Thermodynamics, enzyme reactions

While hydrolysis is a thermodynamically favored reaction, the amide and phosphoester bonds of polypeptides and ohgonucleotides are stable in the aqueous environment of the cell. This seemingly paradoxic behavior reflects the fact that the thermodynamics governing the equihbrium of a reaction do not determine the rate at which it will take place. In the cell, protein catalysts called enzymes are used to accelerate the rate... 

The relationship between reaction velocity and enzyme concentration (in the absence of self-association of the enzyme) should also be adjusted such that reaction rate is linearly related to catalyst concentration, [Etotai]- Initial rates typically fail to obtain if [Etotai] = 0-01 [Ajmitiai where [Ajinitiai is the initial substrate concentration. As a general rule, the substrate concentration will not have changed more than 5-10% of its value over the initial rate phase of the reaction. This rule-of-thumb applies only to thermodynamically favorable reactions, and investigators are well advised to limit substrate consumption to well below 5%. 

A commonly held belief is that, for an enzyme reaction within a metabolic pathway, a large excess of catalytic capacity relative to a pathway s metabolic flux ensures that a given step is at or near thermodynamic equilibrium. Brooks recently treated the kinetic behavior of reaction schemes one might judge to be at equilibrium, and he showed that individual steps can remain far from equilibrium, even at a high ratio of an enzyme s flux to a pathway s steady-state flux. His calculations indicate that whether a reaction is near equilibrium depends on (a) the overall flux through the enzyme locus and (b) the kinetic parameters of the other enzymes in the pathway. S. P. Brooks (1996) Biochem. Cell Biol. 74, 411. 

It is thus a higher form of molecular "behaviour than selective com-plexation alone and involves two stages of information input. Enzyme reactions are examples of such processes, as well as, for instance, drug-receptor interactions. Two substrates could, in principle, display very similar thermodynamic and kinetic complexation behaviour (no selection) but still only one of them may be able to undergo a specific reaction (because of geometrical differences, for instance) and thus be recognized. 

In terms of thermodynamics, two situations may arise in biocatalytic self-assembly (1) the enzyme reaction and self-assembly process are both favoured in isolation, or (2) the enzyme reaction itself is thermodynamically unfavoured but involves a small change in free energy that can be overcome by the overall free energy change from the stabilisation of the self-assembled structure. The latter gives rise to a fully reversible system that operates under thermodynamic control (Fig. 4). 

Fig. 6 Dynamic combinatorial peptide library that expioits enzyme reactions to control self-assembly processes under thermodynamic controi. (a) Emergence of the potentiai peptide derivatives of varying length in a library of interconverting molecules formed from the staring materials of Fmoc L/L2 system. Fmoc-Ls is preferentially formed. Corresponding AFM images of the fibrillar structures formed at 5 min after the addition of enzyme, and the sheet-like structures observed after 2000 h show that redistribution of the derivatives is accompanied by the remodelling from fibres (Fmoc L3) to sheet-like structures (Fmoc L5). (b) HPLC analysis of the composition of the system reveals the formation and the stabilisation of Fmoc-Ls over time. Modified from [21]...

Many enzymic reactions have high negative AG° values, for example glycosyl or peptide bond hydrolysis reactions in aqueous media, oxidations with oxygen as substrate etc. Some thermodynamic data of industrially applied enzymic reactions are described by Bmns and Schulze (1962), Tewari (1990) and Biselli, Kragl and Wandrey (1995). 

Suggest a sequence of reasonable steps for this process on the basis that sulfides, RSR, are both excellent nucleophiles and good leaving groups. It is implicit that all steps will be enzyme-catalyzed, although the way the enzymes function is unknown. Each step must be energetically reasonable because enzymes, like other catalysts, cannot induce thermodynamically unfavorable reactions. 

Note that the hydrolysis of two high-energy phosphate bonds in ATP provides the energy source for the reaction. The inorganic pyrophosphate, PPi, is subsequently broken down to two phosphate ions by inorganic pyrophosphatase. The action of this enzyme means that very little PPi remains in the cell, making the synthesis of the fatty acyl-CoA favored. This is an example of metabolic coupling, the process whereby a thermodynamically unfavored reaction is allowed because it shares an intermediate (in this case PPO with a favored one. 

