Kinetics of the hydrolysis of N-benzoyl-l-serine methyl ester catalysed by bromelain and by papain. Analysis of modifier mechanisms by lattice nomography, computational methods of parameter evaluation for substrate-activated catalyses and consequences of postulated non-productive binding in bromelain- and papain-catalysed hydrolyses

1. N-Benzoyl-l-serine methyl ester was synthesized and evaluated as a substrate for bromelain (EC 3.4.22.4) and for papain (EC 3.4.22.2). 2. For the bromelain-catalysed hydrolysis at pH7.0, plots of [S(0)]/v(i) (initial substrate concn./initial velocity) versus [S(0)] are markedly curved, concave downwards. 3. Analysis by lattice nomography of a modifier kinetic mechanism in which the modifier is substrate reveals that concave-down [S(0)]/v(i) versus [S(0)] plots can arise when the ratio of the rate constants that characterize the breakdown of the binary (ES) and ternary (SES) complexes is either less than or greater than 1. In the latter case, there are severe restrictions on the values that may be taken by the ratio of the dissociation constants of the productive and non-productive binary complexes. 4. Concave-down [S(0)]/v(i) versus [S(0)] plots cannot arise from compulsory substrate activation. 5. Computational methods, based on function minimization, for determination of the apparent parameters that characterize a non-compulsory substrate-activated catalysis are described. 6. In an attempt to interpret the catalysis by bromelain of the hydrolysis of N-benzoyl-l-serine methyl ester in terms of substrate activation, the general substrate-activation model was simplified to one in which only one binary ES complex (that which gives rise directly to products) can form. 7. In terms of this model, the bromelain-catalysed hydrolysis of N-benzoyl-l-serine methyl ester at pH7.0, I=0.1 and 25 degrees C is characterized by K(m) (1) (the dissociation constant of ES)=1.22+/-0.73mm, k (the rate constant for the breakdown of ES to E+products, P)=1.57x10(-2)+/-0.32x10(-2)s(-1), K(a) (2) (the dissociation constant that characterizes the breakdown of SES to ES and S)=0.38+/-0.06m, and k' (the rate constant for the breakdown of SES to E+P+S)=0.45+/-0.04s(-1). 8. These parameters are compared with those in the literature that characterize the bromelain-catalysed hydrolysis of alpha-N-benzoyl-l-arginine ethyl ester and of alpha-N-benzoyl-l-arginine amide; K(m) (1) and k for the serine ester hydrolysis are somewhat similar to K(m) and k(cat.) for the arginine amide hydrolysis and K(as) and k' for the serine ester hydrolysis are somewhat similar to K(m) and k(cat.) for the arginine ester hydrolysis. 9. A previous interpretation of the inter-relationships of the values of k(cat.) and K(m) for the bromelain-catalysed hydrolysis of the arginine ester and amide substrates is discussed critically and an alternative interpretation involving substantial non-productive binding of the arginine amide substrate to bromelain is suggested. 10. The parameters for the bromelain-catalysed hydrolysis of the serine ester substrate are tentatively interpreted in terms of non-productive binding in the binary complex and a decrease of this type of binding by ternary complex-formation. 11. The Michaelis parameters for the papain-catalysed hydrolysis of the serine ester substrate (K(m)=52+/-4mm, k(cat.)=2.80+/-0.1s(-1) at pH7.0, I=0.1, 25.0 degrees C) are similar to those for the papain-catalysed hydrolysis of methyl hippurate. 12. Urea and guanidine hydrochloride at concentrations of 1m have only small effects on the kinetic parameters for the hydrolysis of the serine ester substrate catalysed by bromelain and by papain.     

Evaluation of rate constants for enzyme-catalysed reactions by the jackknife technique. Application to liver alcohol dehydrogenase.

