A partial-propensity formulation of the stochastic simulation algorithm for chemical reaction networks with delays

Several real-world systems, such as gene expression networks in biological cells, contain coupled chemical reactions with a time delay between reaction initiation and completion. The non-Markovian kinetics of such reaction networks can be exactly simulated using the delay stochastic simulation algorithm (dSSA). The computational cost of dSSA scales with the total number of reactions in the network. We reduce this cost to scale at most with the smaller number of species by using the concept of partial reaction propensities. The resulting delay partial-propensity direct method (dPDM) is an exact dSSA formulation for well-stirred systems of coupled chemical reactions with delays. We detail dPDM and present a theoretical analysis of its computational cost. Furthermore, we demonstrate the implications of the theoretical cost analysis in two prototypical benchmark applications. The dPDM formulation is shown to be particularly efficient for strongly coupled reaction networks, where the number of reactions is much larger than the number of species.     

The effects of connectivity, coherence, and trapping on energy transfer in simple light-harvesting systems studied using the Haken-Strobl model with diagonal disorder

The problem of electronic energy transfer in a network of two-level systems coupled to a single trapping site is investigated using a simple Haken-Strobl model with diagonal disorder. The goal is to illustrate how the trapping time T(trap), coherence time T(d), and molecular topology all affect the overall efficiency of a light-harvesting network. Several issues are identified that need to be considered in the design of an optimal energy transfer network, including the dephasing-induced decoupling the trap from the rest of the network, the nonlinear dependence of trapping rate on the coherence time, and the role of network size and connectivity in determining the effect of the coherence time on efficiency. There are two main conclusions from this work. First, there exists an optimum combination of trapping time and coherence time, which will give the most rapid population transfer to the trap. These values are not in general the shortest trapping time and the longest coherence time, as would be expected based on rate equation models and/or simple considerations from previous analytical results derived for the Haken-Strobl model in an infinite system. Second, in the coherent regime, where T(d) is longer than the other relevant timescales, population trapping in a finite system can be suppressed by quantum interference effects, whose magnitude is sensitive to the molecular geometry. Suggestions for possible methods of observing such effects are discussed. These results provide a qualitative framework for quantum coherence and molecular topology into account for the design of covalent light-harvesting networks with high energy transfer efficiencies.     

Coarse-graining Calcium Dynamics on Stochastic Reaction-diffusion Lattice Model

We develop a coarse grained (CG) approach for efficiently simulating calcium dynamics in the endoplasmic reticulum membrane based on a fine stochastic lattice gas model. By grouping neighboring microscopic sites together into CG cells and deriving CG reaction rates using local mean field approximation, we perform CG kinetic Monte Carlo (kMC) simulations and find the results of CG-kMC simulations are in excellent agreement with that of the microscopic ones. Strikingly, there is an appropriate range of coarse proportion m, corresponding to the minimal deviation of the phase transition point compared to the microscopic one. For fixed m, the critical point increases monotonously as the system size increases, especially, there exists scaling law between the deviations of the phase transition point and the system size. Moreover, the CG approach provides significantly faster Monte Carlo simulations which are easy to implement and are directly related to the microscopics, so that one can study the system size effects at the cost of reasonable computational time.     

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.     

Computational analysis of phosphoproteomics: progresses and perspectives

Phosphorylation is one of the most essential post-translational modifications (PTMs) of proteins, regulates a variety of cellular signaling pathways, and at least partially determines the biological diversity. Recent progresses in phosphoproteomics have identified more than 100,000 phosphorylation sites, while this number will easily exceed one million in the next decade. In this regard, how to extract useful information from flood of phosphoproteomics data has emerged as a great challenge. In this review, we summarized the leading edges on computational analysis of phosphoproteomics, including discovery of phosphorylation motifs from phosphoproteomics data, systematic modeling of phosphorylation network, analysis of genetic variation that influences phosphorylation, and phosphorylation evolution. Based on existed knowledge, we also raised several perspectives for further studies. We believe that integration of experimental and computational analyses will propel the phosphoproteomics research into a new phase.     

