Mechanism-based chemical understanding of chiral symmetry breaking in the Soai reaction. A combined probabilistic and deterministic description of chemical reactions

The experimentally observed distribution of enantiomers in the Soai reaction is interpreted in this Article on the basis of a chemical mechanism using a newly developed stochastic kinetic method, accelerated Monte Carlo simulation combined with deterministic continuation and symmetrization. The method is in principle suitable for handling large mechanisms with realistic particle numbers and could be useful for any case where the kinetics of a process shows inherent random fluctuations. The mechanism shows how a slow initial reaction combined with efficient and highly enantioselective autocatalysis can give rise to chiral symmetry breaking under completely nonchiral external conditions.     

Simple model for transport phenomena: microscopic construction of Maxwell demonlike engine

We present a microscopic Hamiltonian framework to develop Maxwell demonlike engine. Our model consists of an equilibrium thermal bath and a nonequilibrium bath, latter generated by driving with an external stationary, Gaussian noise. The engine we develop can be considered as a device to extract work by modifying internal fluctuations. Our theoretical analysis focuses on finding the essential ingredients necessary for generating fluctuation induced transport under nonequilibrium condition. An important outcome of our model is that the net motion occurs when the nonlinear bath is modulated by the external noise, creating the nonzero effective temperature even when the temperature of both the baths are the same.     

Signal transduction in a coupled hormone system: selective explicit internal signal stochastic resonance and its control

Cooperative interactions of signal transduction and environmental noise are investigated with a coupled hormone system, in which selective explicit internal signal stochastic resonance (EISSR) is observed. More specifically, the large peak of a period-2 oscillation (i.e., a strong signal) is greatly amplified by the environmental noise while the small peak (i.e., a weak signal) does not exhibit cooperative interactions with noise. The EISSR phenomenon could be controlled by adjusting the frequency or amplitude of an external signal and a critical amplitude for external signal is found. Significantly, the maximal signal-to-noise ratio increases almost linearly with the increment of control parameter, despite that the magnitude of the large peak is decreased. In addition, the noise does not alter the fundamental frequencies of the strong signal and the weak signal, which implicates that the system can keep its intrinsic oscillatory state and resist the effect of environmental fluctuations.     

Fluctuating lattice-Boltzmann model for complex fluids

We develop and test numerically a lattice-Boltzmann (LB) model for nonideal fluids that incorporates thermal fluctuations. The fluid model is a momentum-conserving thermostat, for which we demonstrate how the temperature can be made equal at all length scales present in the system by having noise both locally in the stress tensor and by shaking the whole system in accord with the local temperature. The validity of the model is extended to a broad range of sound velocities. Our model features a consistent coupling scheme between the fluid and solid molecular dynamics objects, allowing us to use the LB fluid as a heat bath for solutes evolving in time without external Langevin noise added to the solute. This property expands the applicability of LB models to dense, strongly correlated systems with thermal fluctuations and potentially nonideal equations of state. Tests on the fluid itself and on static and dynamic properties of a coarse-grained polymer chain under strong hydrodynamic interactions are used to benchmark the model. The model produces results for single-chain diffusion that are in quantitative agreement with theory.     

Stochastic resonance in circadian rhythms

The effect of fluctuations in the two-variable discrete delay model proposed earlier by us [1] for the circadian rhythm of the fungal species Neurospora Crassa is studied. We have investigated the effect of parametric and additive noise in two different regimes namely, steady-state and Period-1 regimes. It is found that under the influence of noise coherent oscillations are generated in the steady-state. Oscillations are preserved and robust to a wide range of noise intensity in the Period-1 regime. The oscillations in both these regimes are always found to be close to the circadian period (21.5 h). Coherence resonance is observed when parametric or velocity additive noise is added near the Hopf bifurcation. Finally, the implications of fluctuations in circadian rhythms are discussed. This article is dedicated to Professor Karl Jug on the occassion of his sixtyfifth birthday.     

Reciprocating motion on the nanoscale

This paper analyzes the confined motion of a Brownian particle fluctuating between two conformational states with different potential profiles and different position-dependent rate constants of the transitions, the fluctuations arising from both thermal (equilibrium) and external (nonequilibrium) noise. The model illustrates a mechanism to transduce, on the nanoscale, the energy of nonequilibrium fluctuations into mechanical energy of reciprocating motion. Expressions for the reciprocating velocity and the efficiency of energy conversion are derived. These expressions are treated in more detail in the slow-fluctuation (quasi-equilibrium) regime, by simple perturbation theory arguments, and in the fast fluctuation limit, in terms of the potential of mean force. A notable observation is that the generalized driving force of the reciprocating motion is caused by two sources: the energy contribution due to the difference between the potential profiles of the states and the entropic contribution due to the difference between the position-dependent rate constants. Two illustrative examples are presented, where one of the two sources can be ignored and an exact solution is allowed. Among other aspects, we also discuss the ways to construct a molecular motor based on the reciprocating engine.     

