Kinetic analysis of a general model of activation of aspartic proteinase zymogens involving a reversible inhibitor. I. Kinetic analysis

Starting from a simple general reaction mechanism of activation of aspartic proteinases zymogens involving a uni- and a bimolecular simultaneous activation route and a reversible inhibition step, the time course equation of the zymogen, inhibitor and activated enzyme concentrations have been derived. Likewise, expressions for the time required for any reaction progress and the corresponding mean activation rates as well as the half-life of the global zymogen activation have been derived. An experimental design and kinetic data analysis is suggested to estimate the kinetic parameters involved in the reaction mechanism proposed.     

Novel ways to prevent proteolysis - prophytepsin and proplasmepsin II

The recently determined crystal structures of two aspartic proteinase zymogens, prophytepsin from barley and proplasmepsin II from the malarial parasite Plasmodium falciparum, have provided new insights into zymogen inactivation. Prophytepsin shows a variation of the mechanism of inhibition used by the well-known gastric aspartic proteinase zymogens, whereas proplasmepsin II uses a completely new mode of inactivation.     

Competitive and uncompetitive inhibitors simultaneously acting on an autocatalytic zymogen activation reaction

The time course of the residual enzyme activity of a general model consisting of an autocatalytic zymogen activation process inhibited by an irreversible competitive inhibitor and an irreversible uncompetitive inhibitor has been studied. Approached analytical expressions which furnish the time course of the residual enzyme activity from the onset of the reaction depending on the rate constants and initial concentration have been obtained. The goodness and limitations of the analytical equations were checked by comparing with the results obtained from the numerical integration, i.e. with the simulated progress curves. A dimensionless parameter giving the relative contributions of both the activation and the inhibitions routes is suggested, so that the value of this parameter determines whether the activation or the inhibitions routes prevail or if both processes are balanced during the time for which the analytical expressions are valid. The effects of the initial zymogen, free enzyme and inhibitors concentrations are analysed. Finally an experimental design and kinetic data analysis is proposed to evaluate simultaneously the kinetic parameters involved and to discriminate between different zymogen activation processes which can be considered particular cases of the general model.     

Novel ways to prevent proteolysis — prophytepsin and proplasmepsin II

The recently determined crystal structures of two aspartic proteinase zymogens, prophytepsin from barley and proplasmepsin II from the malarial parasite Plasmodium falciparum, have provided new insights into zymogen inactivation. Prophytepsin shows a variation of the mechanism of inhibition used by the well-known gastric aspartic proteinase zymogens, whereas proplasmepsin II uses a completely new mode of inactivation.     

Competitive and uncompetitive inhibitors simultaneously acting on an autocatalytic zymogen activation reaction

The time course of the residual enzyme activity of a general model consisting of an autocatalytic zymogen activation process inhibited by an irreversible competitive inhibitor and an irreversible uncompetitive inhibitor has been studied. Approached analytical expressions which furnish the time course of the residual enzyme activity from the onset of the reaction depending on the rate constants and initial concentration have been obtained. The goodness and limitations of the analytical equations were checked by comparing with the results obtained from the numerical integration, i.e. with the simulated progress curves. A dimensionless parameter giving the relative contributions of both the activation and the inhibitions routes is suggested, so that the value of this parameter determines whether the activation or the inhibitions routes prevail or if both processes are balanced during the time for which the analytical expressions are valid. The effects of the initial zymogen, free enzyme and inhibitors concentrations are analysed. Finally an experimental design and kinetic data analysis is proposed to evaluate simultaneously the kinetic parameters involved and to discriminate between different zymogen activation processes which can be considered particular cases of the general model.     

Linear mixed irreversible inhibition of the autocatalytic activation of zymogens. Kinetic analysis checked by simulated progress curves

Autocatalytic zymogen activation is a phenomenon of great importance for understanding some fundamental physiological processes involved in the enzyme regulation of gastrointestinal-tract enzymes, blood coagulation, fibrinolysis and the complement system. Examples of such processes are the activation of prekallikrein, trypsinogen and pepsinogen, all of which are controlled by natural proteinase inhibitors. This work studies the kinetics of a general autocatalytic zymogen activation process overlapped by two two-step irreversible inhibitions, i.e. a linear mixed irreversible inhibition. The kinetic equations for the whole course of the reaction are derived for this mechanism. In addition, we determine the corresponding kinetics for a number of particular cases of the general model analyzed, i.e. for reversible and irreversible non-competitive, competitive and uncompetitive inhibition systems which are considered particular cases of the general mechanism studied. The kinetic behavior of the system is related to a parameter, a dimensionless quantity, which shows whether the inhibition or the activation route prevails, in a similar way to that which we have previously carried out for other mechanisms. Finally, based on the kinetic equations obtained, a procedure for discriminating between the different mechanisms considered is suggested. The results of this contribution can be directly applied to most physiological autocatalytic zymogen activations in the presence of an inhibitor, allowing their complete kinetic characterization and suggesting procedures for varying the relative weight of the catalytic and inhibition routes or for changing the predominant route.     

