Efficiency analysis of reaction rate calculation methods using analytical models I: The 2D sharp barrier

We analyze the efficiency of different methods for the calculation of reaction rates in the case of two simple analytical benchmark systems. Two classes of methods are considered: the first are based on the free energy calculation along a reaction coordinate and the calculation of the transmission coefficient, the second on the sampling of dynamical pathways. We give scaling rules for how this efficiency depends on barrier height and width, and we hand out simple optimization rules for the method-specific parameters. We show that the path sampling methods, using the transition interface sampling technique, become exceedingly more efficient than the others when the reaction coordinate is not the optimal one.Comment: 22 pages, 5 figure

Ab Initio Molecular Dynamics Study of Aqueous Solvation of Ethanol and Ethylene

The structure and dynamics of aqueous solvation of ethanol and ethylene are studied by DFT-based Car-Parrinello molecular dynamics. We did not find an enhancement of the structure of the hydrogen bonded network of hydrating water molecules. Both ethanol and ethylene can easily be accommodated in the hydrogen-bonded network of water molecules without altering its structure. This is supports the conclusion from recent neutron diffraction experiments that there is no hydrophobic hydration around small hydrophobic groups. Analysis of the electronic charge distribution using Wannier functions shows that the dipole moment of ethanol increases from 1.8 D to 3.1 D upon solvation, while the apolar ethylene molecule attains an average dipole moment of 0.5 D. For ethylene, we identified configurations with $\pi$-H bonded water molecules, that have rare four-fold hydrogen-bonded water coordination, yielding instantaneous dipole moments of ethylene of up to 1 D. The results provide valuable information for the improvement of empirical force fields, and point out that for an accurate description of the aqueous solvation of ethanol, and even of the apolar ethylene, polarizable force fields are required.Comment: 15 pages, 10 figures, 4 tables, revtex4, submitted to J. Chem. Phy

Reaction rate calculation by parallel path swapping

The efficiency of path sampling simulations can be improved considerably using the approach of path swapping. For this purpose, we have devised a new algorithmic procedure based on the transition interface sampling technique. In the same spirit of parallel tempering, paths between different ensembles are swapped, but the role of temperature is here played by the interface position. We have tested the method on the denaturation transition of DNA using the Peyrard-Bishop-Dauxois model. We find that the new algorithm gives a reduction of the computational cost by a factor 20.Comment: 5 pages, 3 figure

Efficient path sampling on multiple reaction channels

Due to the time scale problem, rare events are not accessible by straight forward molecular dynamics. The presence of multiple reaction channels complicates the problem even further. The feasibility of the standard free energy based methods relies strongly on the success in finding a proper reaction coordinate. This can be very difficult task in high-dimensional complex systems and even more if several distinct reaction channels exist. Moreover, even if a proper reaction coordinate can be found, ergodic sampling will be a challenge. In this article, we discuss the recent advancements of path sampling methods to tackle this problem. We argue why the path sampling methods, via the transition interface sampling technique, is less sensitive to the choice of reaction coordinate. Moreover, we review a new algorithm, parallel path swapping, that can dramatically improve the ergodic sampling of trajectories for the multiple reaction channel systems.Comment: 7 pages, 4 figures. Article submitted for the proceedings of the Conference on Computational Physics, Brussels 200

The dynamics of the DNA denaturation transition

The dynamics of the DNA denaturation is studied using the Peyrard-Bishop-Dauxois model. The denaturation rate of double stranded polymers decreases exponentially as function of length below the denaturation temperature. Above Tc, the rate shows a minimum, but then increases as function of length. We also examine the influence of sequence and solvent friction. Molecules having the same number of weak and strong base-pairs can have significantly different opening rates depending on the order of base-pairs.Comment: 6 pages, 6 figures, to be published in Europhysics Letter

Rate constants for diffusive processes by partial path sampling

We introduce a path sampling method for the computation of rate constants for systems with a highly diffusive character. Based on the recently developed algorithm of transition interface sampling (TIS) this procedure increases the efficiency by sampling only parts of complete transition trajectories confined within a certain region. The algorithm assumes the loss of memory for highly diffusive progression along the reaction coordinate. We compare the new technique to the TIS method for a simple diatomic system and show that the computation time of the new method scales linearly, instead of quadraticaly, with the length of the diffusive barrier. The validity of the memory loss assumption is also discussed.Comment: 12 pages, including 8 figures, RevTeX

A Novel Path Sampling Method for the Calculation of Rate Constants

We derive a novel efficient scheme to measure the rate constant of transitions between stable states separated by high free energy barriers in a complex environment within the framework of transition path sampling. The method is based on directly and simultaneously measuring the fluxes through many phase space interfaces and increases the efficiency with at least a factor of two with respect to existing transition path sampling rate constant algorithms. The new algorithm is illustrated on the isomerization of a diatomic molecule immersed in a simple fluid.Comment: 14 pages, including 13 figures, RevTeX

Can one predict DNA Transcription Start Sites by studying bubbles?

It has been speculated that bubble formation of several base-pairs due to thermal fluctuations is indicatory for biological active sites. Recent evidence, based on experiments and molecular dynamics (MD) simulations using the Peyrard-Bishop-Dauxois model, seems to point in this direction. However, sufficiently large bubbles appear only seldom which makes an accurate calculation difficult even for minimal models. In this letter, we introduce a new method that is orders of magnitude faster than MD. Using this method we show that the present evidence is unsubstantiated.Comment: 4 pages, 3 figures, accepted for publication in physical review letter

Comment on "A generalized Langevin formalism of complete DNA melting transition"

We show that the calculated DNA denaturation curves for finite (Peyrard-Bishop-Dauxois (PBD) chains are intrinsically undefined.Comment: 2 pages. Accepted for EP

Improving the mesoscopic modeling of DNA denaturation dynamics

Although previously developed mesoscopic DNA models have successfully reproduced thermodynamic denaturation data, recent studies show that these overestimate the rate of denaturation by orders of magnitude. Using adapted Peyrard–Bishop–Dauxois (PBD) models, we have calculated the denaturation rates of several DNA hairpins and made comparison with experimental data. We show that the addition of a barrier at the onsite potential of the PBD model gives a more accurate description of the unzipping dynamics of short DNA sequences. The new models provide a refined theoretical insight on the dynamical mechanisms of unzipping which can have implications for the understanding of transcription and replication processes. Still, this class of adapted PBD models seems to have a fundamental limitation which implies that it is not possible to get agreement with available experimental results on the dynamics of long DNA sequences and at the same time maintain the good agreement regarding its thermodynamics. The reason for this is that the denaturation rate of long DNA chains is not dramatically lowered by the additional barrier—as the base-pairs that open are more likely to remain open, facilitating the opening of the full DNA molecule. Some care has to be taken, since experimental techniques suitable to the study of denaturation rates of long sequences seem not to agree with other experimental data on short DNA sequences. Further research, both theoretical and experimental, is therefore needed to resolve these inconsistencies—which will be a starting point for new minimalistic models that are able to describe both thermodynamics and dynamics at a predictive level.Spanish Ministry of Economy, Industry and Competitiveness (BES-2013-065453, FIS2012-38827) and the University of Burgos and the Anders Jahre fund (Project 40105000