The presteady state reaction of chemically modified cytochromes c with cytochrome oxidase.

Determination of the presteady state kinetics of the reaction of purified beef cytochrome oxidase and of the high affinity complex between native horse cytochrome c and the beef oxidase with native 4-carboxy-2,6-dinitrophenyllysine horse cytochromes c singly modified at residue 7, 13, 25, 27, 60, 72, 86, or 87 and 2,4,6-trinitrophenyllysine horse cytochrome c modified at residue 13, demonstrated that 1) the high affinity interaction domain on the surface of cytochrome c mapped in this fashion is indistinguishable from that determined by the steady state polarographic kinetic analysis (Ferguson-Miller, S., Brautigan, D. L., and Margoliash, E. (1978) J. Biol. Chem. 253, 149-159). 2) The low affinity enzymic interaction domain is indistinguishable from the high affinity domain. 3) The inhibition of the low affinity reaction, observed with the modified cytochromes c as measured by the presteady state assay is greater than that determined by the steady state polarographic kinetics. This results from the fact that the two sites are interacting (Osheroff, N., Speck, S. H., Margoliash, E., Verrman, E. C. I., Wilms, J., Konig, B. W., and Muijsers, A. 0. (1983) J. Biol. Chem. 258,57315738) and that for the presteady state kinetics the high affinity site is occupied by a tightly bound native cytochrome c, while for the polarographic assay it is occupied by a more weakly bound modified cytochrome c. 4) The bimjolecular rate constant (k,) for the reaction of 4-carboxy-2,6-dinitrophenyllysine 13 horse cytochrome c with beef cytochrome oxidase varies with ionic strength. From a plot of In k1 as a function of P" the rate constants at zero and infinite ionic strength were estimated. These values were used to calculate that the effective charge on purified beef cytochrome oxidase is in the range of -8 to -10.5e. 5) The effect of

