Mass action ratio

Figure 13. The Gibbs energy available from a reaction, A B, depends on its displacement from equilibrium when IB)/IA) = K. The AC value is plotted against the mass-action ratio, and this is the value when B1/ A] is maintained constant in the steady state if the rate of substrate supply and substrate removal is constant.

The relationship of AG to the displacement from thermodynamic equilibrium becomes obvious if Eq. (24) is rewritten in terms of the mass-action ratio T of the participating molecules... 

As long as the mass-action ratio of the involved molecules is below its equilibrium value, the reaction proceeds towards chemical equilibrium. It should be emphasized that the value of AG entails no predication about the time scale in which chemical equilibrium is attained. 

Finally, the theory for the bioenergetics and kinetics of microtubule assembly and disassembly of microtubules has been extended by Hill and Kirschner (1983). They consider the coupling of nucleotide hydrolysis in terms of the energetics of the [GTP]/[GDP][PJ mass action ratio, the possible effects of force imparted by attachment of tubules to barriers on the rate constants, and other intriguing aspects of protomer-polymer exchange kinetics and thermodynamics. Unfortunately, much of their theory remains to be tested, and an evaluation of its importance in revealing the subtleties of assembly/disassembly remains for future investigations. 

The ratio of the concentrations of product and substrate ([B]/[A]) for a reaction in a living organism is known as the mass action ratio and is given the symbol F. The constant, AG°, is known as the standard free energy change and is constant for a particular reaction at a given temperature. Its value depends upon the equilibrium constant, which is the ratio of concentrations of product and substrate when the reaction is at equilibrium... 

To calculate the value of the mass action ratio (F), the concentrations of the substrate(s) and product(s) of the reaction must be measured in the tissue/organ without perturbing the physiological state of the tissue. This is not a simple task. (The experimental details of how this can be done are given in Chapter 3.)... 

Because many cells maintain ATP, ADP, and AMP concentrations at or near the mass action ratio of the adenylate kinase reaction, the cellular content of this enzyme is often quite high. A consequence of such abundance is that, even after extensive purification, many proteins and enzymes contain traces of adenylate kinase activity. The presence of this kinase can confound the quantitative analysis of processes that either require ADP or are carried out in the presence of both ATP and AMP. Furthermore, the equilibrium of any reaction producing ADP may be altered if adenylate kinase activity is present. To minimize the effect of adenylate kinase, one can utilize the bisubstrate geometrical analogues Ap4A and ApsA to occupy simultaneously both substrate binding pockets of this kinase . Typical inhibitory concentrations are 0.4 and 0.2 mM, respectively. Of course, as is the case for the use of any inhibitor, one must always determine whether Ap4A or ApsA has a direct effect on a particular reaction under examination. For example. Powers et al studied the effect of a series of o ,co-di-(adenosine 5 )-polyphosphates (e.g., ApnA, where n =... 

Constant ratio methods are also employed to maintain mass action ratios in measurements of isotope exchange at equilibrium. 

The energy charge quotient has a value of unity (or, 1.00) when only ATP is present and a value of zero when only AMP is present. Thus, the adenine nucleotide system is said to be fully charged at EC = 1 and fully discharged at EC = 0. At intermediate values, the adenine nucleotides are interconverted by adenylate kinase, and their concentrations are constrained by the adenylate kinase mass action ratio ... 

The equilibrium constant for a dissociation reaction is usually referred to as the dissociation constant ( d), and the products of that dissociation are then written in the numerator. For reactions not at equilbrium, the value for the product of the concentrations of all products divided by the product of the concentrations of all reactants is frequently referred to as the mass action ratio. See Association Constant Dissociation Constant Mass Action Ratio... 

To maintain equilibrium, attention must be given to the mass-action ratio, which is the multiplicand of product concentrations (that is, [P], [Q], eic.) divided by the product of the substrate concentrations (that is, [A], [B], eta) ... 

EQUIL SOETWARE, BIOMINERALIZATION EQUATIONS OF STATE EQUI-EFFEOTIVE DOSE/MOLARITY RATIO EQUILIBRIUM EQUILIBRIUM OONSTANT ASSOCIATION CONSTANT DISSOCIATION CONSTANT MASS ACTION RATIO... 

PHYSICAL ORGANIC CHEMISTRY NOMENCLATURE MARQUARDT ALGORITHM COMRUTER ALGORITHMS SOFTWARE MASS-ACTION RATIO Mass-action ratio, determination,... 