The developed H+ concentration gradient plus an electric potential across the membrane supply the driving force for ATP synthesis from ADP and Pi, a thermodynamically unfavorable reaction catalyzed by ATP synthase (Karrasch and Walker, 1999). The latter is a mitochondrial enzyme located on, and spanning, the inner mitochondrial membrane. At least when in submitochondrial particles, ATP synthase saturation kinetics involve ADP positive site-site interactions in catalysis. One group has proposed that ADP saturation in vivo also shows site-site interactions ( , the interaction or Hill coefficient increasing from 1, meaning no interaction, to 2) however, others have not found this, so this issue at this time must be considered to remain unresolved. 

All life processes are the result of enzyme activity. In fact, life itself, whether plant or animal, involves a complex network of enzymatic reactions. An enzyme is a protein that is synthesized in a living cell. It catalyzes a thermodynamically possible reaction so that the rate of the reaction is compatible with the numerous biochemical processes essential for the growth and maintenance of a cell. The synthesis of an enzyme thus is under tight metabolic regulations and controls that can be genetically or environmentally manipulated sometimes to cause the overproduction of an enzyme by the cell. An enzyme, like chemical catalysts, in no way modifies the equilibrium constant or the free energy change of a reaction. 

Thermodynamic concepts are useful to apply to the study of enzyme-mediated enzyme kinetics. Through a variety of reaction mechanisms, specific enzymes catalyze specific biochemical reactions to turn over faster than they would without the enzyme present. Making use of the fact that enzymes are not able to alter the overall thermodynamics (free energy, etc.) of a chemical reaction, we can develop sets of mathematical constraints that apply to the kinetic constants of enzyme reaction mechanism. 

Applications of thermodynamics in biology 1.7.1 Enzyme reaction mechanisms... 

The determination of flow control coefficients is difficult, and requires the independent variation of the activity of all the enzymes within the pathway. Based on linear nonequilibrium thermodynamics, the kinetics of enzyme reactions can be described by the linear functions of the change in Gibbs free energy. This yields a direct relation between the elasticity coefficients and the change in Gibbs free energy for the reactions in a simple two-step pathway. 

We have attempted to integrate chemical concepts throughout the text. They include the mechanistic basis for the action of selected enzymes, the thermodynamic basis for the folding and assembly of proteins and other macromolecules, and the structures and chemical reactivity of the common cofactors. These fundamental topics underlie our understanding of all biological processes. Our goal is not to provide an encyclopedic examination of enzyme reaction mechanisms. 

Some of the principles of thermodynamics were introduced in Chapter 1 —notably the idea offree energy (G). To fully understand how enzymes operate, we need to consider two thermodynamic properties of the reaction (1) the free-energy difference (A G) between the products and reactants and (2) the energy required to initiate the conversion of reactants to products. The former determines whether the reaction will be spontaneous, whereas the later determines the rate of the reaction. Enzymes affect only the latter. First, we will consider the thermodynamics of reactions and then, in Section 8.3. the rates of reactions. 

Under standard conditions, A cannot be spontaneously converted into B and C, because AG° is positive. However, the conversion of B into D under standard conditions is thermodynamically feasible. Because free-energy changes are additive, the conversion of A into C and D has a AG° of — 13kJmol ( —3kcalmoU ), which means that it can occur spontaneously under standard conditions. Thus, a thermodynamically unfavorable reaction can be driven by a thermodynamically favorable reaction to which it is coupled. In this example, the reactions are coupled by the shared chemical intermediate B. Thus, metabolic pathways are formed by the coupling of enzyme-catalyzed reactions such that the overall free energy of the pathway is negative. 

The varit Hoff method has been the most commonly applied technique to determine thermodynamic parameters. A MEDLINE search of varit Hoff reveals over 500 publications between 1966 and 2002. The application to enzyme reaction is well known. More recently, this method has been applied to ligand-receptor inter-... 

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