Temperature-jump studies on benzeneboronic acid-serine protease interactions. Subtilisin and alpha-chymotrypsin.

The interactions of benzeneboronic acid (BBA) as a transition state analog with subtilisin (EC 3.4.21.4) and with alpha-chymotrypsin (EC 3.4.21.1) were investigated kinetically by the temperature-jump method using pH indicators. For both enzymes, the concentration dependence of the relaxation time was consistent with a two-step mechanism involving a fast bimolecular association followed by a slow, unimolecular process. The possibility of a trigonal-tetrahedral interconversion of BBA at the active site of the enzyme is discussed.     

Elementary processes in the interaction of serine protease with a possible transition state analog. Subtillisin-benzeneboronic acid system.

The interaction of benzeneboronic acid(BBA), a possible transition state analog, with subtilisin BPN' [EC 3.4.21.14] was studied by the temperature-jump method at various pH's, temperatures and in D2O as well as H2O. From analysis of the concentration dependence of the relaxation times, it was suggested that the subtillsin-BBA interactions consist of at least two elementary steps, a fast bimolecular association followed by a slow unimolecular process. Similar concentration dependence was observed at pH 6.1-6.7 at 25degrees. However, in D2O the reciprocal relaxation times generally decreased compared to those in H2O and became concentration-independent below pD 6.5. The relaxation times were influenced considerably by the temperature. From these results, the slow unimolecular process was assigned to the trigonal-tetrahedral interconversion of BBA at the active site of the enzyme.     

A study of heat of formation of acetyl-alpha-chymotrypsin intermediate by stopped flow calorimetry

The catalytic hydrolysis of p-nitrophenyl acetate by alpha-chymotrypsin was studied by stopped-flow calorimetry and spectrophotometry at pH 8.0 and 25 degrees C. The initial burst and subsequent steady state of the reaction were observed by rapid calorimetry and spectrophotometry. Based on the three-step mechanism established for the enzymatic reaction, E + S in equilibrium ES leads to acetyl-E + P1 (p-nitrophenol) leads to E + P1 + acetic acid, the enthalpy change of formation of the acetyl enzyme from ES complex was estimated to be -29 kJ . mol-1.     

PH-dependence of the steady-state rate of a two-step enzymic reaction.

1. The pH-dependence is considered of a reaction between E and S that proceeds through an intermediate ES under "Briggs-Haldane' conditions, i.e. there is a steady state in ES and [S]o greater than [E]T, where [S]o is the initial concentration of S and [E]T is the total concentration of all forms of E. Reactants and intermediates are assumed to interconvert in three protonic states (E equilibrium ES; EH equilibrium EHS; EH2 equilibrium EH2S), but only EHS provides products by an irreversible reaction whose rate constant is kcat. Protonations are assumed to be so fast that they are all at equilibrium. 2. The rate equation for this model is shown to be v = d[P]/dt = (kcat.[E]T[S]o/A)/[(KmBC/DA) + [S]o], where Km is the usual assembly of rate constants around EHS and A-D are functions of the form (1 + [H]/K1 + K2/[H]), in which K1 and K2 are: in A, the molecular ionization constants of ES; in B, the analogous constants of E; in C and D, apparent ionization constants composed of molecular ionization constants (of E or ES) and assemblies of rate constants. 3. As in earlier treatments of this type of reaction which involve either the assumption that the reactants and intermediate are in equilibrium or the assumption of Peller & Alberty [(1959) J. Am. Chem. Soc. 81, 5907-5914] that only EH and EHS interconvert directly, the pH-dependence of kcat. is determined only by A. 4. The pH-dependence of Km is determined in general by B-C/A-D, but when reactants and intermediate are in equilibrium, C identical to D and this expression simplifies to B/A. 5. The pH-dependence of kcat./Km, i.e. of the rate when [S]o less than Km, is not necessarily a simple bell-shaped curve characterized only by the ionization constants of B, but is a complex curve characterized by D/B-C. 6. Various situations are discussed in which the pH-dependence of kcat./Km is determined by assemblies simpler than D/B-C. The special situation in which a kcat./Km-pH profile provides the molecular pKa values of the intermediate ES complex is delineated.     

Kinetics of the interaction of alpha-chymotrypsin with trypsin kallikrein inhibitor (Kunitz) in which the reactive-site peptide bond Lys-15--Ala-16 is split.

