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 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.     

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.     

Understanding the regulation of aspartate metabolism using a model based on measured kinetic parameters

The aspartate‐derived amino‐acid pathway from plants is well suited for analysing the function of the allosteric network of interactions in branched pathways. For this purpose, a detailed kinetic model of the system in the plant model Arabidopsis was constructed on the basis of in vitro kinetic measurements. The data, assembled into a mathematical model, reproduce in vivo measurements and also provide non‐intuitive predictions. A crucial result is the identification of allosteric interactions whose function is not to couple demand and supply but to maintain a high independence between fluxes in competing pathways. In addition, the model shows that enzyme isoforms are not functionally redundant, because they contribute unequally to the flux and its regulation. Another result is the identification of the threonine concentration as the most sensitive variable in the system, suggesting a regulatory role for threonine at a higher level of integration.     

A Simple Self-Maintaining Metabolic System: Robustness,Autocatalysis, Bistability

A living organism must not only organize itself from within; it must also maintain its organization in the face of changes in its environment and degradation of its components. We show here that a simple (M,R)-system consisting of three interlocking catalytic cycles, with every catalyst produced by the system itself, can both establish a non-trivial steady state and maintain this despite continuous loss of the catalysts by irreversible degradation. As long as at least one catalyst is present at a sufficient concentration in the initial state, the others can be produced and maintained. The system shows bistability, because if the amount of catalyst in the initial state is insufficient to reach the non-trivial steady state the system collapses to a trivial steady state in which all fluxes are zero. It is also robust, because if one catalyst is catastrophically lost when the system is in steady state it can recreate the same state. There are three elementary flux modes, but none of them is an enzyme-maintaining mode, the entire network being necessary to maintain the two catalysts.     

Modulation of metabolite concentrations with no net effect on fluxes

The concentration of a metabolite in a metabolic system can be varied without affecting any other concentrations or any fluxes by varying the concentrations of two inhibitors, one a competitive inhibitor of the enzyme that produces the metabolite, the other a competitive inhibitor of the enzyme that consumes it. The two concentrations need to be varied in opposite directions in such a way that the they add up to 100% when each is expressed as a percentage of the concentration that gives the desired flux in the absence of the other. The general approach can be extended to systems in which the inhibited enzymes do not catalyse consecutive reactions.     

Further localization of the gene for nevoid basal cell carcinoma syndrome (NBCCS) in 15 Australasian families: Linkage and loss of heterozygosity

Nevoid basal cell carcinoma syndrome (NBCCS; basal cell nevus syndrome or Gorlin syndrome) is a cancer-predisposition syndrome characterized by multiple basal cell carcinomas (BCCs) and diverse developmental defects. The gene for NBCCS has been mapped to 9q23.1-q31 in North American and European families. In addition, loss of heterozygosity (LOH) for genetic markers in this region has been detected in sporadic BCCs, indicating that the NBCCS gene is probably a tumor-suppressor gene. In this study we have determined that the NBCCS gene is also linked to this region in Australasian pedigrees and that there is no significant evidence of heterogeneity. We have defined the localization of the gene by multipoint and haplotype analysis of 15 families, using four microsatellite markers. LOH at these loci was detected in 50% of sporadic BCCs, a rate that is significantly higher than that in other skin lesions used as controls.     

Interpretation of the difference index as a guide to protein sequence identity

The expected behaviour of the “difference index” (Metzger, Shapiro, Mosimann & Vinton, 1968) has been examined under simple assumptions. Provided that it is only used to compare the compositions of proteins of equal or near-equal length, it can be interpreted to provide an estimate of the number of differences between the two sequences. Results with several pairs of proteins are in good agreement with estimates obtained by an alternative approach described previously (Cornish-Bowden, 1977).