Thermodynamic framework for design of reaction rate equations and schemes

2009 ◽  
Vol 74 (9) ◽  
pp. 1375-1401 ◽  
Author(s):  
Miloslav Pekař
Keyword(s):  
Experimental Data ◽  
Reaction Network ◽  
Phenomenological Theory ◽  
Reaction Scheme ◽  
Rate Function ◽  
Irreversible Thermodynamics ◽  
Mass Action ◽  
Rate Equations ◽  
Additional Hypothesis ◽  
Reaction Schemes

It has been shown previously that rational thermodynamics provides general foundations of mass-action kinetic law from the principles of continuum, irreversible thermodynamics. Practical outcomes of this phenomenological theory are analyzed and compared with traditional kinetic approaches on the example of N2O decomposition. It is revealed that classical rate equations are only simplified forms of a polynomial approximation to a general rate function proved by the continuum thermodynamics. It is also shown that various special considerations that have been introduced formerly as additional hypothesis to satisfactorily describe experimental data are naturally included in the thermodynamic approach. The method, in addition, makes it possible to obtain more general mass-action-type rate equations that give better description of experimental data than the traditional ones. The method even reverses the classical kinetic paradigm – reaction scheme directly follows from the rate equation. Data fitting by this method also indicates connections to distinctions between processes at the molecular level and their representation by some macroscopic reaction network. The role of dependent and independent reactions in reaction kinetics and reaction schemes is clarified. A selected example demonstrates that this thermodynamic methodology may improve our design and understanding of thermodynamically and mathematically necessary and sufficient reaction schemes. The phenomenological theory thus sheds new, “thermodynamic” light on what has been and is done by generations of kineticists and gives new hints how to do it in a way consistent with non-equilibrium thermodynamics.

scholarly journals Rates of reactions catalysed by a dimeric enzyme. Effects of the reaction scheme and the kinetic parameters on co-operativity

1991 ◽  
Vol 280 (1) ◽  
pp. 131-137 ◽  
Author(s):  
H Ishikawa ◽  
H Ogino ◽  
H Oshida
Keyword(s):  
Substrate Inhibition ◽  
Reaction Scheme ◽  
Rate Equations ◽  
Kinetic Behaviour ◽  
Hill Coefficients ◽  
S Curve ◽  
Almost All ◽  
The Hill ◽  
Rate Behaviour ◽  
Reaction Schemes

For the reaction S in equilibrium P catalysed by a dimeric enzyme, the reaction schemes are considered on the basis of the KNF model. For each of the ten possible schemes, the rate equation is derived on the basis of the combined steady-state and rapid-equilibrium assumptions. The curves of the plots of initial velocity v versus the substrate concentration [S] and the Hill coefficients h calculated from the rate equations depend strongly on the reaction scheme and the parameter X1. This parameter is defined by log (KS2/KS1) and is a measure of the relative affinities of the first and second protomers for the substrate. When X1 less than 0, v-[S] curves for some schemes exhibit negative co-operativity (h less than 1.0) and v-[S] curves for other schemes are similar to that of the Michaelis-Menten scheme, indicating that, even if there is interaction between the distinct protomers, sigmoidal rate behaviour is not necessarily observed. When X1 greater than 0, all the reaction schemes except one, which shows substrate-inhibition kinetic behaviour, exhibit sigmoidal kinetic behaviour (h greater than 1.0), and at the limit of X1 much greater than 0 the Hill coefficients attain the maximum possible value of 2.0. Furthermore, we have found that, even if X1 = 0, the v-[S] curve for almost all the schemes considered in the present work does not necessarily agree with that for the Michaelis-Menten scheme. This means that the deviation of the v-[S] curve from a hyperbola can be observed even if there is no interaction between the distinct protomers.

scholarly journals A numerical approach for detecting switch-like bistability in mass action chemical reaction networks with conservation laws

2022 ◽  
Vol 23 (1) ◽  
Author(s):  
Brandon C Reyes ◽  
Irene Otero-Muras ◽  
Vladislav A Petyuk
Keyword(s):  
Conservation Laws ◽  
Signaling Pathways ◽  
Chemical Reaction ◽  
Reaction Network ◽  
Chemical Reaction Networks ◽  
Mass Action ◽  
Numerical Continuation ◽  
Rate Equations ◽  
Reaction Networks ◽  
Bistable Switch

