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PubMed2005

Kinetic theory of nucleation based on a first passage time analysis: improvement by the density-functional theory.

A recent kinetic theory of nucleation [see, e.g., E. Ruckenstein and B. Nowakowski, J. Colloid Interface Sci. 137, 583 (1990)] is based on molecular interactions and avoids the traditional thermodynamics. The rate of emission of molecules from a cluster is found via a first passage time analysis. This time is calculated by solving the single-molecule master equation for the probability distribution function of a surface molecule located in the potential field created by the cluster. The liquid cluster was assumed to have sharp boundaries and uniform density. In the present paper, this assumption is removed by using the density-functional theory to find the density profiles. Thus, more accurate calculations of the potential field created by the cluster, its emission rate, and nucleation rate are obtained. The modified theory is illustrated by numerical calculations for a molecular pair interaction potential combining the dispersive attraction with the hard-sphere repulsion.

Journal Article↗
PubMed2006

Theoretical analysis of internal fluctuations and bistability in CO oxidation on nanoscale surfaces.

The bistable CO oxidation on a nanoscale surface is characterized by a limited number of reacting molecules on the catalytic area. Internal fluctuations due to finite-size effects are studied by the master equation with a Langmuir-Hinshelwood mechanism for CO oxidation. Analytical solutions can be found in a reduced one-component model after the adiabatic elimination of one variable which in our case is the oxygen coverage. It is shown that near the critical point, with decreasing surface area, one cannot distinguish between two macroscopically stable stationary states. This is a consequence of the large fluctuations in the coverage which occur on a fast time scale. Under these conditions, the transition times between the macroscopic states also are no longer separated from the short-time scale of the coverage fluctuations as is the case for large surface areas and far away from the critical point. The corresponding stationary solutions of the probability distribution and the mean first passage times calculated in the reduced model are supported by numerics of the full two-component model.

Journal Article↗
PubMed2006

The influence of ultrafast laser pulses on electron transfer in molecular wires studied by a non-Markovian density-matrix approach.

New features of molecular wires can be observed when they are irradiated by laser fields. These effects can be achieved by periodically oscillating fields but also by short laser pulses. The theoretical foundation used for these investigations is a density-matrix formalism where the full system is partitioned into a relevant part and a thermal fermionic bath. The derivation of a quantum master equation, either based on a time-convolutionless or time-convolution projection-operator approach, incorporates the interaction with time-dependent laser fields nonperturbatively and is valid at low temperatures for weak system-bath coupling. From the population dynamics the electrical current through the molecular wire is determined. This theory including further extensions is used for the determination of electron transport through molecular wires. As examples, we show computations of coherent destruction of tunneling in asymmetric periodically driven quantum systems, alternating currents and the suppression of the directed current by using a short laser pulse.

Journal Article↗
PubMed2006

Grand canonical Markov model: a stochastic theory for open nonequilibrium biochemical networks.

In this paper we present the results of a stochastic model of reversible biochemical reaction networks that are being driven through an open boundary, such that the system is interacting with its surrounding environment with explicit material exchange. The stochastic model is based on the master equation approach and is intimately related to the grand canonical ensemble of statistical mechanics. We show that it is possible to analytically calculate the joint probability function of the random variables describing the number of molecules in each state of the system for general linear networks. Definitions of reaction chemical potentials and conductances follow from inherent properties of this model, providing a description of energy dissipation in the system. We are also able to suggest novel methods for experimentally determining reaction fluxes and biochemical affinities at nonequilibrium steady state as well as the overall network connectivity.

Algorithms↗
PubMed2006

Amplification of molecular traffic control in catalytic grains with novel channel topology design.

We investigate the conditions for reactivity enhancement of catalytic processes in porous solids by the use of molecular traffic control (MTC). With dynamic Monte-Carlo simulations and continuous-time master equation theory applied to the high concentration regime, we obtain a quantitative description of the MTC effect for a network of intersecting single-file channels in a wide range of grain parameters and for optimal external operating conditions. Implementing the concept of MTC in models with specially designed alternating bimodal channels, we find the efficiency ratio (compared with a topologically and structurally similar reference system without MTC) to be enhanced with increasing grain diameter, a property verified for the first time for a MTC system. Even for short intersection channels, MTC leads to a reactivity enhancement of up to approximately 65%. This suggests that MTC may significantly enhance the efficiency of a catalytic process for small as well as large porous particles with a suitably chosen binary channel topology.

Journal Article↗
PubMed2006

Relaxation dynamics and structural isomerism in Nb10 and Nb10+.

