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Register a new userFree-Energy Calculations in Protein Folding by Generalized-Ensemble Algorithms
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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.
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We present generalized-ensemble algorithms for isobaric-isothermal molecular simulations. In addition to the multibaric-multithermal algorithm and replica-exchange method for the isobaric-isothermal ensemble, which have already been proposed, we propose a simulated tempering method for this ensemble. We performed molecular dynamics simulations with these algorithms for an alanine dipeptide system in explicit water molecules to test the effectiveness of the algorithms. We found that these generalized-ensemble algorithms are all useful for conformational sampling of biomolecular systems in the isobaric-isothermal ensemble.
In complex systems such as spin systems and protein systems, conventional simulations in the canonical ensemble will get trapped in states of energy local minima. We employ the generalized-ensemble algorithms in order to overcome this multiple-minima problem. Three well-known generalized-ensemble algorithms, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described. We then present three new generalized-ensemble algorithms based on the combinations of the three methods. Effectiveness of the new methods are tested with a Potts model and protein systems.
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.
Searching for characteristic signatures of a higher order phase transition (specifically of order three or four), we have calculated the spatial profiles and the energies of a spatially varying order parameter in one dimension. In the case of a $p^{th}$ order phase transition to a superconducting ground state, the free energy density depends on temperature as $a^p$, where $a = a_o(1-T/T_c)$ is the reduced temperature. The energy of a domain wall between two degenerate ground states is $epsilon_p simeq a^{p-1/2}$. We have also investigated the effects of a supercurrent in a narrow wire. These effects are limited by a critical current which has a temperature dependence $J_c(T) simeq a^{(2p-1)/2}$. The phase slip center profiles and their energies are also calculated. Given the suggestion that the superconducting transtion in bkbox, for $x = 0.4$, may be of order four, these predictions have relevance for future experiments.
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