Kinetic energy decomposition scheme based on information theory

We proposed a novel kinetic energy decomposition analysis based on information theory. Since the Hirshfeld partitioning for electron densities can be formulated in terms of Kullback–Leibler information deficiency in information theory, a similar partitioning for kinetic energy densities was newly proposed. The numerical assessments confirm that the current kinetic energy decomposition scheme provides reasonable chemical pictures for ionic and covalent molecules, and can also estimate atomic energies using a correction with viral ratios.     

A constant-time kinetic Monte Carlo algorithm for simulation of large biochemical reaction networks

The time evolution of species concentrations in biochemical reaction networks is often modeled using the stochastic simulation algorithm (SSA) [Gillespie, J. Phys. Chem. 81, 2340 (1977)]. The computational cost of the original SSA scaled linearly with the number of reactions in the network. Gibson and Bruck developed a logarithmic scaling version of the SSA which uses a priority queue or binary tree for more efficient reaction selection [Gibson and Bruck, J. Phys. Chem. A 104, 1876 (2000)]. More generally, this problem is one of dynamic discrete random variate generation which finds many uses in kinetic Monte Carlo and discrete event simulation. We present here a constant-time algorithm, whose cost is independent of the number of reactions, enabled by a slightly more complex underlying data structure. While applicable to kinetic Monte Carlo simulations in general, we describe the algorithm in the context of biochemical simulations and demonstrate its competitive performance on small- and medium-size networks, as well as its superior constant-time performance on very large networks, which are becoming necessary to represent the increasing complexity of biochemical data for pathways that mediate cell function.     

Steady-state parameter sensitivity in stochastic modeling via trajectory reweighting

Parameter sensitivity analysis is a powerful tool in the building and analysis of biochemical network models. For stochastic simulations, parameter sensitivity analysis can be computationally expensive, requiring multiple simulations for perturbed values of the parameters. Here, we use trajectory reweighting to derive a method for computing sensitivity coefficients in stochastic simulations without explicitly perturbing the parameter values, avoiding the need for repeated simulations. The method allows the simultaneous computation of multiple sensitivity coefficients. Our approach recovers results originally obtained by application of the Girsanov measure transform in the general theory of stochastic processes [A. Plyasunov and A. P. Arkin, J. Comput. Phys. 221, 724 (2007)]. We build on these results to show how the method can be used to compute steady-state sensitivity coefficients from a single simulation run, and we present various efficiency improvements. For models of biochemical signaling networks, the method has a particularly simple implementation. We demonstrate its application to a signaling network showing stochastic focussing and to a bistable genetic switch, and present exact results for models with linear propensity functions.     

A data-integrated method for analyzing stochastic biochemical networks

Variability and fluctuations among genetically identical cells under uniform experimental conditions stem from the stochastic nature of biochemical reactions. Understanding network function for endogenous biological systems or designing robust synthetic genetic circuits requires accounting for and analyzing this variability. Stochasticity in biological networks is usually represented using a continuous-time discrete-state Markov formalism, where the chemical master equation (CME) and its kinetic Monte Carlo equivalent, the stochastic simulation algorithm (SSA), are used. These two representations are computationally intractable for many realistic biological problems. Fitting parameters in the context of these stochastic models is particularly challenging and has not been accomplished for any but very simple systems. In this work, we propose that moment equations derived from the CME, when treated appropriately in terms of higher order moment contributions, represent a computationally efficient framework for estimating the kinetic rate constants of stochastic network models and subsequent analysis of their dynamics. To do so, we present a practical data-derived moment closure method for these equations. In contrast to previous work, this method does not rely on any assumptions about the shape of the stochastic distributions or a functional relationship among their moments. We use this method to analyze a stochastic model of a biological oscillator and demonstrate its accuracy through excellent agreement with CME/SSA calculations. By coupling this moment-closure method with a parameter search procedure, we further demonstrate how a model's kinetic parameters can be iteratively determined in order to fit measured distribution data.     

Petri Net Based Metabolic Network Parameters Fitting with GPU Acceleration

Classical Petri net has been applied into biological analysis, especially as a qualitative model for biochemical pathways analysis, but lack of the ability for quantitative kinetic simulations. In our study, we presented an integration work of the qualitative model–Petri nets with the quantitative approach‐ordinary differential equations (ODEs) for the modeling and analysis of metabolic networks. As an application of our study, the computational modeling of arachidonic acid (AA) biochemical network was provided. A Petri net was set up to present the constraint‐based dynamic simulations on AA metabolic network combined with the validated ODEs model. Furthermore, Graphics Processing Unit (GPU) was adopted to accelerate the calculation of kinetic parameters unavailable from experiments. Our results have indicated that the proposed simulation method was practicable and useful with GPU acceleration, and provides new clues for the large‐scale qualitative and quantitative models of biochemical networks.     