Adaptation of the behaviour of an aspartic proteinase inhibitor by relocation of a lysine residue by one helical turn

In addition to self-inhibition of aspartic proteinase zymogens by their intrinsic proparts, the activity of certain members of this enzyme family can be modulated through active-site occupation by extrinsic polypeptides such as the small IA3 protein from Saccharomyces cerevisiae. The unprecedented mechanism by which IA3 helicates to inhibit its sole target aspartic proteinase locates an i, i+4 pair of charged residues (Lys18+Asp22) on an otherwise-hydrophobic face of the amphipathic helix. The nature of these residues is not crucial for effective inhibition, but re-location of the lysine residue by one turn (+4 residues) in the helical IA3 positions its side chain in the mutant IA3-proteinase complex in an orientation essentially identical to that of the key lysine residue in zymogen proparts. The binding of the extrinsic mutant IA3 shows pH dependence reminiscent of that required for the release of intrinsic zymogen proparts so that activation can occur.     

The high-resolution crystal structure of porcine pepsinogen.

The structure of porcine pepsinogen at pH 6.1 has been refined to an R-factor of 0.173 for data extending to 1.65 A. The final model contains 180 solvent molecules and lacks density for residues 157-161. The structure of this aspartic proteinase zymogen possesses many of the characteristics of pepsin, the mature enzyme. The secondary structure of the zymogen consists predominantly of beta-sheet, with an approximate 2-fold axis of symmetry. The activation peptide packs into the active site cleft, and the N-terminus (1P-9P) occupies the position of the mature N-terminus (1-9). Thus changes upon activation include excision of the activation peptide and proper relocation of the mature N-terminus. The activation peptide or residues of the displaced mature N-terminus make specific interactions with the substrate binding subsites. The active site of pepsinogen is intact; thus the lack of activity of pepsinogen is not due to a deformation of the active site. Nine ion pairs in pepsinogen may be important in the advent of activation and involve the activation peptide or regions of the mature N-terminus which are relocated in the mature enzyme. The activation peptide-pepsin junction, 44P-1, is characterized by high thermal parameters and weak density, indicating a flexible structure which would be accessible to cleavage. Pepsinogen is an appropriate model for the structures of other zymogens in the aspartic proteinase family.     

Kinetic analysis of a simplified scheme of autocatalytic zymogen activation.

Proteolytic enzymes are usually biosynthesized as somewhat larger inactive precursors known as zymogens. These zymogens must undergo an activation process, usually a limited proteolysis, to attain their catalytic activity. When the activating enzyme and the activated enzyme coincide, the process is an autocatalytic zymogen activation. In the present study, a kinetic analysis of the entire progress curve for the autocatalytic zymogen activation reactions is presented. On the basis of the kinetic equations, a novel procedure is developed to evaluate the kinetic parameters of the reactions. This procedure is particularly useful for the fast zymogen autoactivation reactions. As two examples, the novel procedure is used to analyse the autocatalytic activation of bovine trypsinogen and human blood coagulation factor XII (Hageman factor).     

Contribution of the intra- and intermolecular routes in autocatalytic zymogen activation: application to pepsinogen activation

Taking as the starting point a recently suggested reaction scheme for zymogen activation involving intra- and intermolecular routes and the enzyme-zymogen complex, we carry out a complete analysis of the relative contribution of both routes in the process. This analysis suggests the definition of new dimensionless parameters allowing the elaboration, from the values of the rate constants and initial conditions, of the time course of the contribution of the two routes. The procedure mentioned above related to a concrete reaction scheme is extrapolated to any other model of autocatalytic zymogen activation involving intra- and intermolecular routes. Finally, we discuss the contribution of both of the activating routes in pepsinogen activation into pepsin using the values of the kinetic parameters given in the literature.     