Modified trypsin kallikrein inhibitor (I*), with the reactive-site peptide bond Lys-15--Ala-16 split, reacts with alpha-chymotrypsin (E) via an intermediate X to the stable tetrahedral complex C:E + I in equilibrium X leads to C. Formation X constitutes a fast pre-equilibrium (equilibrium constant Kx = 7 X 10(-5) M, association rate constant kx = 4 X 10(3)M-1s-1) to the slow reaction X leads to C (rate constant kc = 2 X 10(-3) s-1), all values at pH 7.5. No intermediate X is observed when alpha-chymotrypsin reacts with I*-OMe in which the carboxyl group of Lys-15 is esterified by methanol. This observation as well as the different pH dependence of the overall association rate constants in the case of I* and I*-OMe indicate tha formation of X precedes formation of the acyl enzyme in the catalytic pathway. The data are compared to the similar results obtained with beta-trypsin and I* or I*-OMe.     

Identification of mechanism of enzyme/transport process in the system of "enzyme/ transporter--substrate--effector" using the "ratio" method

Using equilibrium assumption the analysis of kinetics of enzyme/transport process has been developed. In the course of this process the enzyme can interact simultaneously with substrate S and effector E and as a result two products are generated: P1 (from substrate) and P2 (from effector) after catalytic effect of enzyme or transportation across the biological membrane. It has been demonstrated that the ratio (R = V0,1/V0,2) of initial rates of formation of reaction products P, (V0,1) and P2 (V0,2) represented in linearized form as a dependence on concentration of both substrate S0 and effector E0 allows to identify a specific mechanism of the present process. An algorithm of such identification has been developed.     

Kinetic characteristics of the ATP-pyrophosphate isotope exchange catalyzed by RNA ligase from T4 bacteriophage

The dependence of initial rate v0 of ATP--PPi exchange reaction catalyzed by RNA-ligase of bacteriophage T4 on the concentration of ATP(s), pyrophosphate (z) and Mgcl2 has been determined. The dependence of v0 on s and z described by the equation v0 = k-1k2E0/(k-1 + K2) (1 + K1/s + k2/z) has been obtained for the reaction of E + S in equilibrium ES in equilibrium E1 + Z, where E--enzyme, E1--adenylylenzyme, S--ATP, Z--pyrophosphate, K1 and K2--constants of equilibrium, k-1, k2--velocity constants of transition of ES to E + S and E1 + Z, E0--complete concentration of enzyme. The low inhibition of the ATP--PPi exchange by the acceptor A(pA)2 and donors pAp, p(Ap)3, pCp has been shown. The dependence of v0 on the concentration of MgCl2 is consent with the incorporation of only dimagnesium salts of substrates in the isotope-exchange reaction.     

Catalytic mechanism of C-C hydrolase MhpC from Escherichia coli: kinetic analysis of His263 and Ser110 site-directed mutants

C-C hydrolase MhpC (2-hydroxy-6-keto-nona-1,9-dioic acid 5,6-hydrolase) from Escherichia coli catalyses the hydrolytic C-C cleavage of the meta-ring fission product on the phenylpropionic acid catabolic pathway. The crystal structure of E. coli MhpC has revealed a number of active-site amino acid residues that may participate in catalysis. Site-directed mutants of His263, Ser110, His114, and Ser40 have been analysed using steady-state and stopped-flow kinetics. Mutants H263A, S110A and S110G show 10(4)-fold reduced catalytic efficiency, but still retain catalytic activity for C-C cleavage. Two distinct steps are observed by stopped-flow UV/Vis spectrophotometry, corresponding to ketonisation and C-C cleavage: H263A exhibits very slow ketonisation and C-C cleavage, whereas S110A and S110G exhibit fast ketonisation, an intermediate phase, and slow C-C cleavage. H114A shows only twofold-reduced catalytic efficiency, ruling out a catalytic role, but shows a fivefold-reduced K(M) for the natural substrate, and an ability to process an aryl-containing substrate, implying a role for His114 in positioning of the substrate. S40A shows only twofold-reduced catalytic efficiency, but shows a very fast (500 s(-1)) interconversion of dienol (317 nm) to dienolate (394 nm) forms of the substrate, indicating that the enzyme accepts the dienol form of the substrate. These data imply that His263 is responsible for both ketonisation of the substrate and for deprotonation of water for C-C cleavage, a novel catalytic role in a serine hydrolase. Ser110 has an important but non-essential role in catalysis, which appears not to be to act as a nucleophile. A catalytic mechanism is proposed involving stabilisation of reactive intermediates and activation of a nucleophilic water molecule by Ser110.     