Ti T o whom reprint requests should be addressed. temperature on the bimolecular rate constants yields an enthalpy of activation (-16.5 kcal mol") that remains approximately the same for the native and modified cytochromes c tested. Similarly, the large positive entropy of activation (+30 cal K-' mol") does not vary significantly for those cytochromes c modified outside of the enzymic interaction domain, while it decreases maximally to about half the value observed with native cytochrome c for the preparations modified within the enzymic interaction domain, accounting for their extremely low activity.
The interaction of cytochrome c with cytochrome oxidase, the two components of the terminal segment of the mitochondrial respiratory chain, have been the subject of numerous kinetic studies (see reviews in Refs. [1][2][3]. From stopped flow experiments, the second order rate constant for the initial reaction of cytochrome c with purified cytochrome oxidase ( k l ) was invariably found to be very fast. The values observed vary from lo6 M" s-' in 100 mM phosphate buffer (4) to greater than 2 X 10' M" s-l in 5 mM phosphate buffer (5-8). The latter is only a minimal estimate, the reaction having been completed within the mixing time of the apparatus.
Extrapolation of In kl as a function of 11'* to zero ionic strength, from data obtained at higher ionic strengths at which k , can be measured accurately, yields values as high as 10" M" s-' for horse cytochrome c reacting with purified beef oxidase (9).
The bimolecular rate constant for a reaction between two proteins is generally not more than lo6 M" s" (10) and, assuming that the two proteins are uncharged, an upper limit of approximately 10" M" s-' can be calculated from the encounter frequency (11). The latter value is reached when the reaction is diffusion controlled, namely, when every collision between reactants results in a reaction. If the proteins are oppositely charged, the upper limit of encounter frequency is about 10" M" s-l (11). The area on the surface of cytochrome c at which the molecule interacts with cytochrome oxidase has been mapped in several ways. Cytochromes c chemically modified at single lysyl residues by a variety of substituent moieties are inhibited in their reaction with the enzyme (12)(13)(14)(15)(16), and certain lysines are shielded from chemical reaction in complexes of purified cytochrome oxidase and cytochrome c (17). Both sets of results demonstrate that the enzyme interaction domain is a well defined and restricted area on the "front" surface of the protein that includes a large proportion of the exposed heme edge and is centered at the point at which the positive end of the dipole axis crosses the surface of the molecule near the P-carbon of phenylalanine 82 (18,19). Thus, cytochrome c and cytochrome oxidase require a specific orientation for electron transfer to occur, decreasing the probability of the reaction and therefore the value of k l .
However, two factors enhance the bimolecular rate constant. First, it has long been known that the reaction between cytochrome c and cytochrome oxidase is strongly inhibited as the ionic strength is increased (1-3), indicating that the proteins are oppositely charged, and thus have an increased encounter frequency. Second, the strongly asymmetric distribution of charges on cytochrome c leads to a dipole moment of over 300 debye (19,20), oriented so as to facilitate the correct alignment of the two macromolecules for electron transfer. That cytochrome oxidase has electrostatic properties complementary to those of cytochrome c can only be surmised at this time. The fact that the two proteins can be shown to have co-evolved in the primate line of evolutionary descent (9) supports such a supposition.
The present study examines the presteady state reaction of purified beef heart cytochrome oxidase with eight different CDNPI-lysine-modified preparations of horse cytochrome c (15,16,21,22), and TNP-lysine 13 horse cytochrome c (23,24). With the exception of the TNP-modified protein, it was found that the relative order of the activities of these derivatives in the high affinity reaction with cytochrome oxidase corresponds to the relative order of both the Knt values obtained by steady state kinetic analysis (15, 16) and the KO values determined directly by gel fitration (16). Similar experiments, employing the high affinity complex between native horse cytochrome c and the beef enzyme to study the presteady state low affinity reactions of the modified cytochromes c, demonstrated that the low affinity interaction domain on the molecular surface of cytochrome c is indistinguishable from the high affinity interaction domain. The influence of ionic strength on the bimolecular rate constant for the reaction of CDNP-lysine 13 horse cytochrome c with the beef enzyme was studied over a wide range of ionic strengths. It was found that the plot of In kl as a function of I"* deviates from linearity. However, over an intermediate range of 0.08 to 0.22 M, such plots are apparently linear, and the differences in the slopes for the native, TNP-and CDNPderivatized cytochromes c are approximately consistent with the corresponding changes in the net charge of the protein.
The k , values determined as a function of ionic strength were used to estimate the net charge of cytochrome oxidase. From the influence of temperature on the bimolecular rate constant, it was found that the enthalpy of activation, A H $ , is approximately the same for the different chemically modified cytochromes c, while the entropy of activation, ASS, is clearly decreased for those cytochromes c that are modified within the enzymic interaction domain, apparently accounting for their extremely low activity.

EXPERIMENTAL PROCEDURES
Cytochrome c was prepared from horse hearts by the procedure of Margoliash and Walasek (25) as modified by Brautigan et al. (26). Chemically modified horse cytochromes c in which a single lysine residue is substituted by CDNP-lysine were prepared according to Brautigan and co-workers (21,22) and Osheroff et al. (16). The derivatives at lysines 7, 13, 25, 27, 60, 72, 86, and 87 were employed. TNP-lsyine 13 horse cytochrome c was prepared by a modification (24) of the procedure of Wada and Okunuki (23). Purified cytochrome c oxidase was prepared from beef hearts by a modifkation (27) of the method of Fowler et al. (28).

