Linear conjugacy of chemical reaction networks

Under suitable assumptions, the dynamic behaviour of a chemical reaction network is governed by an autonomous set of polynomial ordinary differential equations over continuous variables representing the concentrations of the reactant species. It is known that two networks may possess the same governing mass-action dynamics despite disparate network structure. To date, however, there has only been limited work exploiting this phenomenon even for the cases where one network possesses known dynamics while the other does not. In this paper, we bring these known results into a broader unified theory which we call conjugate chemical reaction network theory. We present a theorem which gives conditions under which two networks with different governing mass-action dynamics may exhibit the same qualitative dynamics and use it to extend the scope of the well-known theory of weakly reversible systems.     

Double hopf-bifurcation in plane quadratic mass-action systems

We consider models of open two-variable quadratic mass-action systems which may be regarded as the simplest nonlinear systems that can exhibit exotic behaviour. They occur in various branches of physics and biology such as ecology, solid, state physics and — most well-known — in chemistry and biochemistry. In this work it is shown that in spite of their simplicity these models cannot only undergo a normal but also a simultaneous Hopf-bifurcation to limit cycles at two different point of phase space. These limit cycles are found to always have opposite character of stability, thus giving rise to bistability of a limit cycle and a stationary point exterior to it. An example of a simple chemical reaction scheme with the delineated behaviour is presented.     

Computing sparse and dense realizations of reaction kinetic systems

A numerical procedure for finding the sparsest and densest realization of a given reaction network is proposed in this paper. The problem is formulated and solved in the framework of mixed integer linear programming (MILP) where the continuous optimization variables are the nonnegative reaction rate coefficients, and the corresponding integer variables ensure the finding of the realization with the minimal or maximal number of reactions. The mass-action kinetics is expressed in the form of linear constraints adjoining the optimization problem. More complex realization problems can also be solved using the proposed framework by modifying the objective function and/or the constraints appropriately.     

Diffusion chaos in the Lotke-Volterra stochastic model

It is shown that a chaotic state exists in the Lotke-Volterra model because of diffusion control in a bimolecular reaction chain; this stochastic model is used to show that irregularities occur only when there are two intermediate reaction products and are related to deviation from the mass-action law.Translated from Teoreticheskaya i éksperimental'naya Khimiya, Vol. 24, No. 1, pp. 1–8, January–February, 1988.     

Micellar effect upon the reaction of tris(4,7-diphenyl-1,10-phenanthrolinedisulphonato)iron(II) ion with hydroxide in water

Summary Reaction of tris(4,7-diphenyl-1,10-phenanthrolinedisulphonato)iron(II) ion with hydroxide ion is strongly accelerated by cationic micellar systems. Kinetics both in water and in cationic micelles are consistent with a mechanism of consecuive reactions with a reversible step, and the rate constants have been determined. Results in micelles are explained in terms of thepseudo-phase ion-exchange and mass-action kinetics models, and they show that micelles speed the reaction by an authentic catalytic effect by stabilization of transition state of the reaction.     

Atoms of multistationarity in chemical reaction networks

Chemical reaction systems are dynamical systems that arise in chemical engineering and systems biology. In this work, we consider the question of whether the minimal (in a precise sense) multistationary chemical reaction networks, which we propose to call ‘atoms of multistationarity,’ characterize the entire set of multistationary networks. Our main result states that the answer to this question is ‘yes’ in the context of fully open continuous-flow stirred-tank reactors (CFSTRs), which are networks in which all chemical species take part in the inflow and outflow. In order to prove this result, we show that if a subnetwork admits multiple steady states, then these steady states can be lifted to a larger network, provided that the two networks share the same stoichiometric subspace. We also prove an analogous result when a smaller network is obtained from a larger network by ‘removing species.’ Our results provide the mathematical foundation for a technique used by Siegal- Gaskins et al. of establishing bistability by way of ‘network ancestry.’ Additionally, our work provides sufficient conditions for establishing multistationarity by way of atoms and moreover reduces the problem of classifying multistationary CFSTRs to that of cataloging atoms of multistationarity. As an application, we enumerate and classify all 386 bimolecular and reversible two-reaction networks. Of these, exactly 35 admit multiple positive steady states. Moreover, each admits a unique minimal multistationary subnetwork, and these subnetworks form a poset (with respect to the relation of ‘removing species’) which has 11 minimal elements (the atoms of multistationarity).     