X-ray crystallographic study of boronic acid adducts with subtilisin BPN' (Novo). A model for the catalytic transition state.

We have studied the structures of adducts formed between subtilisin BPN' and both benzeneboronic acid and 2-phenylethaneboronic acid by x-ray diffraction techniques. Electron density and difference maps at 2.5 A resolution were computed with phases calculated from a partially refined structure of the native enzyme (R = 0.23 at 2.0 A). Both adducts contain a covalent bond between Ogamma of the catalytic Ser-221 and the inhibitor boron atom. The boron atom is coordinated tetrahedrally, with one of the two additional boronic acid oxygen atoms lying in the "oxyanion hole" and the other at the leaving group site identified in previous studies (ROBERTUS, J.D., Kraut, J. ALDEN, R.A., and BIRKTOFT, J.J. (1972) Biochemistry 11, 4293-4303). Moreover, the previously postulated structure of the tetrahedral intermediate for substrate hydrolysis is isosteric with these boronic acid adducts, which can therefore be considered good models for the transition state complex (KOEHLER, K.K., and LIENHARD, G.E. (1972) Biochemistry 10, 2477-2483). These observations further support the suggestion that an important contribution to stabilization of this transition state complex, relative to both the Michaelis complex and the acyl intermediate, occurs as a consequence of hydrogen bond donation to the substrate carbonyl oxygen atom from the side chain amido group of Asn-155 and from the backbone amido group of Ser-221.     

Sequence of the gene encoding an alkaline serine proteinase of Bacillus pumilus TYO-67

The complete nucleotide sequence of the gene encoding an alkaline serine proteinase (aprP) of Bacillus pumilus TYO-67 was determined. The sequence analysis showed an open reading frame of 1,149 bp (383 amino acids) that encoded a signal peptide consisting of 29 residues and a propeptide of 79 residues. The deduced 3 amino acid residues, D32, H64, and S221, were identical with 3 essential amino acids in the catalytic center of subtilases. The sequence around these residues revealed that APRP was a new member of the true subtilisin subgroup of the subtilisin family. The highest homology was found in subtilisin NAT at 64.4% in the DNA sequence. The residue S189 of APRP was different from those of other subtilases.     

Accelerated refolding of subtilisin BPN' by tertiary-structure-forming mutants of its propeptide

The propeptide of subtilisin BPN', which functions as an intramolecular chaperone and a temporary inhibitor of subtilisin, is unique in that it acquires its three-dimensional structure by formation of a complex with the cognate protease. We previously showed that the successive amino acid replacements Ala47-->Phe, Gly13-->Ile, and Val65-->Ile in the propeptide to increase its hydrophobicity resulted in formation of a tertiary structure, accompanied by increased ability to bind to the protease and increased resistance to proteolysis. In this study, we examined the effects of these tertiary-structure-forming mutations on the intramolecular chaperone activity of the propeptide. The successive amino acid replacements mentioned above were introduced into pro-subtilisin*, possessing a Ser221-->Ala mutation in the catalytic residue. Refolding experiments were started by rapid dilution of the denatured pro-subtilisin*, and formation of tertiary structure in subtilisin was monitored kinetically by increase in tryptophan fluorescence. The wild-type pro-subtilisin* was found to refold with a rate constant of 4.8 x 10(-3) s(-1) in the equation describing an intramolecular process. The Ala47-->Phe replacement in the propeptide resulted in a 1.2-fold increase in the rate constant of subtilisin refolding. When the additional replacement Gly13-->Ile was introduced, refolding of subtilisin was substantially accelerated, and its kinetics could be fitted to a double exponential process composed of a fast phase with a rate constant of 2.1 x 10(-2) s(-1) and a slow phase with a rate constant of 4.5 x 10(-3) s(-1). The rate constant of the fast phase was increased slightly by a further replacement, Val65-->Ile. Since the slow phase is considered to correspond to proline isomerization, we concluded that tertiary-structure-forming mutations in the propeptide produce positive effects on its intramolecular chaperone activity through acceleration of the propeptide-induced formation of the tertiary structure of subtilisin BPN'.     

