Shinnosuke Kawai

Diversity in ATP concentrations in a single bacterial cell population revealed by quantitative single-cell imaging

Recent advances in quantitative single-cell analysis revealed large diversity in gene expression levels between individual cells, which could affect the physiology and/or fate of each cell. In contrast, for most metabolites, the concentrations were only measureable as ensemble averages of many cells. In living cells, adenosine triphosphate (ATP) is a critically important metabolite that powers many intracellular reactions. Quantitative measurement of the absolute ATP concentration in individual cells has not been achieved because of the lack of reliable methods. In this study, we developed a new genetically-encoded ratiometric fluorescent ATP indicator “QUEEN”, which is composed of a single circularly-permuted fluorescent protein and a bacterial ATP binding protein. Unlike previous FRET-based indicators, QUEEN was apparently insensitive to bacteria growth rate changes. Importantly, intracellular ATP concentrations of numbers of bacterial cells calculated from QUEEN fluorescence were almost equal to those from firefly luciferase assay. Thus, QUEEN is suitable for quantifying the absolute ATP concentration inside bacteria cells. Finally, we found that, even for a genetically-identical Escherichia coli cell population, absolute concentrations of intracellular ATP were significantly diverse between individual cells from the same culture, by imaging QUEEN signals from single cells.

Control over differentiation of a metastable supramolecular assembly in one and two dimensions

Molecular self-assembly under kinetic control is expected to yield nanostructures that are inaccessible through the spontaneous thermodynamic process. Moreover, time-dependent evolution, which is reminiscent of biomolecular systems, may occur under such out-of-equilibrium conditions, allowing the synthesis of supramolecular assemblies with enhanced complexities. Here we report on the capacity of a metastable porphyrin supramolecular assembly to differentiate into nanofibre and nanosheet structures. Mechanistic studies of the relationship between the molecular design and pathway complexity in the self-assembly unveiled the energy landscape that governs the unique kinetic behaviour. Based on this understanding, we could control the differentiation phenomena and achieve both one- and two-dimensional living supramolecular polymerization using an identical monomer. Furthermore, we found that the obtained nanostructures are electronically distinct, which illustrates the pathway-dependent material properties.

Dynamic pathways to mediate reactions buried in thermal fluctuations. I. Time-dependent normal form theory for multidimensional Langevin equation

We present a novel theory which enables us to explore the mechanism of reaction selectivity and robust functions in complex systems persisting under thermal fluctuation. The theory constructs a nonlinear coordinate transformation so that the equation of motion for the new reaction coordinate is independent of the other nonreactive coordinates in the presence of thermal fluctuation. In this article we suppose that reacting systems subject to thermal noise are described by a multidimensional Langevin equation without a priori assumption for the form of potential. The reaction coordinate is composed not only of all the coordinates and velocities associated with the system (solute) but also of the random force exerted by the environment (solvent) with friction constants. The sign of the reaction coordinate at any instantaneous moment in the region of a saddle determines the fate of the reaction, i.e., whether the reaction will proceed through to the products or go back to the reactants. By assuming the statistical properties of the random force, one can know a priori a well-defined boundary of the reaction which separates the full position-velocity space in the saddle region into mainly reactive and mainly nonreactive regions even under thermal fluctuation. The analytical expression of the reaction coordinate provides the firm foundation on the mechanism of how and why reaction proceeds in thermal fluctuating environments.

Dynamic pathways to mediate reactions buried in thermal fluctuations. II. Numerical illustrations using a model system

The framework recently developed for the extraction of a dynamic reaction coordinate to mediate reactions buried in thermal fluctuation is examined with a model system. Numerical simulations are carried out for an underdamped Langevin equation with the Müller-Brown potential surface, which contains three wells and two saddles, and are compared to the prediction by the theory. Reaction probabilities for specific initial conditions of the system as well as their average over the Boltzmann distribution are investigated in the position space and in a space spanned by the position coordinates and the velocities of the system. The nonlinear couplings between the reactive and the nonreactive modes are shown to have significant effects on the reactivity in the model system. The magnitude and the direction of the nonlinear effect are different for the two saddles, which is found to be correctly reproduced by our theory. The whole position-velocity space of the model system is found to be divided into the two distinct regions: One is of mainly reactive (with reaction probability more than half) initial conditions and the other, the mainly nonreactive (with reaction probability less than half) ones. Our theory can actually assign their boundaries as the zero of the statistical average of the new reaction coordinate as an analytical functional of both the original position coordinates and velocities of the system (solute), as well as of the random force and the friction constants from the environment (solvent). The result validates the statement in the previous paper that the sign of the reaction coordinate thus extracted determines the fate of the reaction. Physical interpretation of the reactivity under thermal fluctuation that is naturally derived, thanks to the analyticity of the theoretical framework, is also exemplified for the model system.

Hierarchy of reaction dynamics in a thermally fluctuating environment

Nonlinear dynamics in the passage over a rank-one saddle is investigated as a function of temperature in the presence of stochastic, thermal fluctuation. The analyses are based on a framework we developed recently adopting a multidimensional underdamped Langevin equation (without any assumption for the form of the potential of mean force). The framework can in principle provide a single coordinate to enable us to predict the final destination of the reaction in a thermally fluctuating media. At each temperature, the preciseness or the error of the reaction coordinate is evaluated in capturing the true reaction dynamics at different levels of approximations. By using the Müller-Brown potential as an illustrative example, it is found that a hierarchy of dynamical structure exists in the region of a rank-one saddle, in which the crossing dynamics qualitatively changes as the temperature increases. We discuss the mechanism of how the reaction coordinate persists, which provides a boundary of the reaction to divide the phase space into the reactive and the nonreactive regions, even in the presence of thermal fluctuation.

