Reaction flux

To find the total reaction flux, equation (A3.12.12) must be integrated between the limits equal to 0 and E -E, so that... 

Some of the earliest attempts to address the difficulties associated with making kinetic measurements at immiscible liquid-liquid interfaces were made by Lewis [16,17] using the stirred cell design illustrated in Fig. 2. The Lewis cell employs direct contact between the two immiscible liquids, and reaction rates are evaluated by measuring concentration changes in the bulk of one of the two phases, usually by a batch extraction technique. The rate of change of concentration, dc/dt, is related to the interfacial reaction flux, 7, by... 

Assuming a first-order rate law with respect to hydrogen, with a kinetic constant kc, the maximum rate of chemical reaction (mol s-1 mL3) is obtained when the hydrogen concentration reaches equilibrium (Ch,l=C ,i) and the corresponding maximum reaction flux ( m(mol s 1) results in Eq. (19). 

The reverse of reaction (3.44) has no effect until the system has equilibrated, at which point the two coefficients d In Yco/d In and d In Yco/d In f44b are equal in magnitude and opposite in sense. At equilibrium, these reactions are microscopically balanced, and therefore the net effect of perturbing both rate constants simultaneously and equally is zero. However, a perturbation of the ratio (A 44f/A 44b = K44) has the largest effect of any parameter on the CO equilibrium concentration. A similar analysis shows reactions (3.17) and (3.20) to become balanced shortly after the induction period. A reaction flux (rate-of-production) analysis would reveal the same trends. 

Because the UI is defined in terms of the reaction flux at the surface, it is not appropriate to understand the effectiveness of species that are not expected to react at the deposition surface. For example, in the diamond system neither the CH4 nor H2 introduced as reagents is expected to react at the surface. Since the gas-supply cost depends only on the reagents (regardless of whether they participate directly in surface reactions), another measure of reactor effectiveness needs to be considered. 

When microscopic reversibility is present in a complex system composed of many particles, every elementary process in a forward direction is balanced by one in the reverse direction. The balance of forward and backward rates is characteristic of the equilibrium state, and detailed balance exists throughout the system. Microscopic reversibility therefore requires that the forward and backward reaction fluxes in Fig. 2.1 be equal, so that... 

This model predicts that 98% of the reaction flux will go through the pathway with glucose adding first when both glucose and MgATP are present at Km levels. At higher MgATP levels both pathways would carry nearly equal flux (30). 

For confidence in the accuracy of /cHa.b> it is important that the curvature in Fig. 11.2A corresponds to an increase of two-fold or greater in the slope. Too often, the third-order term in Equation 11.2 (/cha b) is inaccurate because it derives from a very small fraction of the total reaction flux, and needs confirmation. Data for the enolisation of acetone are reproduced in Fig. 11.3, which shows that substantial differences between observed rate constants and calculated values not including the third-order term are seen only at high concentration of the acid-base pair [2]. Concentrations of acid-base pairs are between 0 and 2 M, and there are no major specific salt or solvent effects. This is important as the high... 

Percentages represent reaction flux taken by the acid catalyst indicated. 

In atmospheric chemistry, kinetic isotope effects have been measured for the reaction of hydroxyl radicals with acetone using the relative-rate method over a range of temperatures.334 Water vapour had relatively little effect on rates. Product studies have allowed partitioning of the reaction flux into routes that produce acetic acid directly, and secondary processes. 

Kinetic data indicate that the hydrolysis of 5-2,4-dinitrophenyl 4,-hydroxythioben-zoate (61) in mild alkaline solutions (pH 8-11) most likely follows a dissociative, ElcB pathway, through a p-oxoketene intermediate, whereas at higher pH values an associative mechanism carries the reaction flux (Scheme 18). LFER relationships obtained from a kinetic study on the alkaline hydrolyses of substituted 5-aryl 4 -hydroxythiobenzoates seem to suggest that the associative pathway is a concerted, one-step process, rather than the classical mechanism via a tetrahedral intermediate.51... 

These results are particularly interesting in that on closer examination they indicate by comparison with conventional quench cross section measurements (16), which refer to all loss channels, that the chemical reaction flux is quite minor. The interaction between excited Na or Li with either H20 or H2 proceeds predominately and quite efficiently via a physical non-adiabatic quench-... 

Each of the reactions (r) contributing to the overall metabolic activity has a characteristic molar enthalpy, A,//b (J moL1), where subscript B indicates that any given reaction stoichiometry must be divided by vB (v = stoichiometric number) to give a stoichiometric form of unity (IVbI = 1). Each is calculated from the balanced reaction stoichiometry and enthalpy of formation. If this value is multiplied by the measured chemical reaction flux, JB (mol s 1 m-1), then the reaction enthalpy flux, JhO mo -3), is obtained,... 

The situation becomes much less problematic if the reaction in Eq. 3.1 is considered only at equilibrium. Equilibrium states are steady states in which the net reaction fluxes to produce products or reactants, regardless of the reaction pathway, are equal and opposite. From the perspective of chemical thermodynamics, equilibrium states are unique and independent of thermodynamic path. Thus these states can be described by a unique set of chemical species irrespective of the intermediate steps of their formation. Dissolution- precipitation reactions and the chemical species that affect them at equilibrium can be described by an extension of the methodology discussed in Section 2.4 (cf. Fig. 

