism and break down the porphyrin scaffold to sequester the Fe2+ ion via a heme oxygenase. Recent studies have revealed that certain pathogens can anaerobically degrade heme. Our own research has shown that one such pathway proceeds via NADH-dependent heme degradation, which has been identified in a family of hemoproteins from a range of bacteria. HemS, from Yersinia enterocolitica, is the main focus of this work, along with HmuS (Yersinia pestis), ChuS (Escherichia coli) and ShuS (Shigella dysenteriae). We combine experiments, Energy Landscape Theory, and a bioinformatic investigation to place these homologues within a wider phylogenetic context. A subset of these hemoproteins are known to bind certain DNA promoter regions, suggesting not only that they can catalytically degrade heme, but that they are also involved in transcriptional modulation responding to heme flux. Many of the bacterial species responsible for these hemoproteins (including those that produce HemS, ChuS and ShuS) are known to specifically target oxygen-depleted regions of the gastrointestinal tract. A deeper understanding of anaerobic heme breakdown processes exploited by these pathogens could therefore prove useful in the development of future strategies for disease prevention.

Nearly reducible finite Markov chains: Theory and algorithms

Finite Markov chains, memoryless random walks on complex networks, appear commonly as models for stochastic dynamics in condensed matter physics, biophysics, ecology, epidemiology, economics, and elsewhere. Here, we review exact numerical methods for the analysis of arbitrary discrete- and continuous-time Markovian networks. We focus on numerically stable methods that are required to treat nearly reducible Markov chains, which exhibit a separation of characteristic timescales and are therefore ill-conditioned. In this metastable regime, dense linear algebra methods are afflicted by propagation of error in the finite precision arithmetic, and the kinetic Monte Carlo algorithm to simulate paths is unfeasibly inefficient. Furthermore, iterative eigendecomposition methods fail to converge without the use of nontrivial and system-specific preconditioning techniques. An alternative approach is provided by state reduction procedures, which do not require additional a priori knowledge of the Markov chain. Macroscopic dynamical quantities, such as moments of the first passage time distribution for a transition to an absorbing state, and microscopic properties, such as the stationary, committor, and visitation probabilities for nodes, can be computed robustly using state reduction algorithms. The related kinetic path sampling algorithm allows for efficient sampling of trajectories on a nearly reducible Markov chain. Thus, all of the information required to determine the kinetically relevant transition mechanisms, and to identify the states that have a dominant effect on the global dynamics, can be computed reliably even for computationally challenging models. Rare events are a ubiquitous feature of realistic dynamical systems, and so the methods described herein are valuable in many practical applications.

Graph transformation and shortest paths algorithms for finite Markov chains

The graph transformation (GT) algorithm robustly computes the mean first-passage time to an absorbing state in a finite Markov chain. Here we present a concise overview of the iterative and block formulations of the GT procedure and generalize the GT formalism to the case of any path property that is a sum of contributions from individual transitions. In particular, we examine the path action, which directly relates to the path probability, and analyze the first-passage path ensemble for a model Markov chain that is metastable and therefore numerically challenging. We compare the mean first-passage path action, obtained using GT, with the full path action probability distribution simulated efficiently using kinetic path sampling, and with values for the highest-probability paths determined by the recursive enumeration algorithm (REA). In Markov chains representing realistic dynamical processes, the probability distributions of first-passage path properties are typically fat-tailed and therefore difficult to converge by sampling, which motivates the use of exact and numerically stable approaches to compute the expectation. We find that the kinetic relevance of the set of highest-probability paths depends strongly on the metastability of the Markov chain, and so the properties of the dominant first-passage paths may be unrepresentative of the global dynamics. Use of a global measure for edge costs in the REA, based on net productive fluxes, allows the total reactive flux to be decomposed into a finite set of contributions from simple flux paths. By considering transition flux paths, a detailed quantitative analysis of the relative importance of competing dynamical processes is possible even in the metastable regime.

