Free energy surfaces

In the last decade L-Lactate Dehydrogenase (LDH) has become an extremely useful marker in both clinical diagnosis and in monitoring the course of many human diseases. It has been assumed from the 80s that the full catalytic process of LDH starts with the binding of the cofactor and the substrate followed by the enclosure of the active site by a mobile loop of the protein before the reaction to take place. In this paper we show that the chemical step of the LDH catalyzed reaction can proceed within the open loop conformation, and the different reactivity of the different protein conformations would be in agreement with the broad range of rate constants measured in single molecule spectrometry studies. Starting from a recently solved X-ray diffraction structure that presented an open loop conformation in two of the four chains of the tetramer, QM/MM free energy surfaces have been obtained at different levels of theory. Depending on the level of theory used to describe the electronic s...

Enzyme promiscuity attracts the interest of the industrial and academic sectors because of its application in the design of biocatalysts. The amidase activity of Candida antarctica lipase B (CALB) on two different substrates has been studied by theoretical quantum mechanics/molecular mechanics methods, supported by experimental kinetic measurements. The aim of the study is to understand the substrate promiscuity of CALB in this secondary reaction and the origin of its promiscuous catalytic activity. The computational results predict activation free energies in very good agreement with the kinetic data and confirm that the activity of CALB as an amidase, despite depending on the features of the amide substrate, is dictated by the electrostatic effects of the protein. The protein polarizes and activates the substrate as well as stabilizes the transition state, thus enhancing the rate constant. Our results can provide guides for future designs of biocatalysts based on electrostatic arguments.

Flying Gaussian method simulates multiple replicas of the studied system and enhances sampling by disfavoring replicas to simultaneously sample similar states. The bias potential used for this enhancement is highly dynamic when looking at individual replica, which raises concerns about the accuracy of free-energy surfaces predicted by reweighing methods. Here we show that the bias potential can be considered as static when looking at the simulation from a multisystem perspective. We present two equations that can be used to predict the free-energy surface, and we demonstrate their convergence.

In this paper a computational study of the two possible inhibition mechanisms of rhodesain cysteine protease by the dipeptidyl enoate Cbz-Phe-Leu-CH=CH-CO2C2H5 has been carried out by means of molecular dynamics simulations with hybrid QM/MM potentials. The low free energy barriers confirm that the Cys25 residue can attack both Cβ and C1 atoms of the inhibitor, confirming a dual mode of action in the inhibition of the rhodesain by enoates. According to the results, the inhibition process through the Cys25 attack on the Cβ atom of the inhibitor is an exergonic and irreversible process, while the inhibition process when Cys25 attacks on the C1 atom of the inhibitor is and exergonic but reversible process. The interactions between the inhibitor and rhodesain suggest that P2 is the most important fragment to consider in the design of new efficient inhibitors of rhodesain. These results may be useful for the design of new inhibitors of rhodesain and other related cysteine proteases based on dipeptidyl enoates scaffolds.

The environmental problems derived from the generalized plastic consumption and disposal could find a friendly solution in enzymatic biodegradation. Recently, two hydrolases from Ideonella sakaiensis 201-F6 and the metagenome-derived leafbranch compost cutinase (LCC), more specially the improved ICCG variant, have revealed degradation activity toward poly ethylene terephthalate (PET). In the present study, the reaction mechanism of this polymer breakage is studied at an atomic level by multiscale QM/MM molecular dynamics simulations, using semiempirical and DFT Hamiltonians to describe the QM region. The obtained free energy surfaces confirmed a characteristic fourstep path for both systems, with activation energies in agreement with the experimental observations. Structural analysis of the evolution of the active site along the reaction progress and the study of electrostatic effects generated by the proteins reveal the similarity in the behavior of the active site of these two enzymes. The origin of the apparent better performance of the LCC-ICCG protein over PETase must be due to its capabilities of working at higher temperature and its intrinsic relationship with the crystallinity grade of the polymer. Our results may be useful for the development of more efficient enzymes in the biodegradation of PET.