The general modifier ("allosteric") unireactant enzyme mechanism: redundant conditions for reduction of the steady state velocity equation to one that is first degree in substrate and effector

The general unireactant modifier mechanism in the absence of product can be described by the following linked reactions: E + S k1 in equilibrium k-1 ES k3----E + P; E + I k5 in equilibrium k-5 EI; EI + S k2 in equilibrium k-2 ESI k4----EI + P; and ES + I k6 in equilibrium k-6 ESI where S is a substrate and I is an effector. A full steady state treatment yields a velocity equation that is second degree in both [S] and [I]. Two different conditions (or assumptions) permit reduction of the velocity equation to one that is first degree in [S] and [I]. These are (a) that k-2k3 = k-1k4 (Frieden, C., J. Biol. Chem. 239, pp. 3522-3531, (1964)) and (b) that the I-binding reactions are at equilibrium (Reinhart, G. D., Arch. Biochem. Biophys. 224, pp. 389-401 (1983)). It is shown that each condition gives rise to the other (i.e., if the I-binding reactions are at equilibrium, then k-2k3 must equal k-1k4 and vice-versa). If one assumes equilibrium for the I-binding steps, the velocity equation derived by the method of Cha (J. Biol. Chem. 243, pp. 820-825 (1968)) is apparently second degree in [I] (Segel, I. H., Enzyme Kinetics, p. 838, Wiley-Interscience (1975)), but reduces to a first degree equation when the relationship derived by Frieden is inserted. If one starts by assuming a single equilibrium condition for I binding, e.g., k-5[EI] = k5[E][I] or k-6[ESI] = k6[ES][I], then a traditional algebraic manipulation of the remaining steady state equations provides first degree expressions for the concentrations of all enzyme species and also discloses the Frieden relationship.     

The use of intrinsic protein fluorescence to quantitate enzyme-bound persulfide and to measure equilibria between intermediates in rhodanese catalysis

The intrinsic fluorescence of the enzyme rhodanese is quenched by as much as 30% when sulfur is transferred to the free enzyme form, E, giving the sulfur-substituted enzyme, ES. This fluorescence change (lambda ex = 295 nm and lambda em = 335 nm) has been used to quantitate the E and ES forms which are isolatable, obligatory intermediates in rhodanese catalysis. Fluorescence titration was performed using cyanide to irreversibly remove sulfur from ES. The results show a stoichiometry corresponding to 1 bound sulfur/molecule of the ES form of rhodanese (Mr = 33,000). The fluorescence changes were used to measure the concentrations of E and ES when these were in reversible equilibria induced by interactions with the substrates S2O3(2-) and SO3(2-). These results were compared with an equilibrium constant derived from published kinetic studies for the reaction (formula; see text) The very close agreement between the physical and kinetic methods indicate that there are no significant concentrations of intermediates other than E and ES. Overall, the results are compatible with the formation of a persulfide intermediate in rhodanese catalysis and are consistent with conclusions from x-ray crystallography and absorption spectroscopy. In addition, these procedures offer a facile method to measure equilibria between catalytic intermediates in the rhodanese reaction using functionally relevant concentrations.     

Binding of the recombinant proteinase inhibitor eglin c from leech Hirudo medicinalis to human leukocyte elastase, bovine alpha-chymotrypsin and subtilisin Carlsberg: thermodynamic study

