Non-equilibrium reactions

How relevant are these phenomena First, many oscillating reactions exist and play an important role in living matter. Biochemical oscillations and also the inorganic oscillatory Belousov-Zhabotinsky system are very complex reaction networks. Oscillating surface reactions though are much simpler and so offer convenient model systems to investigate the realm of non-equilibrium reactions on a fundamental level. Secondly, as mentioned above, the conditions under which nonlinear effects such as those caused by autocatalytic steps lead to uncontrollable situations, which should be avoided in practice. Hence, some knowledge about the subject is desired. Finally, the application of forced oscillations in some reactions may lead to better performance in favorable situations for example, when a catalytic system alternates between conditions where the catalyst deactivates due to carbon deposition and conditions where this deposit is reacted away. 

Gibbs free energy and equilibrium and non-equilibrium reactions... 

The large and negative value for hexokinase indicates that this enzyme catalyses the reaction only in the direction of glucose 6-phosphate formation, i.e. it is a non-equilibrium reaction in vivo. In contrast, the low value for phosphoglucoisomerase indicates that it is a reaction that is close to equilibrium in vivo, that is, it can proceed in either direction. AG valnes for all the reactions of glycolysis indicate that those catalysed by hexokinase, phosphorylase, phos-phofractokinase and pyrnvate kinase are non-eqnilibrinm the others are near eqnilibrinm (Fignre 2.6). 

Near-equilibrium and non-equilibrium reactions This steady-state condition is usually achieved by the presence, in the pathway, of two classes of reactions those that are very close to equilibrium (near-equilibrium) and those that are far removed from equilibrium (non-equilibrium). The difference between these two types of reactions can be explained both thermodynamically (above) and kinetically (in Chapter 3). 

One of the enzymes that catalyses a non-equilibrium reaction approaches saturation with substrate, so that it is the flux-generating step, (i.e. the beginning of the pathway). 

Figure 3.27 Representation of the rates ofthefonvard and reverse reactions for non- and near-equilibrium reactions in one reaction in a hypothetical pathway. The values represent actual rates, not rate constants. The net flux through the pathway is given by (1/f-l/r). In the non-equilibrium reaction, the rate of the forward reaction dominates, so that the net flux is almost identical to this rate. In the near-equilibrium reaction, both forward and reverse rates are almost identical but considerably in excess of the flux.

The pathway for gluconeogenesis is shown in Figures 6.23 and 6.24. Some of the reactions are catalysed by the glycolytic enzymes i.e. they are the near-equilibrium. The non-equilibrium reactions of glycolysis are those catalysed by hexokinase (or glucokinase, in the liver), phosphofructokinase and pyruvate kinase and, in order to reverse these steps, separate and distinct non-equilibrium reactions are required in the gluconeogenic pathway. These reactions are ... 

Figure 6.24 The gluconeogenic pathway indicating the glycolytic and gluconeogenic non-equilibrium reactions. The non-equilibrium reactions provide for the substrate cycles. (See Chapter 3 for a discussion of substrate cycles and their role in regulation.)...

Citrate synthase, isocitrate dehydrogenase and oxogluta-rate dehydrogenase are key enzymes regulating the flux through the cycle all three catalyse non-equilibrium reactions (Chapter 3). 

Figure 9.26 (a) Near-equUibiium and non-equilibrium reactions in the electron transfer chain. The electron transfer chain is considered to be the Latter part of the physiological Krebs cycle (see above). The non-equilibrium processes are the Krebs cycle and the terminal reaction cytochrome oxidase. All other reactions are near-equilibrium, including the ATP-generating reactions. These are not shown in the figure, (b) The similarity of electron transfer chain and glycolysis in the position of near-equilibrium/non-equilibrium reactions, in the two pathways. In both cases, non-equilibrium reactions are at the beginning and at the end of the processes (see Chapters 2 and 3 for description of these terms and the means by which such reactions can be identified). 