So far, the effect of product inhibition has not been considered. Inhibited enzyme electrodes have been discussed in a collection of publications by Albery et at. [42, 44, 45]. Solving our equations by applying a steady-state analysis, and including the effects of product inhibition within the film, results in the following expression for the homogeneous reaction flux, f, within the polymer layer [48],... 

The last step to building a simulation of a well mixed system such as the one illustrated in Figure 3.1 is to define the mathematical form of the reaction fluxes in Equations (3.2) and (3.3). The simplest possible rate law for reaction fluxes is the well-known law of mass action. 

Net flux for nearly irreversible reactions is proportional to reverse flux In computational modeling of biochemical systems, the approximation that certain reactions are irreversible is often invoked. In this section, we explore the consequences of such an approximation, and show that the flux through nearly irreversible enzyme-mediated reactions is proportional to the reverse reaction flux. 

The flux expressions for this model of Section 3.1.4.2 violate certain physical constraints on reaction fluxes. What constraints are violated Under what circumstances will these violations be important ... 

The data and associated model fits used to obtain these kinetic constants are shown in Figures 4.10 through 4.12. These data on quasi-steady reaction flux as functions of reactant and inhibitor concentrations are obtained from a number of independent sources, as described in the figure legends. Note that the data sets were obtained under different biochemical states. In fact, it is typical that data on biochemical kinetics are obtained under non-physiological pH and ionic conditions. Therefore the reported kinetic constants are not necessarily representative of the biochemical states obtained in physiological systems. 

Can a phosphorylation-dephosphorylation switch be more sensitive to the level of kinase concentration than n = 1 as given in Equation 5.12 We note that the kinetic scheme in Equation (4.7) is obtained under the assumption of no Michaelis-Menten saturation. Since this assumption may not be realistic, let us move on to study the enzyme kinetics in Figure (5.2) in terms of saturable Michaelis-Menten kinetics. The mechanism by which saturating kinetics of the kinase and phosphatase leads to sensitive switch-like behavior is illustrated in Figure 5.4. The reaction fluxes as a function of / (the ratio [S ]/Sc) for two cases are plotted. The first case (switch off)... 

We start our analysis of the TCA cycle kinetics by examining the predicted steady state production of NADH as a function of the NAD and ADP concentrations. From Equation (6.31) we see that there can be no net flux through the TCA cycle when concentration of either NAD or ADP, which serve as substrates for reactions in the cycle, is zero. Thus when the ratios [ATP]/[ADP] and [NADH]/[NAD] are high, we expect the TCA cycle reaction fluxes to be inhibited by simple mass action. In addition, the allosteric inhibition of several enzymes (for example inhibition of pyruvate dehydrogenase by NADH and ACCOA) has important effects. 

To understand how the TCA cycle responds kinetically to changes in demand, we can examine the predictions in time-dependent reaction fluxes in response to changes in the primary controlling variable NAD. Figure 6.4 plots predicted reaction fluxes for pyruvate dehydrogenase, aconitase, fumarase, and malate dehydrogenase in response to an instantaneous change in NAD. The initial steady state is obtained... 

The aconitase flux (reaction 3) and the fumarase flux (reaction 8) display overshoots that are small compared to pyruvate dehydrogenase. The aconitase reaction flux reaches a peak value that is only a few percent greater than the final steady state value. The fumarase flux does overshoot the final steady state, but the overshoot is too small to be observed on the scale plotted. This behavior occurs because these reactions are downstream of any reactions directly using NAD as a substrate. Therefore their response is muted compared to reactions that are directly controlled byNAD/NADH. 

Analysis of biochemical systems, with their behaviors constrained by the known system stoichiometry, falls under the broad heading constraint-based analysis, a methodology that allows us to explore computationally metabolic fluxes and concentrations constrained by the physical chemical laws of mass conservation and thermodynamics. This chapter introduces the mathematical formulation of the constraints on reaction fluxes and reactant concentrations that arise from the stoichiometry of an integrated network and are the basis of constraint-based analysis. 

Algebraic analysis of this equation reveals that mass-balanced solutions exist if and only if bA = bs- Equation (9.5) can be simplified to J2 = h = J —bA. Thus, mass balance does not provide unique values for the internal reaction fluxes. In fact, for this example, solutions exist for... 

In addition to the stoichiometric mass-balance constraint, constraints on reaction fluxes and species concentration arise from non-equilibrium steady state biochemical thermodynamics [91]. Some constraints on reaction directions are... 

As briefly outlined in Section 6.3, one of the theoretical frameworks in quantitative analysis of metabolic networks is metabolic control analysis. In metabolic control analysis, the enzyme elasticity coefficients provide empirical constraints between the metabolites concentrations and the reaction fluxes. These constraints can be considered in concert with the interdependencies in the J and c spaces that are imposed by the network stoichiometry. If the coefficients elk = (c / Ji)dJi/dck are known, then these values bind the fluxes and concentrations to a hyperplane in the (J, c) space. 

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