The effect of pH and temperature on the apparent association equilibrium constant (Ka) for the binding of the recombinant proteinase inhibitor eglin c from leech Hirudo medicinalis to human leukocyte elastase (EC 3.4.21.37), bovine alpha-chymotrypsin (EC 3.4.21.1) and subtilisin Carlsberg (EC 3.4.21.14) has been investigated. On lowering the pH from 9.5 to 4.5, values of Ka for eglin c binding to the serine proteinases considered decrease thus reflecting the acid-pK shift of the invariant histidyl catalytic residue (His57 in human leukocyte elastase and bovine alpha-chymotrypsin, and His64 in subtilisin Carlsberg) from congruent to 6.9, in the free enzymes, to congruent to 5.1, in the enzyme:inhibitor adducts. At pH 8.0, values of the apparent thermodynamic parameters for eglin c binding are: human leukocyte elastase - Ka = 1.0 x 10(10) M-1, delta G phi = -13.4 kcal/mol, delta H phi = +1.8 kcal/mol, and delta S phi = +52 entropy units; bovine alpha-chymotrypsin -Ka = 5.0 x 10(9) M-1, delta G phi = -13.0 kcal/mol, delta H phi = +2.0 kcal/mol, and delta S phi = +51 entropy units; and subtilisin Carlsberg - Ka = 6.6 x 10(9) M-1, delta G phi = -13.1 kcal/mol, delta H phi = +2.0 kcal/mol, and delta S phi = +51 entropy units (values of Ka, delta G phi and delta S phi were obtained at 21 degrees C; values of delta H phi were temperature independent over the range explored, i.e. between 10 degrees C and 40 degrees C; 1 kcal = 4184J).(ABSTRACT TRUNCATED AT 250 WORDS)     

Mechanisms of the multiphasic kinetics in the folding and unfolding of globular proteins

The multiphasic kinetics of the protein folding and unfolding processes are examined for a “cluster model” with only two thermodynamically stable macroscopic states, native (N) and denatured (D), which are essentially distributions of microscopic states. The simplest kinetic schemes consistent with the model are: N-(fast) → I-(slow) → D for unfolding and N ← (fast)-D₂ ← (slow)-D₁ for refolding. The fast phase during the unfolding process can be visualized as the redistribution of the native population N to I within its free energy valley. Then, this population crosses over the free energy barrier to the denatured state D in the slow phase. Therefore, the macrostate I is a kinetic intermediate which is not stable at equilibrium. For the refolding process, the initial equilibrium distribution of the denatured state D appears to be separated into D₁ and D₂ in the final condition because of the change in position of the free energy barrier. The fast refolding species D₂ is due to the “leak” from the broadly distributed D state, while the rest is the slow refolding species D₁, which must overpass the free energy barrier to reach N. At an early stage of the folding process the amino acid chain is considered to be composed of several locally ordered regions, which we call clusters, connected by random coil chain parts. Thus, the denatured state contains different sizes and distributions of clusters depending on the external condition. A later stage of the folding process is the association of smaller clusters. The native state is expressed by a maximum-size cluster with possible fluctuation sites reflecting this association. A general discussion is given of the correlation between the kinetics and thermodynamics of proteins from the overall shape of the free energy function. The cluster model provides a conceptual link between the folding kinetics and the structural patterns of globular proteins derived from the X-ray crystallographic data.     

The role of Pro-239 in the catalysis and heat stability of subtilisin E

Site-directed mutagenesis was employed to analyze the role of an alpha-helix containing catalytic Ser-221 of subtilisin E. Pro-239 located at the carboxy-terminal end of the alpha-helix was first replaced with Gly to examine the role of Pro-239 in the catalysis and stability of subtilisin E. The mutation was found to decrease both the catalytic rate (kcat) and the heat stability. This result strongly suggests that Pro-239 plays an important role in the maintenance of the alpha-helix, affecting the functioning of the active site. Various amino acid substitutions at position 239 were attempted to obtain the active subtilisins from Gly-239 subtilisin. Lys- and Arg-substitutions were found to result in more active and stable subtilisins than the Gly-239 subtilisin. In particular, the Arg-239 mutant showed enhanced heat stability compared with the wild type. These results demonstrate the important role of the alpha-helix containing catalytic Ser-221 in the catalysis as well as in the heat stability of subtilisin.     

Random mutagenesis to enhance the activity of subtilisin in organic solvents: Characterization of Q103R subtilisin E

Q103R subtilisin E was isolated following random mutagenesis and screening for improved activity in the presence of dimethylformamide (DMF). Our goal is to identify the mechanism(s) by which amino acid substitutions can enhance enzyme activity in polar organic solvents. A quantitative framework for comparing substrate binding and catalytic activities of mutant and wild-type enzymes in the presence and absence of DMF is outlined. Kinetic experiments performed at high salt concentration (1M KCl) reveal that the mechanism behind the Q103R variant's enhanced activity toward succinyl-Ala-Ala-Pro-Phe-p-nitroanilide is both electrostatic and nonelectrostatic in origin. Favorable electrostatic interactions between the negatively charged succinyl group of the substrate and the positive charge on Arg 103 are responsible for tighter substrate binding. This conclusion is supported by kinetic experiments performed on the related substrate Ala-Ala-Pro-Phe-p-nitroanilide and the hydrolysis kinetics of the Q103E, Q103K, and Q103S variants constructed by site-directed mutagenesis. These results highlight the importance of the choice of the substrate used to screen for improvements in catalytic activity.     

