Temperature-dependences of the kinetics of reactions of papain and actinidin with a series of reactivity probes differing in key molecular recognition features

Enzymes and reactivity probes

Methods of purification of actinidin [9] and papain [10], which include the production of fully active enzymes by covalent chromatography (reviewed in [11]), have been described previously, as have their active-centre content and evaluation by spectroscopic titration at 343 nm (ϵ₃₄₃=8080 M⁻¹·cm⁻¹) using 2,2′-dipyridyl disulphide as titrant [12].

The syntheses and characterization of the seven reactivity probes used in the present work (shown in Figure 1) have been described previously in connection with pH-dependence studies: ethyl 2-pyridyl disulphide (1) [13]; 2-(acetoxy)ethylene 2′-pyridyl disulphide (2) [14]; 2-(acetamido)ethylene 2′-pyridyl disulphide (3) [15]; 2-(N′-acetyl-L-phenylalanyl)hydroxyethylene 2′-pyridyl disulphide (4) [10] and its D-enantiomer (5) [16]; 2-(N′-acetyl-L-phenylalanylamino)ethylene 2′-pyridyl disulphide (6) [15] and its D-enantiomer (7) [17].

SF (stopped-flow) kinetics

Kinetic studies on the reactions of the catalytic site thiol groups of papain and actinidin with the reactivity probes were performed by using a Hi-Tech Scientific SF spectrophotometer, kinetics workstation, and data acquisition and analysis software. Monochromator entrance and exit slit widths were set at 0.5 mm. The sample handling unit was fitted with a UG5 bandpass filter to eliminate stray light and was configured for thermostatically controlled temperature cycling. Temperature control was achieved using a Grant LTD6 water bath.

Reactions were carried out in the low-temperature coefficient (dpK_a/dT=0.0028 [18]) KH₂PO₄/NaOH buffer, pH 6.7, I 0.1 M, at ten different temperatures in the range 4–30 °C under (pseudo) first-order conditions with [probe]≥20 times [enzyme thiol]. The stock solution of the phosphate buffer was prepared at I 0.3 M and was diluted to provide a solution containing the reactivity probe at I 0.1 M in one of the syringes of the SF spectrophotometer. The other syringe contained the enzyme in 0.1 M KCl. Mixing of equal volumes of these two solutions maintained I 0.1 M in the reaction chamber. The pH was checked to be 6.7 in the effluent from the reaction chamber and in dummy reaction mixtures. The release of pyridine-2-thione was monitored at 343 nm. Values of the observed first-order rate constants (k_obs) were obtained by fitting the equation for a single exponential process,

where P₁=A_∞−A₀, P₂=k_obs and P₃=A_∞, to the absorbance (A)−time (t) data collected as multiple superimposable traces by the SF system.

Determination of activation parameters

Values of entropy of activation (ΔS^‡) and enthalpy of activation (ΔH^‡) were determined by linear regression of the left-hand side of eqn (1) on 1000/T, where T is the absolute temperature and 1000 is a convenient scaling factor:

(1)

Eqn (1) is a convenient transform of the Eyring equation (see the Results and Discussion section) in which R is the gas constant (8.13145 J·mol⁻¹·K⁻¹), k_B is Boltzmann's constant, h is Planck's constant and the value of ln(k_B/h) is 23.76. The regression provides −ΔH^‡ as the slope of the linear plot and ΔS^‡ as the ordinate intercept.

Temperature-dependent kinetics: aspects of analysis

The well-known Arrhenius and Eyring equations used in chemical kinetics can be properly applied to reactions of enzymes and sensibly interpreted providing that: (i) a restricted temperature range that avoids denaturation (often taken to be 0–50 °C) is used, (ii) account is taken of the temperature-dependence of acid dissociation constants, and (iii) the mechanistic significance of the rate parameter is known and lacking in complexity. In the present study, it was possible to: (i) restrict the temperature range to 4–30 °C, where the enzymes are conformationally stable without detriment to the analysis, (iii) study the reactions at pH 6.7, a value around which the rate constants change only slightly with change in pH in the range ∼6–8, and (iii) determine the second-order rate constant (k) for the enzyme–probe reactions whose mechanistic significance (reaction of the catalytic site cysteinyl thiol group with the neutral probe molecule) is well defined and is the same for each probe.

