Cleland nomenclature

Symbols for substrates and products, respectively, in multisubstrate enzyme-catalyzed reactions. In all ordered reaction mechanisms, A represents the first substrate to bind, B is the second, eta, whereas P denotes the first product to be released, Q represents the second, eta See Cleland Nomenclature... 

In Cleland nomenclature, the initial velocity and individual rate constants are designated by lower case italicized letters (e.g., v, k, k2, etc.). Dissociation, Michaelis, and equilibrium constants utilize an upper case italicized K with the appropriate unitalicized lower case subscript. For example, the equilibrium constant would be symbolized by whereas the Michaelis constant for substrate B would be designated by K. Dissociation constants for a Michaelis complex contain a subscript i and a letter for the dissociating ligand (e.g., for the EA binary complex, the dissociation constant would be Ki ). Maximum velocities are designated by a capital italicized V, usually with a subscript 1 or 2 depending on whether the forward or reverse reaction is referred to. (If the numerical subscript is not provided, the forward reaction is assumed. In most cases, the unitalicized subscript max is also provided.)... 

If the standard form of the rate expression is to be used with Michaelis constants, maximum velocities, etc.) (See Cleland Nomenclature), then both the numerator and denominator are divided by the coefficient of the [A][B] term appearing in the denominator (i.e., divide by the coefficient of the term containing all of the substrates utilized in the reaction raised to the power equal to the stoichiometry number of each substrate). Thus, the ordered Bi Bi expression becomes... 

The Cleland nomenclature (Cleland, 1963a) for enzyme reactions follows ... 

TABLE 7.2. Cleland Nomenclature for Bisubstrate Reactions Exemplified ... 

Examples of the bisubstrate reactions according to Cleland nomenclature are listed in Table 7.2. 

The simplest enzyme-catalyzed reaction involves a single substrate going to a single product. The system is called Uni Uni in the commonly used Cleland nomenclature. The reaction sequence is ... 

A binds to free E with a dissociation constant Ka (also called Ku, in the Cleland nomenclature). B binds to free E with a dissociation constant -Kb (or Kn). The binding of one substrate may alter the affinity of the enzyme for the other. Thus, A binds to EB with a dissociation constant ctKa. Since the overall equilibrium constant between A and E must be the same regardless of the path taken, B binds to EA with a dissociation constant aKs. o Ka is the same as Km (the K for A at saturating [B]). ocKb is the same as (the for B at saturating [A]). If the rate-limidng step is the slow conversion of EAB to EPQ, we can derive the velocity equation for the forward reaction in the absence of P and Q in the usual manner. In fact, the only difference between the rapid equilibrium random bireactant system and noncompetitive or linear mixed-type inhibition is that now the ternary complex (EAB) is catalyticaUy active, while ESI was not. 

The Northrop-Cleland nomenclature system for isotope effects greatly simplifies their discussion the non-abundant isotope and, in the case of secondary effects, site of substitution are written as superscripts to V or VjK in parentheses, so that °(F/A) refers to an a-deuterium kinetic isotope effect on kcatZ-Klm and (K) refers to an effect on kcat- The effects on individual rate and equilibrium constants are written as superscripts is the p-tritium effect on an equilibrium constant and " k+2 is the effect on the k+2 step. Although in principle potentially ambiguous (e.g. could in principle refer to or the relatively short-lived F), in practice any ambiguity is resolved from the context. 

TABLE 11.5 Cleland nomenclature for bisubstrate reactions exemplified. Three common kinetic mechanisms for bisubstrate enzymatic reactions are exemplified. The forward rate equations for the order bi bi and ping pong bi hi are derived according to the steady-state assumption, whereas that of the random bi bi is based on the quasi-equilibrium assumption. These rate equations are first order in both A and B, and their double reciprocal plots (1A versus 1/A or 1/B) are linear. They are convergent for the order bi bi and random bi bi but parallel for the ping pong bi bi due to the absence of the constant term (KiaKb) in the denominator. These three kinetic mechanisms can be further differentiated by their product inhibition patterns (Cleland, 1963b)... 