The structure, energetics, and interconversion of isomers of Nb10 and Nb10+ are studied using density functional theory with Gaussian basis sets, using guess structures derived from basin-hopping simulations with the Finnis-Sinclair [Philos. Mag. A 50, 45 (1984)] potential. These results are used as input to a master equation approach to model the relaxation of these clusters. Ionization potentials are calculated for all relevant minima, as are the infrared spectra. On the basis of these data, and known experimental results, plausible explanations are given for the biexponential reaction kinetics observed for Nb10 and Nb10+ with respect to small molecule adsorbates. In principle, this approach could be extended to investigate any midsized transition metal cluster that exhibits structural isomerism.

Journal Article↗
PubMed2006

A kinetic approach to the theory of heterogeneous nucleation on soluble particles during the deliquescence stage.

Deliquescence is the dissolution of a solid nucleus in a liquid film formed on the nucleus due to vapor condensation. Previously, the kinetics of deliquescence was examined in the framework of the capillarity approximation which involves the thermodynamic interfacial tensions for a thin film and the approximation of uniform density therein. In the present paper we propose a kinetic approach to the theory of deliquescence which avoids the use of the above macroscopic quantities for thin films. The rates of emission of molecules from the liquid film into the vapor and from the solid core into the liquid film are determined through a first passage time analysis whereas the respective rates of absorption are calculated through the gas kinetic theory. The first passage time is obtained by solving the single-molecule master equation for the probability distribution of a "surface" molecule moving in a potential field created by the cluster. Furthermore, the time evolution of the liquid film around the solid core is described by means of two mass balance equations which involve the rates of absorption and emission of molecules by the film at its two interfaces. When the deliquescence of an ensemble of solid particles occurs by means of large fluctuations, the time evolution of the distribution of composite droplets (liquid film+solid core) with respect to the independent variables of state is governed by a Fokker-Planck kinetic equation. When both the vapor and the solid soluble particles are single component, this equation has the form of the kinetic equation of binary nucleation. A steady-state solution for this equation is obtained by the method of separation of variables. The theory is illustrated with numerical calculation regarding the deliquescence of spherical particles in a water vapor with intermolecular interactions of the Lennard-Jones kind. The new approach allows one to qualitatively explain an important feature of experimental data on deliquescence, namely the occurrence of nonsharp deliquescence, a feature that the previous deliquescence theory based on classical thermodynamics could not account for.

Journal Article↗
PubMed2006

Statistics of subthreshold neuronal voltage fluctuations due to conductance-based synaptic shot noise.

Neurons in the central nervous system, and in the cortex in particular, are subject to a barrage of pulses from their presynaptic populations. These synaptic pulses are mediated by conductance changes and therefore lead to increases or decreases of the neuronal membrane potential with amplitudes that are dependent on the voltage: synaptic noise is multiplicative. The statistics of the membrane potential are of experimental interest because the measurement of a single subthreshold voltage can be used to probe the activity occurring across the presynaptic population. Though the interpulse interval is not always significantly smaller than the characteristic decay time of the pulses, and so the fluctuations have the nature of shot noise, the majority of results available in the literature have been calculated in the diffusion limit, which is valid for high-rate pulses. Here the effects that multiplicative conductance noise and shot noise have on the voltage fluctuations are examined. It is shown that both these aspects of synaptic drive sculpt high-order features of the subthreshold voltage distribution, such as the skew. It is further shown that the diffusion approximation can only capture the effects arising from the multiplicative conductance noise, predicting a negative voltage skew for excitatory drive. Exact results for the full dynamics are derived from a master-equation approach, predicting positively skewed distributions with long tails in voltage ranges typical for action potential generation. It is argued that, although the skew is a high-order feature of subthreshold voltage distributions, the increased probability of reaching firing threshold suggests a potential role for shot noise in shaping the neuronal transfer function.

Action Potentials↗
PubMed2006

Rotranslational state-to-state rates and spectral representation of inelastic collisions in low-temperature molecular hydrogen.

Inelastic collisions in natural H2 are studied from the experimental and theoretical points of view between 10 and 140 K. Rotational populations and number densities measured by Raman spectroscopy along supersonic expansions of H2 provide the link between experimental and theoretical rotranslational state-to-state rate coefficients of H2 in the vibrational ground state. These rates are calculated in the close-scattering approach with the MOLSCAT code employing a recent ab initio H2-H2 potential. The calculated rates are assessed by means of a master equation describing the time evolution of the experimental rotational populations. The feasibility for obtaining the rates on the sole basis of the experiment is discussed. The dominant processes j(1)j(2)-->j'(1)j'(2) in the investigated thermal range are found to be 21-->01 >30-->12 >31-->11, proving the importance of double processes such as 30-->12. Good agreement is found between theory and experiment, as well as with earlier ultrasonic measurements of relaxation times. A spectral representation is proposed in order to visualize quantitatively the collisional contributions in any nonequilibrium time evolving process.