For many reactions, the increase in k with increase in temperature is described by the Arrhenius equation (eqn 2) where E_a, the activation energy, in terms of transition state theory, is equal to ΔH^‡+RT.

(2)

Transition state theory leads to the Eyring equation (eqn 3, in which ΔG^‡ is the free energy of activation) or eqn (4) and division throughout of eqn (4) by T leads to the logarithmic form, eqn (5).

(3)

(4)

(5)

The form of the Eyring equation (eqn 1, see the Materials and methods section) convenient for analysis is obtained from eqn (5) by multiplying through by and collecting terms in R. Regression analysis provides values of ΔS^‡ and ΔH^‡ directly.

Despite the well-known long extrapolation to 0 K required to obtain the value of ΔS^‡ and the relatively large standard errors on this parameter, conclusions drawn from temperature-dependence studies that, as in the present study, rely on the sign of ΔS^‡ (positive or negative) and not only on its magnitude are usually not affected by the error inherent in the extrapolation process (see, for example, [19]).

Dependence on non-covalent interactions of ΔS^‡ and ΔH^‡ for the reactions of papain and actinidin with the 2-pyridyl disulphide reactivity probes 1–7 at pH 6.7

The values of ΔS^‡ and ΔH^‡ for the two sets of enzyme–probe reactions, together with those of ΔG^‡ at 298 K calculated as ΔH^‡−TΔS^‡, are collected in Table 1, and a typical linear plot derived from eqn (1) (for the reaction of papain with the substrate-analogue probe 6) is shown in Figure 2. The variations, particularly in ΔS^‡, for the reactions of papain are considered first and then compared with those for the reactions of actinidin.

Reactions of papain

For the reactions of papain with the ‘featureless’ probe, CH₃-CH₂-S-S-2-Py (where 2-Py is 2-pyridyl) (1), ΔS^‡ has a large negative value (−79.9±4.0 J·mol⁻¹·K⁻¹), as expected, because of the restriction of the motion of the probe in the transition state, and the probable minimal disruption of the water network in the active centre of the enzyme owing to the lack of recognition features in the small alkyl group of 1. When provision is made for the possibility first of one hydrogen bond [between the backbone N-H of Gly⁶⁶ and the carbonyl O of CH₃CO-O-[CH₂]₂-S-S-2-Py (2)] and then also of a second hydrogen bond [between the backbone carbonyl O of Asp¹⁵⁸ and the N-H of the amide group of CH₃CO-NH-[CH₂]₂-S-S-2-Py (3)], the values of ΔS^‡ become progressively less negative (from (−79.9±4.0 to −60.5±4.0 to −37.1±2.0 J·mol⁻¹·K⁻¹). In these three cases, the negative values of ΔS^‡ are characteristic of transition states that are more ordered than the corresponding ground states. The progressive decrease in their negativity could be accounted for by the increased probability of an appropriate transition-state geometry. The changes in transition-state geometry consequent on provision of various recognition interactions in these reactions may be inferred from marked changes in shapes of pH–k profiles [16,17].

The most striking changes in ΔS^‡ arise when the probe is equipped with phenylalanine at P₂ as a potential occupant for the major recognition site for papain, the hydrophobic S₂ subsite. For the reaction of CH₃CO-[L-Phe]-NH-[CH₂]₂-S-S-2-Py (6), the probe containing both a P₁-P₂ amide bond and L-phenylalanine at P₂, which has a pH–k profile with a shape strikingly similar to that of a pH–k_cat/K_m profile, i.e. maximal activity around pH 6, ΔS^‡ has become large and positive (+57.7±7.0 J·mol⁻¹·K⁻¹). The effectiveness of this reaction at pH values around 6 suggest a high probability of a well-organized transition state in which the thiolate component of the catalytic site ion pair and the Im⁺H component are correctly positioned to act as nucleophile and hydrogen bond donor respectively. The fact that this reaction is characterized also by a large positive entropy of activation, however, suggests a third component which provides for a less-ordered structure in the transition state than in the ground state. The most obvious candidate for this additional component is the water network of the active centre. This leads to the view that desolvation resulting from binding of the substrate-like probe 6 in the transition state conformation with consequent release of bound water molecules allows both components of the ion pair to be involved synchronously in the reaction, and is most likely to be the cause of the large positive value of ΔS^‡.