Immediately after the passage of an action potential, the Na ion channels close spontaneously and cannot be re-opened for a period of time. This is the refractory period. An action potential therefore cannot proceed in the opposite direction, i.e. it is unidirectional, which imposes a direction on propagation of the whole action potential. This is analogous to the means by which directionality is achieved in a metabolic pathway or a signalling sequence of reactions within either process there is at least one irreversible (non-equilibrium) reaction which provides directionality (Chapter 2). 

In any signalling process, it is essential that the signal travels only in one direction (e.g. action potential in a nerve, signalling in hormone action). To do this, non-equilibrium reactions must be included in the sequence. 

Today, non-equilibrium reaction theory has been developed. Unlike the absolute rate theory, it does not require the fulfilment of the Maxwell-Boltzmann distribution. Calculations are carried out on large computers, enabling one to obtain abundant information on the dynamics of elementary chemical acts. The present situation is extensively clarified in the proceed-dings of two symposia in the U.S.A. [23, 24]. 

Insert the non-equilibrium reaction concentrations into the equilibrium expression to obtain a reaction quotient, Q. 

Table m. A. 2 - Comparison of the Energetics of Non-Equilibrium Reactions with their Equilibrium Alternatives ... 

MC is also successful in far from equilibrium processes encountered in the areas of diffusion and reaction. It is precisely this class of non-equilibrium reaction/diffusion problems that is of interest here. Chemical engineering applications of MC include crystal growth (this is probably one of the first areas where physicists applied MC), catalysis, reaction networks, biology, etc. MC simulations provide the stochastic solution to a time-dependent master equation... 

A substrate cycle is produced when a non-equilibrium reaction in the forward direction of a pathway is opposed by another non-equUibrium reaction in the reverse direction of the pathway. The two opposing reactions must be catalyzed by separate enzymes. 

The decarboxylases used by different C4 plants (malic enzyme, PEP carboxy-kinase) are believed to catalyse a non-equilibrium reaction. Little is known, however, about the regulatory characteristics of these enzymes. 

Most recently we have investigated ultrafast ET (as fast as ca. 10 3 j-l) between excited dye and weakly polar electron-donating solvent molecules [10-14]. These systems have several interesting features. (1) The electron donor and acceptor are in contact and there is no translational difhision to induce ET. (2) Non-equilibrium reaction caused by solvent dynamics can be observed. (3) Some systems have a rate of ET much faster than that of solvent relaxation. In this case the reaction is mainly due to the nuclear dynamics and is independent of solvent dynamics. (4) A clear substituent effect of electron acceptor molecules on the rates of ET is observed. 

In order to understand the regulation of the TCA cycle, it is necessary to look at the AG values for the various reactions and the kinetic properties of the enzymes. Values for the non-equilibrium reactions are tabulated below as Table 9.4 ... 

In general, flux through the glycolytic pathway is regulated by the activity of hexokinase, 6-phosphofructo-l-kinase, and pyruvate kinase. These enzymes have in common that the metabolic steps they catalyze are non-equilibrium reactions. All other enzymes in the glycolytic pathway appear to catalyze a near-equilibrium reaction and are, therefore, not subject to regulation of the conversion of glucose to pyruvate or lactate. 

The application of Monte-Carlo simulations to non-equilibrium reaction systems in heterogeneous catalysis started by Ziff, Gulari and Barshad on the lattice-gas version of a simple Langmuir-Hinshelwood model of CO oxidation on a transition metal surface. The ZGB-model is a lattice-gas version of the Langmuir-Hinshelwood-model of CO oxidation. 

Similarly to the case of non-equilibrium reaction (11-17) assuming vibrational excitation of the nitrogen molecules, the reaction rate of dissociation process (11-20) can be expressed as... 

Table IV also shows a comparison between DBzlC and PhCH2Cl as alkylating agents. High selectivity (>99%) in monobenzylation is always observed with DBzlC (entries 1-3), whereas PhCH2Cl had lower selectivity (entry 4). This reaction probably uses the mechanism already described for DMC. As in the case for DMC, the driving force for the monobenzylation is the non-equilibrium reaction following the Ba]2 mechanism.

Volk, R Bathelt, H. Performance parameters of explosives equihbrium and non-equilibrium reactions. Propellants, Explosives, Pyrotechnics 2002, 27, 136-141. 

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