Steady-state measurements of enzyme-catalysed reactions are capable of providing more information about the rate constants of the individual steps than is commonly obtained. We have applied a combination of the jackknife and non-linear regression techniques to measurements of the rate of oxidation of ethanol by NAD+, catalysed by alcohol dehydrogenase from horse liver. This has permitted values and confidence intervals to be assigned to the eight rate constants that characterize the binding of ethanol and NAD+ in random order to the enzyme, and to the net rate constant kcat. for the breakdown of the ternary complex.     

Evaluation of distribution-free confidence limits for enzyme kinetic parameters

Monte Carlo experiments have been used to test the robustness of distribution-free confidence limits for the parameters of the Michaelis-Menten equation (Porter & Trager, 1977). When used in conjunction with the modified form of the direct linear plot (Cornish-Bowden & Eisenthal, 1978), they prove to be more robust than least-squares confidence limits. In circumstances where the least-squares assumptions are correct, the distribution-free confidence limits define the parameters somewhat less precisely than the corresponding least-squares confidence limits, but this effect is negligible unless there are eight or fewer observations.     

Hexokinase and 'glucokinase' in liver metabolism

Rat liver contains four hexokinase isoenzymes, one of which, despite often being called 'glucokinase', is no more specific for glucose than the others. However, it does differ from them in displaying a sigmoid kinetic response to glucose, requiring much higher glucose concentrations for activity, and being insensitive to physiological concentrations of glucose 6-phosphate.     

Estimation of the dissociation constants of enzyme-substrate complexes from steady-state measurements. Interpretation of pH-independence of Km.

If the Michaelis constant of an enzyme-catalysed reaction is independent of pH under conditions where the catalytic constant varies with pH, it is equal to the thermodynamic dissociation constant of the enzyme-substrate complex. This is true for realistic mechanisms in which binding and catalytic steps, are clearly distinguished, as well as for the simpler mechanisms that have been considered previously. It is also true for a mechanism in which a bell-shaped pH profile for the catalytic constant results from a change of rate-limiting step with pH. The relaxation time for ionization of a typical group in unbuffered solutions at 25 degrees C is of the order of 0.1 ms at the longest, and is much shorter in buffered solutions. Thus ionizations in almost all enzyme mechanisms can properly be treated as equilibria, provided that ionization is not accompanied by a slow, compulsory change in conformation.     

Diagnostic uses of the Hill (Logit and Nernst) plots.

Analysis of the Hill plot for ligand-binding studies shows that it can adopt a variety of shapes other than a straight line. The shape of the curve can yield valuable information about the details of the binding process. In some cases it is possible to discriminate between models of co-operativity without the need for curve-fitting by computer.     

Detection of errors of interpretation in experiments in enzyme kinetics

Although modern statistical computing will often be the method of choice for analyzing kinetic data, graphic methods provide an important supplement that ought not to be neglected. Residual plots, or plots of differences between observed and calculated values against variables not expected to be correlated with these differences, permit a rapid judgment of whether data have been correctly interpreted and analyzed. The rapid increase in the frequency with which artificially modified or mutated enzymes are studied is making it less and less safe to assume that enzymes are stable under assay conditions, and there is thus an increased need for methods to check for enzyme stability, and a method for doing this is briefly described. Finally, the Scatchard plot (together with the Eadie-Hofstee plot) is used as an example to discuss the dangers of publishing derived information unaccompanied by any primary data.     

Stoicheiometric analysis in studies of metabolism

Stoicheiometric analysis of metabolic pathways provides a systematic way of determining which metabolite concentrations are subject to constraints, information that may otherwise be very difficult to recognize in a large branched pathway. The procedure involves representing the pathway structure in the form of a matrix and then carrying out row operations to convert the matrix into "row echelon form": this is a form in which as many as possible of the elements on the main diagonal are non-zero, and all of the elements below the main diagonal are zero. If exactly the same operations are carried out on a unit matrix of order equal to the number of intermediate metabolites in the pathway, the resulting matrix allows the stoicheiometric constraints to be read off directly.