The effect on ΔS^‡ of removing the possibility of hydrogen bonding of the probe to the backbone carbonyl O of Asp¹⁵⁸ while retaining L-phenylalanine at P₂ was investigated by comparison of the value for the reaction of CH₃CO-[L-Phe]-O-[CH₂]₂-S-S-2-Py (4) with that for the reaction of probe 6. Removal of the possibility of the (P₁)-NH···O=C<(Asp¹⁵⁸) hydrogen bond results in a substantial decrease in the value of ΔS^‡ from +57.7±7.0 to +18.7±4.1 J·mol⁻¹·K⁻¹. The fact that ΔS^‡ for the reaction of probe 5, the D-enantiomer of 4 (−19.0±4.4 J·mol⁻¹·K⁻¹) is substantially less negative than that for the reaction of probe 2 which lacks the D-phenylalanine moiety (−60.5±4.0 J·mol⁻¹·K⁻¹) provides evidence for the binding of (P₂)-D-phenylalanine to papain (see [17] for a discussion of this phenomenon deduced by model building). It is noteworthy that ΔS^‡ for the reaction of probe 5 is still negative and becomes positive for the D-enantiomer only when the possibility of hydrogen bonding to Asp¹⁵⁸ is restored in probe 7. This supports the conclusion suggested by the relative values of difference kinetic specificity energies [16], that transition state geometry in reactions of papain is determined by interdependent binding interactions in the S₂-subsite, S₁-S₂ intersubsite region and catalytic site. The present study also suggests that selective desolvation of the regions of the active centre participates in the binding site–catalytic site coupling process.

Reactions of actinidin

ΔS^‡ for the reactions of the featureless probe (1) is even more negative (−112.1±6.9 J·mol⁻¹·K⁻¹) than for the analogous reaction of papain (−79.9±4.0 J·mol⁻¹·K⁻¹), possibly indicating even more restriction of the motion of the probe in the transition state. As in the case of the papain reactions, incorporation of the P₁-P₂ hydrogen bonding systems in the P₁-P₂ ester probe (2) and the P₁-P₂ amide probe (3) results in the progressive decrease in the negativity of ΔS^‡ from −112.1±6.9 to −42.2±3.8 to −34.5±6.3 J·mol⁻¹·K⁻¹, presumably reflecting the increased probability of binding with appropriate orientation in the transition state. Although the probability of an appropriate transition-state geometry is increased by the opportunity to form the additional trans-cleft hydrogen bond, the mechanism of the reaction of actinidin is different from that of papain. Thus, whereas for papain there is substantial reaction involving activation of the leaving group by hydrogen bond donation by the Im⁺H component of the catalytic site ion pair, the reaction of actinidin is mainly with the formally protonated probe (pK_a ∼2.5). This conclusion arises from the observation of maximal activity at pH 6 for the papain reaction, but at pH 3–4 for the actinidin reaction (see [16,17]).

