Davide Branduardi

PLUMED: a portable plugin for free-energy calculations with molecular dynamics

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.

PLUMED 2: New feathers for an old bird

Enhancing sampling and analyzing simulations are central issues in molecular simulation. Recently, we introduced PLUMED, an open-source plug-in that provides some of the most popular molecular dynamics (MD) codes with implementations of a variety of different enhanced sampling algorithms and collective variables (CVs). The rapid changes in this field, in particular new directions in enhanced sampling and dimensionality reduction together with new hardware, require a code that is more flexible and more efficient. We therefore present PLUMED 2 here—a complete rewrite of the code in an object-oriented programming language (C++). This new version introduces greater flexibility and greater modularity, which both extends its core capabilities and makes it far easier to add new methods and CVs. It also has a simpler interface with the MD engines and provides a single software library containing both tools and core facilities. Ultimately, the new code better serves the ever-growing community of users and contributors in coping with the new challenges arising in the field.

From A to B in free energy space

The authors present a new method for searching low free energy paths in complex molecular systems at finite temperature. They introduce two variables that are able to describe the position of a point in configurational space relative to a preassigned path. With the help of these two variables the authors combine features of approaches such as metadynamics or umbrella sampling with those of path based methods. This allows global searches in the space of paths to be performed and a new variational principle for the determination of low free energy paths to be established. Contrary to metadynamics or umbrella sampling the path can be described by an arbitrary large number of variables, still the energy profile along the path can be calculated. The authors exemplify the method numerically by studying the conformational changes of alanine dipeptide.

Nucleotide-dependent conformational states of actin

The influence of the state of the bound nucleotide (ATP, ADP-Pi, or ADP) on the conformational free-energy landscape of actin is investigated. Nucleotide-dependent folding of the DNase-I binding (DB) loop in monomeric actin and the actin trimer is carried out using all-atom molecular dynamics (MD) calculations accelerated with a multiscale implementation of the metadynamics algorithm. Additionally, an investigation of the opening and closing of the actin nucleotide binding cleft is performed. Nucleotide-dependent free-energy profiles for all of these conformational changes are calculated within the framework of metadynamics. We find that in ADP-bound monomer, the folded and unfolded states of the DB loop have similar relative free-energy. This result helps explain the experimental difficulty in obtaining an ordered crystal structure for this region of monomeric actin. However, we find that in the ADP-bound actin trimer, the folded DB loop is stable and in a free-energy minimum. It is also demonstrated that the nucleotide binding cleft favors a closed conformation for the bound nucleotide in the ATP and ADP-Pi states, whereas the ADP state favors an open confirmation, both in the monomer and trimer. These results suggest a mechanism of allosteric interactions between the nucleotide binding cleft and the DB loop. This behavior is confirmed by an additional simulation that shows the folding free-energy as a function of the nucleotide cleft width, which demonstrates that the barrier for folding changes significantly depending on the value of the cleft width.

The Unfolded Ensemble and Folding Mechanism of the C-Terminal GB1 β-Hairpin

In this work, we shed new light on a much-studied case of beta-hairpin folding by means of advanced molecular dynamics simulations. A fully atomistic description of the protein and the solvent molecule is used, together with metadynamics, to accelerate the sampling and estimate free-energy landscapes. This is achieved using the path collective variables approach, which provides an adaptive description of the mechanism under study. We discover that the folding mechanism is a multiscale process where the turn region conformation leads to two different energy pathways that are connected by elongated structures. The former displays a stable 2:4 native-like structure in which an optimal hydrophobic packing and hydrogen bond pattern leads to 8 kcal/mol of stabilization. The latter shows a less-structured 3:5 beta-sheet, where hydrogen bonds and hydrophobic packing provide only 2.5 kcal/mol of stability. This perspective is fully consistent with experimental evidence that shows this to be a prototypical two-state folder, while it redefines the nature of the unfolded state.

Metadynamics with Adaptive Gaussians.

Metadynamics is an established sampling method aimed at reconstructing the free-energy surface relative to a set of appropriately chosen collective variables. In standard metadynamics, the free-energy surface is filled by the addition of Gaussian potentials of preassigned and typically diagonal covariance. Asymptotically the free-energy surface is proportional to the bias deposited. Here, we consider the possibility of using Gaussians whose variance is adjusted on the fly to the local properties of the free-energy surface. We suggest two different prescriptions: one is based on the local diffusivity and the other on the local geometrical properties. We further examine the problem of extracting the free-energy surface when using adaptive Gaussians. We show that the standard relation between the bias and the free energy does not hold. In the limit of narrow Gaussians an explicit correction can be evaluated. In the general case, we propose to use instead a relation between bias and free energy borrowed from umbrella sampling. This relation holds for all kinds of incrementally deposited bias. We illustrate on the case of alanine dipeptide the advantage of using adaptive Gaussians in conjunction with the new free-energy estimator both in terms of accuracy and speed of convergence.