Thermodynamic profiles of penicillin G hydrolysis catalyzed by wild-type and Met----Ala168 mutant penicillin acylases from Kluyvera citrophila

The Met-168 residue in penicillin acylase from Kluyvera citrophila was changed to Ala by oligonucleotide site-directed mutagenesis. The Ala-168 mutant exhibited different substrate specificity than wild-type and enhanced thermal stability. The thermodynamic profiles for penicillin G hydrolysis catalyzed by both enzymes were obtained from the temperature dependence of the steady-state kinetic parameters Km and kcat. The high values of enthalpy and entropy of activation determined for the binding of substrate suggest that an induced-fit-like mechanism takes place. The Met----Ala168 mutation unstabilizes the first transition-state (E..S not equal to) and the enzyme-substrate complex (ES) causing a decrease in association equilibrium and specificity constants in the enzyme. However, no change is observed in the acyl-enzyme formation. It is concluded that residue 168 is involved in the enzyme conformational rearrangements caused by the interaction of the acid moiety of the substrate at the active site.     

Cryoenzymic studies on actomyosin ATPase. Evidence that the degree of saturation of actin with myosin subfragment 1 affects the kinetics of the binding of ATP

The initial steps of actomyosin subfragment 1 (acto-S1) ATPase (dissociation and binding of ATP) were studied at -15 degrees C with 40% ethylene glycol as antifreeze. The dissociation kinetics were followed by light scattering in a stopped-flow apparatus, and the binding of ATP was followed by the ATP chase method in a rapid-flow quench apparatus. The data from the chase experiments were fitted to E + ATP in equilibrium (K1) E.ATP----(k2) E*ATP, where E is acto-S1 or S1. The kinetics of the binding of ATP to acto-S1 were sensitive to the degree of saturation of the actin with S1. There was a sharp transition with actin nearly saturated with S1: when the S1 to actin ratio was low, the kinetics were fast (K1 greater than 300 microM, k2 greater than 40 s-1); when it was high, they were slow (K1 = 14 microM, k2 = 2 s-1). With S1 alone K1 = 12 microM and k2 = 0.07 S-1. With acto heavy meromyosin (acto-HMM) the binding kinetics were the same as with saturated acto-S1, regardless of the HMM to actin ratio. The dissociation kinetics were independent of the S1 to actin ratio. Saturation kinetics were obtained with Kd = 460 microM and kd = 75 S-1. The data for the saturated acto-S1 could be fitted to a reaction scheme, but for lack of structural information the abrupt dependence of the ATP binding kinetics upon the S1 to actin ratio is difficult to explain.(ABSTRACT TRUNCATED AT 250 WORDS)     

Directed coevolution of stability and catalytic activity in calcium-free subtilisin

We have coevolved high activity and hyperstability in subtilisin by sequentially randomizing 12 amino acid positions in calcium-free subtilisin. The optimal amino acid for each randomized site was chosen based on stability and catalytic properties and became the parent clone for the next round of mutagenesis. Together, the 12 selected mutations increased the half-life of calcium-free subtilisin at elevated temperature by 15,000-fold. The catalytic properties of the mutants were examined against a range of substrates. In general, only mutations occurring at or near the substrate-binding surface have measurable effects on catalytic constants. No direct influence of stability on catalytic properties was observed. A high-stability mutant, Sbt140, was a more efficient enzyme in terms of k(cat)/K(m) than a commercial version of subtilisin across a range of substrates but had a lower k(cat) against tight-binding substrates. The reason for this behavior was discerned by examining microscopic rate constants for the hydrolysis of a tight-binding peptide substrate. Burst kinetics were observed for this substrate, indicating that acylation is not rate-limiting. Although acylation occurs at the rate of substrate binding, k(cat) is attenuated by the slow release of the N-terminal product. Natural evolution appears to have optimized catalytic activity against a range of sequences by achieving a balance between substrate binding and the rate of release of the N-terminal product.