Hybrid modeling and simulation of stochastic effects on progression through the eukaryotic cell cycle

The eukaryotic cell cycle is regulated by a complicated chemical reaction network. Although many deterministic models have been proposed, stochastic models are desired to capture noise in the cell resulting from low numbers of critical species. However, converting a deterministic model into one that accurately captures stochastic effects can result in a complex model that is hard to build and expensive to simulate. In this paper, we first apply a hybrid (mixed deterministic and stochastic) simulation method to such a stochastic model. With proper partitioning of reactions between deterministic and stochastic simulation methods, the hybrid method generates the same primary characteristics and the same level of noise as Gillespie's stochastic simulation algorithm, but with better efficiency. By studying the results generated by various partitionings of reactions, we developed a new strategy for hybrid stochastic modeling of the cell cycle. The new approach is not limited to using mass-action rate laws. Numerical experiments demonstrate that our approach is consistent with characteristics of noisy cell cycle progression, and yields cell cycle statistics in accord with experimental observations.     

Transient Substrate‐Induced Catalyst Formation in a Dynamic Molecular Network

In biology enzyme concentrations are continuously regulated, yet for synthetic catalytic systems such regulatory mechanisms are underdeveloped. We now report how a substrate of a chemical reaction induces the formation of its own catalyst from a dynamic molecular network. After complete conversion of the substrate, the network disassembles the catalyst. These results open up new opportunities for controlling catalysis in synthetic chemical systems.     

Stochastic self-assembly of incommensurate clusters

Nucleation and molecular aggregation are important processes in numerous physical and biological systems. In many applications, these processes often take place in confined spaces, involving a finite number of particles. Analogous to treatments of stochastic chemical reactions, we examine the classic problem of homogeneous nucleation and self-assembly by deriving and analyzing a fully discrete stochastic master equation. We enumerate the highest probability steady states, and derive exact analytical formulae for quenched and equilibrium mean cluster size distributions. Upon comparison with results obtained from the associated mass-action Becker-D?ring equations, we find striking differences between the two corresponding equilibrium mean cluster concentrations. These differences depend primarily on the divisibility of the total available mass by the maximum allowed cluster size, and the remainder. When such mass "incommensurability" arises, a single remainder particle can "emulsify" the system by significantly broadening the equilibrium mean cluster size distribution. This discreteness-induced broadening effect is periodic in the total mass of the system but arises even when the system size is asymptotically large, provided the ratio of the total mass to the maximum cluster size is finite. Ironically, classic mass-action equations are fairly accurate in the coarsening regime, before equilibrium is reached, despite the presence of large stochastic fluctuations found via kinetic Monte-Carlo simulations. Our findings define a new scaling regime in which results from classic mass-action theories are qualitatively inaccurate, even in the limit of large total system size.     

A graph-theoretic method for detecting potential Turing bifurcations

The conditions for diffusion-driven (Turing) instabilities in systems with two reactive species are well known. General methods for detecting potential Turing bifurcations in larger reaction schemes are, on the other hand, not well developed. We prove a theorem for a graph-theoretic condition originally given by Volpert and Ivanova [Mathematical Modeling (Nauka, Moscow, 1987) (in Russian), p. 57] for Turing instabilities in a mass-action reaction-diffusion system involving n substances. The method is based on the representation of a reaction mechanism as a bipartite graph with two types of nodes representing chemical species and reactions, respectively. The condition for diffusion-driven instability is related to the existence of a structure in the graph known as a critical fragment. The technique is illustrated using a substrate-inhibited bifunctional enzyme mechanism which involves seven chemical species.     