Coarse master equation from Bayesian analysis of replica molecular dynamics simulations

We use Bayesian inference to derive the rate coefficients of a coarse master equation from molecular dynamics simulations. Results from multiple short simulation trajectories are used to estimate propagators. A likelihood function constructed as a product of the propagators provides a posterior distribution of the free coefficients in the rate matrix determining the Markovian master equation. Extensions to non-Markovian dynamics are discussed, using the trajectory "paths" as observations. The Markovian approach is illustrated for the filling and emptying transitions of short carbon nanotubes dissolved in water. We show that accurate thermodynamic and kinetic properties, such as free energy surfaces and kinetic rate coefficients, can be computed from coarse master equations obtained through Bayesian inference.     

Effects of diffusion on long-range electron transfer

The competition between diffusive hops and direct tunneling of solvated electrons to scavenger molecules in solid classes has been discussed in the literature. We have considered these two reaction paths in terms of stationary kinetic diffusion equations and multiphonon electron-transfer rate theory, and for coupling of the solvated electron to a broad continuum of nuclear modes. Diffusion can only be expected to be important for less polar glasses.     

Effect of the surface-stimulated mode on the kinetics of homogeneous crystal nucleation in droplets

The thermodynamics of surface-stimulated crystal nucleation demonstrates that if at least one of the facets of the crystal is only partially wettable by its melt, then it is thermodynamically more favorable for the nucleus to form with that facet at the droplet surface rather than within the droplet. So far, however, the kinetic aspects of this phenomenon had not been studied at all. In the present paper, a kinetic theory of homogenous crystal nucleation in unary droplets is proposed by taking into account that a crystal nucleus can form not only in the volume-based mode (with all its facets within the droplet) but also in the surface-stimulated one (with one of its facets at the droplet surface). The theory advocates that even in the surface-stimulated mode crystal nuclei initially emerge (as subcritical clusters) homogeneously in the subsurface layer, not "pseudo-heterogeneously" at the surface. A homogeneously emerged subcritical crystal can become a surface-stimulated nucleus due to density and structure fluctuations. This effect contributes to the total rate of crystal nucleation (as the volume-based mode does). An explicit expression for the total per-particle rate of crystal nucleation is derived. Numerical evaluations for water droplets suggest that the surface-stimulated mode can significantly enhance the per-particle rate of crystal nucleation in droplets as large as 10 microm in radius. Possible experimental verification of the proposed theory is discussed.     

Thermal shrinkage of oriented semicrystalline poly(ethylene terephthalate)

The shrinkage of commercial oriented poly(ethylene terephthalate) filaments was studied within the framework of the kinetic theory of rubberlike elasticity. Previous workers had found that the shrinkage and optical behavior of amorphous polymers could be satisfactorily explained in terms of this theory. Such an analysis is now applied to semicrystalline samples of moderate and high draw ratios (from 2× to 6×). It was found in this work that the thermal shrinkage force behavior as well as the optical anisotropy as a function of stretch can be explained in terms of the theory of rubberlike elasticity, if the following reasonable assumption is made: the average number of statistical segments per network chain in the noncrosslinked sample increases as a function of the draw ratio. A possible mechanism for such behavior is the relaxation of some of the chain entaglements due to the strain imposed externally on the fiber.     

Role of cooperativity in protein folding and protein mosaic assemblage relevance for protein conformational diseases

Biological systems are organized in intricate and highly structured networks with hierarchies and multiple scales. Cells can be considered as "meso-scale level" systems placed between the "macro-scale level" (systems of cellular networks) and the "micro-scale level" (systems of molecular networks). In fact, cells represent complex biochemical machineries made by networks of molecules connected by biochemical reactions. Thus, the brain should be studied as a system of "networks of networks". Recently, the existence of a Global Molecular Network (GMN) enmeshing the entire CNS was proposed. This proposal is based on the evidence that the extra-cellular matrix is a dynamic molecular structure capable of storing and releasing signals and of interacting with receptors and proteins on the cell membranes. Proteins have a special role in molecular networks since they can be assembled into high-order molecular complexes, which have been defined as Protein Mosaics (PM). Protein monomers in a PM (the "tesserae" of the mosaic) can interact via classical and non-classical cooperativity behaviour involving allosteric interactions. In the present paper, new features of allostery and cooperativity for protein folding, assemblage and topological features of PM will be discussed. Against this background, alterations in PM via allosteric modulations and non-classical cooperativity mechanisms may lead to protein aggregates like beta amyloid fibrils. Such aggregates cause pathological changes in the GMN structure and function leading to neurodegenerative diseases such as Alzheimer's disease. Thus, a novel view of the so called Protein Conformational Diseases (PCD) is proposed.     