Equilibrium density fluctuations and the rate of a Langmuir-Hinshelwood type reaction on microcrystal particles

We investigate the effect of restricting the area of planes of microcrystals and equilibrium density fluctuations in components of binary mixtures on partial isotherms of the adsorption of binary mixtures of molecules and the rate of a surface reaction of the Langmuir-Hinshelwood type. Adsorption of components of mixture is considered in a large canonical assembly, and the rate of an elementary step is calculated in kinetic regime. The value of a section of the surface on a plane contains a number of adsorption centers in the range of 10 to 10⁵. The effect of the structure of a heterogeneous surface on the rate of the considered reaction is studied. The effect of the density fluctuations of adsorbed molecules on partial adsorption isotherms and fluctuations in the rate of reaction on heterogeneous surfaces is discussed. It is shown that the greatest effect of density fluctuations on the rate of a step is observed at low fillings of each plane of a particle and at the almost complete filling of a plane.     

Internal noise stochastic resonance in CO oxidation on nm-sized palladium particles

The constructive roles of noise and disorder in nonlinear system have been extensively studied in the last two decades. Among them the most well known phenomenon is stochastic resonance[1], which demon-strates that noise can help a nonlinear system to det…     

Electrochemical control of bifurcation points for stochastic resonance in a model of the photosensitive belousov‐zhabotinsky reaction

We present a model of the Belousov‐Zhabotinsky reaction with external controls. The Oregonator model is modified to include three different control parameters, i.e., flow rate, light intensity, and electric current. Applying cathodic or anodic current shifts bifurcation points in an opposite direction in a two‐parameter space spanned by light intensity and flow rate. This external control enables steady states to be sensitive to noise in the two‐parameter space. The use of shifting bifurcation points is discussed in relation with stochastic resonance.     

Enhancement of stochastic oscillations by colored noise or internal noise in NO reduction by CO on small platinum surfaces

In this paper, based on the stochastic model of NO reduction by CO on Pt crystal surfaces and taking Gaussian colored noise as external fluctuations of the NO partial pressure, we study the effect of the colored noise on the internal noise-induced stochastic oscillations (INSOs) and the effect of internal noise on the colored noise-induced stochastic oscillations (CNSOs). It is found that the INSO can be enhanced by the colored noise with appropriate correlation time or noise strength and, interestingly, the CNSO can be enhanced by the internal noise as well and, moreover, the enhanced CNSO can reach the best oscillatory states repetitively via proper internal noises. This effect of the internal noise is different from its effect on the stochastic oscillations induced by the external Gaussian white noise, which probably results from the interaction of the correlated colored noise and the internal noise.     

Intermittent single-molecule interfacial electron transfer dynamics

We report on single-molecule studies of photosensitized interfacial electron transfer (ET) processes in Coumarin 343 (C343)-TiO(2) nanoparticles (NP) and Cresyl Violet (CV(+))-TiO(2) NP systems, using time-correlated single-photon counting coupled with scanning confocal fluorescence microscopy. Fluorescence intensity trajectories of individual dye molecules adsorbed on a semiconductor NP surface showed fluorescence fluctuations and blinking, with time constants distributed from milliseconds to seconds. The fluorescence fluctuation dynamics were found to be inhomogeneous from molecule to molecule and from time to time, showing significant static and dynamic disorders in the interfacial ET reaction dynamics. We attribute fluorescence fluctuations to the interfacial ET reaction rate fluctuations, associating redox reactivity intermittency with the fluctuations of molecule-TiO(2) electronic and Franck-Condon coupling. Intermittent interfacial ET dynamics of individual molecules could be characteristic of a surface chemical reaction strongly involved with and regulated by molecule-surface interactions. The intermittent interfacial reaction dynamics that likely occur among single molecules in other interfacial and surface chemical processes can typically be observed by single-molecule studies but not by conventional ensemble-averaged experiments.     

Complex chemical kinetics in single enzyme molecules: Kramers's model with fractional Gaussian noise

A model of barrier crossing dynamics governed by fractional Gaussian noise and the generalized Langevin equation is used to study the reaction kinetics of single enzymes subject to conformational fluctuations. The direct application of Kramers's flux-over-population method to this model yields analytic expressions for the time-dependent transmission coefficient and the distribution of waiting times for barrier crossing. These expressions are found to reproduce the observed trends in recent simulations and experiments.     

