Cleland notation

Phosphocreatine is an important energy source in muscle. Sequential random reactions can also be depicted in the Cleland notation. 

Haldane relationships are relationships between the equilibrium constant and the various kinetic constants defined for a given mechanism. They exist because we define for each mechanism more kinetic parameters than there are independently determinable parameters. They are of two types, kinetic and thermodynamic, and every mechanism has at least one of each. Thermodynamic Haldanes consist of the cross product of reciprocal dissociation constants for the substrates and dissociation constants for the products (i.e., the product of equilibrium constants for each step in the mechanism). For mechanisms with at least three substrates, the Cleland notation defines dissociation constants as K, values (i.e., /fia, ib, K c, etc.), but for Ordered Uni Bi and Bi Bi mechanisms, Cleland defined the dissociation constants of the inner substrates differently (4). The dissociation constants for A and Q were and /(jq, but that for B was... 

Above Cleland notation, showing order of binding and removal of substrates and products. Be-iow Eiectron transfer to oxygen and substrate via cytochrome P450 reductase and cytochrome P450. 

Three possible kinetic mechanisms for a two-substrate/two-product reaction depicted in Cleland notation. Substrates are designated as A and B , products as C and D while E represents the enzyme and E is a covalently modified enzyme that forms transiently as part of the normal catalytic pathway in the ping-pong mechanism. 

Restricting ourselves to the rapid equilibrium approximation (as opposed to the steady-state approximation) and adopting the notation of Cleland [158 160], the most common enzyme-kinetic mechanisms are shown in Fig. 8. In multisubstrate reactions, the number of participating reactants in either direction is designated by the prefixes Uni, Bi, or Ter. As an example, consider the Random Bi Bi Mechanism, depicted in Fig. 8a. Following the derivation in Ref. [161], we assume that the overall reaction is described by vrbb = k+ [EAB — k EPQ. Using the conservation of total enzyme... 

The general reaction scheme for this mechanism can be drawn as shown below using Cleland s notation. 

In its original form, Cleland s notation had only single arrows thus this mechanism would be written as... 

In the ordered sequential mechanism, the coenzyme always binds first and the lactate is always released first. This sequence can be represented as follows in a notation developed by W. Wallace Cleland ... 

The sequential mechanisms can be subdivided in those which have a compulsory order and those which have a random order of S binding. These mechanisms are often described with the popular shorthand notation given by Cleland (1963), in which uni, bi, ter, etc, denote the number of S and P species. The /Cm values of the various reactants are concentration values at which half of the maxi-... 

Two types of reaction schemes are usually considered. Below we will use the notation of Cleland for denoting reactants and products. In sequential mechanism both substrates bind to the enzyme before any product is released. Such mechanism can be ordered with an obligatory order of addition of substrates and release of products. Substrate A binds E first, giving an EA complex. Then B binds to EA, giving a ternary complex (EAB). A and B are converted to products P and Q on (EAB), giving an (EPQ) complex. P dissociates first from (EPQ), then Q from EQ, regenerating E. 

All kinetic mechanisms can be presented in shorthand notations the most popular is that proposed by Cleland (1963). However, the reader is warned that he or she wiU find other systems in the literature, as weU as in this book, and will have to examine the definitions given for the kinetic constants in each case. 

The shorthand notation of Cleland is illustrated with the example of an Ordered Bi Bi mechanism ... 

When there is more than one substrate (see Multisubstrate enzymes), the kinetics may be second order (or pseudo-second-order. See Cleland s short notation). The equation for a second order reaction is A + B iib P, where kj is the bimolecular rate constant, and V = k2[A][B], All chemical reactions are reversible andd eventually reach an equilibrium in which the rates of the forward and reverse reactions are equal. 

Multi-substrate enzymes (see) catalyse reactions of two or more substrates. Such enzymes can form a number of different complexes (known as enzyme species) with one or both substrates and/or products. The order in which these species are formed may be random or ordered. Cleland s short notation (see) is a convenient way of representing the possibilities. The kinetics of such reactions become extremely complicated enzyme networks (see Enzyme graphs) provide a means of sununarizing them. To evaluate the kinetic data for such systems, one must resort to a computer. Furthermore, the information gained from steady-state experiments may not be sufficient. A number of methods of very rapid measiu ement have been used to investigate the pre-steady-state condition of reactions, including stopped flow, temperature jump and flash methods. 

Multisubstrate enzymes enzymes that require two or more substrates in order to catalyse a particular reaction. Accordingly, the enzyme forms a ternary (two substrates), quaternary (three substrates), etc. complex. Many enzymes are of this type, e.g. NAD-dependent dehydrogenases must bind both the substrate and NADt See Cleland s short notation. 

Cullen (1990) The public inquiry into the piper alpha disaster. HMSO Cm 1310 Emmet L, Cleland G (2002) Graphical notations, narratives and persuasion a pliant systems approach to hypertext tool design. In Proc ACM Hypertext, College Park, Maryland, USA Eurocontrol (2003) ESARR6 Software in ATM systems. 

Two types of reaction schemes are usually considered. Below, we will use the notation of Cleland for denoting reactants and products. In sequential mechanism, both substrates bind to the enzyme before any product is released. Such mechanism can be ordered with an obligatory order of substrates addition and products release. 

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