Reconstructing the equilibrium Boltzmann distribution from well‐tempered metadynamics

Bonomi, Massimiliano; Barducci, Alessandro; Parrinello, Michele

doi:10.1002/jcc.21305

Cited by 316 publications

(464 citation statements)

References 62 publications

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“…In well-tempered metadynamics, the reconstruction of the distribution of variables different from the CVs is particularly simple since for long time periods the amount of bias added decreases to zero and the system approaches equilibrium. The algorithm described by Bonomi et al 54 consists of three different steps: (1) Accumulate the histogram of the CVs plus the other variables of interest between two updates of the bias potential. (2) When a new Gaussian is added, evolve the histogram as equation (2):…”

Section: Methodsmentioning

confidence: 99%

Activation of G-protein-coupled receptors correlates with the formation of a continuous internal water pathway

et al. 2014

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Recent crystal structures of G-protein-coupled receptors (GPCRs) have revealed ordered internal water molecules, raising questions about the functional role of those waters for receptor activation that could not be answered by the static structures. Here, we used molecular dynamics simulations to monitor-at atomic and high temporal resolutionconformational changes of central importance for the activation of three prototypical GPCRs with known crystal structures: the adenosine A 2A receptor, the b 2 -adrenergic receptor and rhodopsin. Our simulations reveal that a hydrophobic layer of amino acid residues next to the characteristic NPxxY motif forms a gate that opens to form a continuous water channel only upon receptor activation. The highly conserved tyrosine residue Y 7.53 undergoes transitions between three distinct conformations representative of inactive, G-protein activated and GPCR metastates. Additional analysis of the available GPCR crystal structures reveals general principles governing the functional roles of internal waters in GPCRs.

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Section: Methodsmentioning

confidence: 99%

Activation of G-protein-coupled receptors correlates with the formation of a continuous internal water pathway

et al. 2014

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“…We used the procedure described in Bonomi et al to calculate the time-dependent probability distribution of the conformations along the gating charge variable Q and thus estimate the free-energy profile along this CV (47). Briefly, assuming that the system is at instantaneous equilibrium under the internal potential U(r) and the bias potential along a collective variable s(r), V(s(r)), the probability distribution at time t can be written as Pðr,tÞ = e −βfUðrÞ+VðsðrÞ,tÞg R e −βfUðr′Þ+Vðsðr′Þ,tÞg dr′…”

Section: Methodsmentioning

confidence: 99%

“…3B. To calculate the free-energy profile along this new CV, we used all of the configurations visited during the biased metadynamics trajectories after assigning an appropriate weight to each of them, as described in Bonomi et al (47). Strikingly, the free energy as a function of Q is extremely smooth (Fig.…”

Section: Free-energy Surface In the Extended Collective Variable Spacementioning

confidence: 99%

Free-energy landscape of ion-channel voltage-sensor–domain activation

Delemotte

Kasimova

Klein

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

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Voltage sensor domains (VSDs) are membrane-bound protein modules that confer voltage sensitivity to membrane proteins. VSDs sense changes in the transmembrane voltage and convert the electrical signal into a conformational change called activation. Activation involves a reorganization of the membrane protein charges that is detected experimentally as transient currents. These so-called gating currents have been investigated extensively within the theoretical framework of so-called discrete-state Markov models (DMMs), whereby activation is conceptualized as a series of transitions across a discrete set of states. Historically, the interpretation of DMM transition rates in terms of transition state theory has been instrumental in shaping our view of the activation process, whose free-energy profile is currently envisioned as composed of a few local minima separated by steep barriers. Here we use atomistic level modeling and well-tempered metadynamics to calculate the configurational free energy along a single transition from first principles. We show that this transition is intrinsically multidimensional and described by a rough free-energy landscape. Remarkably, a coarse-grained description of the system, based on the use of the gating charge as reaction coordinate, reveals a smooth profile with a single barrier, consistent with phenomenological models. Our results bridge the gap between microscopic and macroscopic descriptions of activation dynamics and show that choosing the gating charge as reaction coordinate masks the topological complexity of the network of microstates participating in the transition. Importantly, full characterization of the latter is a prerequisite to rationalize modulation of this process by lipids, toxins, drugs, and genetic mutations.Kv1.2 | voltage-gated ion channels | gating kinetics | electrophysiology | metadynamics V oltage sensor domains (VSDs) are key players of diverse physiological processes involving changes in transmembrane (TM) potential: electrical impulse propagation, cellular contraction, and activation of metabolic pathways are only few possible examples (1). As such, they are the target of toxins produced by many venomous animals (2) and are becoming a popular target for drug development (3). Most of what we know about VSDs comes from the study of voltage-gated cation channels, mainly potassium and sodium selective ones, each containing four distinct VSDs. VSDs are formed by a bundle of four TM helices (S1-S4) (4-7). The S4 segment contains a series of positively charged residues, called gating charges, arranged along its inward-facing side. This segment confers to VSDs their sensitivity to external voltages, by translating vertically in response to voltage changes (Fig. 1A), and determines their voltage dependency, which is tuned by the number of S4 charges and their specific interactions with their environment (8, 9).For several decades, the molecular details of the VSD activation mechanism have been investigated extensively using diverse experimental techniques such...

