Here we present a program aimed at free-energy calculations in molecular systems. It consists of a series of routines that can be interfaced with the most popular classical molecular dynamics (MD) codes through a simple patching procedure. This leaves the possibility for the user to exploit many different MD engines depending on the system simulated and on the computational resources available. Free-energy calculations can be performed as a function of many collective variables, with a particular focus on biological problems, and using state-of-the-art methods such as metadynamics, umbrella sampling and Jarzynski-equation based steered MD. The present software, written in ANSI-C language, can be easily interfaced with both fortran and C/C++ codes.

Trp-cage is a designed 20-residue polypeptide that, in spite of its size, shares several features with larger globular proteins. Although the system has been intensively investigated experimentally and theoretically, its folding mechanism is not yet fully understood. Indeed, some experiments suggest a two-state behavior, while others point to the presence of intermediates. In this work we show that the results of a bias-exchange metadynamics simulation can be used for constructing a detailed thermodynamic and kinetic model of the system. The model, although constructed from a biased simulation, has a quality similar to those extracted from the analysis of long unbiased molecular dynamics trajectories. This is demonstrated by a careful benchmark of the approach on a smaller system, the solvated Ace-Ala3-Nme peptide. For the Trp-cage folding, the model predicts that the relaxation time of 3100 ns observed experimentally is due to the presence of a compact molten globule-like conformation. This state has an occupancy of only 3% at 300 K, but acts as a kinetic trap. Instead, non-compact structures relax to the folded state on the sub-microsecond timescale. The model also predicts the presence of a state at of 4.4 Å from the NMR structure in which the Trp strongly interacts with Pro12. This state can explain the abnormal temperature dependence of the and chemical shifts. The structures of the two most stable misfolded intermediates are in agreement with NMR experiments on the unfolded protein. Our work shows that, using biased molecular dynamics trajectories, it is possible to construct a model describing in detail the Trp-cage folding kinetics and thermodynamics in agreement with experimental data.

Na+/Ca2+ exchangers utilize the Na+ electrochemical gradient across the plasma membrane to extrude intracellular Ca2+, and play a central role in Ca2+ homeostasis. Here, we elucidate their mechanisms of extracellular ion recognition and exchange through a structural analysis of the exchanger from Methanococcus jannaschii (NCX_Mj) bound to Na+, Ca2+ or Sr2+ in various occupancies and in an apo state. This analysis defines the binding mode and relative affinity of these ions, establishes the structural basis for the anticipated 3Na+:1Ca2+ exchange stoichiometry, and reveals the conformational changes at the onset of the alternating-access transport mechanism. An independent analysis of the dynamics and conformational free-energy landscape of NCX_Mj in different ion-occupancy states, based on enhanced-sampling molecular-dynamics simulations, demonstrates that the crystal structures reflect mechanistically relevant, interconverting conformations. These calculations also reveal the mechanism by which the outward-to-inward transition is controlled by the ion-occupancy state, thereby explaining the emergence of strictly-coupled Na+/Ca2+ antiport.

The binding mechanism of a peptide substrate (Thr-Ile-Met-Met-Gln-Arg, cleavage site p2-NC of the viral polyprotein) to wild-type HIV-1 protease has been investigated by 1.6 micros biased all-atom molecular dynamics simulations in explicit water. The configuration space has been explored biasing seven reaction coordinates by the bias-exchange metadynamics technique. The structure of the Michaelis complex is obtained starting from the substrate outside the enzyme within a backbone rmsd of 0.9 A. The calculated free energy of binding is -6 kcal/mol, and the kinetic constants for association and dissociation are 1.3 x 10(6) M(-1) s(-1) and 57 s(-1), respectively, consistent with experiments. In the main binding pathway, the flaps of the protease do not open sizably. The substrate slides inside the enzyme cavity from the tight lateral channel. This may contrast with the natural polyprotein substrate which is expected to bind by opening the flaps. Thus, mutations might influence differently the binding kinetics of peptidomimetic ligands and of the natural substrate.