Energy Landscape for the Membrane Fusion Pathway in Influenza A Hemagglutinin From Discrete Path Sampling

The conformational change associated with membrane fusion for Influenza A Hemagglutinin is investigated with a model based upon pre- and post-fusion structures of the HA2 component. We employ computational methods based on the potential energy landscape framework to obtain an initial path connecting these two end points, which provides the starting point for refinement of a kinetic transition network. Here we employ discrete path sampling, which provides access to the experimental time and length scales via geometry optimization techniques to identify local minima and the transition states that connect them. We then analyse the distinct phases of the predicted pathway in terms of structure and energetics, and compare with available experimental data and previous simulations. Our results provide the foundations for future work, which will address the effect of mutations, changes in pH, and incorporation of additional components, especially the HA1 chain and the fusion peptide.

Analysis of the Ub to Ub-CR Transition in Ubiquitin

A new conformation has recently been reported for ubiquitin (Ub). This invisible conformation (Ub-CR), where the C-terminal tail is retracted, has a key functional role in phosphorylation of the Ser65 residue, a trigger for PINK1 and Parkin dependent mitophagy. Here we calculate the transition mechanism and associated rates for the Ub to Ub-CR pathway in the wild-type protein and a selection of mutants. We predict a cooperative one-step process with a transition state that resembles the Ub configuration, characterized by a loss of all interactions of the C-terminal tail with surrounding residues, and an open ubiquitin scaffold. The calculated observables agree well with reported values, and we make a range of predictions to guide future experiments. In particular, the effect of mutations on the pathway and the corresponding structural ensembles should have observable consequences. This feedback between theory and experiment promises new insight into key cellular processes.

Exploring Energy Landscapes

Recent advances in the potential energy landscapes approach are highlighted, including both theoretical and computational contributions. Treating the high dimensionality of molecular and condensed matter systems of contemporary interest is important for understanding how emergent properties are encoded in the landscape and for calculating these properties while faithfully representing barriers between different morphologies. The pathways characterized in full dimensionality, which are used to construct kinetic transition networks, may prove useful in guiding such calculations. The energy landscape perspective has also produced new procedures for structure prediction and analysis of thermodynamic properties. Basin-hopping global optimization, with alternative acceptance criteria and generalizations to multiple metric spaces, has been used to treat systems ranging from biomolecules to nanoalloy clusters and condensed matter. This review also illustrates how all this methodology, developed in the context of chemical physics, can be transferred to landscapes defined by cost functions associated with machine learning.

Exploring biomolecular energy landscapes

The potential energy landscape perspective provides both a conceptual and a computational framework for predicting, understanding and designing molecular properties. In this Feature Article, we highlight some recent advances that greatly facilitate structure prediction and analysis of global thermodynamics and kinetics in proteins and nucleic acids. The geometry optimisation procedures, on which these calculations are based, can be accelerated significantly using local rigidification of selected degrees of freedom, and through implementations on graphics processing units. Results of progressive local rigidification are first summarised for trpzip1, including a systematic analysis of the heat capacity and rearrangement rates. Benchmarks for all the essential optimisation procedures are then provided for a variety of proteins. Applications are then illustrated from a study of how mutation affects the energy landscape for a coiled-coil protein, and for transitions in helix morphology for a DNA duplex. Both systems exhibit an intrinsically multifunnel landscape, with the potential to act as biomolecular switches.

Energy Landscapes for the Aggregation of Aβ17-42

The aggregation of the Aβ peptide (Aβ_1-42) to form fibrils is a key feature of Alzheimer's disease. The mechanism is thought to be a nucleation stage followed by an elongation process. The elongation stage involves the consecutive addition of monomers to one end of the growing fibril. The aggregation process proceeds in a stop-and-go fashion and may involve off-pathway aggregates, complicating experimental and computational studies. Here we present exploration of a well-defined region in the free and potential energy landscapes for the Aβ_17-42 pentamer. We find that the ideal aggregation process agrees with the previously reported dock-lock mechanism. We also analyze a large number of additional stable structures located on the multifunnel energy landscape, which constitute kinetic traps. The key contributors to the formation of such traps are misaligned strong interactions, for example the stacking of F19 and F20, as well as entropic contributions. Our results suggest that folding templates for aggregation are a necessity and that aggregation studies could employ such species to obtain a more detailed description of the process.