We report a fully general technique addressing a long standing challenge of calculating conformational free energy differences between various states of a polymer chain from simulations using explicit solvent force fields. The main feature of our method is a special mapping variable, a path coordinate, which continuously connects two conformations. The path variable has been designed to preserve locality in the phase space near the path endpoints. We avoid the problem of sampling the unfolded states by creating an artificial confinement ''tube" in the phase space that prevents the molecule from unfolding without affecting the calculation of the desired free energy difference. We applied our technique to compute the free energy difference between two native-like conformations of the small protein Trp-cage using the CHARMM force field with explicit solvent. We verified this result by comparing it with an independent, significantly more expensive calculation. Overall, the present study suggests that the new method of computing free energy differences between polymer chain conformations is accurate and highly computationally efficient.

Many biologically interesting functions such as allosteric switching or protein-ligand binding are determined by the kinetics and mechanisms of transitions between various conformational substates of the native basin of globular proteins. To advance our understanding of these processes, we constructed a two-dimensional free energy surface (FES) of the native basin of a small globular protein, Trp-cage. The corresponding order parameters were defined using two native substructures of Trp-cage. These calculations were based on extensive explicit water all-atom molecular dynamics simulations. Using the obtained two-dimensional FES, we studied the transition kinetics between two Trp-cage conformations, finding that switching process shows a borderline behavior between diffusive and weakly-activated dynamics. The transition is well-characterized kinetically as a biexponential process. We also introduced a new one-dimensional reaction coordinate for the conformational transition, finding reasonable qualitative agreement with the two-dimensional kinetics results. We investigated the distribution of all the 38 native nuclear magnetic resonance structures on the obtained FES, analyzing interactions that stabilize specific lowenergy conformations. Finally, we constructed a FES for the same system but with simple dielectric model of water instead of explicit water, finding that the results were surprisingly similar in a small region centered on the native conformations. The dissimilarities between the explicit and implicit model on the larger-scale point to the important role of water in mediating interactions between amino acid residues.

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Molecular dynamics (MD) simulations have become a standard tool to correlate the structure and function of biomolecules, and significant advances have been made in the study of proteins and their complexes. A major drawback of conventional MD simulations is the difficulty and cost of obtaining converged results, especially when exploring potential energy surfaces containing considerable energy barriers. This limits the wide use of MD calculations to determine the thermodynamic properties of biomolecular processes. Alternatively, a wide range of Structure-Based Models (SBMs) has been used in the literature to unravel the basic mechanisms of biomolecular dynamics. Here we introduce SBMOpenMM, a Python library to build force fields for SBMs, that uses the OpenMM framework to create and run SBM simulations. The code is flexible, user-friendly, and profits from the high customizability and performance provided by the OpenMM platform.

We report a fully general technique addressing a long standing challenge of calculating conformational free energy differences between various states of a polymer chain from simulations using explicit solvent force fields. The main feature of our method is a special mapping variable, a path coordinate, which continuously connects two conformations. The path variable has been designed to preserve locality in the phase space near the path endpoints. We avoid the problem of sampling the unfolded states by creating an artificial confinement ''tube" in the phase space that prevents the molecule from unfolding without affecting the calculation of the desired free energy difference. We applied our technique to compute the free energy difference between two native-like conformations of the small protein Trp-cage using the CHARMM force field with explicit solvent. We verified this result by comparing it with an independent, significantly more expensive calculation. Overall, the present study suggests that the new method of computing free energy differences between polymer chain conformations is accurate and highly computationally efficient.

Long timescale (>1 ms) molecular dynamics simulations of protein folding offer a powerful tool for understanding the atomic-scale interactions that determine a protein's folding pathway and stabilize its native state. Unfortunately, when the simulated protein fails to fold, it is often unclear whether the failure is due to a deficiency in the underlying force fields or simply a lack of sufficient simulation time. We examine one such case, the human Pin1 WW domain, using the recently developed deactivated morphing method to calculate free energy differences between misfolded and folded states. We find that the force field we used favors the misfolded states, explaining the failure of the folding simulations. Possible further applications of deactivated morphing and implications for force field development are discussed.