Kinetic analysis of a general model of activation of aspartic proteinase zymogens involving a reversible inhibitor. II. Contribution of the uni- and bimolecular activation routes

From the kinetic study carried out in part I of this series (preceding article) an analysis quantifying the relative contribution to the global process of the uni- and bimolecular routes has been carried out. This analysis suggests a way to predict the time course of the relative contribution as well as the effect on this relative weight of the initial zymogen, inhibitor and activating enzyme concentrations.     

Kinetic behaviour of proenzymes activation in the presence of different inhibitors for both activating and activated enzymes

In the present paper, a kinetic analysis of a general model for proenzyme activation, where the activating enzyme and also the activated one are reversibly inhibited in two steps by two different inhibitors, has been performed. The cases in which both inhibitors are the same, or in which the inhibition is irreversible (only one or the two inhibition routes) are treated as particular cases of the general model. In addition, the kinetic behaviour of many other proenzyme activation systems involving inhibition, particular cases of the reaction scheme under study, can be obtained. The total number of particular cases for the general model under study is 370, so this approach offers to the scientific community working in limited proteolysis regulation for the first time a method based on general solutions which only needs to be specified to their concrete problem of zymogen activation. Finally, new adimensional parameters are introduced, allowing the knowledgement, in the case that any of the inhibition routes is irreversible, the relative weight of both activation and irreversible inhibition routes.     

Kinetic analysis of zymogen autoactivation in the presence of a reversible inhibitor.

Limited proteolysis is a highly specific irreversible process, which can serve to initiate physiological function by converting a precursor protein into a biologically active form. When the activating enzyme and the activated enzyme coincide, the process is an autocatalytic zymogen activation (i.e. reactions in which the zymogens serves as a substrate for the corresponding active enzyme). The activity of proteases is frequently regulated by the binding of specific protease inhibitors. Thus, to understand the biological regulation of proteolysis, one must understand the role of protease inhibitors. In the present study, a detailed kinetic analysis of autocatalytic reaction modulated by a reversible inhibitor is represented. On the basis of the kinetic equation, a novel procedure is developed to evaluate the kinetic parameters of the reaction. As an example of the application of this method, effects of acetamidine, p-amidinobenzamidine and benzamidine on the autoactivation of trypsinogen by trypsin were studied.     

Secretion by yeast of the zymogen form of Mucor rennin, an aspartic proteinase of Mucor pusillus, and its conversion to the mature form

The Mucor rennin gene encoding a prepro-form of the fungal aspartic proteinase from Mucor pusillus was expressed under the control of the yeast GAL7 promoter in Saccharomyces cerevisiae. An inactive zymogen of the enzyme with the 44-amino-acid pro-sequence was identified in the medium during the initial stage of cultivation. Processing of the purified zymogen to the mature enzyme proceeded autocatalytically under the acidic conditions. The rate of processing was accelerated by an increase in the concentration of the zymogen or addition of the mature enzyme. The in vitro processing was inhibited by inhibitors for the aspartic proteinases. The zymogen with no proteinase activity due to a mutation at the active site residue, Asp, was still processed at a relatively slower rate in a wild-type strain of yeast, but no processing occurred in the pep4-3 mutant strain of S. cerevisiae deficient in yeast proteinase A. Thus, Mucor rennin is excreted in a form of zymogen, which is then processed in the yeast secretion pathway mainly by the autocatalytic proteolysis but, alternatively, by a proteinase of yeast.     

Evolution in the structure and function of aspartic proteases

Aspartic proteases (EC3.4.23) are a group of proteolytic enzymes of the pepsin family that share the same catalytic apparatus and usually function in acid solutions. This latter aspect limits the function of aspartic proteases to some specific locations in different organisms; thus the occurrence of aspartic proteases is less abundant than other groups of proteases, such as serine proteases. The best known sources of aspartic proteases are stomach (for pepsin, gastricsin, and chymosin), lysosomes (for cathepsins D and E), kidney (for renin), yeast granules, and fungi (for secreted proteases such as rhizopuspepsin, penicillopepsin, and endothiapepsin). These aspartic proteases have been extensively studied for their structure and function relationships and have been the topics of several reviews or monographs (Tang: Acid Proteases, Structure, Function and Biology. New York: Plenum Press, 1977; Tang: J Mol Cell Biochem 26:93-109, 1979; Kostka: Aspartic Proteinases and Their Inhibitors. Berlin: Walter de Gruyter, 1985). All mammalian aspartic proteases are synthesized as zymogens and are subsequently activated to active proteases. Although a zymogen for a fungal aspartic protease has not been found, the cDNA structure of rhizopuspepsin suggests the presence of a "pro" enzyme (Wong et al: Fed Proc 44:2725, 1985). It is probable that other fungal aspartic proteases are also synthesized as zymogens. It is the aim of this article to summarize the major models of structure-function relationships of aspartic proteases and their zymogens with emphasis on more recent findings. Attempts will also be made to relate these models to other aspartic proteases.     