Brittle fracture of entangled polymers

A stochastic model is presented to calculate the number of chain segments entangled about a unit plane when the segment length is a stochastic variable. This crossing density to which the brittle fracture energy and the critical strength of entangled polymers scale is a function of the number of moles of entanglement network strands per unit volume and the mesh size of the entanglement network. Experimental results of the molecular weight dependence of the fracture energy and strength validate the theoretical predictions.     

Kinetic growth models at different biological development levels

The quasi-chemical biological growth model suggested earlier was used to derive kinetic equations for population growth of various biological species. A cycle of sequential stages of population development can be represented in the form of quasi-chemical equations; the kinetic equations describing the development cycle allow the population size changes to be predicted quantitatively depending on the conditions. As distinct from the extrapolation-simulation model, the kinetic parameters in kinetic biological growth models are the experimental population growth characteristics. The models developed were verified and parametrically identified on the basis of the experimental data to show that they were in agreement with experiment to within measurement errors.     

Discovery of network motifs based on induced subgraphs using a dynamic expansion tree

Biological networks are powerful representations of topological features in biological systems. Finding network motifs in biological networks is a computationally hard problem due to their huge size and abrupt increase of search space with the increase of motif size. Motivated by the computational challenges of network motif discovery and considering the importance of this topic, an efficient and scalable network motif discovery algorithm based on induced subgraphs in a dynamic expansion tree is proposed. This algorithm uses a pruning strategy to overcome the space limitation of the static expansion tree. The proposed algorithm can identify large network motifs up to size 15 by significantly reducing the computationally expensive subgraph isomorphism checks. Further, the present work avoids the unnecessary growth of patterns that do not have any statistical significance. The runtime performance of the proposed algorithm outperforms most of the existing algorithms for large network motifs.     

Stochastic diffusion interactions and coarsening in a system of droplets growing from a supersaturated gas mixture

In this work we study diffusion interactions among liquid droplets growing in stochastic population by condensation from supersaturated binary gas mixture. During the postnucleation transient regime collective growth of liquid droplets competing for the available water vapor decreases local supersaturation leading to the increase of critical radius and the onset of coarsening process. In coarsening regime the growth of larger droplets is prevailing noticeably broadening the droplet size-distribution function when the condensation process becomes more intensive than the supersaturation yield. Modifications in the kinetic equation are discussed and formulated for a stochastic population of liquid droplets when diffusional interactions among droplets become noteworthy. The kinetic equation for the droplet size-distribution function is solved together with field equations for the mass fraction of disperse liquid phase, mass fraction of water vapor component of moist air, and temperature during diffusion-dominated regime of droplet coarsening. The droplet size and mass distributions are found as functions of the liquid volume fraction, showing considerable broadening of droplet spectra. It is demonstrated that the effect of latent heat of condensation considerably changes coarsening process. The coarsening rate constant, the droplet density (number of droplets per unit volume), the screening length, the mean droplet size, and mass are determined as functions of the temperature, pressure, and liquid volume fraction.     

Geometric and Topological Analysis of Three-Dimensional Porous Media: Pore Space Partitioning Based on Morphological Skeletonization

This article presents a versatile, rigorous, and efficient methodology for extracting various geometric and topological parameters of 3D discrete porous media. The new approach takes advantage of the morphological skeleton of the pore structure-a lower dimensional representation of the pore space akin to the topological "deformation retract". The skeleton is derived by a fully parallel thinning algorithm that fulfils two essential requirements: it generates a medial axis and preserves the connectivity of the pore space. Topological analysis is accomplished by classifying all skeleton points as node or link (branch) points according to the concept of lambda-adjacency in 3D discrete space. In this manner, node coordination number and link length distributions are directly obtained from the skeleton. Pore necks (throats) are identified through a search for minima in the hydraulic radius of individual pore space channels outlined by skeleton links. In addition to the determination of the size distribution of the constrictions (pore necks) that control nonwetting phase invasion, improved estimates of the distributions of effective hydraulic and electric conductivity of individual pore space channels are obtained. Furthermore, erection of planes at the location of pore necks results in partitioning of the pore space into its constituent pores. This enables the characterization of the pore space in terms of a pore volume distribution. The new methodology is illustrated by application to a regular cubic pore network and irregularly shaped 2D and 3D pore networks generated by stochastic simulation. In the latter case, important new results are obtained concerning the sensitivity of geometric and topological properties of the microstructure to the parameters of stochastic simulation, namely, the porosity and correlation function. It is found that model porous media reconstructed from the same porosity and correlation function can exhibit marked differences in geometry and connectivity, which correlate with differences in specific surface area. Copyright 2000 Academic Press.     

