Bifurcating trajectory of non-diffractive electromagnetic Airy pulse

The explicit expression for spatial-temporal Airy pulse is derived from the Maxwell's equations in paraxial approximation. The trajectory of the pulse in the time-space coordinates is analysed. The existence of a bifurcation point that separates regions with qualitatively different features of the pulse propagation is demonstrated. At this point the velocity of the pulse becomes infinite and the orientation of it changes to the opposite

All-Atom Molecular Dynamics Simulations of Whole Viruses

Classical molecular dynamics modeling of whole viruses or their capsids in explicit water is discussed, and known examples from the literature are analyzed. Only works on all-atom modeling in explicit water are included. Physical chemistry of the whole system is the focus, which includes the structure and dynamics of the biomolecules as well as water and ion behavior in and around the virus particle. It was demonstrated that in most investigations molecular phenomena that currently can not be studied experimentally are successfully reproduced and explained by the simulations. These include, for example, transport and distribution of ions inside viruses that ultimately connected to their stability, the hydrodynamic pressure in the capsid related to viruses’ elastic properties, the role of metal ions in virus swelling, and others. Current and future tendencies in the development of all-atom virus simulations are outlined

21-residue peptide's dynamics at and between elementary structural transitions

Elementary conformational changes of the backbone of a 21-residue peptide A5(A3RA)3A are studied using molecular dynamics simulations in explicit water. The processes of the conformational transitions and the regimes of stationary fluctuations between them are investigated using minimal perturbations of the system. The perturbations consist of a few degrees rotation of the velocity of one of the systems' atoms and keep the system on the same energy surface. It is found that (i) the system dynamics is insignificantly changed by the perturbations in the regimes between the transitions; (ii) it is very sensitive to the perturbations just before the transitions that prevents the peptide from making the transitions; and (iii) the perturbation of any atom of the system, including distant water molecules is equally effective in preventing the transition. The latter implies strongly collective dynamics of the peptide and water during the transitions

Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework, the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore, it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare´ return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare´ theorem

Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds)

Complexity of classical dynamics of molecular systems. II. Finite statistical complexity of a water-Na+ system

The computational mechanics approach has been applied to the orientational behavior of water molecules in a molecular dynamics simulated water–Na + system. The distinctively different statistical complexity of water molecules in the bulk and in the first solvation shell of the ion is demonstrated. It is shown that the molecules undergo more complex orientational motion when surrounded by other water molecules compared to those constrained by the electric field of the ion. However the spatial coordinates of the oxygen atom shows the opposite complexity behavior in that complexity is higher for the solvation shell molecules. New information about the dynamics of water molecules in the solvation shell is provided that is additional to that given by traditional methods of analysis

Water network dynamics at the critical moment of a peptide's ß-turn formation:a molecular dynamics study

All-atom molecular dynamics simulations for a single molecule of Leu-Enkephalin in aqueous solution have been used to study the role of the water network during the formation of ß-turns. We give a detailed account of the intramolecular hydrogen bonding, the water-peptide hydrogen bonding, and the orientation and residence times of water molecules focusing on the short critical periods of transition to the stable ß-turns. These studies suggest that, when intramolecular hydrogen bonding between the first and fourth residue of the ß-turn is not present, the disruption of the water network and the establishment of water bridges constitute decisive factors in the formation and stability of the ß-turn. Finally, we provide possible explanations and mechanisms for the formations of different kinds of ß-turns

Complexity of classical dynamics of molecular systems. I. Methodology

Methods for the calculation of complexity have been investigated as a possible alternative for the analysis of the dynamics of molecular systems. “Computational mechanics” is the approach chosen to describe emergent behavior in molecular systems that evolve in time. A novel algorithm has been developed for symbolization of a continuous physical trajectory of a dynamic system. A method for calculating statistical complexity has been implemented and tested on representative systems. It is shown that the computational mechanics approach is suitable for analyzing the dynamic complexity of molecular systems and offers new insight into the process

Controlling protein molecular dynamics:how to accelerate folding while preserving the native state

The dynamics of peptides and proteins generated by classical molecular dynamics (MD) is described by using a Markov model. The model is built by clustering the trajectory into conformational states and estimating transition probabilities between the states. Assuming that it is possible to influence the dynamics of the system by varying simulation parameters, we show how to use the Markov model to determine the parameter values that preserve the folded state of the protein and at the same time, reduce the folding time in the simulation. We investigate this by applying the method to two systems. The first system is an imaginary peptide described by given transition probabilities with a total folding time of 1 micros. We find that only small changes in the transition probabilities are needed to accelerate (or decelerate) the folding. This implies that folding times for slowly folding peptides and proteins calculated using MD cannot be meaningfully compared to experimental results. The second system is a four residue peptide valine-proline-alanine-leucine in water. We control the dynamics of the transitions by varying the temperature and the atom masses. The simulation results show that it is possible to find the combinations of parameter values that accelerate the dynamics and at the same time preserve the native state of the peptide. A method for accelerating larger systems without performing simulations for the whole folding process is outlined