A kinetic and equilibrium study of the denaturation of aspartic proteinases from the fungi, Endothia parasitica and Mucor miehei

Kinetic and equilibrium analyses of the denaturation of Endothia parasitica and Mucor miehei aspartic proteinases were performed using enzyme activity and ultraviolet absorption as indices of denaturation. Denaturation of these proteinases was shown to be irreversible, suggesting that the conformations of these aspartic proteinases may be predetermined in their zymogens. Thermal and guanidine hydrochloride denaturation of these proteinases produced first-order, two-state, kinetic behaviour. Equilibrium unfolding transitions of these proteinases were highly cooperative but not entirely coincident in the two indices employed, suggesting some deviation from two-state character. Oxidation to remove 37.8% of the carbohydrate of M. miehei glycoproteinase with sodium metaperiodate resulted in a substantial decrease in both kinetic and equilibrium stabilities without modification of the amino acid composition or specific activity. In addition, gel filtration subsequent to equilibrium studies indicated that partial removal of the carbohydrate from M. miehei proteinase promoted autolysis under denaturing conditions.     

Kinetics of an autocatalytic zymogen reaction in the presence of an inhibitor coupled to a monitoring reaction

A global kinetic analysis of a model consisting of an autocatalytic zymogen-activation process, in which an irreversible inhibitor competes with the zymogen for the active site of the proteinase, and a monitoring coupled reaction, in which the enzyme acts upon one of its substrates, is presented. This analysis is based on the progress curves of any of the two products released in the monitoring reaction. The general solution is applied to an important particular case in which rapid equilibrium conditions prevail. Finally, we suggest a procedure to predict whether the inhibition or activation route dominates in the steady state of the system. These results generalize our previous analysis of simpler mechanisms.     

Molecular mechanisms for the conversion of zymogens to active proteolytic enzymes.

Proteolytic enzymes are synthesized as inactive precursors, or "zymogens," to prevent unwanted protein degradation, and to enable spatial and temporal regulation of proteolytic activity. Upon sorting or appropriate compartmentalization, zymogen conversion to the active enzyme typically involves limited proteolysis and removal of an "activation segment." The sizes of activation segments range from dipeptide units to independently folding domains comprising more than 100 residues. A common form of the activation segment is an N-terminal extension of the mature enzyme, or "prosegment," that sterically blocks the active site, and thereby prevents binding of substrates. In addition to their inhibitory role, prosegments are frequently important for the folding, stability, and/or intracellular sorting of the zymogen. The mechanisms of conversion to active enzymes are diverse in nature, ranging from enzymatic or nonenzymatic cofactors that trigger activation, to a simple change in pH that results in conversion by an autocatalytic mechanism. Recent X-ray crystallographic studies of zymogens and comparisons with their active counterparts have identified the structural changes that accompany conversion. This review will focus upon the structural basis for inhibition by activation segments, as well as the molecular events that lead to the conversion of zymogens to active enzymes.     

Kinetics of autocatalytic zymogen activation measured by a coupled reaction: pepsinogen autoactivation

A kinetic study was performed of a model for an autocatalytic zymogen activation process involving both intra- and intermolecular routes, to which a chromogenic reaction in which the active enzyme acts upon one of its substrates was coupled to continuously monitor the reaction. Kinetic equations describing the evolution of species involved in the system with time were obtained. These equations are valid for any zymogen autocatalytic activation process under the same initial conditions. Experimental design and kinetic data analysis procedures to evaluate the kinetic parameters, based on the derived kinetic equations, are suggested. In addition, a dimensionless distribution coefficient was defined, which shows mathematically whether the intra- or the intermolecular route prevails once the kinetic parameters involved in the system are known. The validity of the results obtained was checked using simulated curves for the species involved. As an example of application of the method, the system is experimentally illustrated by the continuous monitoring of pepsinogen transformation to pepsin.