Sparse learning of stochastic dynamic equations

With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems, which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastics SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy, and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential, and the projected dynamics of a two-dimensional diffusion process

Protein Design is a Key Factor for Subunit-subunit Association

Fundamental questions about the role of the quaternary structures are addressed using a statistical mechanics off-lattice model of a dimer protein. The model, in spite of its simplicity, captures key features of the monomer-monomer interactions revealed by atomic force experiments. Force curves during association and dissociation are characterized by sudden jumps followed by smooth behavior and form hysteresis loops. Furthermore, the process is reversible in a finite range of temperature stabilizing the dimer. It is shown that in the interface between the two monomeric subunits the design procedure naturally favors those amino acids whose mutual interaction is stronger. Furthermore it is shown that the width of the hysteresis loop increases as the design procedure improves, i.e. stabilizes more the dimer.Comment: submitted to "Proceedings of the National Academy of Sciences, USA

Folding Lennard-Jones proteins by a contact potential

We studied the possibility to approximate a Lennard Jones interaction by a pairwise contact potential. First we used a Lennard-Jones potential to design off-lattice, protein-like heteropolymer sequences, whose lowest energy (native) conformations were then identified by Molecular Dynamics. Then we turned to investigate whether one can find a pairwise contact potential, whose ground states are the contact maps associated with these native conformations. We show that such a requirement cannot be satisfied exactly - i.e. no such contact parameters exist. Nevertheless, we found that one can find contact energy parameters for which an energy minimization procedure, acting in the space of contact maps, yields maps whose corresponding structures are close to the native ones. Finally we show that when these structures are used as the initial point of a Molecular Dynamics energy minimization process, the correct native folds are recovered with high probability.Comment: submitted to "Proteins: Structure, Function, and Genetics

CYTISINE AND CYTISINE DERIVATIVES. MORE THAN SMOKING CESSATION AIDS

Cytisine, a natural bioactive compound that is mainly isolated from plants of the Leguminosae family (especially the seeds of Laburnum anagyroides), has been marketed in central and eastern Europe as an aid in the clinical management of smoking cessation for more than 50 years. Its main targets are neuronal nicotinic acetylcholine receptors (nAChRs), and pre-clinical studies have shown that its interactions with various nAChR subtypes located in different areas of the central and peripheral nervous systems are neuroprotective, have a wide range of biological effects on nicotine and alcohol addiction, regulate mood, food intake and motor activity, and influence the autonomic and cardiovascular systems. Its relatively rigid conformation makes it an attractive template for research of new derivatives. Recent studies of structurally modified cytisine have led to the development of new compounds and for some of them the biological activities are mediated by still unidentified targets other than nAChRs, whose mechanisms of action are still being investigated. The aim of this review is to describe and discuss: 1) the most recent pre-clinical results obtained with cytisine in the fields of neurological and non-neurological diseases; 2) the effects and possible mechanisms of action of the most recent cytisine derivatives; and 3) the main areas warranting further research

A geometric interpretation of integrable motions

Integrability, one of the classic issues in galactic dynamics and in general in celestial mechanics, is here revisited in a Riemannian geometric framework, where newtonian motions are seen as geodesics of suitable ``mechanical'' manifolds. The existence of constants of motion that entail integrability is associated with the existence of Killing tensor fields on the mechanical manifolds. Such tensor fields correspond to hidden symmetries of non-Noetherian kind. Explicit expressions for Killing tensor fields are given for the N=2 Toda model, and for a modified Henon-Heiles model, recovering the already known analytic expressions of the second conserved quantity besides energy for each model respectively.Comment: 20 page

On the origin of Phase Transitions in the absence of Symmetry-Breaking

In this paper we investigate the Hamiltonian dynamics of a lattice gauge model in three spatial dimension. Our model Hamiltonian is defined on the basis of a continuum version of a duality transformation of a three dimensional Ising model. The system so obtained undergoes a thermodynamic phase transition in the absence of symmetry-breaking. Besides the well known use of quantities like the Wilson loop we show how else the phase transition in such a kind of models can be detected. It is found that the first order phase transition undergone by this model is characterised according to an Ehrenfest-like classification of phase transitions applied to the configurational entropy. On the basis of the topological theory of phase transitions, it is discussed why the seemingly divergent behaviour of the third derivative of configurational entropy can be considered as the "shadow" of some suitable topological transition of certain submanifolds of configuration space.Comment: 31 pages, 9 figure

Supersymmetric Langevin equation to explore free energy landscapes

The recently discovered supersymmetric generalizations of Langevin dynamics and Kramers equation can be utilized for the exploration of free energy landscapes of systems whose large time-scale separation hampers the usefulness of standard molecular dynamics techniques. The first realistic application is here presented. The system chosen is a minimalist model for a short alanine peptide exhibiting a helix-coil transition.Comment: 9 pages, 9 figures, RevTeX 4 v2: conclusive section enlarged, references adde

Modeling Diffusive Dynamics in Adaptive Resolution Simulation of Liquid Water

We present a dual-resolution molecular dynamics (MD) simulation of liquid water employing a recently introduced Adaptive Resolution Scheme (AdResS). The spatially adaptive molecular resolution procedure allows for changing from a coarse-grained to an all-atom representation and vice-versa on-the-fly. In order to find the most appropriate coarse-grained water model to be employed with AdResS we first study the accuracy of different coarse-grained water models in reproducing the structural properties of the all-atom system. Typically, coarse-grained molecular models have a higher diffusion constant than the corresponding all-atom models due to the reduction in degrees of freedom (DOFs) upon coarse-graining that eliminates the fluctuating forces associated with those integrated-out molecular DOFs. Here, we introduce the methodology to obtain the same diffusional dynamics across different resolutions. We show that this approach leads to the correct description of essential thermodynamic, structural and dynamical properties of liquid water at ambient conditions.Comment: 12 pages, 16 figure