A maximum caliber approach for continuum path ensembles

Funder: Federation of European Biochemical Societies; doi: http://dx.doi.org/10.13039/100012623 Abstract The maximum caliber approach implements the maximum entropy principle for trajectories by maximizing a path entropy under external constraints. The maximum caliber approach can be applied to a diverse set of equilibrium and non-equilibrium problems concerning the properties of trajectories connecting different states of a system. In this review, we recapitulate the basic concepts of the maximum entropy principle and of its maximum caliber implementation for path ensembles, and review recent applications of this approach. In particular, we describe how we recently used this approach to introduce a framework, called here the continuum path ensemble maximum caliber (CoPE-MaxCal) method, to impose kinetic constraints in molecular simulations, for instance to include experimental information about transition rates. Such incorporation of dynamical information can ameliorate inaccuracies of empirical force fields, and lead to improved mechanistic insights. We conclude by offering an outlook for future research. Graphic Abstract </jats:sec

Understanding the nature of "superhard graphite"

Numerous experiments showed that on cold compression graphite transforms into a new superhard and transparent allotrope. Several structures with different topologies have been proposed for this phase. While experimental data are consistent with these models, the only way to solve this puzzle is to find which structure is kinetically easiest to form. Using state-of-the-art molecular-dynamics transition path sampling simulations, we investigate kinetic pathways of the pressure-induced transformation of graphite to various superhard candidate structures. Unlike hitherto applied methods for elucidating nature of superhard graphite, transition path sampling realistically models nucleation events necessary for physically meaningful transformation kinetics. We demonstrate that nucleation mechanism and kinetics lead to $M$-carbon as the final product. $W$-carbon, initially competitor to $M$-carbon, is ruled out by phase growth. Bct-C$_4$ structure is not expected to be produced by cold compression due to less probable nucleation and higher barrier of formation

Exploring the Free Energy Landscape: From Dynamics to Networks and Back

The knowledge of the Free Energy Landscape topology is the essential key to understand many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers are, how the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times or rate constants, and the hierarchical relationship among basins, complete the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, the dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.Comment: PLoS Computational Biology (in press

Probing rare physical trajectories with Lyapunov weighted dynamics

The transition from order to chaos has been a major subject of research since the work of Poincare, as it is relevant in areas ranging from the foundations of statistical physics to the stability of the solar system. Along this transition, atypical structures like the first chaotic regions to appear, or the last regular islands to survive, play a crucial role in many physical situations. For instance, resonances and separatrices determine the fate of planetary systems, and localised objects like solitons and breathers provide mechanisms of energy transport in nonlinear systems such as Bose-Einstein condensates and biological molecules. Unfortunately, despite the fundamental progress made in the last years, most of the numerical methods to locate these 'rare' trajectories are confined to low-dimensional or toy models, while the realms of statistical physics, chemical reactions, or astronomy are still hard to reach. Here we implement an efficient method that allows one to work in higher dimensions by selecting trajectories with unusual chaoticity. As an example, we study the Fermi-Pasta-Ulam nonlinear chain in equilibrium and show that the algorithm rapidly singles out the soliton solutions when searching for trajectories with low level of chaoticity, and chaotic-breathers in the opposite situation. We expect the scheme to have natural applications in celestial mechanics and turbulence, where it can readily be combined with existing numerical methodsComment: Accepted for publication in Nature Physics. Due to size restrictions, the figures are not of high qualit

The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein

The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling approach, and the resulting potential energy surface is visualized by constructing disconnectivity graphs. Owing to topological constraints, the low-lying portion of the landscape consists of three distinct regions, corresponding to the native knotted state and to configurations where either the N- or C-terminus is not yet folded into the knot. The fastest folding pathways from denatured states exhibit early formation of the N-terminus portion of the knot and a rate-determining step where the C-terminus is incorporated. The low-lying minima with the N-terminus knotted and the C-terminus free therefore constitute an off-pathway intermediate for this model. The insertion of both the N- and C-termini into the knot occur late in the folding process, creating large energy barriers that are the rate limiting steps in the folding process. When compared to other protein folding proteins of a similar length, this system folds over six orders of magnitude more slowly.Comment: 19 page