The thermodynamic feasibility of a reaction with precipitating products can be assessed by comparing the mass action ratio to the equilibrium constant of a reaction. This requires estimation of solubilities, using melting points of reactants in combination with the reaction equilibrium constant [39]. 

Methods have been developed for the prediction of aqueous solubilities of organic compounds and therefore for the prediction of the mass action ratio Zsa, [48-50]. 

It has been theoretically derived that the favorability of solid-to-solid conversion is solvent independent [30]. Practical evidence was presented that the mass action ratio and equilibrium constant varied in the same proportions as the solvent was changed (Figure 12.4) [45]. 

Figure 12.4 Comparison of the mass action ratio and equilibrium constants for peptide synthesis in different solvents at aw 0.70, at 30°C [45]. The light bars are equilibrium constants (Keq) obtained from four individual experiments.

The dark bars represent the measured saturated mass action ratio (Zsat). Note that the difference between the two parameters is similar in all the solvents. 

The direction of a reaction can be assessed straightforwardly by comparing the equilibrium constant (Keq) and the ratio of the product solubility to the substrate solubility (Zsat) [39]. In the case of the zwitterionic product amoxicillin, the ratio of the equilibrium constant and the saturated mass action ratio for the formation of the antibiotic was evaluated [40]. It was found that, at every pH, Zsat (the ratio of solubilities, called Rs in that paper) was about one order of magnitude greater in value than the experimental equilibrium constant (Zsat > Keq), and hence product precipitation was not expected and also not observed experimentally in a reaction with suspended substrates. The pH profile of all the compounds involved in the reaction (the activated acyl substrate, the free acid by-product, the antibiotic nucleus, and the product) could be predicted with reasonable accuracy, based only on charge and mass balance equations in combination with enzyme kinetic parameters [40]. 

Free Energy Required for ATP Synthesis under Physiological Conditions In the cytosol of rat hepato-cytes, the mass-action ratio, Q, is... 

Recall from Chapter 13 that the actual free-energy change, AG, is determined by the standard free-energy change, AG °, and the mass-action ratio, Q, which is the ratio [products]/ reactants] (see Eqn 13-3). For step (tT... 

Note that this expression is true only when reactants and products are at their equilibrium concentrations, where AG = 0. At any other set of concentrations, AG is not zero. Recall (from Chapter 13) that the ratio of products to substrates (the mass action ratio, Q) determines the magnitude and sign of AG and therefore the amount of free energy released during the reaction ... 

Because an alteration of this mass action ratio profoundly influences every reaction that involves ATP, organisms have been under strong evolutionary pressure to develop regulatory mechanisms that respond to the [ATP]/[ADP] ratio. Similar arguments show the importance of maintaining appropriate [NADH]/[NAD+] and [NADPH]/[NADP+] ratios. 

ATP synthase 704 FiATPase 708 rotational catalysis 711 P/O ratio 712 P/2e ratio 712 acceptor control 716 mass-action ratio 716 light-dependent reactions 723 light reactions 723 carbon-assimilation reactions 723 carbon-fixation reaction 723 thylakoid 724 stroma 724 exciton transfer 725 chlorophylls 725... 

An interesting experiment is to allow oxidative phosphorylation to proceed until the mitochondria reach state 4 and to measure the phosphorylation state ratio Rp, which equals the value of [ATP] / [ADP][PJ that is attained. This mass action ratio, which has also been called the "phosphorylation ratio" or "phosphorylation potential" (see Chapter 6 and Eq. 6-29), often reaches values greater than 104-105 M 1 in the cytosol.164 An extrapolated value for a zero rate of ATP hydrolysis of log Rf) = 6.9 was estimated. This corresponds (Eq. 6-29) to an increase in group transfer potential (AG of hydrolysis of ATP) of 39 kj/mol. It follows that the overall value of AG for oxidation of NADH in the coupled electron transport chain is less negative than is AG. If synthesis of three molecules of ATP is coupled to electron transport, the system should reach an equilibrium when Rp = 106 4 at 25°C, the difference in AG and AG being 3RT In Rp = 3 x 5.708 x 6.4 = 110 kj mol-1. This value of Rp is, within experimental error, the same as the maximum value observed.165 There apparently is an almost true equilibrium among NADH, 02 and the adenylate system if the P/O ratio is 3. 

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