Nonlinear dynamical effects on reaction rates in thermally fluctuating environments

A framework to calculate the rate constants of condensed phase chemical reactions of manybody systems is presented without relying on the concept of transition state. The theory is based on a framework we developed recently adopting a multidimensional underdamped Langevin equation in the region of a rank-one saddle. The theory provides a reaction coordinate expressed as an analytical nonlinear functional of the position coordinates and velocities of the system (solute), the friction constants, and the random force of the environment (solvent). Up to moderately high temperature, the sign of the reaction coordinate can determine the final destination of the reaction in a thermally fluctuating media, irrespective of what values the other (nonreactive) coordinates may take. In this paper, it is shown that the reaction probability is analytically derived as the probability of the reaction coordinate being positive, and that the integration with the Boltzmann distribution of the initial conditions leads to the exact reaction rate constant when the local equilibrium holds and the quantum effect is negligible. Because of analytical nature of the theory taking into account all nonlinear effects and their combination with fluctuation and dissipation, the theory naturally provides us with the firm mathematical foundation of the origin of the reactivity of the reaction in a fluctuating media.

Reactivity boundaries for chemical reactions associated with higher-index and multiple saddles

Yutaka Nagahata, Hiroshi Teramoto, 2 Chun-Biu Li, 3, 4 Shinnosuke Kawai, 2 and Tamiki Komatsuzaki 2, 4, ∗ Graduate School of Life Science, Hokkaido University, Kita 12, Nishi 6,Kita-ku, Sapporo 060-0812, Japan Molecule and Life Nonlinear Sciences Laboratory, Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan Graduate School of Science, Department of Mathematics, Hokkaido University, Kita 12, Nishi 6,Kita-ku, Sapporo 060-0812, Japan Research Center for Integrative Mathematics, Hokkaido University, Kita 20, Nishi 10, Kita-Ku, Sapporo, Hokkaido, 001-0020, Japan (Dated: May 11, 2014)

Dynamic reaction coordinate in thermally fluctuating environment in the framework of the multidimensional generalized Langevin equations.

A framework recently developed for the extraction of a dynamic reaction coordinate to mediate reactions buried in a multidimensional Langevin equation is extended to the generalized Langevin equations without a priori assumption of the forms of the potential (in general, nonlinearly coupled systems) and the friction kernel. The equation of motion with memory effect can be transformed into an equation without memory at the cost of an increase in the dimensionality of the system, and hence the theoretical framework developed for the (nonlinear) Langevin formulation can be generalized to the non-Markovian process with colored noise. It is found that the increased dimension can be physically interpreted as effective modes of the fluctuating environment. As an illustrative example, we apply this theory to a multidimensional generalized Langevin equation for motion on the Müller-Brown potential surface with an exponential friction kernel. Numerical simulations find a boundary between the highly reactive region and the less reactive region in the space of initial conditions. The location of the boundary is found to depend significantly on both the memory kernel and the nonlinear couplings. The theory extracts a reaction coordinate whose sign determines the fate of the reaction taking into account thermally fluctuating environments, memory effect, and nonlinearities. It is found that the location of the boundary of reactivity is satisfactorily reproduced as the zero of the statistical average of the new reaction coordinate, which is an analytical functional of both the original position coordinates and velocities of the system, and of the properties of the environment.

Derivation of the generalized Langevin equation in nonstationary environments.

The generalized Langevin equation (GLE) is extended to the case of nonstationary bath. The derivation starts with the Hamiltonian equation of motion of the total system including the bath, without any assumption on the form of Hamiltonian or the distribution of the initial condition. Then the projection operator formulation is utilized to obtain a low-dimensional description of the system dynamics surrounded by the nonstationary bath modes. In contrast to the ordinary GLE, the mean force becomes a time-dependent function of the position and the velocity of the system. The friction kernel is found to depend on both the past and the current times, in contrast to the stationary case where it only depends on their difference. The fluctuation-dissipation theorem, which relates the statistical property of the random force to the friction kernel, is also derived for general nonstationary cases. The resulting equation of motion is as simple as the ordinary GLE, and is expected to give a powerful framework to analyze the dynamics of the system surrounded by a nonstationary bath.

Why and how do systems react in thermally fluctuating environments

Many chemical reactions, including those of biological importance, take place in thermally fluctuating environments. Compared to isolated systems, there arise markedly different features due to the effects of energy dissipation through friction and stochastic driving by random forces reflecting the fluctuation of the environment. Investigation of how robustly the system reacts under the influence of thermal fluctuation, and elucidating the role of thermal fluctuation in the reaction are significant subjects in the study of chemical reactions. In this article, we start with overviewing the generalized Langevin equation (GLE), which has long been used and continues to be a powerful tool to describe a system surrounded by a thermal environment. It has been also generalized further to treat a nonstationary environment, in which the conventional fluctuation-dissipation theorem no longer holds. Then, within the framework of the Langevin equation we present a method recently developed to extract a new reaction coordinate that is decoupled from all the other coordinates in the region of a rank-one saddle linking the reactant and the product. The reaction coordinate is buried in nonlinear couplings among the original coordinates under the influence of stochastic random force. It was ensured that the sign of this new reaction coordinate (= a nonlinear functional of the original coordinates, velocities, friction, and random force) at any instant is sufficient to determine in which region, the reactant or the product, the system finally arrives. We also discuss how one can extend the method to extract such a coordinate from the GLE framework in stationary and nonstationary environments, where memory effects exist in dynamics of the reaction.