Cooperativity in enzymes

Equation (4.31) gives us the equilibrium binding in the case of dual cooperativity, yet it does not tell us what cooperative binding has to do with enzyme kinetics. To illustrate the role of cooperativity in enzyme kinetics, consider the following... 

Substrate Inhibition Substrate inhibition represents another example of cooperativity in enzyme kinetic reactions, but of a different profile than described to this point. With substrate inhibition kinetics, the velocity of a reaction increases (as expected for hyperbolic profiles) to an apex, however, beyond this point the velocity of the reaction decreases with increasing substrate concentrations (Fig. 4.7). 

Cooperativity in enzyme action and servomechanism-type control of enzyme activity are important principles of metabolic control which we have already encountered. Separately or in concert, they introduce nonlinearity into the kinetic behavior of a pathway. It is noteworthy that nonlinearity is at the heart of the genesis of oscillations as well. 

Kauss, H. and Swanson, A.L. (1969) Cooperation of enzymes responsible for polymerization and methylation in pectin biosynthesis. ZJ aturforsch. 24 28-33. 

Pyruvate kinase (PK) is one of the three postulated rate-controlling enzymes of glycolysis. The high-energy phosphate of phosphoenolpyruvate is transferred to ADP by this enzyme, which requires for its activity both monovalent and divalent cations. Enolpyruvate formed in this reaction is converted spontaneously to the keto form of pyruvate with the synthesis of one ATP molecule. PK has four isozymes in mammals M, M2, L, and R. The M2 type, which is considered to be the prototype, is the only form detected in early fetal tissues and is expressed in many adult tissues. This form is progressively replaced by the M( type in the skeletal muscle, heart, and brain by the L type in the liver and by the R type in red blood cells during development or differentiation (M26). The M, and M2 isozymes display Michaelis-Menten kinetics with respect to phosphoenolpyruvate. The Mj isozyme is not affected by fructose-1,6-diphosphate (F-1,6-DP) and the M2 is al-losterically activated by this compound. Type L and R exhibit cooperatively in... 

Flodstrom, S., L. Wamgard, S. Ljungquist, and U.G. Ahlborg. 1988. Inhibition of metabolic cooperation in vitro and enhancement of enzyme altered foci incidence in rat liver by the pyrethroid insecticide fenvalerate. Arch. Toxicol. 61 218-223. 

Figure 11. Allosteric regulation A conformational change of the active site of an enzyme induced by reversible binding of an effector molecule (A). The model of Monod, Wyman, and Changeux (B) Cooperativity in the MWC is induced by a shift of the equilibrium between the T and R state upon binding of the receptor. Note that the sequential dissociation constants Kr and KR do not change. The T and R states of the enzyme differ in their catalytic properties for substrates. Both plots are adapted from Ref. 140. See color insert.

The indirect correlation is the major source of cooperativity in biochemical systems, such as hemoglobin (Chapter 6) or allosteric enzymes (Chapter 8). The model treated in this section is the simplest binding model having indirect correlation. We now examine some of the outstanding properties of the indirect correlation... 

The book is organized in nine chapters and eleven appendices. Chapters 1 and 2 introduce the fundamental concepts and definitions. Chapters 3 to 7 treat binding systems of increasing complexity. The central chapter is Chapter 4, where all possible sources of cooperativity in binding systems are discussed. Chapter 8 deals with regulatory enzymes. Although the phenomenon of cooperativity here is manifested in the kinetics of enzymatic reactions, one can translate the description of the phenomenon into equilibrium terms. Chapter 9 deals with some aspects of solvation effects on cooperativity. Here, we only outline the methods one should use to study solvation effects for any specific system. 

To understand the basic role served by vitamins in human health, we need to retreat to chapter 9 for a moment. We discussed there the nature of an amazing group of proteins, the catalysts of living systems, enzymes. Many enzymes are perfectly happy to work by themselves and they do work by themselves. Others, in contrast, require a partner for their catalytic functions. These partners are known by the generic name of coenzymes. Basically, they cooperate with enzymes in getting the catalytic job accomplished. Although his name implies that he worked... 

Hunter T, Cooper JA, In Enzyme Control by Protein Phosphorylation. (Eds Boyer PD, Krebs EG), p. 191. Academic Press, New York, 1986. 

Thiamine diphosphate (TPP, 3), in cooperation with enzymes, is able to activate aldehydes or ketones as hydroxyalkyl groups and then to pass them on to other molecules. This type of transfer is important in the transketo-lase reaction, for example (see p. 152). Hydroxyalkyl residues also arise in the decarboxylation of 0x0 acids. In this case, they are released as aldehydes or transferred to lipoamide residues of 2-oxoacid dehydrogenases (see p. 134). The functional component of TPP is the sulfur- and nitrogen-containing thiazole ring. 

Each subunit of the enzyme binds acetyl residues as thioesters at two different SH groups at one peripheral cysteine residue (CysSH) and one central 4-phosphopante-theine group (Pan-SH). Pan-SH, which is very similar to coenzyme A (see p. 12), is covalently bound to a protein segment of the synthase known as the acyl-carrier protein (ACP). This part functions like a long arm that passes the substrate from one reaction center to the next. The two subunits of fatty acid synthase cooperate in this process the enzyme is therefore only capable of functioning as a dimer. 

A centrifugation technique used to determine the oligomeric or monomeric status of an enzyme during catalysis. For example, this method can address such questions as Is the catalytically active form of the enzyme a dimer or monomer Is there cooperativity in the interconversion between the forms ... 

In a series of papers, we have proposed the torsional mechanism of energy transduction and ATP synthesis, the only unified and detailed molecular mechanism of ATP synthesis to date [16-20,56] which addresses the issues of ion translocation in Fq [16, 20, 56], ionmotive torque generation in Fq [16, 20, 56], torque transmission from Fq to Fj [17,18], energy storage in the enzyme [17], conformational changes in Fj [18], and the catalytic cycle of ATP synthesis [18, 19]. We have also studied the thermodynamic and kinetic aspects of ATP synthesis [19,20,41,42,56]. A kinetic scheme has been developed and mathematically analyzed to obtain a kinetic model relating the rate of ATP synthesis to pHjn and pH m in the Fq portion and the adenine nucleotide concentrations in the Fj portion of ATP synthase. Analysis of these kinetic models reveals a wealth of mechanistic details such as the absence of cooperativity in the Fj portion of ATP synthase, order of substrate binding and product release events, and kinetic inequivalence of ApH and Aip. 

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