W. W. Cleland. The kinetics of enzyme catalyzed reactions with two or more substrates or products. I. Nomenclature and rate equations. Biochim. Biopkys. Acta. 67, 104 137 (1963). 

Selectivity is an intrinsic properly of enzymatic catalysis. [3] Following the nomenclature proposed by Cleland [24, 25], the pseudo second-order rate constant for the reaction of a substrate with an enzyme, kml/KM, is known as the specificity constant, ksp. [26] To express the relative rates of competing enzymatic reactions, involving any type of substrates, the ratio of the specificity constants appears to be the parameter of choice [3]. Since the authoritative proposition by Sih and coworkers [27], the ratio of specificity constants for the catalytic conversion of enantiomeric substrates, R and S, is commonly known as the enantiomeric ratio or E -value (Equation 1) ... 

Enzymes are biocatalysts, as such they facilitate rates of biochemical reactions. Some of the important characteristics of enzymes are summarized. Enzyme kinetics is a detailed stepwise study of enzyme catalysis as affected by enzyme concentration, substrate concentrations, and environmental factors such as temperature, pH, and so on. Two general approaches to treat initial rate enzyme kinetics, quasi-equilibrium and steady-state, are discussed. Cleland s nomenclature is presented. Computer search for enzyme data via the Internet and analysis of kinetic data with Leonora are described. 

Common practice Cleland s nomenclature Equations Figures... 

The nomenclature of Cleland is very versatile and can be applied to even more complex inhibition patterns that occur in double reciprocal plots. In addition, the nomenclature of Cleland is also applicable to double reciprocal plots for bisubstrate and tiisubstrate reactions, in the absence and in the presence of the products of reaction, which makes this nomenclamre even more versatile. 

The velocity equations for bisubstrate and trisubstrate reactions are usually formidable if expressed in terms of individual rate constants, especially in the steady-state treatment. The resulting equations are almost useless until the rate constants are grouped into relatively simple kinetic constants that can be experimentally determined (Chapter 4). Various methods for grouping the individual rate constants have been developed by Alberty (1953), DaMel (1957), Bloomfield et al. (1962), Wong Hanes (1962), Cleland (1963), Mahler Cordes (1966), Segel (1975), and others. The nomenclature of Cleland is now in general use. 

In Cleland s nomenclature, substrates are designated by the letters A, B, and C in the order which they add to the enzyme, and products by the letters P, Q, and R in order in which they leave the enz5mie. There are two types of enzyme forms those which are stable on the timescale of several minutes or more, and those which are basically enzyme-reactant complexes and wiU dissociate on a timescale of seconds or milliseconds. Stable enzyme forms are designated E, F, and G. The stable forms can usually be isolated by chemical methods and latter shown to transfer the group they are carrying to one of the reactants. 

In rapid equilibrium systems, all inhibition constants represent the tme dissociation constants of respective enzyme complexes. The nomenclature of Cleland, described in Section 8.1, is sufficient to describe most kinetic constants. However, for those constants that are leading to the formation of dead-end complexes (Xas. Khq, Kha, /Cjip), novel or extra descriptions are necessary (Cleland, 1967). Since all enzyme forms in reaction (8.35) are in the thermodynamic equilibrium, the novel constants are mutually related by the following relationships ... 

The nomenclature of Cleland is now in general use although the nomenclature ofDalziel has been often used in the older literature other methods did not stand the test of time (Purich Allison, 2000). 

We shall compare the nomenclature of Cleland and the nomenclature of Dalziel with the example of an Ordered Bi Bi mechanism, described in... 

In Cleland s nomenclature, the concentrations of two substrates are indicated as A and B, and in Dalziel s nomenclature as Si and Sa- In Cleland s nomenclature, the maximal velocity is Vi, the MichaeUs constants and K, and the inhibition constant KjA-In DaMel s nomenclature, kinetic factors have the following meaning ... 

This nomenclature has been introduced by Cleland (1963), but other descriptions of bisubstrate mechanisms are also found in the biochemical literature. For example, a sequential addition in bisubstrate reactions, an Ordered Bi Bi mechanism is also called a compulsory-order ternary-complex mechanism whereas a Random Bi Bi mechanism is called a random-order ternary-complex... 

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