Journal Article↗
PubMed2006

An ignored but most favorable channel for NCO+C2H2 reaction.

The NCO+C(2)H(2) reaction has been considered as a prototype for understanding the chemical reactivity of the isocyanate radical towards unsaturated hydrocarbons in fuel-rich combustion. It has also been proposed to provide an effective route for formation of oxazole-containing compounds in organic synthesis, and might have potential applications in interstellar processes. Unfortunately, this reaction has met mechanistic controversy both between experiments and between experiments and theoretical calculations. In this paper, detailed theoretical investigations at the Becke's three parameter Lee-Yang-Parr-B3LYP6-31G(d), B3LYP6-311++G(d,p), quadratic configuration interaction with single and double excitations QCISD6-31G(d), and Gaussian-3 levels are performed for the NCO+C(2)H(2) reaction, covering various entrance, isomerization, and decomposition channels. Also, the highly cost-expensive coupled-cluster theory including single and double excitations and perturbative inclusion of triple excitations CCSD(T)/aug-cc-pVTZ single-point energy calculation is performed for the geometries obtained at the Becke's three parameter Lee-Yang-Parr-B3LYP6-311++G(d,p) level. A previously ignored yet most favorable channel via a four-membered ring intermediate with allyl radical character is found. However, formation of P(3) H+HCCNCO and the five-membered ring channel predicted by previous experimental and theoretical studies is kinetically much less competitive. With the new channel, master equation rate constant calculations over a wide range of temperatures (298-1500 K) and pressures (10-560 Torr) show that the predicted total rate constants exhibit a positive-temperature dependence and no distinct pressure dependence effect. This is in qualitative agreement with available experimental results. Under the experimental conditions, the predicted values are about 50% lower than the latest experimental results. Also, the branching ratio variations of the fragments P(2) HCN+HCCO and P(5) OCCHCN+H as well as the intermediates L1 HCHCNCO, r4 cCHCHNC-O, and L5 NCHCHCO are discussed with respect to the temperature and pressure. Future experimental reinvestigations are strongly desired to test the newly predicted channel for the model NCO+C(2)H(2) reaction. Implications of the present results in various fields are discussed.

Journal Article↗
PubMed1992

Interurban migration and the dynamics of a system of cities: 1. The stochastic framework with an application to the French urban system.

"A stochastic framework for the modelling of interurban migration is presented. The model is an extension of a recently developed master-equation approach to interregional migration. The population dynamics of the French urban system, described by a set of 78 cities, is investigated within the period 1954-82. The importance of synergy effects (self-reinforcing collective effects) as well as socioeconomic macrovariables for the understanding of urban dynamics becomes obvious. A forecasting of urban dynamics...[up to the year 2002 confirms] this result and [gives] further insight into the nested structure of urban systems."

Demography↗
PubMed2004

Stability and dynamics of crystals and glasses of motorized particles.

Many of the large structures of the cell, such as the cytoskeleton, are assembled and maintained far from equilibrium. We study the stabilities of various structures for a simple model of such a far-from-equilibrium organized assembly in which spherical particles move under the influence of attached motors. From the variational solutions of the many-body master equation for Brownian motion with motorized kicking we obtain a closed equation for the order parameter of localization. Thus, we obtain the transition criterion for localization and stability limits for the crystalline phase and frozen amorphous structures of motorized particles. The theory also allows an estimate of nonequilibrium effective temperatures characterizing the response and fluctuations of motorized asemblies.

Chemical Phenomena↗
PubMed2005

Delay-induced stochastic oscillations in gene regulation.

The small number of reactant molecules involved in gene regulation can lead to significant fluctuations in intracellular mRNA and protein concentrations, and there have been numerous recent studies devoted to the consequences of such noise at the regulatory level. Theoretical and computational work on stochastic gene expression has tended to focus on instantaneous transcriptional and translational events, whereas the role of realistic delay times in these stochastic processes has received little attention. Here, we explore the combined effects of time delay and intrinsic noise on gene regulation. Beginning with a set of biochemical reactions, some of which are delayed, we deduce a truncated master equation for the reactive system and derive an analytical expression for the correlation function and power spectrum. We develop a generalized Gillespie algorithm that accounts for the non-Markovian properties of random biochemical events with delay and compare our analytical findings with simulations. We show how time delay in gene expression can cause a system to be oscillatory even when its deterministic counterpart exhibits no oscillations. We demonstrate how such delay-induced instabilities can compromise the ability of a negative feedback loop to reduce the deleterious effects of noise. Given the prevalence of negative feedback in gene regulation, our findings may lead to new insights related to expression variability at the whole-genome scale.

