Free energy calculations of a proton transfer reaction by simulated tempering umbrella sampling first principles molecular dynamics simulations

A new simulated tempering method, which is referred to as simulated tempering umbrella sampling, for calculating the free energy of chemical reactions is proposed. First principles molecular dynamics simulations with this simulated tempering were performed in order to study the intramolecular proton transfer reaction of malonaldehyde in aqueous solution. Conformational sampling in reaction coordinate space can be easily enhanced with this method, and the free energy along a reaction coordinate can be calculated accurately. Moreover, the simulated tempering umbrella sampling provides trajectory data more efficiently than the conventional umbrella sampling method.Comment: 5 pages, (Revtex4-1), 3 figure

Amino-acid-dependent main-chain torsion-energy terms for protein systems

Many commonly used force fields for protein systems such as AMBER, CHARMM, GROMACS, OPLS, and ECEPP have amino-acid-independent force-field parameters of main-chain torsion-energy terms. Here, we propose a new type of amino-acid-dependent torsion-energy terms in the force fields. As an example, we applied this approach to AMBER ff03 force field and determined new amino-acid-dependent parameters for $\psi$ and $\psi'$ angles for each amino acid by using our optimization method, which is one of the knowledge-based approach. In order to test the validity of the new force-field parameters, we then performed folding simulations of $\alpha$-helical and $\beta$-hairpin peptides, using the optimized force field. The results showed that the new force-field parameters gave structures more consistent with the experimental implications than the original AMBER ff03 force field.Comment: 10 pages, (Revtex4.1), 3 tables, 6 figure

Generalized-Ensemble Algorithms for the Isobaric-Isothermal Ensemble

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.Comment: 6 pages, (Revtex4), 4 figure

Replica-Exchange Molecular Dynamics Simulations for Various Constant Temperature Algorithms

In the replica-exchange molecular dynamics method, where constant-temperature molecular dynamics simulations are performed in each replica, one usually rescales the momentum of each particle after replica exchange. This rescaling method had previously been worked out only for the Gaussian constraint method. In this letter, we present momentum rescaling formulae for four other commonly used constant-temperature algorithms, namely, Langevin dynamics, Andersen algorithm, Nos\'{e}-Hoover thermostat, and Nos\'{e}-Poincar\'{e} thermostat. The effectiveness of these rescaling methods is tested with a small biomolecular system, and it is shown that proper momentum rescaling is necessary to obtain correct results in the canonical ensemble.Comment: 6 pages, (Revtex4), 4 figure

Multicanonical Algorithm, Simulated Tempering, Replica-Exchange Method, and All That

We discuss multi-dimensional generalizations of multicanonical algorithm, simulated tempering, and replica-exchange method. We generalize the original potential energy function $E_0$ by adding any physical quantity $V$ of interest as a new energy term with a coupling constant $\lambda$. We then perform a multi-dimensional multicanonical simulation where a random walk in $E_0$ and $V$ space is realized. We can alternately perform a multi-dimensional simulated tempering simulation where a random walk in temperature $T$ and parameter $\lambda$ is realized. The results of the multi-dimensional replica-exchange simulations can be used to determine the weight factors for these multi-dimensional multicanonical and simulated tempering simulations.Comment: 4 pages, (Revtex4), 2 figure

Optimizations of protein force fields

In this Chapter we review our works on force fields for molecular simulations of protein systems. We first discuss the functional forms of the force fields and present some extensions of the conventional ones. We then present various methods for force-field parameter optimizations. Finally, some examples of our applications of these parameter optimization methods are given and they are compared with the results from the existing force-fields.Comment: 56 pages, (Springer Verlag global LaTeX2e support for multi authored books), 28 figures, 13 table

Designed-walk replica-exchange method for simulations of complex systems

We propose a new implementation of the replica-exchange method (REM) in which replicas follow a pre-planned route in temperature space instead of a random walk. Our method satisfies the detailed balance condition in the proposed route. The method forces tunneling events between the highest and lowest temperatures to happen with an almost constant period. The number of tunneling counts is proportional to that of the random-walk REM multiplied by the square root of moving distance in temperature space. We applied this new implementation to two kinds of REM and compared the results with those of the conventional random-walk REM. The test system was a two-dimensional Ising model, and our new method reproduced the results of the conventional random-walk REM and improved the tunneling counts by three times or more than that of the random-walk REM.Comment: 6 pages, 3 figures, 1 table; methods are the same before, but results and some references are added, table is update

An Efficient Simulation Protocol for Determining the Density of States: Combination of Replica-Exchange Wang-Landau Method and Multicanonical Replica-Exchange Method

By combining two generalized-ensemble algorithms, Replica-Exchange Wang-Landau (REWL) method and Multicanonical Replica-Exchange Method (MUCAREM), we propose an effective simulation protocol to determine the density of states with high accuracy. The new protocol is referred to as REWL-MUCAREM, and REWL is first performed and then MUCAREM is performed next. In order to verify the effectiveness of our protocol, we performed simulations of a square-lattice Ising model by the three methods, namely, REWL, MUCAREM, and REWL-MUCAREM. The results showed that the density of states obtained by the REWL-MUCAREM is more accurate than that is estimated by the two methods separately.Comment: 12 pages, , (Revtex4-1), 5 figure

Deterministic replica-exchange method without pseudo random numbers for simulations of complex systems

We propose a replica-exchange method (REM) which does not use pseudo random numbers. For this purpose, we first give a conditional probability for Gibbs sampling replica-exchange method (GSREM) based on the heat bath method. In GSREM, replica exchange is performed by conditional probability based on the weight of states using pseudo random numbers. From the conditional probability, we propose a new method called deterministic replica-exchange method (DETREM) that produces thermal equilibrium distribution based on a differential equation instead of using pseudo random numbers. This method satisfies the detailed balance condition using a conditional probability of Gibbs heat bath method and thus results can reproduce the Boltzmann distribution within the condition of the probability. We confirmed that the equivalent results were obtained by REM and DETREM with two-dimensional Ising model. DETREM can avoid problems of choice of seeds in pseudo random numbers for REM using a differential equation.Comment: 12 pages, 1 table, 11 figures, auto-correlation function and time series of internal state are adde

Application of Simulated Tempering and Magnetizing to a Two-Dimensional Potts Model

We applied the simulated tempering and magnetizing (STM) method to the two-dimensional three-state Potts model in an external magnetic field in order to perform further investigations of the STM's applicability. The temperature as well as the external field are treated as dynamical variables updated during the STM simulations. After we obtained adequate information for several lattice sizes $L$ (up to $160\times 160$), we also performed a number of conventional canonical simulations of large lattices, especially in order to illustrate the crossover behavior of the Potts model in external field with increasing $L$. The temperature and external field for larger lattice size simulations were chosen by extrapolation of the detail information obtained by STM. We carefully analyzed the crossover scaling at the phase transitions with respect to the lattice size as well as the temperature and external field. The crossover behavior is clearly observed in the simulations in agreement with theoretical predictions.Comment: 21 pages, 21 figure