Energy landscape picture of supercooled liquids: Application of a generalized random energy model

The thermodynamic and kinetic anomalies of supercooled liquids are analyzed from the perspective of energy landscapes. A mean field model, a generalized random energy model of liquids is developed, which exhibits a dynamical transition of the onset of slow dynamics at T_0, alteration of the nature of motion from the saddle-to-saddle to minimum-to-minimum motion at T_c, and an ideal glass transition at T_k. If the energy spectrum of the configurations has a low energy tail, the model also allows a thermodynamic liquid-liquid transition at T_l. The liquid-liquid transition of the model is correlated to the kinetic fragile-strong transition accompanied by the anomalous slowing down of motion. Fragility of the system is classified in terms of features of the energy landscape such as ruggedness of the potential energy surface, size of the cooperative motion invoked in a transition from one configuration to another, and energy needed to deform the local structure in the cooperative motion. A simple relation is found between diffusion constant, D and the saddle index of the potential energy surface, f, as $D \propto f^{a}$, where a depends on the size of the cooperative motion.Comment: to appear in J. Chem. Phy

Effects of the DNA state fluctuation on single-cell dynamics of self-regulating gene

A dynamical mean-field theory is developed to analyze stochastic single-cell dynamics of gene expression. By explicitly taking account of nonequilibrium and nonadiabatic features of the DNA state fluctuation, two-time correlation functions and response functions of single-cell dynamics are derived. The method is applied to a self-regulating gene to predict a rich variety of dynamical phenomena such as anomalous increase of relaxation time and oscillatory decay of correlations. Effective "temperature" defined as the ratio of the correlation to the response in the protein number is small when the DNA state change is frequent, while it grows large when the DNA state change is infrequent, indicating the strong enhancement of noise in the latter case.Comment: 18 pages, 5 figure

Organization of fast and slow chromatin revealed by single-nucleosome dynamics

Understanding chromatin organization and dynamics is important since they crucially affect DNA functions. In this study, we investigate chromatin dynamics by statistically analyzing single-nucleosome movement in living human cells. Bi-modal nature of the mean squared displacement distribution of nucleosomes allows for a natural categorization of the nucleosomes as fast and slow. Analyses of the nucleosome-nucleosome correlation functions within these categories along with the density of vibrational modes show that the nucleosomes form dynamically correlated fluid regions, i.e., dynamic domains of fast and slow nucleosomes. Perturbed nucleosome dynamics by global histone acetylation or cohesin inactivation indicate that nucleosome-nucleosome interactions along with tethering of chromatin chains organize nucleosomes into fast and slow dynamic domains. A simple polymer model is introduced, which shows the consistency of this dynamic domain picture. Statistical analyses of single-nucleosome movement provide rich information on how chromatin is dynamically organized in a fluid manner in living cells

Testing the transition state theory in stochastic dynamics of a genetic switch

Stochastic dynamics of chemical reactions in a mutually repressing two-gene circuit is numerically simulated. The circuit has a rich variety of different states when the kinetic change of DNA status is slow. The stochastic switching transition between those states are compared with the theoretical estimation of the switching rate derived from the idea similar to the transition state theory. Even though the circuit is kept far from equilibrium, the method gives a consistent explanation of the switching kinetics for a wide range of parameters. The transition state theory-like estimation, however, fails to describe transitions involving the state which has the extremely small numbers of protein molecules

Stable stochastic dynamics in yeast cell cycle

Chemical reactions in cell are subject to intense stochastic fluctuations. An important question is how the fundamental physiological behavior of cell is kept stable against those noisy perturbations. In this paper a stochastic model of cell cycle of budding yeast is constructed to analyze the effects of noise on the cell cycle oscillation. The model predicts intense noise in levels of mRNAs and proteins, and the simulated protein levels explain the observed statistical tendency of noise in populations of synchronous and asynchronous cells. In spite of intense noise in levels of proteins and mRNAs, cell cycle is stable enough to bring the largely perturbed cells back to the physiological cyclic oscillation. The model shows that consecutively appearing fixed points are the origin of this stability of cell cycle.Comment: main text, 2 supporting texts, 3 supplementary table