Conformational Changes and Gating at the Selectivity Filter of Potassium Channels

The translocation of ions and water across cell membranes is a prerequisite for many of lifes processes. K(+) channels are a diverse family of integral membrane proteins through which K(+) can pass selectively. There is an ongoing debate about the nature of conformational changes associated with the opening and closing and conductive and nonconductive states of potassium (K(+)) channels. These changes depend on the membrane potential, the K(+) concentration gradient, and large scale motions of transmembrane helices and associated residues. Experiments also suggest that local structural changes in the selectivity filter may act as the dominant gate referred to as C-type inactivation. Herein we present an extensive computational study on KirBac, which supports the existence of a physical gate or constriction in the selectivity filter (SF) of K(+) channels. Our computations identify a new selectivity filter structure, which is likely associated with C-type inactivation. Specifically, the four peptide chains that comprise the filter adopt an unusual structure in which their dihedrals alternate between left- and right-handed Ramachandran angles, which also justifies the need for conservation of glycine in the K(+) selectivity filter, since it is the only residue able to play this bifunctional role.

Investigating the Mechanism of Substrate Uptake and Release in the Glutamate Transporter Homologue GltPh through Metadynamics Simulations

A homeostatic concentration of glutamate in the synaptic cleft ensures a correct signal transduction along the neuronal network. An unbalance in this concentration can lead to neuronal death and to severe neurodegenerative diseases such as Alzheimers or Parkinsons. Glutamate transporters play a crucial role in this respect because they are responsible for the reuptake of the neurotransmitter from the synaptic cleft, thus controlling the glutamate concentration. Understanding the molecular mechanism of this transporter can provide the possibility of an exogenous control. Structural studies have shown that this transporter can assume at least three conformations, thus suggesting a pronounced dynamical behavior. However, some intermediate states that lead to the substrate internalization have not been characterized and many aspects of the transporter mechanism still remain unclear. Here, using metadynamics simulations, we investigate the substrate uptake from the synaptic cleft and its release in the intracellular medium. In addition, we focus on the role of ions and substrate during these processes and on the stability of the different conformations assumed by the transporter. The present dynamical results can complement available X-ray data and provide a thorough description of the entire process of substrate uptake, internalization, and release.

A Catalytic Mechanism for Cysteine N-Terminal Nucleophile Hydrolases, as Revealed by Free Energy Simulations

The N-terminal nucleophile (Ntn) hydrolases are a superfamily of enzymes specialized in the hydrolytic cleavage of amide bonds. Even though several members of this family are emerging as innovative drug targets for cancer, inflammation, and pain, the processes through which they catalyze amide hydrolysis remains poorly understood. In particular, the catalytic reactions of cysteine Ntn-hydrolases have never been investigated from a mechanistic point of view. In the present study, we used free energy simulations in the quantum mechanics/molecular mechanics framework to determine the reaction mechanism of amide hydrolysis catalyzed by the prototypical cysteine Ntn-hydrolase, conjugated bile acid hydrolase (CBAH). The computational analyses, which were confirmed in water and using different CBAH mutants, revealed the existence of a chair-like transition state, which might be one of the specific features of the catalytic cycle of Ntn-hydrolases. Our results offer new insights on Ntn-mediated hydrolysis and suggest possible strategies for the creation of therapeutically useful inhibitors.

Covalent Inhibitors of Fatty Acid Amide Hydrolase: A Rationale for the Activity of Piperidine and Piperazine Aryl Ureas

Recently, covalent drugs have attracted great interest in the drug discovery community, with successful examples that have demonstrated their therapeutic effects. Here, we focus on the covalent inhibition of the fatty acid amide hydrolase (FAAH), which is a promising strategy in the treatment of pain and inflammation. Among the most recent and potent FAAH inhibitors (FAAHi), there are the cyclic piperidine and piperazine aryl ureas. FAAH hydrolyzes efficiently the amide bond of these compounds, forming a covalent enzyme-inhibitor adduct. To rationalize this experimental evidence, we performed an extensive computational analysis centered on piperidine-based PF750 (1) and piperazine-based JNJ1661010 (2), two potent lead compounds used to generate covalent inhibitors as clinical candidates. We found that FAAH induces a distortion of the amide bond of the piperidine and piperazine aryl ureas. Quantum mechanics/molecular mechanics ΔE(LUMO-HOMO) energies indicate that the observed enzyme-induced distortion of the amide bond favors the formation of a covalent FAAH-inhibitor adduct. These findings could help in the rational structure-based design of novel covalent FAAHi.