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Exploring high‐dimensional free energy landscapes of chemical reactions

Focus Article

Nisanth N. Nair, Shalini Awasthi

Published Online: Nov 16 2018

DOI: 10.1002/wcms.1398

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Molecular dynamics (MD) techniques are widely used in computing free energy changes for conformational transitions and chemical reactions, mainly in condensed matter systems. Most of the MD‐based approaches employ biased sampling of a priori selected coarse‐grained coordinates or collective variables (CVs) and thereby accelerate otherwise infrequent transitions from one free energy basin to the other. A quick convergence in free energy estimations can be achieved by enhanced sampling of large number of CVs. Conventional enhanced sampling approaches become exponentially slower with increasing dimensionality of the CV space, and thus they turn out to be highly inefficient in sampling high‐dimensional free energy landscapes. Here, we focus on some of the novel methods that are designed to overcome this limitation. In particular, we discuss four methods: bias‐exchange metadynamics, parallel‐bias metadynamics, adiabatic free energy dynamics/temperature‐accelerated MD, and temperature‐accelerated sliced sampling. The basic idea behind these techniques is presented and applications using these techniques are illustrated. Advantages and disadvantages of these techniques are also delineated. This article is categorized under: Structure and Mechanism > Reaction Mechanisms and Catalysis Molecular and Statistical Mechanics > Free Energy Methods Theoretical and Physical Chemistry > Statistical Mechanics

A cartoon showing the issues with metadynamics sampling when the free energy surface along the crucial reactive collective variable (CV) is broad and unbound.(Reprinted with permission from Reference . Copyright 2018 John Wiley and Sons)

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Changes in the crystal structures of benzene explored by TAMD/d‐AFED.(Reprinted with permission from Reference . Copyright 2018 American Physical Society)

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Basic idea behind the TAMD/d‐AFED method is shown graphically. Here, auxiliary variables, s, are introduced and are coupled with the CVs, S, with a harmonic potential. The s degrees of freedom are connected to a thermostat with inverse temperature _, while the physical system coordinates, S, are thermostatted to an inverse temperature β, with . Free energy of the system at β along the CVs can be computed directly from the probability distribution of s at

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Reaction pathways of γ‐ketohydroperoxid explored by PBMetaD.(Reprinted with permission from Reference . Copyright 2018 American Chemical Society)

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Sketch showing the working of PBMetaD. Here, low‐dimensional free energy surfaces are sampled parallely within the same replica. Height of the Gaussian bias added along one CV is scaled according to the bias added along other CVs. Reweighting methods can recover the high‐dimensional free energy landscapes

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(a–g) Free energy profiles along different CVs used in the BEMetaD simulation of Trp‐cage protein folding. These free energy profiles are made based on the metadynamics bias constructed in each replica; figures (h, i) are the structures of the folded and the “pseudo‐folded” states of the protein.(Reprinted with permission from Reference . Copyright 2018 American Chemical Society)

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A sketch demonstrating the basic idea behind the BEMetaD method. Here, the arrows are showing exchanges between two randomly selected replicas, which are attempted frequently. The biases added are shown in red. A reweighting procedure could be used to reconstruct the high‐dimensional free energy surface

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A schematic representation of the working principle of the temperature‐accelerated sliced sampling (TASS) method is shown for a case with three collective variables (CVs), S₁, S₂, and S₃. Note that for h = 1, ⋯, M number of independent molecular dynamics (MD) simulations with umbrella biases W₁(s₁),⋯, W_M(s₁), are performed independently. Here, metadynamics bias potential (V_b) is applied along s₂ (only). All the auxiliary variables {s_α} are connected to a thermostat with inverse temperature and the physical system is thermostatted to an inverse temperature β, with

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Free energy surface for the reverse acylation of the aztreonam drug catalyzed by class‐C β lactamase enzyme is shown. Here, the nine‐dimensional free energy surface is projected to CV1‐CV2 space. Contour lines are drawn at 2 kcal/mol intervals. Subfigures (b), (c), and (d) show representative snapshots of EI, EIa, and ES. Atom colors: S (yellow), O (red), N (blue), C (black), H (white). Protein backbone is shown as transparent ribbons.(Reprinted with permission from Reference . Copyright 2018 American Chemical Society)

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