The autocatalytic reaction system with a small number of molecules is studied numerically by stochastic particle simulations. A novel state due to fluctuation and discreteness in molecular numbers is found, characterized as an extinction of molecule species alternately in the autocatalytic reaction loop. Phase transition to this state with changes of the system size and flow is studied, while a single-molecule switch of the molecule distributions is reported. The relevance of the results to intracellular processes is briefly discussed.

The mammalian genome is organized into submegabase-sized chromatin domains (CDs) including topologically associating domains, which have been identified using chromosome conformation capture-based methods. Single-nucleosome imaging in living mammalian cells has revealed subdiffusively dynamic nucleosome movement. It is unclear how single nucleosomes within CDs fluctuate and how the CD structure reflects the nucleosome movement. Here, we present a polymer model wherein CDs are characterized by fractal dimensions and the nucleosome fibers fluctuate in a viscoelastic medium with memory. We analytically show that the mean-squared displacement (MSD) of nucleosome fluctuations within CDs is subdiffusive. The diffusion coefficient and the subdiffusive exponent depend on the structural information of CDs. This analytical result enabled us to extract information from the single-nucleosome imaging data for HeLa cells. Our observation that the MSD is lower at the nuclear periphery region than the interior region indicates that CDs in the heterochromatin-rich nuclear periphery region are more compact than those in the euchromatin-rich interior region with respect to the fractal dimensions as well as the size. Finally, we evaluated that the average size of CDs is in the range of 100–500 nm and that the relaxation time of nucleosome movement within CDs is a few seconds. Our results provide physical and dynamic insights into the genome architecture in living cells.

Analyzing nonlinear conformational relaxation dynamics in elastic networks corresponding to two classical motor proteins, we find that they respond by well defined internal mechanical motions to various initial deformations and that these motions are robust against external perturbations. We show that this behavior is not characteristic for random elastic networks. However, special network architectures with such properties can be designed by evolutionary optimization methods. Using them, an example of an artificial elastic network, operating as a cyclic machine powered by ligand binding, is constructed.complex systems ͉ protein machines ͉ molecular motors ͉ evolutionary optimization U nderstanding design principles of single-molecule machines is a major challenge. Experimental and theoretical studies of proteins, acting as motors (1-5), ion pumps (6-8), or channels (6, 9), and enzymes (10-14), show that their operation involves functional conformational motions (see ref. 15). Such motions are slow and cannot therefore be reproduced by full molecular dynamics simulations. Within the last decade, approximate descriptions based on elastic network models of proteins have been developed (16)(17)(18)(19)(20)(21). In this approach, structural elements of a protein are viewed as identical point particles, with two particles connected by an elastic string if the respective elements lie close enough in the native state of the considered protein. Thus, a network of elastic connections corresponding to a protein is constructed. So far, the attention has been focused on linear dynamics of elastic networks, characterized in terms of their normal vibrational modes. It has been found that ligand-induced conformational changes in many proteins agree with the patterns of atomic displacements in their slowest vibrational modes (refs. 22-25 and see also refs. 26 and 27), even though nonlinear elastic effects must become important for large deviations from the equilibrium (28, 29). The focus of this article is on nonlinear relaxation phenomena in elastic networks seen as complex dynamical systems.Generally, a machine is a mechanical device that performs ordered internal motions that are robust against external perturbations. In machines representing single molecules, energy is typically supplied in discrete portions, through individual reaction events. Therefore, their cycles consist of the processes of conformational relaxation that follow after energetic excitations. For a robust machine operation, special nonlinear relaxation dynamics is required. We expect that, starting from a broad range of initial deformations, such dynamical systems would return to the same final equilibrium state. Moreover, the relaxation would proceed along a well defined trajectory (or a low-dimensional manifold), rapidly approached starting from different initial states and robust against external perturbations. These attractive relaxation trajectories would define internal mechanical motions of the machine inside its operation cycle.This special confor...

G protein-coupled receptors (GPCRs) are major drug targets. Developing a method to measure the activities of GPCRs is essential for pharmacology and drug screening. However, it is difficult to measure the effects of a drug by monitoring the receptor on the cell surface; thus, changes in the concentrations of downstream signaling molecules, which depend on the signaling pathway selectivity of the receptor, are often used as an index of receptor activity. We show that single-molecule imaging analysis provides an alternative method for assessing the effects of ligands on GPCRs. Using total internal reflection fluorescence microscopy (TIRFM), we monitored the dynamics of the diffusion of metabotropic glutamate receptor 3 (mGluR3), a class C GPCR, under various ligand conditions. Our single-molecule tracking analysis demonstrated that increases and decreases in the average diffusion coefficient of mGluR3 quantitatively reflected the ligand-dependent inactivation and activation of receptors, respectively. Through experiments with inhibitors and dual-color single-molecule imaging analysis, we found that the diffusion of receptor molecules was altered by common physiological events associated with GPCRs, including G protein binding, and receptor accumulation in clathrin-coated pits. We also confirmed that agonist also decreased the average diffusion coefficient for class A and B GPCRs, demonstrating that this parameter is a good index for estimating ligand effects on many GPCRs regardless of their phylogenetic groups, the chemical properties of the ligands, or G protein-coupling selectivity.