A particularly marked difference between the reactions of actinidin and papain occurs when the hydrogen bond acceptor (the ester carbonyl O in probe 2) is augmented by (P₂)-L-phenylalanine in probe 4. In the papain reaction, this addition results in ΔS^‡ changing from markedly negative (−60.5±4.0 J·mol⁻¹·K⁻¹) to substantially positive (+18.7±4.1 J·mol⁻¹·K⁻¹). In the actinidin reaction, however, it remains substantially negative (−21.4±8.0 J·mol⁻¹·K⁻¹), although less negative than the value for the amide probe 3 devoid of the L-phenylalanine moiety. This suggests that, although binding of the L-phenylalanine moiety contributes to a correct transition-state geometry for nucleophilic attack of the thiolate anion of actinidin, desolvation is not as effective as in the papain reaction. Another striking difference between the reactions of the two enzymes is that changing the chirality of the phenylalanine moiety from L-phenylalanine in 4 to D-phenylalanine in 5 results in a marked change in ΔS^‡ from +18.7±4.1 J·mol⁻¹·K⁻¹ to −19.0±4.4 J·mol⁻¹·K⁻¹ for the papain reaction, but essentially no change for the actinidin reaction (both approx. −21 J·mol⁻¹·K⁻¹). This suggests that binding either of the enantiomeric phenylalanine moieties to actinidin does not achieve a good fit of probes 4 and 5 in the hydrophobic pocket of the S₂ subsite. This is in accord with the prediction from the crystal structure of actinidin [8] which reveals a shorter pocket than that in papain [7]. A significantly better fit is achieved for the L-phenylalanine enantiomer; however, when provision is made also for the (P₁)>N-H···O=C<(Asp¹⁶¹) hydrogen bond by changing the P₁-P₂ ester bond in 4 to the P₁-P₂ amide bond in 6. Reaction of actinidin with 6 is characterized by a positive ΔS^‡ (+12.1±1.2 J·mol⁻¹·K⁻¹), indicating more effective desolvation, although less effective than in the papain reaction (ΔS^‡=+57.7±7.0 J·mol⁻¹·K⁻¹). The change in structure from the L-phenylalanine enantiomer 6 to the D-enantiomer 7 which results in the decrease in ΔS^‡ from +57.7±7.0 to +11.0±5.5 J·mol⁻¹·K⁻¹ for the papain reaction, results in a similar change for the actinidin reaction, in this case from +12.1±1.2 to −18.2±3.3 J·mol⁻¹·K⁻¹. In both cases, therefore, the binding mode of the D-phenylalanine moiety differs from that of the L-phenylalanine moiety with respect to the (P₂)-binding pocket. This contrasts with the lack of dependence on P₂ chirality for actinidin when the possibility of the (P₁)>N-H···O=C<(Asp¹⁵⁸) hydrogen bond is missing (in probes 4 and 5). This emphasizes the interdependence of P₂/S₂ subsite and P₁-P₂/S₁-S₂ intersubsite binding.

Differences in the relative changes in ΔH^‡ and ΔS^‡ that characterize reactions of papain and actinidin with the substrate-derived reactivity probes 2–7

Linear relationships between enthalpies and entropies occur widely in molecular associations particularly those involving hydrogen bonding (see, for example, [20–22]). Whether such relationships arise at least in part from chemical causation (extrathermodynamic relationships, isokinetic effect, enthalpy–entropy compensation effect) as against a dominant statistical compensation pattern has been the subject of much debate (see, for example, [22] and references therein). The analysis of enthalpy–entropy compensation reported by Cornish-Bowden [23] necessitates extreme caution in discussion of this phenomenon. In the present paper, we report the differences observed in the temperature-dependent kinetic characteristics of some analogous reactions of papain and actinidin that are influenced by non-covalent interactions and point out possible correlations with our results from other types of kinetic study reported previously.

Linear dependence of ΔH^‡ on ΔS^‡ was observed for the reactions of papain with the substrate-derived probes 2–7 (plot not shown; data in Table 1). Evidence for chemical causation suggested by Krug et al. [24,25] includes a substantial difference between the compensation temperature, T_c (the approximate value of which is provided by the slope of the ΔH^‡ against ΔS^‡ plot) and the average experimental temperature, and a linear relationship between ΔH^‡ and ΔG^‡. These two criteria appear to be met in the present work (T_c=200 K, average temperature 295 K; linear plot not shown, results in Tables 1 and 2).

Such chemical causation as may exist in enthalpy–entropy compensation is generally considered to be at least partly due to the perturbation, release or change in the state of water consequent upon ligand binding by the protein. This may reflect the responsiveness of proteins to ligand binding [26], and the compensation effect for the reactions of papain correlates well with the responsiveness of papain to changes in the structure of the substrate-derived probes 2–6 detected by the changes in the pH–k profiles [16,17]. The much lower sensitivity of the compensation effect for the corresponding reactions of actinidin (Table 1) and the clustering of the ΔG^‡/ΔH^‡ data (Table 2) contrast markedly with the results for papain and correlate with the relative insensitivity of the pH–k profiles for the actinidin reactions to respond to structural change in the probes. The absence of substantial differences in ΔH^‡ for the reactions of the substrate-derived probes with actinidin could result from the masking of an enzyme-mediated decrease in enthalpy of activation by an endothermic conformational change as suggested by Jencks [27] for the deacylation of a series of acyl α-chymotrypsins. Such an interpretation of the temperature-dependent kinetic data for the reactions of actinidin might be related to the kinetically significant change(s) in conformation detected uniquely for actinidin by using a specific thionoester substrate [28,29].