Algorithms↗
PubMed2000

Stochastic focusing: fluctuation-enhanced sensitivity of intracellular regulation.

Many regulatory molecules are present in low copy numbers per cell so that significant random fluctuations emerge spontaneously. Because cell viability depends on precise regulation of key events, such signal noise has been thought to impose a threat that cells must carefully eliminate. However, the precision of control is also greatly affected by the regulatory mechanisms' capacity for sensitivity amplification. Here we show that even if signal noise reduces the capacity for sensitivity amplification of threshold mechanisms, the effect on realistic regulatory kinetics can be the opposite: stochastic focusing (SF). SF particularly exploits tails of probability distributions and can be formulated as conventional multistep sensitivity amplification where signal noise provides the degrees of freedom. When signal fluctuations are sufficiently rapid, effects of time correlations in signal-dependent rates are negligible and SF works just like conventional sensitivity amplification. This means that, quite counterintuitively, signal noise can reduce the uncertainty in regulated processes. SF is exemplified by standard hyperbolic inhibition, and all probability distributions for signal noise are first derived from underlying chemical master equations. The negative binomial is suggested as a paradigmatic distribution for intracellular kinetics, applicable to stochastic gene expression as well as simple systems with Michaelis-Menten degradation or positive feedback. SF resembles stochastic resonance in that noise facilitates signal detection in nonlinear systems, but stochastic resonance is related to how noise in threshold systems allows for detection of subthreshold signals and SF describes how fluctuations can make a gradual response mechanism work more like a threshold mechanism.

Animals↗
PubMed2000

Dynamical principles in biological processes: a model of charge migration in proteins and DNA.

The generalized master equations (GMEs) that contain multiple time scales have been derived quantum mechanically. The GME method has then been applied to a model of charge migration in proteins that invokes the hole hopping between local amino acid sites driven by the torsional motions of the floppy backbones. This model is then applied to analyze the experimental results for sequence-dependent long-range hole transport in DNA reported by Meggers et al. [Meggers, E., Michel-Beyerle, M. E., & Giese, B. (1998) J. Am. Chem. Soc. 120, 12950-12955]. The model has also been applied to analyze the experimental results of femtosecond dynamics of DNA-mediated electron transfer reported by Zewail and co-workers [Wan, C., Fiebig, T., Kelley, S. O., Treadway, C. R., Barton, J. K. & Zewail, A. H. (1999) Proc. Natl. Acad. Sci. USA 96, 6014-6019]. The initial events in the dynamics of protein folding have begun to attract attention. The GME obtained in this paper will be applicable to this problem.

Base Sequence↗
PubMed1972

Dynamics of fluorescence polarization in macromolecules.

Reexamination of the theory of fluorescence time dependence owing to rotational diffusion of rigid macromolecules reveals deficiencies or hidden restrictions in each of the previous treatments. The correct master equation has five exponential decay terms, with preexponential factors that depend upon the diffusion constants and, in a completely symmetrical fashion, upon the orientations of absorbing and emitting dipoles.

Diffusion↗
PubMed1981

On the density matrix approach of intramolecular relaxation processes.

In this paper we derive the generalized master equations for the S(1) system coupled with the S(2) system, with the S(1) and S(2) systems embedded in a heat bath. This formalism can be applied to a number of problems like vibrational redistribution, dynamic effect of vibrational relaxation on electronic relaxation in condensed media, etc. In this paper the importance of the memory function associated with a relaxation process is emphasized.

Journal Article↗
PubMed1985

Anomalous properties of a simple small-volume membrane transport system at steady state.

We investigate the transport of a single ligand L, between two macroscopic baths with different concentrations of L, by a simple membrane system. The center of this system is a very small volume V that might contain N = 0, 1, 2,... molecules of L. Access to V from either bath is by means of a single binding site for L. The steady-state properties of this simple system are studied exactly by a discrete-N master-equation approach. It is found that the mean concentration of L in V, c = N/V, is not a significant quantity either kinetically or thermodynamically. Further, the chemical potential of L in V is not defined and hence the overall thermodynamic force on L between the two baths cannot be subdivided at V. In fact, because V is small, the transport system must be treated as an indivisible system with interdependent parts. In the limit when V and N are very large, V becomes in effect a third macroscopic bath and two well-defined transport subsystems emerge (between V and either bath).

Journal Article↗