Na + /Ca 2+ exchangers (NCXs) are ubiquitous membrane transporters with a key role in Ca 2+ homeostasis and signaling. NCXs mediate the bidirectional translocation of either Na + or Ca 2+ , and thus can catalyze uphill Ca 2+ transport driven by a Na + gradient, or vice versa. In a major breakthrough, a prokaryotic NCX homolog (NCX_Mj) was recently isolated and its crystal structure determined at atomic resolution. The structure revealed an intriguing architecture consisting of two inverted-topology repeats, each comprising five transmembrane helices. These repeats adopt asymmetric conformations, yielding an outward-facing occluded state. The crystal structure also revealed four putative ion-binding sites, but the occupancy and specificity thereof could not be conclusively established. Here, we use molecular-dynamics simulations and free-energy calculations to identify the ion configuration that best corresponds to the crystallographic data and that is also thermodynamically optimal. In this most probable configuration, three Na + ions occupy the so-called S ext , S Ca , and S int sites, whereas the S mid site is occupied by one water molecule and one H + , which protonates an adjacent aspartate side chain (D240). Experimental measurements of Na + /Ca 2+ and Ca 2+ /Ca 2+ exchange by wild-type and mutagenized NCX_Mj confirm that transport of both Na + and Ca 2+ requires protonation of D240, and that this side chain does not coordinate either ion at S mid . These results imply that the ion exchange stoichiometry of NCX_Mj is 3:1 and that translocation of Na + across the membrane is electrogenic, whereas transport of Ca 2+ is not. Altogether, these findings provide the basis for further experimental and computational studies of the conformational mechanism of this exchanger.secondary transporters | membrane antiporters | ion specificity | CaCA superfamily | molecular-dynamics simulations C a 2+ signals control a variety of cellular processes essential for the basic function of multiple organs. In cardiac cells, for example, Ca 2+ release from the sarcoplasmic reticulum is a necessary step for heart contraction, whereas Ca 2+ extrusion from the cell is required for cardiac relaxation. These fluctuations in the cytosolic Ca 2+ concentration underlie the initiation of the heartbeat (1, 2). Na + /Ca 2+ exchangers (NCXs) play a central role in the homeostasis of cellular Ca 2+ (3-5). These integral membrane proteins are ubiquitous in many types of tissues including the heart, brain, and kidney (4), and consequently their dysfunction is associated with numerous human pathologies such as cardiac arrhythmia, hypertension, skeletal muscle dystrophy, and postischemic brain damage (5). NCXs facilitate the translocation of either Ca 2+ or Na + across the membrane; thus, they can harness a transmembrane sodium motive force to energize Ca 2+ transport against a concentration gradient. For example, the cardiac exchanger NCX1 mediates the extrusion of intracellular Ca 2+ driven by a Na + transmembrane gradient maintained by the Na ...

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Metadynamics is a powerful sampling technique that uses a nonequilibrium history-dependent process to reconstruct the free-energy surface as a function of the relevant collective variables s . In Bussi [Phys. Rev. Lett. 96, 090601 (2006)] it is proved that, in a Langevin process, metadynamics provides an unbiased estimate of the free energy F(s) . We here study the convergence properties of this approach in a multidimensional system, with a Hamiltonian depending on several variables. Specifically, we show that in a Monte Carlo metadynamics simulation of an Ising model the time average of the history-dependent potential converge to F(s) with the same law of an umbrella sampling performed in optimal conditions (i.e., with a bias exactly equal to the negative of the free energy). Remarkably, after a short transient, the error becomes approximately independent on the filling speed, showing that even in out-of-equilibrium conditions metadynamics allows recovering an accurate estimate of F(s) . These results have been obtained introducing a functional form of the history-dependent potential that avoids the onset of systematic errors near the boundaries of the free-energy landscape.

We introduce an enhanced-sampling method for molecular dynamics (MD) simulations referred to as ensemble-biased metadynamics (EBMetaD). The method biases a conventional MD simulation to sample a molecular ensemble that is consistent with one or more probability distributions known a priori, e.g., experimental intramolecular distance distributions obtained by double electron-electron resonance or other spectroscopic techniques. To this end, EBMetaD adds an adaptive biasing potential throughout the simulation that discourages sampling of configurations inconsistent with the target probability distributions. The bias introduced is the minimum necessary to fulfill the target distributions, i.e., EBMetaD satisfies the maximum-entropy principle. Unlike other methods, EBMetaD does not require multiple simulation replicas or the introduction of Lagrange multipliers, and is therefore computationally efficient and straightforward in practice. We demonstrate the performance and accuracy of the method for a model system as well as for spin-labeled T4 lysozyme in explicit water, and show how EBMetaD reproduces three double electron-electron resonance distance distributions concurrently within a few tens of nanoseconds of simulation time. EBMetaD is integrated in the open-source PLUMED plug-in (www.plumed-code.org), and can be therefore readily used with multiple MD engines.