Stochastic transitions: Paths over higher energy barriers can dominate in the early stages

The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two (or more) possible pathways that the system can take, the time available for the transition to occur is crucially important. The well-known results of reaction rate theory for determining the rates of the transitions apply in the long-time limit. However, at short times, the system can instead choose to pass over higher energy barriers with much higher probability, as long as the distance to travel in phase space is shorter. We construct two simple models to illustrate this general phenomenon. We also present an extension of the gMAM algorithm of Vanden-Eijnden and Heymann [J. Chem. Phys. {\bf 128}, 061103 (2008)] to determine the most likely path at both short and long times.Comment: 7 pages, 5 Figure

Path-metadynamics: A computational study of conformational transitions in proteins

The biological functions of proteins are ultimately governed by the dynamical properties of their large conformational transitions rooted on multidimensional free energy landscapes. Straightforward molecular dynamics simulation provides a mechanistically detailed picture of conformational transitions, but is hampered by the long timescales of these processes, which are rare events compared to the molecular timescales. In order to overcome these difficulties, we present in this thesis a new method, path-metadynamics, for the study of rare events. Path-metadynamics aims to explore high dimensional free energy landscapes and determine local likely transition pathways. The formalism works within the framework of a history-dependent bias potential applied to a flexible path-variable. Control of the sampling of the orthogonal modes recovers the average path and the minimum free energy path as limiting cases. Simultaneously the bias potential estimates the free energy profile along the path. The method has trivial scaling with the number of order parameters and this makes it suitable for the study of complex transitions. We have applied path-metadynamics to investigate the partial unfolding of a relevant photoreceptor, the photoactive yellow protein, and the formation/dissociation mechanism of a coiled coil, the leucine zipper domain. Our results demonstrate that path-metadynamics enables the calculation of rate constants, the localization of transition states, and the mapping of the free energy along a transition path described on a high-dimensional space. The likely transition paths obtained provide unique molecular insight about the protein conformational changes investigated. This approach opens a new way for studying complex rare events transitions

Path finding on high-dimensional free energy landscapes

We present a method for determining the average transition path and the free energy along this path in the space of selected collective variables. The formalism is based upon a history-dependent bias along a flexible path variable within the metadynamics framework but with a trivial scaling of the cost with the number of collective variables. Controlling the sampling of the orthogonal modes recovers the average path and the minimum free energy path as the limiting cases. The method is applied to resolve the path and the free energy of a conformational transition in alanine dipeptide

Insights into the nonclassical crystallization of M(II) in the biomineralization process

Microorganisms coexist in nature and interact with various metal ions and metallic compounds, ultimately affecting their migration rates, circulation processes, and distribution states in the environment; microorganisms participate in every step of the biogeochemical cycle with metal ions. The core processes of metal-ion biomineralization involve the combination of metal ions and organic matter, electron transfer between microbial minerals, the transformation of complexes, and changes in the valence or oxidation states of cations. Significant evidence of biological action has been found in sedimentary deposits or key zones on the surface of the earth for many metal ions present in the divalent state, or higher, as stable compounds in nature. Therefore, investigations of the nonclassical crystallization of M(II)-M(VI) in the biomineralization process could lead to a better understanding of biogeochemical cycles and energy transfer between ions, minerals, and bacteria in different environments. This chapter mainly reviews the nonclassical crystallization behaviors occurring in the biomineralization processes of divalent Ca, Mg, Sr, Pb, Ni, Cu, and Zn cations. First, the divalent cations are discussed in relation to travertine to consider the nonclassical crystallization behaviors of Ca(II) for biomineralization, and second, the nonclassical crystallization behaviors in the biomineralization processes with divalent Sr, Pb, Ni, Cu, and Zn by plants and microbes are discussed