Eliminating fast reactions in stochastic simulations of biochemical networks: a bistable genetic switch

In many stochastic simulations of biochemical reaction networks, it is desirable to "coarse grain" the reaction set, removing fast reactions while retaining the correct system dynamics. Various coarse-graining methods have been proposed, but it remains unclear which methods are reliable and which reactions can safely be eliminated. We address these issues for a model gene regulatory network that is particularly sensitive to dynamical fluctuations: a bistable genetic switch. We remove protein-DNA and/or protein-protein association-dissociation reactions from the reaction set using various coarse-graining strategies. We determine the effects on the steady-state probability distribution function and on the rate of fluctuation-driven switch flipping transitions. We find that protein-protein interactions may be safely eliminated from the reaction set, but protein-DNA interactions may not. We also find that it is important to use the chemical master equation rather than macroscopic rate equations to compute effective propensity functions for the coarse-grained reactions.     

Fluorescence quenching by reversible excimer formation: Kinetics and yield predictions for a classical potential association-dissociation model

Fluorescence quenching by reversible excimer formation is studied on the assumption that excimer formation and dissociation can be modelled as entering and leaving the attractive region of an monomer excited-monomer interaction potential by diffusion. To get some general insight in the kinetic consequences of such a type of modelling, the simple case of an attractive square-well potential is investigated. It is shown that three different kinetic regimes have to be distinguished: Two "reversible" ones in case of slow excimer radiative decay, in which the quenching kinetics can be formulated by Markovian or non-Markovian rate equations with both excimer formation and excimer dissociation terms, and an effectively "irreversible" regime if the excimer radiative decay is too rapid to allow the excimer equilibration. In the latter case a dissociation coefficient can no longer be defined and the quenching kinetics can only be predicted on the basis of generalized rate equations of a net-excimer-formation type. It is shown how the quenching constant formula must be generalized to be applicable in all kinetic situations.     

On the precision of quasi steady state assumptions in stochastic dynamics

Many biochemical networks have complex multidimensional dynamics and there is a long history of methods that have been used for dimensionality reduction for such reaction networks. Usually a deterministic mass action approach is used; however, in small volumes, there are significant fluctuations from the mean which the mass action approach cannot capture. In such cases stochastic simulation methods should be used. In this paper, we evaluate the applicability of one such dimensionality reduction method, the quasi-steady state approximation (QSSA) [L. Menten and M. Michaelis, "Die kinetik der invertinwirkung," Biochem. Z 49, 333369 (1913)] for dimensionality reduction in case of stochastic dynamics. First, the applicability of QSSA approach is evaluated for a canonical system of enzyme reactions. Application of QSSA to such a reaction system in a deterministic setting leads to Michaelis-Menten reduced kinetics which can be used to derive the equilibrium concentrations of the reaction species. In the case of stochastic simulations, however, the steady state is characterized by fluctuations around the mean equilibrium concentration. Our analysis shows that a QSSA based approach for dimensionality reduction captures well the mean of the distribution as obtained from a full dimensional simulation but fails to accurately capture the distribution around that mean. Moreover, the QSSA approximation is not unique. We have then extended the analysis to a simple bistable biochemical network model proposed to account for the stability of synaptic efficacies; the substrate of learning and memory [J. E. Lisman, "A mechanism of memory storage insensitive to molecular turnover: A bistable autophosphorylating kinase," Proc. Natl. Acad. Sci. U.S.A. 82, 3055-3057 (1985)]. Our analysis shows that a QSSA based dimensionality reduction method results in errors as big as two orders of magnitude in predicting the residence times in the two stable states.     

Nonempirical statistical theory for atomic evaporation from nonrigid clusters: applications to the absolute rate constant and kinetic energy release

A high energy atomic cluster undergoing frequent structural isomerization behaves like a liquid droplet, from which atoms or molecules can be emitted. Even after evaporation, the daughter cluster may still keep changing its structure. We study the dynamics of such an evaporation process of atomic evaporation. To do so, we develop a statistical rate theory for dissociation of highly nonrigid molecules and propose a simple method to calculate the absolute value of classical phase-space volume for a potential function that has many locally stable basins. The statistical prediction of the final distribution of the released kinetic energy is also developed. A direct application of the Rice-Ramsperger-Kassed-Marcus (RRKM) theory to this kind of multichannel chemical reaction is prohibitively difficult, unless further modeling and/or assumptions are made. We carry out a completely nonempirical statistical calculation for these dynamical quantities, in that nothing empirical is introduced like remodeling (or reparametrization) of artificial potential energy functions or recalibration of the phase-space volume referring to other "empirical" values such as those estimated with the molecular dynamics method. The so-called dividing surface is determined variationally, at which the flux is calculated in a consistent manner with the estimate of the phase-space volume in the initial state. Also, for the correct treatment of a highly nonrigid cluster, the phase-space volume and flux are estimated without the separation of vibrational and rotational motions. Both the microcanonical reaction rate and the final kinetic energy distribution thus obtained have quite accurately reproduced the corresponding quantities given by molecular dynamics calculations. This establishes the validity of the statistical arguments, which in turn brings about the deeper physical insight about the evaporation dynamics.     

