Yes / In this article we briefly review the Boxed Molecular Dynamics (BXD) method, which allows analysis of thermodynamics and kinetics in complicated molecular systems. BXD is a multiscale technique, in which thermodynamics and long-time dynamics are recovered from a set of short-time simulations. In this article, we review previous applications of BXD to peptide cyclization, diamond etching, solution-phase organic reaction dynamics, and desorption of ions from self-assembled monolayers (SAMs). We also report preliminary results of simulations of diamond etching mechanisms and protein unfolding in AFM experiments. The latter demonstrate a correlation between the protein’s structural motifs and its potential of mean force (PMF). Simulations of these processes by standard molecular dynamics (MD) is typically not possible, since the experimental timescales are very long. However, BXD yields well-converged and physically meaningful results. Compared to other methods of accelerated MD, our BXD approach is very simple; it is easy to implement, and it provides an integrated approach for simultaneously obtaining both thermodynamics and kinetics. It also provides a strategy for obtaining statistically meaningful dynamical results in regions of configuration space that standard MD approaches would visit only very rarely. / DRG is grateful for funding from a Royal Society Research Fellowship. JB and DVS acknowledge the support of EPSRC (Grant No EP/E009824/1). E.M.-N. and S.A.V. are grateful to the “Centro de Supercomputación de Galicia (CESGA)” for the use of its computational resources, as well as to “Ministerio de Economía y Competitividad” (Grant No. CTQ2009-12588) for financial support. DS and E.M.-N. acknowledge the Leverhulme Trust for funding the E.M.-N. visit to Leeds by the grant “Accelerated classical and quantum molecular dynamics and its applications” (Grant No. VP1-2012-013).

The differences between refolding mechanisms of sperm whale apomyoglobin subsequent to three different unfolding conditions have been examined by atomistic level computer simulations. The three unfolding conditions used in this work are high-temperature, low temperature and low pH. The folding of this protein has been extensively studied experimentally, providing a large data base of folding parameters which can be probed using simulations. The crystal structure of sperm whale myoglobin was taken from Protein Data Bank, followed by the removal of the heme unit and a subsequent energy minimization was performed in order to generate the native apomyoblogin form. Thus, the native conformation of apomyoglobin utilized is the same in all the three different refolding simulations done in the present work. The differences are the way the initial unfolded conformations were obtained. The refolding trajectories were obtained at room temperature using the Stochastic Difference Equation in Length algorithm. The results reveal differences between the three refolding routes. In contrast to previous molecular simulations that modeled low pH denaturation, an extended intermediate with large helical content was not observed in the refolding simulations from the high-temperature unfolded state. Otherwise, a structural collapse occurs without formation of helices or native contacts. Once the protein structure is more compact (radius of gyration less than 18 angstroms) secondary and tertiary structures appear. The low pH simulations show some agreement with the low pH experimental data and previous molecular dynamics simulations, like formation of a conformation having radius of gyration around 20 angstroms and large helical content. And the refolding simulations after the low temperature unfolding present differences in the properties of apomyoglobin folding route, comparing to the other two previous conditions. The collapse of the protein during folding occurs later in the simulation when compared with high-temperature denaturing state, but earlier when compared to low pH simulations. These differences strongly suggest that a protein can follow different folding routes, depending on the nature and the structure of the unfolded state.

Cette thèse porte sur l’étude des propriétés qualitatives des solutions des équations des ondes et de la chaleur semi-linéaires. Les résultats qui y sont décrits sont les suivants. Les deux premiers concernent l’existence et la description de dynamiques explosives de concentration en temps fini de l’état stationnaire à symétrie radiale dans le régime dit énergie surcritique ; en outre, pour l’équation des ondes la stabilité de ces phénomènes est étudiée dans le cas radial, et pour l’équation de la chaleur le cas plus général d’un domaine borné avec conditions de Dirichlet au bord est considéré. Le troisième porte sur la classification des dynamiques possibles près de l’état stationnaire radial pour l’équation de la chaleur dans le régime dit énergie critique, trois scénarios ayant lieu : la stabilisation, l’instabilité par explosion auto-similaire à profil explosif constant en espace, et l’instabilité par dissipation vers la solution nulle. Enfin, le quatrième a pour objet l’existence et la stabilité de profils explosifs auto-similaires non constants en espace pour l’équation de la chaleur dans le cas énergie surcritique / This thesis is devoted to the study of qualitative properties for solutions to the semilinear heat and wave equations. The results that are described are the following. The first two concern the existence and description of blow-up dynamics in which the radially symmetric stationary state is concentrated in finite time in the so-called energy supercritical regime; in addition, for the wave equation the stability of these phenomena is studied in the radial case, and for the heat equation the more general case of a bounded domain with Dirichlet condition at the boundary is considered. The third one deals with the classification of the possible dynamics near the radial stationary state for the heat equation in the so-called energy critical regime, where three scenarii occur: stabilization, instability by blow-up with the constant in space blow-up profile, and instability by dissipation to the null solution. Eventually, in the forth result we investigate the existence and the stability of self-similar blow-up profiles that are not constant in space, for the heat equation in the energy supercritical case