The enhanced extended phenomenological kinetics method to deal with timescale disparity problem among different reaction pathways

Kinetic Monte Carlo method can provide valuable mechanistic insights for catalytic systems. Nonetheless, it suffers from the notorious problem of timescale disparity due to the existence of the complex catalytic network that consists of fast events and slow events. Previously, we have proposed the extended phenomenological kinetics (XPK) method that effectively deals with the timescale disparity problem between diffusion and reaction. However, it remains a great challenge to simulate systems with timescale disparity among different reaction pathways, which is important when selectivity is the major concern. In this study, we implement the enhanced XPK method to address this problem. The new algorithm works by identifying states connected through fast transitions and compressing them into a “superstate” when the chosen states satisfy a local steadystate condition. This state compression algorithm simplifies the reaction network by concealing the fast transitions. The accuracy and efficiency of the algorithm are demonstrated by two model systems: selective catalytic hydrogenation and selective catalytic decomposition. The enhanced XPK method is expected to be beneficial to the kinetic simulations of catalytic systems, especially those with complex reaction networks.     

Environmental effects on hydrogen bonded systems: A quantum chemical study of proton relay model systems

In this paper an application of a reaction field theory of solvent effects has been made to study proton transfer mechanisms in hydrogen bonded systems coupled to an environment. The latter is simulated with reaction fields having variable strength and direction (defined with respect to the supermolecule's total dipole moment direction), together with superposed uniform external electric fields. Changes in proton potential curves and some other properties of a model water dimer and a water trimer are reported. The results are discussed in relation to relevant phenomena in biology and biochemistry, namely proton relay systems in enzymatic catalysis.     

硫酸羟胺与水合肼对B-Z反应的影响

化学振荡与生化、生理现象关系密切，有维生素C参与的化学振荡反应也很引人注目．赵学庄等对维生素C存在的B－Z反应的振荡行为与机理进行了研究．他们的实验表明，当加入维生素C时，B-Z反应的诱导期增长，振荡周期增大，振荡寿命缩短，与向反应体系加入等量的Br-所产生的影响是一致的，并由此推断，维生素C对B－Z反应的影响可能是由维生素C与BrO反应生成Br-抑制了此反应的化学振荡，据此，凡是能与BrO反应生成Br-的物质，其对B－Z反应的影响必将类似于维生素C，硫酸羟胺与水合肼就属于此类物质．本文初步研究了它们对B－Z反应的影…     

Determination of complex reaction mechanisms. Analysis of chemical, biological and genetic networks

We present several methods of determining, not guessing, complex chemical reaction mechanisms and their functions. One method is based on the theory of correlation functions of measured time series of concentrations of chemical species; another is on measurements of temporal responses of concentrations to various perturbations of arbitrary magnitude; a third deals with the analysis of oscillatory systems; a fourth is on the use of genetic algorithms to determine functions of chemical reaction networks. All methods are applicable to chemical, biochemical, and biological reaction systems and to genetic networks and systems biology. The methods depend on the design of appropriate experiments on the whole system and corresponding theories for interpretation that lead to information on the causal chemical connectivity of species, on reaction pathways, on reaction mechanisms, on control centers in the system, and on functions of the system. The first three methods require no assumption of a model or hypothesis, nor extensive calculations, unlike the interpretation of measurements made on a gene network at only one time.     

Inferring gene regulatory networks from temporal expression profiles under time-delay and noise

Ordinary differential equations (ODE) have been widely used for modeling and analysis of dynamic gene networks in systems biology. In this paper, we propose an optimization method that can infer a gene regulatory network from time-series gene expression data. Specifically, the following four cases are considered: (1) reconstruction of a gene network from synthetic gene expression data with noise, (2) reconstruction of a gene network from synthetic gene expression data with time-delay, (3) reconstruction of a gene network from synthetic gene expression data with noise and time-delay, and (4) reconstruction of a gene network from experimental time-series data in budding yeast cell cycle.     