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“…Several of them are based on the application of a suitable external bias potential (12)(13)(14) that speeds up configurational sampling and permits free energies to be evaluated and transition rates to be computed (22)(23)(24). Here, we shall use well-tempered (WT) metadynamics to enhance the nucleation of urea crystals from aqueous solutions and compute free-energy profile associated to this event (25). To this aim, we build on our recent study of homogeneous nucleation in pure urea where we have identified collective variables that well describe the process of nucleation (9).…”

mentioning

confidence: 99%

Molecular-dynamics simulations of urea nucleation from aqueous solution

Salvalaglio

Perego

Giberti

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

160

231

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Despite its ubiquitous character and relevance in many branches of science and engineering, nucleation from solution remains elusive. In this framework, molecular simulations represent a powerful tool to provide insight into nucleation at the molecular scale. In this work, we combine theory and molecular simulations to describe urea nucleation from aqueous solution. Taking advantage of well-tempered metadynamics, we compute the freeenergy change associated to the phase transition. We find that such a free-energy profile is characterized by significant finite-size effects that can, however, be accounted for. The description of the nucleation process emerging from our analysis differs from classical nucleation theory. Nucleation of crystal-like clusters is in fact preceded by large concentration fluctuations, indicating a predominant two-step process, whereby embryonic crystal nuclei emerge from dense, disordered urea clusters. Furthermore, in the early stages of nucleation, two different polymorphs are seen to compete.T he nucleation of crystals from solution plays an important role in a variety of chemical and engineering processes. However, the very small scale that characterizes the early stages of nucleation makes its experimental study rather challenging. In this regard, molecular simulations play an important role and much work has been devoted to the study of homogeneous nucleation in simple model systems like Lennard-Jones particles or hard spheres (1-3). More recently, growing attention has been paid to the computer simulation of nucleation from solution of organic and inorganic materials (4-11).However, these simulations have to face an important challenge. Nucleation is a typical example of a rare event occurring on a timescale that is much longer than what atomistic simulations can typically afford. The problem is most easily understood if we focus on molecular dynamics (MD), which is the sampling method used here but it plagues other methods as well. In MD, the shortest timescale to be used for a correct integration of the equation of motion is dictated by the fastest atomic motions such as vibrations or rotations. Due to this constraint in the integration step, present MD simulations can reach timescales up to microseconds unless specific hardware, accessible only to few, is used. Even in this case the scale of the accessible times can be stretched only to the milliseconds range, a far cry from the much longer scale of nucleation phenomena.These timescale limitations affect molecular simulations in several other research fields, such as ligand protein binding, protein folding, or slow chemical reactions, to name just a few. To overcome this limit, many enhanced sampling methods have been proposed (12-21). Several of them are based on the application of a suitable external bias potential (12-14) that speeds up configurational sampling and permits free energies to be evaluated and transition rates to be computed (22)(23)(24). Here, we shall use well-tempered (WT) metadynamics to enhance the nucleation...

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Reconstructing the equilibrium Boltzmann distribution from well‐tempered metadynamics

Cited by 316 publications

References 62 publications

Activation of G-protein-coupled receptors correlates with the formation of a continuous internal water pathway

Activation of G-protein-coupled receptors correlates with the formation of a continuous internal water pathway

Free-energy landscape of ion-channel voltage-sensor–domain activation

Molecular-dynamics simulations of urea nucleation from aqueous solution

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