Knowledge of the Free Energy Landscape topology is the essential key to understanding 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 there are, what 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 and rate constants, or hierarchical relationships among basins, completes 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, dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.

We analyze theoretically the effects of excluded-volume interactions between motors on the dynamics of a cargo driven by multiple motors. The model considered shares much in common with others recently proposed in the literature, with the addition of direct interaction between motors and motor back steps. The cargo is assumed to follow a continuum Langevin dynamics, while individual motors evolve following a Monte Carlo algorithm based on experimentally accessible probabilities for discrete forward and backward jumps, and attachment and detachment rates. The links between cargo and motors are considered as nonlinear springs. By means of numerical simulations we compute the relevant quantities characterizing the dynamical properties of the system, and we compare the results to those for noninteracting motors. We find that interactions lead to quite relevant changes in the force-velocity relation for cargo, with a considerable reduction of the stall force, and also cause a notable decrease of the run length. These effects are mainly due to traffic-like phenomena in the microtubule. The consideration of several parallel tracks for motors reduces such effects. However, we find that for realistic values of the number of motors and the number of tracks, the influence of interactions on the global parameters of transport of cargo are far from being negligible. Our studies also provide an analysis of the relevance of motor back steps on the modeling, and of the influence of different assumptions for the detachment rates. In particular, we discuss these two aspects in connection with the possibility of observing processive back motion of cargo at large load forces.

We study the properties of discrete breathers, also known as intrinsic localized modes, in the one-dimensional Frenkel-Kontorova lattice of oscillators subject to damping and external force. The system is studied in the whole range of values of the coupling parameter, from C=0 (uncoupled limit) up to values close to the continuum limit (forced and damped sine-Gordon model). As this parameter is varied, the existence of different bifurcations is investigated numerically. Using Floquet spectral analysis, we give a complete characterization of the most relevant bifurcations, and we find (spatial) symmetry-breaking bifurcations that are linked to breather mobility, just as it was found in Hamiltonian systems by other authors. In this way moving breathers are shown to exist even at remarkably high levels of discreteness. We study mobile breathers and characterize them in terms of the phonon radiation they emit, which explains successfully the way in which they interact. For instance, it is possible to form "bound states" of moving breathers, through the interaction of their phonon tails. Over all, both stationary and moving breathers are found to be generic localized states over large values of C, and they are shown to be robust against low temperature fluctuations.

Cations are known to mediate diverse interactions in nucleic acids duplexes but they are critical in the arrangement of four-stranded structures. Here, we use all-atom molecular dynamics simulations with explicit solvent to analyse the mechanical unfolding of representative intramolecular G-quadruplex structures: a parallel, a hybrid and an antiparallel DNA and a parallel RNA, in the presence of stabilising cations. We confirm the stability of these conformations in the presence of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\rm {K}^+$\end{document} central ions and observe distortions from the tetrad topology in their absence. Force-induced unfolding dynamics is then investigated. We show that the unfolding events in the force-extension curves are concomitant to the loss of coordination between the central ions and the guanines of the G-quadruplex. We found lower ruptures forces for the parallel configuration with respect to the antiparallel one, while the behaviour of the force pattern of the parallel RNA appears similar to the parallel DNA. We anticipate that our results will be essential to interpret the fine structure rupture profiles in stretching assays at high resolution and will shed light on the mechanochemical activity of G-quadruplex-binding machinery.