The synergistic catalysis on Co nanoparticles and CoN_x sites of aniline-modified ZIF derived Co@NCs for oxidative esterification of HMF

An efficient sustainable and scalable strategy for the synthesis of porous cobalt/nitrogen co-doped carbons(Co@NCs) via pyrolysis of aniline-modified ZIFs,has been demonstrated.Aniline can coordinate and absorb on the surface of ZIF(ZIF-CoZn3-PhA),accelerate the precipitation of ZIFs,thus resulting in smaller ZIF particle size.Meanwhile,the aniline on the surface of ZIF-CoZn3-PhA promotes the formation of the protective carbon shell and smaller Co nanoparticles,and increases nitrogen content of the catalyst.Because of these prope rties of Co@NC-PhA-3,the oxidative esterification of 5-hydroxymethylfurfural can be carried out under ambient conditions.According to our experimental and computational results,a synergistic catalytic effect between CoN_x sites and Co nanoparticles has been established,in which both Co nanoparticles and CoN_x can activate O_2 while Co nanoparticles bind and oxidize HMF.Moreover,the formation and release of active oxygen species in CoN_x sites are reinfo rced by the electronic interaction between Co nanoparticles and CoN_x.     

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.     

Structural studies of NaPO3-MoO3 glasses by solid-state nuclear magnetic resonance and Raman spectroscopy

Vitreous samples were prepared in the (100 - x)% NaPO(3)-x% MoO(3) (0 相似文献   

Understanding the effect of cobalt particle size on Fischer-Tropsch synthesis: surface species and mechanistic studies by SSITKA and kinetic isotope effect

Co/γ-Al(2)O(3) catalysts with particle sizes in the range of 4-15 nm were investigated by isothermal hydrogenation (IH), temperature programmed hydrogenation (TPH), and steady-state isotopic transient kinetic analysis (SSITKA). Kinetic isotope effect experiments were used to probe possible mechanisms on Co/γ-Al(2)O(3) with different particle size. It was found that CO dissociated on Co/γ-Al(2)O(3) catalysts at 210 °C. The total amount of CO(2) formed following the dissociation depends on the cobalt crystal size. O-Co binding energy was found to be highly dependent on the Co metal particle size, whereas similar C-Co binding energy was found on catalysts with different Co particle size. Very strongly bonded carbon and oxygen surface species increased with decreasing particle size and acted as site blocking species in the methanation reaction. SSITKA experiments showed that the intrinsic activity (1/τ(CH(x))) remained constant as the particle size increased from 4 to 15 nm. The number of surface intermediates (N(CH(x))) increased with increasing particle size. The apparent activation energies were found similar for these catalysts, about 85 kJ/mol. D(2)-H(2) switches further confirmed that the particle size did not change the kinetically relevant steps in the reaction. The reactivity of the active sites on the 4 nm particles was the same as those on the 8, 11, and 15 nm particles, and only the number of total available surface active sites was less on the 4 nm particles than on the others.     