Modulation of electron transfer kinetics by protein conformational fluctuations during early-stage photosynthesis

The kinetics of electron transfer during the early stages of the photosynthetic reaction cycle has recently been shown in transient absorption experiments carried out by Wang et al. [Science 316, 747 (2007)] to be strongly influenced by fluctuations in the conformation of the surrounding protein. A model of electron transfer rates in polar solvents developed by Sumi and Marcus using a reaction-diffusion formalism [J. Chem. Phys. 84, 4894 (1986)] was found to be successful in fitting the experimental absorption curves over a roughly 200 ps time interval. The fits were achieved using an empirically determined time-dependent function that described protein conformational relaxation. In the present paper, a microscopic model of this function is suggested, and it is shown that the function can be identified with the dynamic autocorrelation function of intersegment distance fluctuations that occur in a harmonic potential of mean force under the action of fractional Gaussian noise.     

受迫薛罗格双匣化学反应模型的随机共振

In order to theoretically disclose the linear and nonlinear responses of the Gaussian white noise driven Schrodinger Model of Two Boxes in chemical reaction to a weak periodic perturbation, the rate equation method is used to derive the analytical expression of linear and nonlinear susceptibilities and the signal-to noise ratio according to quadrustable or bistable adiabatic approximations with in different parameter ranges.The analytically approximate result is also compared with that from numerical simulation. For the parameters under concern, the qualitative agreement is observed between the analytic and the numerical first order resonant structures when the noise intensity is not in zero limit. Moreover, the analytic results show that the resonant behavior can occur only in the odd-order harmonic of the model, but the numerical simulation also shows the second-order harmonic resonance, which might be induced by the finite frequency truncations on the Gaussian white noiseor by the indistinguish ability between high-order harmonics and background noise.     

Green's-function reaction dynamics: a particle-based approach for simulating biochemical networks in time and space

We have developed a new numerical technique, called Green's-function reaction dynamics (GFRD), that makes it possible to simulate biochemical networks at the particle level and in both time and space. In this scheme, a maximum time step is chosen such that only single particles or pairs of particles have to be considered. For these particles, the Smoluchowski equation can be solved analytically using Green's functions. The main idea of GFRD is to exploit the exact solution of the Smoluchoswki equation to set up an event-driven algorithm, which combines in one step the propagation of the particles in space with the reactions between them. The event-driven nature allows GFRD to make large jumps in time and space when the particles are far apart from each other. Here, we apply the technique to a simple model of gene expression. The simulations reveal that spatial fluctuations can be a major source of noise in biochemical networks. The calculations also show that GFRD is highly efficient. Under biologically relevant conditions, GFRD is up to five orders of magnitude faster than conventional particle-based techniques for simulating biochemical networks in time and space. GFRD is not limited to biochemical networks. It can also be applied to a large number of other reaction-diffusion problems.     

Spin dynamics of the radical pair in a low magnetic field studied by the transient absorption detected magnetic field effect on the reaction yield and switched external magnetic field

The spin dynamics of the radical pair generated from the photocleavage reaction of (2,4,6-trimethylbenzoyl)diphenylphosphine oxide (TMDPO) in micellar solutions was studied by the time-resolved magnetic field effect (MFE) on the transient absorption (TA) and by a novel technique, absorption detected switched external magnetic field (AD-SEMF). Thanks to the large hyperfine coupling constant (A = 38 mT), a characteristic negative MFE on the radical yield was observed at a magnetic field lower than 60 mT whereas a positive effect due to the conventional hyperfine (HFM) and relaxation mechanisms (RM) was observed at higher magnetic field. The negative effect can be assigned to the mechanism "so-called" low field effect (LFE) mechanism and has been analyzed thoroughly using a model calculation incorporating a fast spin dephasing process. The time scale of the spin mixing process of LFE studied by AD-SEMF is shorter than the lifetime of the recombination kinetics of the radical pair. These results indicate that the LFE originates from the coherent spin motion. This can be interfered from the fast spin dephasing caused by electron spin interaction fluctuations.     

Pt(110)面上CO催化反应速率振荡过程中的相干共振研究:内外涨落的相互作用

Effects of noise on rate oscillations during CO oxidation on Pt(110) surface were investigated, both theo-retically and numerically, by focusing on the interplay of internal noise (IN) due to stochasticity in reaction events, and external noise (EN) resulting from parameter perturbation. The surface is divided into cells of variable size which are assumed to be well mixed, and we consider the behavior inside a single cell. At-tention is paid to parameter regions subthreshold of the deterministic Hopf bifurcation, where noise can induce stochastic oscillations, the signal-to-noise ratio (SNR) of which shows a maximum with the variation of noise intensity, known as coherent resonance (CR). By stochastic normal theory, we show that IN and EN contribute in a weighted additive way to an effective noise that lead to CR, such that SNR shows a ridge shape in the D-1/N plane, where D and 1/N measures the strength of EN and IN, respectively. It is shown that for too large IN (EN), CR behavior with EN (IN) no longer exists. Numerical simulations show good agreements with the theoretical results