Abstract Background Theoretical analysis of signaling pathways can provide a substantial amount of insight into their function. One particular area of research considers signaling pathways capable of assuming two or more stable states given the same amount of signaling ligand. This phenomenon of bistability can give rise to switch-like behavior, a mechanism that governs cellular decision making. Investigation of whether or not a signaling pathway can confer bistability and switch-like behavior, without knowledge of specific kinetic rate constant values, is a mathematically challenging problem. Recently a technique based on optimization has been introduced, which is capable of finding example parameter values that confer switch-like behavior for a given pathway. Although this approach has made it possible to analyze moderately sized pathways, it is limited to reaction networks that presume a uniterminal structure. It is this limited structure we address by developing a general technique that applies to any mass action reaction network with conservation laws. Results In this paper we developed a generalized method for detecting switch-like bistable behavior in any mass action reaction network with conservation laws. The method involves (1) construction of a constrained optimization problem using the determinant of the Jacobian of the underlying rate equations, (2) minimization of the objective function to search for conditions resulting in a zero eigenvalue, (3) computation of a confidence level that describes if the global minimum has been found and (4) evaluation of optimization values, using either numerical continuation or directly simulating the ODE system, to verify that a bistability region exists. The generalized method has been tested on three motifs known to be capable of bistability. Conclusions We have developed a variation of an optimization-based method for the discovery of bistability, which is not limited to uniterminal chemical reaction networks. Successful completion of the method provides an S-shaped bifurcation diagram, which indicates that the network acts as a bistable switch for the given optimization parameters.

scholarly journals Coping with dynamical reaction system topologies using deterministic P modules: a case study of photosynthesis

2020 ◽  
Vol 2 (4) ◽  
pp. 281-289
Author(s):  
Thomas Hinze
Keyword(s):  
Reaction System ◽  
Reaction Network ◽  
Reaction Scheme ◽  
Static Structure ◽  
In Silico Simulation ◽  
External Signals ◽  
Parameter Values ◽  
Substrate Concentrations ◽  
Reaction Schemes

AbstractThe topology of chemical reaction networks is commonly treated as a static structure. This might be sufficient if substrate concentrations and kinetic parameter values exclusively determine the behaviour of all considered reactions. In contrast, numerous phenomena observed in life sciences imply a different nature by dynamical composition of reaction schemes. Single reactions or functional groups of reactions (modules) become activated or deactivated by external signals such as light intensity while the system is in operation. In other scenarios, reactions emerge or disappear while modules can connect to each other or disconnect due to presence or absence of corresponding trigger signals. We capture dynamical reaction network structures by an extended version of deterministic P modules with evaluation of trigger signals which facilitates detailed in-silico simulation studies and hence an easier understanding and prediction of complex biological systems. A case study dedicated to photosynthesis in plants demonstrates its usefulness beyond pure employment of ordinary differential equations by consideration of events, non-differentiable external trigger signals, and thresholds which collaterally modify the underlying reaction scheme.

scholarly journals Genetic recombination as a generalised gradient flow

2021 ◽  
Author(s):  
Frederic Alberti
Keyword(s):  
Arbitrary Number ◽  
Genetic Recombination ◽  
Reaction Network ◽  
Gradient Flow ◽  
Mass Action ◽  
Gradient System ◽  
Gradient Structure ◽  
Law Of Mass Action ◽  
Reversible Chemical Reaction ◽  
Time Partitioning

AbstractIt is well known that the classical recombination equation for two parent individuals is equivalent to the law of mass action of a strongly reversible chemical reaction network, and can thus be reformulated as a generalised gradient system. Here, this is generalised to the case of an arbitrary number of parents. Furthermore, the gradient structure of the backward-time partitioning process is investigated.

scholarly journals Deep search for hydrogen peroxide toward pre- and protostellar objects

