Rare events and free-energy calculations

During the post-doc, my research was mainly focused on the development of methods for the study of rare events in molecular dynamics simulations. In particular, I worked on the improvement of the metadynamics method, and on a new approach which combined metadynamics and parallel tempering, which allowed us to investigate protein folding. I also worked on the modeling of rare-events dynamics in complex systems using a few coarse-grained parameters. I studied a molecular motor and have developed a new scheme for extracting dynamical properties from coarse-grained trajectories. Finally, I am actively involved in the development of PLUMED, a software plugin which can be combined with popular molecular dynamics codes to perform metadynamics and other free-energy simulations.

Does metadynamics work? Here you have a formal proof for Langevin dynamics

G. Bussi, A. Laio and M. Parrinello,
Equilibrium free energies from non-equilibrium metadynamics,
Phys. Rev. Lett. 96, 090601 (2006)
Preprint: arXiv:0804.0175

In this paper we give a formal proof of the fact that metadynamics provides an unbiased estimate for the free energy landscape, at least when the dynamics of the collective variables can be described using the Langevin equation. This is very important since it shows that the fact that the collective variables are kept out of equilibrium has no consequences on the asymptotic accuracy of the results.

Combining metadynamics and parallel tempering: the best from both worlds

G. Bussi, F. L. Gervasio, A. Laio and M. Parrinello,
Free energy landscape for hairpin folding from combined parallel tempering and metadynamics,
J. Am. Chem. Soc. 128, 13435 (2006)

Here we introduce a method which combines metadynamics and parallel tempering and is very promising for the simulation of conformational changes in biomolecules. The method introduced in this paper is available in the parallel version of GROMACS+PLUMED.

The convergence problem of metadynamics resolved

A. Barducci, G. Bussi and M. Parrinello,
Well-tempered metadynamics: a smoothly converging and tunable free-energy method,
Phys. Rev. Lett. 100, 020603 (2008)
Preprint: arXiv:0803.3861

Here we introduce a method which allows to solve one of the problems of standard metadynamics, i.e. convergence, and, as a side product, provides a way to control the size of the explored region in the collective-variable space. This is a great advantage in multidimensional (2, 3 or 4 collective variables) metadynamics calculations.
A movie showing the convergence of well-tempered metadynamics can be seen in the gallery. The method introduced in this paper is available in PLUMED.

Adaptive hills: simplifying the setup of a metadynamics simulation

D. Branduardi, G. Bussi, and M. Parrinello
Metadynamics with adaptive Gaussians
Preprint: arXiv:1205.4300

Here we discuss the possibility of doing metadynamics using Gaussian hills with width automatically chosen. In more than one dimension, we consider also "skewed" hills, which cannot be expressed as products of functions of the collective variables and can in principle provide even better filling. We propose two criteria to choose the width/shape. The first one is based on the history of the visited conformations, whereas the second on the gradients of the collective variables with respect to the atomic positions. Interestingly, these two choices can be considered equivalent to expressing hills width in "time lag" (first case) or "spatial lag" (second case). The methods introduced in this paper are still not available, but will likely be introduced in a future version of PLUMED.

Molecular motors out of equilibrium: a multiscale/multiphysics study

P. Raiteri, G. Bussi, C. S. Cucinotta, A. Credi, J. F. Stoddart and M. Parrinello,
Unravelling the shuttling mechanism in a photoswitchable multicomponent bistable rotaxane,
Angew. Chem. Int. Ed. 47, 3536 (2008)

In this work we study the shuttling of a molecular motor in collaboration with an experimental group, using a combination of computational approaches, ranging from ab initio calculations to advanced classical molecular dynamics and coarse-grained models. We show that the effect of the counter-ions is crucial and should be included in the description of the process.

A plugin to perform metadynamics calculation with your favorite molecular dynamics code

M. Bonomi, D. Branduardi, G. Bussi, C. Camilloni, D. Provasi, P. Raiteri, D. Donadio, F. Marinelli, F. Pietrucci, R. A. Broglia and M. Parrinello,
PLUMED: a portable plugin for free-energy calculations with molecular dynamics,
Comp. Phys. Comm. 180, 1961 (2009)
Preprint: arXiv:0902.0874

PLUMED is a plugin that we have developed which allows one to perform free-energy calculations using metadynamics and other methods. It can be combined with many popular engines for molecular dynamics, including

Visit PLUMED webpage!

Replica exchange: an asynchronous approach

G. Bussi
A simple asynchronous replica-exchange implementation,
Nuovo Cimento Soc. Ital. Fis., C 32, 61 (2009)

Preprint: arXiv:0812.1633

In this proceeding I show that one of the bottlenecks of the replica-exchange method, i.e. interprocess synchronization, can be overcome by implementing it in an asynchronous manner. This improvement is crucial for simulations with hundreds of replicas. Source code is available on request.

Studying the isomerization of small biomolecules with metadynamics

Y. A. Mantz, D. Branduardi, G. Bussi and M. Parrinello,
Ensemble of transition state structures for the cis-trans isomerization of N-methylacetamide,
J. Phys. Chem. B 113, 12521 (2009)

C. Melis, G. Bussi, S. C. R. Lummis and C. Molteni,
Trans-cis switching mechanisms in proline analogues and their relevance for the gating of the 5-
HT receptor,
J. Phys. Chem. B 113, 12148 (2009)

In these works we study the isomerization of small biomolecules in vacuo and in explicit solvent. The first work is methodological and aimed at clarifying some properties of the metadynamics with path collective variables. The second work is an application which is relevant for the interpretation of experimental data on the gating of a ion channel.