This paper explores the driving mechanisms for structural transitions of atomic clusters between oblate and prolate isomers. We employ the hyperspherical coordinates to investigate structural dynamics of a seven-atom cluster at a coarse-grained level in terms of the dynamics of three gyration radii and three principal axes, which characterize overall mass distributions of the cluster. Dynamics of gyration radii is governed by two kinds of forces. One is the potential force originating from the interactions between atoms. The other is the dynamical forces called the internal centrifugal forces, which originate from twisting and shearing motions of the system. The internal centrifugal force arising from twisting motions has an effect of breaking the symmetry between two gyration radii. As a result, in an oblate isomer, activation of the internal centrifugal force that has the effect of breaking the symmetry between the two largest gyration radii is crucial in triggering structural transitions into prolate isomers. In a prolate isomer, on the other hand, activation of the internal centrifugal force that has the effect of breaking the symmetry between the two smallest gyration radii is crucial in triggering structural transitions into oblate isomers. Activation of a twisting motion that switches the movement patterns of three principal axes is also important for the onset of structural transitions between oblate and prolate isomers. Based on these trigger mechanisms, we finally show that selective activations of specific gyration radii and twisting motions, depending on the isomer of the cluster, can effectively induce structural transitions of the cluster. The results presented here could provide further insights into the control of molecular reactions. (C) 2015 AIP Publishing LLC.

This paper explores asymmetric elasticity of a double-stranded helical chain, which serves as a minimal model of biopolymers. The model consists of two elastic chains that mutually intertwine in a right-handed manner, forming a double-stranded helix. A simple numerical experiment for structural relaxation, which reduces the total elastic energy of the model monotonically without thermal fluctuations, reveals possible asymmetric elasticity inherent in the helical chain. It is first shown that a short segment of the double-stranded helical chain has a tendency to unwind when it is bent. It is also shown that a short segment of the helical chain has a tendency to writhe in the left direction upon bending. This tendency gives rise to a propensity for a longer segment of the chain to form a left-handed superhelix spontaneously upon bending. Finally, this propensity of the helical chain to form a left-handed superhelix is proposed to be a possible origin of the uniform left-handed wrapping of DNA around nucleosome core particles in nature. The results presented here could provide deeper insights into the roles and significance of helical chirality of biopolymers. © 2014 American Physical Society.

We study the coupling between shape changes and rotations of molecules in a random environment. As a prototype of molecules or biopolymers that can undergo non-trivial conformational transitions we consider a planar four-atomic molecule, with underdamped dynamics of Langevin-type. In this simplified setting, we can extend the available gauge theory of semi-flexible molecules to the stochastic setting which allows us to analyse and explain geometric phase effects that arise from the internal motion of the molecule. Due to the stochastic nature of the Langevin system, the internal dynamics contains temperature-dependent coriolis forces that arise from the fluctuations of the angular momentum around its mean value zero. All theoretical investigations are supplemented by numerical simulations, in which we specifically investigate the dependence of the orientational shift on the parameters of the Langevin equation, i.e., friction coefficient, atomic masses, temperature and the velocity of deformation of the system. The numerical results confirm our theoretical findings. We further discuss various extension of the analysis, e.g., to the overdamped limit or optimal control. © 2013 Taylor &amp
Francis.

We study the internal resonance, energy transfer, activation mechanism, and control of a model of DNA division via parametric resonance. While the system is robust to noise, this study shows that it is sensitive to specific fine scale modes and frequencies that could be targeted by low intensity electro-magnetic fields for triggering and controlling the division. The DNA model is a chain of pendula in a Morse potential. While the (possibly parametrically excited) system has a large number of degrees of freedom and a large number of intrinsic time scales, global and slow variables can be identified by (1) first reducing its dynamic to two modes exchanging energy between each other and (2) averaging the dynamic of the reduced system with respect to the phase of the fastest mode. Surprisingly, the global and slow dynamic of the system remains Hamiltonian (despite the parametric excitation) and the study of its associated effective potential shows how parametric excitation can turn the unstable open state into a stable one. Numerical experiments support the accuracy of the time-averaged reduced Hamiltonian in capturing the global and slow dynamic of the full system. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4790835]