2020 ◽  
Vol 636 ◽  
pp. A114
Author(s):  
G. W. Fuchs ◽  
D. Witsch ◽  
D. Herberth ◽  
M. Kempkes ◽  
B. Stanclik ◽  
...  
Keyword(s):  
Hydrogen Peroxide ◽  
Solid State ◽  
Water Reservoir ◽  
Reaction Network ◽  
Reaction Scheme ◽  
Young Stellar Objects ◽  
Model Parameters ◽  
Stellar Objects ◽  
Additional Information ◽  
Water Formation

Context. In the laboratory, hydrogen peroxide (HOOH) was proven to be an intermediate product in the solid-state reaction scheme that leads to the formation of water on icy dust grains. When HOOH desorbs from the icy grains, it can be detected in the gas phase. In combination with water detections, it may provide additional information on the water reaction network. Hydrogen peroxide has previously been found toward ρ Oph A. However, further searches for this molecule in other sources failed. Hydrogen peroxide plays a fundamental role in the understanding of solid-state water formation and the overall water reservoir in young stellar objects (YSOs). Without further HOOH detections, it is difficult to assess and develop suitable chemical models that properly take into account the formation of water on icy surfaces. Aims. The objective of this work is to identify HOOH in YSOs and thereby constrain the grain surface water formation hypothesis. Methods. Using an astrochemical model based on previous work in combination with a physical model of YSOs, the sources R CrA-IRS 5A, NGC C1333-IRAS 2A, L1551-IRS 5, and L1544 were identified as suitable candidates for an HOOH detection. Long integration times on the APEX 12 m and IRAM 30 m telescopes were applied to search for HOOH signatures in these sources. Results. None of the four sources under investigation showed convincing spectral signatures of HOOH. The upper limit for HOOH abundance based on the noise level at the frequency positions of this molecule for the source R CrA-IRS 5A was close to the predicted value. For NGC 1333-IRAS 2A, L1544, and L1551-IRS 5, the model overestimated the hydrogen peroxide abundances. Conclusions. HOOH remains an elusive molecule. With only one secure cosmic HOOH source detected so far, namely ρ Oph A, the chemical model parameters for this molecule cannot be sufficiently well determined or confirmed in existing models. Possible reasons for the nondetections of HOOH are discussed.

Kinetic modelling of microalgal growth and fucoxanthin synthesis in photobioreactor

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Xiaojuan Zhang ◽  
Junru Zhao ◽  
Jie Zhang ◽  
Shijing Su ◽  
Luqiang Huang ◽  
...  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Kinetic Parameters ◽  
Kinetic Modelling ◽  
Inhibitory Effect ◽  
Rate Equations ◽  
Phosphorus Concentration ◽  
Model Output ◽  
Nitrogen And Phosphorus ◽  
Nitrogen Phosphorus

Abstract This paper presented a mathematical model to describe the production of fucoxanthin by alga Thalassiosira weissflogi ND-8 in photobioreactor. Our interest was focused on characterizing the effects of nitrogen and phosphorus on the growth of microalgae and on the synthesis of fucoxanthin. The rate equations of microalgal growth, fucoxanthin synthesis and substrate consumptions were formulated. Kinetic parameters of the model and their sensitivities with respect to model output were estimated. The predicted results were compared with experimental data, which showed that this model closely agrees with actual experiment and is able to reflect the growth and metabolism characteristics of microalgae. Our results also indicated that nitrogen plays a major role in the synthesis of fucoxanthin, and the synthesis of fucoxanthin is partially linearly related to the consumption of nitrogen. Phosphorus is primarily consumed in the growth and metabolism of microalgal cells, while excessive phosphorus concentration has an inhibitory effect on the growth of microalgae.