Retention controlling and peak shape simulation in anion chromatography using multiple equilibrium model and stochastic theory

The stochastic theory of chromatography and an equilibrium based approach were used for the prediction of peak shape and retention data of anions. This attempt incorporating the potential advantages of two different chromatographic phenomena for analytical purposes. It is an integrated method to estimate kinetic and thermodynamic properties for the same chromatographic run of ions. The stochastic parameters of eluted anions, such as the residence time of the molecule on the surface of the stationary phase, and the average number of adsorption steps were determined on the basis of a retention database of organic and inorganic anions (formate, chloride, bromide, nitrate, sulphate, oxalate, phosphate) obtained by using carbonate/bicarbonate eluent system at different pHs (9-11) and concentrations (7-13 mM). In the investigated IC system the residence times are much higher and the average number of sorption steps is somewhat smaller than in RP-HPLC. The simultaneous application of the stochastic and the multispecies eluent/analyte model was utilized to peak shape simulation and the retention controlling of various anions under elution conditions of practical importance. The similarities between the measured and the calculated chromatograms indicates the predictive and simulation power of the combined application of the stochastic theory and the multiple species eluent/analyte retention model.     

Incorporating hidden Markov models for identifying protein kinase-specific phosphorylation sites

Protein phosphorylation, which is an important mechanism in posttranslational modification, affects essential cellular processes such as metabolism, cell signaling, differentiation, and membrane transportation. Proteins are phosphorylated by a variety of protein kinases. In this investigation, we develop a novel tool to computationally predict catalytic kinase-specific phosphorylation sites. The known phosphorylation sites from public domain data sources are categorized by their annotated protein kinases. Based on the concepts of profile Hidden Markov Models (HMM), computational models are trained from the kinase-specific groups of phosphorylation sites. After evaluating the trained models, we select the model with highest accuracy in each kinase-specific group and provide a Web-based prediction tool for identifying protein phosphorylation sites. The main contribution here is that we have developed a kinase-specific phosphorylation site prediction tool with both high sensitivity and specificity.     

Polypeptide folding on a conformational‐space network: Dependence of network topology on the structural discretization procedure

Mapping the conformational space of a polypeptide onto a network of conformational states involves a number of subjective choices, mostly in relation to the definition of conformation and its discrete nature in a network framework. Here, we evaluate the robustness of the topology of conformational‐space networks derived from Molecular Dynamics (MD) simulations with respect to the use of different discretization (clustering) methods, variation of their parameters, simulation length and analysis time‐step, and removing high‐frequency motions from the coordinate trajectories. In addition, we investigate the extent to which polypeptide dynamics can be reproduced on the resulting networks when assuming Markovian behavior. The analysis is based on eight 500 ns and eight 400 ns MD simulations in explicit water of two 10‐residue peptides. Three clustering algorithms were used, two of them based on the pair‐wise root‐mean‐square difference between structures and one on dihedral‐angle patterns. A short characteristic path length and a power‐law behavior of the probability distribution of the node degree are obtained irrespective of the clustering method or the value of any of the tested parameters. The average cliquishness is consistently one or two orders of magnitude larger than that of a random realization of a network of corresponding size and connectivity. The cliquishness as function of node degree and the kinetic properties of the networks are found to be most dependent on clustering method and/or parameters. Although Markovian simulations on the networks reproduce cluster populations accurately, their kinetic properties most often differ from those observed in the MD simulations. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Size distribution of folded chain crystal nuclei of polyethylene on active centers

Kinetic equations describing temporal evolution of the size distribution of crystalline nuclei of folded chain polyethylene on active centers are solved numerically. Basic characteristics of nucleation processes (the total number of supercritical nuclei and the size distribution of nuclei) are determined and compared with the experimental data. It is shown that even though the total number of supercritical nuclei coincides with the experimental data, the size distribution prediction fails. This is caused by the fact that the total number of nuclei (usually used in analysis of the experimental data), in contrast to the size distribution of nuclei, represents an integral quantity. Using the experimental data of the steady state size distribution of nuclei enables us to determine thermodynamic parameters (especially interfacial energies) of the studied system more precisely and consequently to correct kinetic parameters to get coincidence of kinetic model with the experimental data in both, the total number of supercritical nuclei and also the size distribution of nuclei.