Escaping free-energy minima

We introduce a novel and powerful method for exploring the properties of the multidimensional free energy surfaces of complex many-body systems by means of a coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates.A characteristic feature of this dynamics is the presence of a history-dependent potential term that, in time, fills the minima in the free energy surface, allowing the efficient exploration and accurate determination of the free energy surface as a function of the collective coordinates. We demonstrate the usefulness of this approach in the case of the dissociation of a NaCl molecule in water and in the study of the conformational changes of a dialanine in solution.Comment: 3 figure

Predicting crystal structures: the Parrinello-Rahman method revisited

By suitably adapting a recent approach [A. Laio and M. Parrinello, PNAS, 99, 12562 (2002)] we develop a powerful molecular dynamics method for the study of pressure-induced structural transformations. We use the edges of the simulation cell as collective variables. In the space of these variables we define a metadynamics that drives the system away from the local minimum towards a new crystal structure. In contrast to the Parrinello-Rahman method our approach shows no hysteresis and crystal structure transformations can occur at the equilibrium pressure. We illustrate the power of the method by studying the pressure-induced diamond to simple hexagonal phase transition in a model of silicon.Comment: 5 pages, 2 Postscript figures, submitte

Soil nutrient cycles as a nonlinear dynamical system

International audienceAn analytical model for the soil carbon and nitrogen cycles is studied from the dynamical system point of view. Its main nonlinearities and feedbacks are analyzed by considering the steady state solution under deterministic hydro-climatic conditions. It is shown that, changing hydro-climatic conditions, the system undergoes dynamical bifurcations, shifting from a stable focus to a stable node and back to a stable focus when going from dry, to well-watered, and then to saturated conditions, respectively. An alternative degenerate solution is also found in cases when the system can not sustain decomposition under steady external conditions. Different basins of attraction for "normal" and "degenerate" solutions are investigated as a function of the system initial conditions. Although preliminary and limited to the specific form of the model, the present analysis points out the importance of nonlinear dynamics in the soil nutrient cycles and their possible complex response to hydro-climatic forcing

Reconstructing the Density of States by History-Dependent Metadynamics

We present a novel method for the calculation of the energy density of states D(E) for systems described by classical statistical mechanics. The method builds on an extension of a recently proposed strategy that allows the free energy profile of a canonical system to be recovered within a pre-assigned accuracy,[A. Laio and M. Parrinello, PNAS 2002]. The method allows a good control over the error on the recovered system entropy. This fact is exploited to obtain D(E) more efficiently by combining measurements at different temperatures. The accuracy and efficiency of the method are tested for the two-dimensional Ising model (up to size 50x50) by comparison with both exact results and previous studies. This method is a general one and should be applicable to more realistic model systems

Jacobson generators, Fock representations and statistics of sl(n+1)

The properties of A-statistics, related to the class of simple Lie algebras sl(n+1) (Palev, T.D.: Preprint JINR E17-10550 (1977); hep-th/9705032), are further investigated. The description of each sl(n+1) is carried out via generators and their relations, first introduced by Jacobson. The related Fock spaces W_p (p=1,2,...) are finite-dimensional irreducible sl(n+1)-modules. The Pauli principle of the underlying statistics is formulated. In addition the paper contains the following new results: (a) The A-statistics are interpreted as exclusion statistics; (b) Within each W_p operators B(p)_1^\pm, ..., B(p)_n^\pm, proportional to the Jacobson generators, are introduced. It is proved that in an appropriate topology the limit of B(p)_i^\pm for p going to infinity is equal to B_i^\pm, where B_i^\pm are Bose creation and annihilation operators; (c) It is shown that the local statistics of the degenerated hard-core Bose models and of the related Heisenberg spin models is p=1 A-statistics.Comment: LaTeX-file, 33 page

Deciphering the folding kinetics of transmembrane helical proteins

Nearly a quarter of genomic sequences and almost half of all receptors that are likely to be targets for drug design are integral membrane proteins. Understanding the detailed mechanisms of the folding of membrane proteins is a largely unsolved, key problem in structural biology. Here, we introduce a general model and use computer simulations to study the equilibrium properties and the folding kinetics of a $C_{\alpha}$-based two helix bundle fragment (comprised of 66 amino-acids) of Bacteriorhodopsin. Various intermediates are identified and their free energy are calculated toghether with the free energy barrier between them. In 40% of folding trajectories, the folding rate is considerably increased by the presence of non-obligatory intermediates acting as traps. In all cases, a substantial portion of the helices is rapidly formed. This initial stage is followed by a long period of consolidation of the helices accompanied by their correct packing within the membrane. Our results provide the framework for understanding the variety of folding pathways of helical transmembrane proteins

First principles simulations of direct coexistence of solid and liquid aluminium

First principles calculations based on density functional theory, with generalised gradient corrections and ultrasoft pseudopotentials, have been used to simulate solid and liquid aluminium in direct coexistence at zero pressure. Simulations have been carried out on systems containing up to 1000 atoms for 15 ps. The points on the melting curve extracted from these simulations are in very good agreement with previous calculations, which employed the same electronic structure method but used an approach based on the explicit calculation of free energies [L. Vo\v{c}adlo and D. Alf\`e, Phys. Rev. B, {\bf 65}, 214105 (2002).]Comment: To appear in Phys. Rev.

Dynamics of ions in the selectivity filter of the KcsA channel

The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic solution. A new approach to the derivation of a Brownian dynamics (BD) model of ion permeation through the filter is discussed, based on unbiased MD simulations. It is shown that depending on additional assumptions, ion’s dynamics can be described either by under-damped Langevin equation with constant damping and white noise or by Langevin equation with a fractional memory kernel. A comparison of the potential of the mean force derived from unbiased MD simulations with the potential produced by the umbrella sampling method demonstrates significant differences in these potentials. The origin of these differences is an open question that requires further clarifications

Direct Observation of Martensitic Phase-Transformation Dynamics in Iron by 4D Single-Pulse Electron Microscopy

The in situ martensitic phase transformation of iron, a complex solid-state transition involving collective atomic displacement and interface movement, is studied in real time by means of four-dimensional (4D) electron microscopy. The iron nanofilm specimen is heated at a maximum rate of ∼10^(11) K/s by a single heating pulse, and the evolution of the phase transformation from body-centered cubic to face-centered cubic crystal structure is followed by means of single-pulse, selected-area diffraction and real-space imaging. Two distinct components are revealed in the evolution of the crystal structure. The first, on the nanosecond time scale, is a direct martensitic transformation, which proceeds in regions heated into the temperature range of stability of the fcc phase, 1185−1667 K. The second, on the microsecond time scale, represents an indirect process for the hottest central zone of laser heating, where the temperature is initially above 1667 K and cooling is the rate-determining step. The mechanism of the direct transformation involves two steps, that of (barrier-crossing) nucleation on the reported nanosecond time scale, followed by a rapid grain growth typically in ∼100 ps for 10 nm crystallites