Structural diversity in binary nanoparticle superlattices

Assembly of small building blocks such as atoms, molecules and nanoparticles into macroscopic structures - that is, 'bottom up' assembly - is a theme that runs through chemistry, biology and material science. Bacteria(1), macromolecules(2) and nanoparticles(3) can self-assemble, generating ordered structures with a precision that challenges current lithographic techniques. The assembly of nanoparticles of two different materials into a binary nanoparticle superlattice (BNSL)(3-7) can provide a general and inexpensive path to a large variety of materials (metamaterials) with precisely controlled chemical composition and tight placement of the components. Maximization of the nanoparticle packing density has been proposed as the driving force for BNSL formation(3,8,9), and only a few BNSL structures have been predicted to be thermodynamically stable. Recently, colloidal crystals with micrometre-scale lattice spacings have been grown from oppositely charged polymethyl methacrylate spheres(10,11). Here we demonstrate formation of more than 15 different BNSL structures, using combinations of semiconducting, metallic and magnetic nanoparticle building blocks. At least ten of these colloidal crystalline structures have not been reported previously. We demonstrate that electrical charges on sterically stabilized nanoparticles determine BNSL stoichiometry; additional contributions from entropic, van der Waals, steric and dipolar forces stabilize the variety of BNSL structures.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62551/1/nature04414.pd

Allostery in Its Many Disguises: From Theory to Applications.

Allosteric regulation plays an important role in many biological processes, such as signal transduction, transcriptional regulation, and metabolism. Allostery is rooted in the fundamental physical properties of macromolecular systems, but its underlying mechanisms are still poorly understood. A collection of contributions to a recent interdisciplinary CECAM (Center Européen de Calcul Atomique et Moléculaire) workshop is used here to provide an overview of the progress and remaining limitations in the understanding of the mechanistic foundations of allostery gained from computational and experimental analyses of real protein systems and model systems. The main conceptual frameworks instrumental in driving the field are discussed. We illustrate the role of these frameworks in illuminating molecular mechanisms and explaining cellular processes, and describe some of their promising practical applications in engineering molecular sensors and informing drug design efforts

Can we predict personality in fish? searching for consistency over time and across contexts

The interest in animal personality, broadly defined as consistency of individual behavioural traits over time and across contexts, has increased dramatically over the last years. Individual differences in behaviour are no longer recognised as noise around a mean but rather as adaptive variation and thus, essentially, raw material for evolution. Animal personality has been considered evolutionary conserved and has been shown to be present in all vertebrates including fish. Despite the importance of evolutionary and comparative aspects in this field, few studies have actually documented consistency across situations in fish. In addition, most studies are done with individually housed fish which may pose additional challenges when interpreting data from social species. Here, we investigate, for the first time in fish, whether individual differences in behavioural responses to a variety of challenges are consistent over time and across contexts using both individual and grouped-based tests. Twenty-four juveniles of Gilthead seabream Sparus aurata were subjected to three individual-based tests: feed intake recovery in a novel environment, novel object and restraining and to two group-based tests: risk-taking and hypoxia. Each test was repeated twice to assess consistency of behavioural responses over time. Risk taking and escape behaviours during restraining were shown to be significantly consistent over time. In addition, consistency across contexts was also observed: individuals that took longer to recover feed intake after transfer into a novel environment exhibited higher escape attempts during a restraining test and escaped faster from hypoxia conditions. These results highlight the possibility to predict behaviour in groups from individual personality traits.European Commission [265957 COPEWELL]; European Social Fund of Andalusia; Foundation for Science and Technology, Portugal [SFRH/BPD/77210/2011]info:eu-repo/semantics/publishedVersio