The hydrolysis of maleimide in alkaline solution

1976 ◽  
Vol 54 (9) ◽  
pp. 1400-1404 ◽  
Author(s):  
Remigio Germano Barradas ◽  
Stephen Fletcher ◽  
John Douglas Porter
Keyword(s):  
Alkaline Solution ◽  
Reaction Scheme ◽  
Rate Equations ◽  
Bulk Concentration ◽  
Rate Of Reaction ◽  
Ph Range ◽  
Derived Data ◽  
Hydrolysis Of

The hydrolysis of maleimide has been investigated in the pH range 8.5–14. Polarographic limiting currents were well-defined, so that the bulk concentration of reactant during reduction could be clearly followed as a function of time. Logarithmic analysis of derived data indicated an arrest in the rate of reaction at circa pH 12, and a reaction scheme is proposed to explain this. In this scheme, the neutral maleimide molecule exists in equilibrium with its anion, and both of these species may undergo hydrolysis at the appropriate pH. From derived rate equations, the pKa of maleimide was found to be 10.0, whilst estimates of the rates of hydrolysis were also calculated.

Electrostatic Generation in Dielectric Fluids: The Viscoelectric Effect

2005 ◽  
Author(s):  
Robert T. Balmer
Keyword(s):  
Experimental Data ◽  
Electric Fields ◽  
Theoretical Basis ◽  
Fluid Motion ◽  
Irreversible Thermodynamics ◽  
Reverse Effect ◽  
Dielectric Fluids ◽  
Electrostatic Generator ◽  
New Type ◽  
Mobile Charges

Simultaneous energy transfer modes have been known to interact to produce unusual “coupled” effects. This coupling now has its theoretical basis in the concept of entropy production (or dissipation or irreversibility) central to nonequilibrium irreversible thermodynamics. Over the years, many examples of coupled phenomena have been identified and studied (thermoelectricity, electrokinetics, piezoelectricity, and so forth). Electrohydrodynamics (the effect of fluid motion on electric fields and the reverse effect of electric fields on fluid motion) can be explained as a thermodynamically coupled phenomenon characterized by the viscous and electrical properties of a fluid that contain mobile charges at the molecular (e.g., ions) or macroscopic (e.g., dust) levels. This is called the “viscoelectric” effect. In the first part of this paper we apply the concepts of irreversible thermodynamics to electrohydrodynamic systems to develop the relevant relationships. The second describes experiments carried out with a new type of Couette electrostatic generator. The resulting experimental data is then discussed in light of the coupled phenomenon relations previously developed.

Theoretical Investigation of Autoignition of Combustible Gas Mixtures in Rapid Compression Machines

2002 ◽  
Author(s):  
Shaoping Shi ◽  
Daniel Lee ◽  
Sandra McSurdy ◽  
Michael McMillian ◽  
Steven Richardson ◽  
...  
Keyword(s):  
Experimental Data ◽  
Theoretical Investigation ◽  
Ignition Delay ◽  
Kinetic Mechanism ◽  
Chemical Kinetic ◽  
Reaction Scheme ◽  
Independent Manner ◽  
Elementary Reactions ◽  
Chemical Kinetic Mechanism ◽  
Rapid Compression

In any theoretical investigation of ignition processes in natural gas reciprocating engines, physical and chemical mechanisms must be adequately modeled and validated in an independent manner. The Rapid Compression Machine (RCM) has been used in the past as a tool to validate both autoignition models as well as turbulent mixing effects. In this study, two experimental cases were examined. In the first experimental case, the experimental measurements of Lee and Hochgreb (1998a) were chosen to validate the simulation results. In their experiments, hydrogen/oxygen/argon mixtures were used as reactants. In the simulations, a reduced chemical kinetic mechanism consisting of 10 species and 19 elementary reactions coupled to a CFD software, Fluent 6, was used to simulate the autoignition. The ignition delay from the simulation agreed very well with that from the experimental data of Lee and Hochgreb, (1998b). In the second case, experimental data derived from an RCM with two opposed, pneumatically driven pistons (Brett et al., 2001) were used to study the autoignition of methane/oxygen/argon mixtures. The reduced chemical kinetic mechanism DRM22, derived from the GRI-Mech reaction scheme coupled to Fluent 6, was applied in the simulations. The DRM22 scheme included 22 species and 104 reactions. When methane/oxygen/argon mixture were simulated for the RCM, the ignition delay deviated about 15% from the experimental results. The simulation approaches as well as the validation results are discussed in detail in this paper. The paper also discusses an evaluation of reduced reaction models available in the literature for subsequent Fluent modeling.

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