This paper explores the mechanisms for dissociation of atomic clusters in terms of internal energy flow and driving forces. We employ the hyperspherical coordinates to investigate internal dynamics of atomic clusters. The hyperspherical coordinates consist of three gyration radii and 3n - 9 hyperangular degrees of freedom that parameterize the shape of an n-atom system in the three-dimensional physical space. The latter 3n - 9 hyperangular degrees of freedom are further classified into three twisting modes and 3n-12 shearing modes. We numerically characterize the patterns of energy flow among the internal degrees of freedom leading to dissociations. It is shown that a large amount of kinetic energy tends to accumulate in the largest gyration radius upon dissociations of the cluster. We also identify some of the twisting and shearing modes that are active right at the instant of dissociation. These modes may be regarded as the triggers that drive dissociation of the cluster by pumping energy into the largest gyration radius. Physically, this pumping of energy is mediated by the internal centrifugal forces that originate from twisting and shearing motions of the system. These results are consistent with theoretical expectations from the equations of motion for gyration radii, and could be an initial step towards the control of large-amplitude collective motions of complex molecular systems. © 2013 by JSME.

This paper gives an account of our recent studies on the mechanisms for chiral selection in super-coiling and wrapping of DNA. We first present a compact model of double-stranded DNA (Model 1), which consists of two elastic chains that mutually intertwine in a right-handed manner to form a double-stranded helix. Numerical analysis of this model suggests an intrinsic propensity of DNA to writhe in the left direction upon bending. Based on this asymmetric elasticity of DNA, we present a further simplified model of DNA (Model 2), which is a single-chained homopolymer with the propensity to writhe in the left direction upon bending. This simplified model is incorporated into a Langevin dynamics study to explore the origin of the uniform left-handed wrapping of DNA around a nucleosome core particle in nature. We finally show that the propensity of DNA to writhe in the left direction upon bending gives rise to the selective left-handed wrapping, provided that the size of the core particle is appropriate. This result suggests the fundamental significance of the asymmetric elasticity of helical biopolymers in their structural dynamics and functions.

A technique based on dynamical systems theory is introduced for the computation of lifetime distributions and rates of chemical reactions and scattering phenomena, even in systems that exhibit non-statistical behavior. In particular, we merge invariant manifold tube dynamics with Monte Carlo volume determination for accurate rate calculations. This methodology is applied to a three-degree-of-freedom model problem and some ideas on how it might be extended to higher-degree-of-freedom systems are presented.

A methodology is given to determine the effect of different mass distributions for triatomic reactions using the geometry of shape space. Atomic masses are incorporated into the non-Euclidean shape space metric after the separation of rotations. Using the equations of motion in this non-Euclidean shape space, an averaged field of velocity-dependent fictitious forces is determined. This force field, as opposed to the force arising from the potential, dominates branching ratios of isomerization dynamics of a triatomic molecule. This methodology may be useful for qualitative prediction of branching ratios in general triatomic reactions.

In a previous study of isomerization dynamics of clusters as a chaotic conservative system, we proposed a temperature, called the microcanonical temperature [C. Seko and K. Takatsuka, J. Chem. Phys. 104, 8613 (1996)], which is expected to characterize a phase space distribution on a constant energy plane. In contrast to the standard view of equal a priori distribution in phase space, we note a fact that this distribution usually becomes sharply localized with a single peak, if projected onto the potential energy coordinate. The microcanonical temperature is defined as a kinetic energy at which this projected distribution takes the maximum value. Then the most probable statistical events should be dominated by those components in vicinity of the peak, provided that the projected distribution is singly and sharply peaked and the associated dynamics is ergodic. The microcanonical temperature can be similarly redefined in the individual potential basins. Here in the present article a numerical fact is highlighted that the inverse of the lifetime of an isomer bears an Arrhenius-type relation with thus defined local microcanonical temperature assigned to the corresponding potential basin. We present an analysis of how the Arrhenius relation can arise. (C) 2000 American Institute of Physics. [S0021-9606(00)50831-9].

We present a theoretical treatment that accounts for the internal-energy dependence of the rate of geometrical isomerization of Ar-7-like clusters in the so-called liquid-like phase (high-energy region). Since many trajectories representing this reaction pass through a broad range of basin boundaries other than the transition state and since there are many channels involved, the reaction rate is not determined by a few local characteristics of the potential surfaces such as the transition state or the reaction coordinates. We therefore propose a reaction rate model which is based on the isotropic inflation of the density of states at the global basin boundaries. (C) 1999 Elsevier Science B.V. All rights reserved.