No Arabic abstract
The microcanonical analysis is shown to be a powerful tool to characterize the protein folding transition and to neatly distinguish between good and bad folders. An off-lattice model with parameter chosen to represent polymers of these two types is used to illustrate this approach. Both canonical and microcanonical ensembles are employed. The required calculations were performed using parallel tempering Monte Carlo simulations. The most revealing features of the folding transition are related to its first-order-like character, namely, the S-bend pattern in the caloric curve, which gives rise to negative microcanonical specific heats, and the bimodality of the energy distribution function at the transition temperatures. Models for a good folder are shown to be quite robust against perturbations in the interaction potential parameters.
We analyse a picture of transport in which two large but finite charged electrodes discharge across a nanoscale junction. We identify a functional whose minimisation, within the space of all bound many-body wavefunctions, defines an instantaneous steady state. We also discuss factors that favour the onset of steady-state conduction in such systems, make a connection with the notion of entropy, and suggest a novel source of steady-state noise. Finally, we prove that the true many-body total current in this closed system is given exactly by the one-electron total current, obtained from time-dependent density-functional theory.
We review uses of the generalized-ensemble algorithms for free-energy calculations in protein folding. Two of the well-known methods are multicanonical algorithm and replica-exchange method; the latter is also referred to as parallel tempering. We present a new generalized-ensemble algorithm that combines the merits of the two methods; it is referred to as the replica-exchange multicanonical algorithm. We also give a multidimensional extension of the replica-exchange method. Its realization as an umbrella sampling method, which we refer to as the replica-exchange umbrella sampling, is a powerful algorithm that can give free energy in wide reaction coordinate space.
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the energy level sets of the Hamiltonian of a system under investigation. In particular, it turns out that peculiar behaviours of thermodynamic observables at a phase transition point are rooted in more fundamental changes of the geometry of the energy level sets in phase space. More specifically, we discuss how microcanonical and geometrical descriptions of phase-transitions are shaped in the special case of $phi^4$ models with either nearest-neighbours and mean-field interactions.
By means of the principle of minimal sensitivity we generalize the microcanonical inflection-point analysis method by probing derivatives of the microcanonical entropy for signals of transitions in complex systems. A strategy of systematically identifying and locating independent and dependent phase transitions of any order is proposed. The power of the generalized method is demonstrated in applications to the ferromagnetic Ising model and a coarse-grained model for polymer adsorption onto a substrate. The results shed new light on the intrinsic phase structure of systems with cooperative behavior.
A geometric analysis of protein folding, which complements many of the models in the literature, is presented. We examine the process from unfolded strand to the point where the strand becomes self-interacting. A central question is how it is possible that so many initial configurations proceed to fold to a unique final configuration. We put energy and dynamical considerations temporarily aside and focus upon the geometry alone. We parameterize the structure of an idealized protein using the concept of a ribbon from differential geometry. The deformation of the ribbon is described by introducing a generic twisting Ansatz. The folding process in this picture entails a change in shape guided by the local amino acid geometry. The theory is reparamaterization invariant from the start, so the final shape is independent of folding time. We develop differential equations for the changing shape. For some parameter ranges, a sine-Gordon torsion soliton is found. This purely geometric waveform has properties similar to dynamical solitons. Namely: A threshold distortion of the molecule is required to initiate the soliton, after which, small additional distortions do not change the waveform. In this analysis, the soliton twists the molecule until bonds form. The analysis reveals a quantitative relationship between the geometry of the amino acids and the folded form.