A synthetic reaction network: chemical amplification using nonequilibrium autocatalytic reactions coupled in time

This article reports a functional chemical reaction network synthesized in a microfluidic device. This chemical network performs chemical 5000-fold amplification and shows a threshold response. It operates in a feedforward manner in two stages: the output of the first stage becomes the input of the second stage. Each stage of amplification is performed by a reaction autocatalytic in Co(2+). The microfluidic network is used to maintain the two chemical reactions away from equilibrium and control the interactions between them in time. Time control is achieved as described previously (Angew. Chem., Int. Ed. 2003, 42, 768) by compartmentalizing the reaction mixture inside plugs which are aqueous droplets carried through a microchannel by an immiscible fluorinated fluid. Autocatalytic reaction displayed sensitivity to mixing; more rapid mixing corresponded to slower reaction rates. Synthetic chemical reaction networks may help understand the function of biochemical reaction networks, the goal of systems biology. They may also find practical applications. For example, the system described here may be used to detect visually, in a simple format, picoliter volumes of nanomolar concentrations of Co(2+), an environmental pollutant.     

Effect of charge regulation on steric mass-action equilibrium for the ion-exchange adsorption of proteins

A thermodynamic formalism is developed for incorporating the effects of charge regulation on the ion-exchange adsorption of proteins under mass-overloaded conditions as described by the steric mass-action (SMA) isotherm. To accomplish this, the pH titration behavior of a protein and the associated adsorption equilibrium of the various charged forms of a protein are incorporated into a model which also accounts for the steric hindrance of salt counterions caused by protein adsorption. For the case where the protein is dilute, the new model reduces to the protein adsorption model described recently by the authors which accounts for charge regulation. Similarly, the new model reduces to the steric mass-action isotherm developed by Brooks and Cramer which applies to mass-overloaded conditions for the case where charge regulation is ignored so that the protein has a fixed charge. Calculations using the new model were found to agree with experimental data for the adsorption of bovine serum albumin (BSA) on an anion-exchange column packing when using reasonable physical properties. The new model was also used to develop an improved theoretical criterion for determining the conditions required for an adsorbed species to displace a protein in displacement chromatography when the pH is near the protein pI.     

INTERACTIONS BETWEEN CATIONIC STARCH AND ANIONIC SURFACTANTS III RHEOLOGY AND STRUCTURE OF THE COMPLEX PHASE

This paper reports on studies of the rheological properties of cationic starch (CS)/ surfactant systems. The degree of substitution of the CS was 0.1 - 0.8. Surfactants investigated were sodium dodecyl sulfate (SDS), potassium octanoate (KOct), sodium decanoate (NaDe)potassium dodecanoate (KDod), sodium oleate (NaOl) and sodium erucate (NaEr). Aggregation of surfactant micelles with the polymer produces a hydrophobic and pseudoplastic gel-like complex phase with low water content and high viscosity. The rheological behavior of the gels is described by the Herschel-Bulkley model. In dilute aqueous solution the CS/surfactant aggregate structure resembles a randomly coiled polymer network, in which polymer molecules are linked by micelles. The rheological data for the gel are compatible with the assumption that the surfactants form liquid crystalline structures with the polymer anchored to the surfactant aggregates, as recently suggested for analogous systems. However, this conjecture needs to be corroborated by more direct determinations of the structure.     

Algorithm to generate reaction pathways for computer-assisted elucidation

An algorithm is introduced that can generate reaction-pathway hypotheses for computer-assisted elucidation. A key aspect of the algorithm is its ability to conjecture reaction intermediates and products that are not input to the algorithm. The formal basis for the conjecture is stoichiometry, i.e., species variables are used in the construction of a pathway, and their molecular formulas are inferred when sufficient stoichiometric constraint is placed on the variables. These conjectured species have a degree of plausibility when the algorithm is used systematically to search for the simplest pathways consistent with given experimental evidence. The MECHEM system for computer-assisted elucidation under development by the author adapts this algorithm to generate initial pathway hypotheses from experimental data. © 1992 by John Wiley & Sons, Inc.