During allosteric motions proteins navigate rugged energy landscapes. Hence, mapping of these multidimensional landscapes into lower dimensional manifolds is important for gaining deeper insights into allosteric dynamics. Using a recently developed computational technique, we calculated the free energy difference between the open and closed states of adenylate kinase, an allosteric protein which was extensively studied previously using both experimental and theoretical approaches. Two independent simulations indicate reasonable convergence of the computed free energy profiles. The numerical value of the open/closed free energy difference is only 1−2 k B T, much smaller than some of the prior estimates. We also found that the conformations structurally close to the open form still retain many LID-NMP contacts, suggesting that the conformational basin of the closed form is larger than expected. The latter suggestion may explain the discrepancy in relative populations of open and closed forms of unligated adenylate kinase, observed in NMR and FRET experiments.

Energy landscape theories have provided a common ground for understanding the protein folding problem, which once seemed to be overwhelmingly complicated. At the same time, the native state was found to be an ensemble of interconverting states with frustration playing a more important role compared to the folding problem. The landscape of the folded protein – the native landscape – is glassier than the folding landscape; hence, a general description analogous to the folding theories is difficult to achieve. On the other hand, the native basin phase volume is much smaller, allowing a protein to fully sample its native energy landscape on the biological timescales. Current computational resources may also be used to perform this sampling for smaller proteins, to build a ‘topographical map’ of the native landscape that can be used for subsequent analysis. Several major approaches to representing this topographical map are highlighted in this review, including the construction of kinetic networks, hierarchical trees and free energy surfaces with subsequent structural and kinetic analyses. In this review, we extensively discuss the important question of choosing proper collective coordinates characterizing functional motions. In many cases, the substates on the native energy landscape, which represent different functional states, can be used to obtain variables that are well suited for building free energy surfaces and analyzing the protein's functional dynamics. Normal mode analysis can provide such variables in cases where functional motions are dictated by the molecule's architecture. Principal component analysis is a more expensive way of inferring the essential variables from the protein's motions, one that requires a long molecular dynamics simulation. Finally, the two popular models for the allosteric switching mechanism, ‘preexisting equilibrium’ and ‘induced fit’, are interpreted within the energy landscape paradigm as extreme points of a continuum of transition mechanisms. Some experimental evidence illustrating each of these two models, as well as intermediate mechanisms, is presented and discussed.

We report a fully general technique addressing a long standing challenge of calculating conformational free energy differences between various states of a polymer chain from simulations using explicit solvent force fields. The main feature of our method is a special mapping variable, a path coordinate, which continuously connects two conformations. The path variable has been designed to preserve locality in the phase space near the path endpoints. We avoid the problem of sampling the unfolded states by creating an artificial confinement "tube" in the phase space that prevents the molecule from unfolding without affecting the calculation of the desired free energy difference. We applied our technique to compute the free energy difference between two native-like conformations of the small protein Trp-cage using the CHARMM force field with explicit solvent. We verified this result by comparing it with an independent, significantly more expensive calculation. Overall, the present study suggests that the new method of computing free energy differences between polymer chain conformations is accurate and highly computationally efficient.

Proteins are highly complex molecules with features exquisitely selected by nature to carry out essential biological functions. Physical chemistry and polymer physics provide us with the tools needed to make sense of this complexity. Upon translation, many proteins fold to a thermodynamically stable form known as the native state. The native state is not static, but consists of a hierarchy of conformations, that are continuously explored through dynamics. In this review we provide a brief introduction to some of the core concepts required in the discussion of the protein native dynamics using energy landscapes ideas. We first discuss recent works which have challenged the structure−function paradigm by demonstrating function in disordered proteins. Next we examine the hierarchical organization in the energy landscapes using atomistic molecular dynamics simulations and principal component analysis. In particular, the role of direct and water-mediated contacts in sculpting the landscape is elaborated. Another approach to studying the native state ensemble is based on choosing high-resolution order parameters for computing one- or two-dimensional free energy surfaces. We demonstrate that 2D free energy surfaces provide rich thermodynamic and kinetic information about the native state ensemble. Brownian dynamics simulations on such a surface indicate that protein conformational dynamics is weakly activated. Finally, we briefly discuss implicit and coarse-grained protein models and emphasize the solvent role in determining native state structure and dynamics.