Torsion in biochemical reaction networks

This article starts in Part I with a simple example of two biochemical reaction networks that are indistinguishable at the macroscopic level but are different at the molecular level and are shown to have significantly different kinetic properties. So, if one completely ignores the fact that reactions advance in discrete steps at the molecular level, then one can fail to distinguish between networks with widely different kinetics. In part II biochemical reaction networks are treated in a general way to discover what property of a network, only seen at the molecular level, affects its kinetics. It is shown that every such network has a unique torsion group which can be described numerically and readily determined by a programmable computation. If the group is found to be the singleton {0} (as is most often the case in practice), then the network is said to be torsion-free and its kinetic properties unaffected by ignoring its discrete character. A chemical reaction network has to be represented algebraically to calculate its torsion group. If the network is to be understood only at the macroscopic level, it can be placed in the context of real vector spaces, but to recognize its discrete character and its torsion group, each vector space is replaced by a discrete subset of that space, where each molecule can be recognized as a distinct and indivisible entity. Next, the process of calculating a torsion group is shown in several cases, including the example in part I. In this particular case it is shown to have the torsion group with 2 elements, reflecting the fact that the substrate molecules become product molecules 2 at a time, with the result that the overall macroscopic reaction is R ⇔ T, whereas at the molecular level it is 2R ⇔ 2T. In general, however, the torsion group of a biochemical reaction network can be any finite additive group, which is a property of the network that can only be seen at the molecular level. Finally, this fact is demonstrated by showing how to construct a hypothetical, but plausible, biochemical reaction network that has any given finite additive group as its torsion group.     

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 an anomalous increase of relaxation time and oscillatory decay of correlations. The 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.     

Detailed chemical kinetic modeling of cyclohexane oxidation

A detailed chemical kinetic mechanism has been developed and used to study the oxidation of cyclohexane at both low and high temperatures. Rules for reaction rate constants are developed for the low-temperature combustion of cyclohexane. These rules can be used for in chemical kinetic mechanisms for other cycloalkanes. Because cyclohexane produces only one type of cyclohexyl radical, much of the low-temperature chemistry of cyclohexane is described in terms of one potential energy diagram showing the reaction of cyclohexyl radical with O2 through five-, six-, and seven-membered-ring transition states. The direct elimination of cyclohexene and HO2 from RO2 is included in the treatment using a modified rate constant of Cavallotti et al. (Proc. Combust. Inst. 2007, 31, 201). Published and unpublished data from the Lille rapid compression machine, as well as jet-stirred reactor data, are used to validate the mechanism. The effect of heat loss is included in the simulations, an improvement on previous studies on cyclohexane. Calculations indicated that the production of 1,2-epoxycyclohexane observed in the experiments cannot be simulated according to the current understanding of low-temperature chemistry. Possible "alternative" H-atom isomerizations leading to different products from the parent O2QOOH radical were included in the low-temperature chemical kinetic mechanism and were found to play a significant role.     

Chromatographic characterization of molecularly imprinted polymers

Recent efforts in the investigation of chromatographic characterization of molecularly imprinted polymers (MIPs) have focused mainly on the nature of heterogeneous binding sites. More data on the thermodynamics than on the kinetic features of MIP columns have been published. The present article addresses the sources of peak broadening and tailing, which are the main drawbacks often associated with imprinted polymers in chromatography for practical applications. With use of the theory of nonlinear chromatography, the peak properties of a MIP column, including the retention and peak broadening and tailing, can be well interpreted. Efforts to improve chromatographic efficiency using MIPs prepared by approaches different from the conventional method, including covalent imprinting and the format of uniformly sized spherical microbeads, are reviewed and discussed. This review leads to the conclusion that nonlinear chromatography theory is useful for characterizing chromatographic features of MIP columns, since a MIP is essentially an affinity-based chromatographic stationary phase. We expect more theoretical and experimental studies on the kinetic aspects of MIP columns, especially the factors influencing the apparent rate constant, as well as the analysis of the influences of mobile-phase composition on the chromatographic performance. In addition to revealing the affinity interaction by molecular recognition, slow nonspecific interactions which may be inherited from the imperfect imprinting and may be involved in the rebinding of the template to MIPs also need to be characterized. Figure The peak broadening and tailing associated often with molecularly imprinted polymers (MIPs) in column chromatography for practical applications can be well characterized by the theory of nonlinear chromatography.