e with Cytochrome Oxidase
Prior to assay, monomeric cytochrome c was separated from any polymeric material, as well as reductant (ascorbate) or oxidant (potassium ferricyanide), by gel fdtration on a column (0.7 X 18 cm) of Sephadex G-50 superfine in 133 m~ acetate (Tris) buffer, pH 7.8, containing 0.25% Tween 20.
The high affinity horse ferricytochrome c -beef cytochrome oxidase complex was prepared by mixing a 1.1 molar excess of cytochrome c with cytochrome oxidase in 5 m~ potassium phosphate buffer, pH 7.0, containing 0.5% Tween 20. The kinetic properties of the complex prepared in this way were identical with those of the complex separated from excess cytochrome c by gel filtration. indicated, with a modified Durrum stopped flow apparatus, in which Presteady state reactions were studied at 10 "C, except where the reaction chamber had an optical path length of 2.0 cm, as previously described (5). The photomultiplier output signal was transferred via a log converter to a Datalab 905 transient recorder as a 1024-point data file, and stored in a Hewlett-Packard 2100A computer. All traces were subjected to a 5-point smoothing procedure. The rate constants were calculated from the initial portion of the reaction trace, employing a nonlinear least squares best fit procedure (5).
The presteady state reaction of ferrocytochrome c with purified cytochrome oxidase, or with the ferricytochrome c . cytochrome oxidase complex, was monitored by following the reduction of the oxidase at 444 nm. The conditions used throughout this study yielded pseudof m t order kinetics. The absorption coefficients (reduced minus oxidized) used for cytochrome c and cytochrome oxidase (cytochrome aa3) were 21.1 m"' cm" at 550 nm (29) and 24.0 m"' cm" at 605 nm (30), respectively.
The ionic strength of potassium phosphate buffers was calculated by an iterative procedure, according to Wilms and co-workers (7,311.

RESULTS
Traces of the change in absorbance at 444 nm, representing the fast reduction of heme a, during the presteady state oxidation of native and singly modified CDNP-and TNPlysine ferrocytochromes c are shown in Fig. 1 were measured as a function of the cytochrome oxidase concentration ( Fig. 2), cytochrome oxidase being present in excess over cytochrome c. The slopes of the lines represent the value of the second order rate constant ( k l ) for the reactions. Although the CDNP-lysine cytochromes c have the same net positive charge (two less than native cytochrome c ) , their reactivities toward cytochrome oxidase differ greatly. Of the proteins examined, CDNP-lysine 13 cytochrome c was the most inhibited, while CDNP-lysine 60 cytochrome c was nearly as active as the native protein. The order of increasing reactivity of the cytochrome c derivatives with cytochrome oxidase was CDNP-lysine 13 < 72 < TNP-lysine 13 < CDNPlysine 86 < 87 < 27 < 25 < 7 < 60 < native. This order is in good agreement with those of the K , and the KO values for the interaction of singly substituted cytochromes c with the high affinity site on cytochrome oxidase, as determined from steady state kinetics and binding measurements (Table I) (15,16).

c with Cytochrome Oxidase 5741
The rate of reaction of a 1:l complex of horse cytochrome c and purified beef cytochrome oxidase with the cytochrome c derivatives as a function of the reactant present in excess, namely the cytochrome c . cytochrome oxidase complex, is shown in Fig. 3. The second order rate constants for the reaction of the complex with the singly substituted cytochrome c derivatives increased in the following order: CDNPlysine-13 < 86 < 87 < TNP-lysine-13 < CDNP-lysine 25 < native. With the exception of TNP-lysine 13 cytochrome c, this order is the same as that obtained for the presteady state reaction of the cytochrome c derivatives with cytochrome oxidase at high ionic strength.
Since all CDNP-lysine cytochromes c have the same net charge, the differences in their activities with cytochrome oxidase has been ascribed, in part, to the fact that certain charged residues on the cytochrome c molecule are involved in the binding of cytochrome c to cytochrome oxidase (15), and also to the distribution of charged residues on the surface of cytochrome c (18,19). To evaluate the effective electrostatic charge on the reacting proteins, the ionic strength dependence of the rate constants was examined. Fig. 4 shows the ionic strength dependence of the rate constants over a range of 80 to 220 mM for the reaction between cytochrome oxidase and some of the cytochrome c derivatives expressed in terms of the equation (32): (1) in which k , is the second order rate constant, kIo the second order rate constant at zero ionic strength, ZA and ZB the net charge numbers of reactants A and B, respectively, I the ionic strength, and A a constant with a value of 0.997 at 10 "C. Although this equation applies to reactions between small ions at low ionic strength (33), an apparent linear relationship between log k1 and I"' was observed in the ionic strength range from 0.08 to 0.22 M. The value of K : was estimated by extrapolation to zero ionic strength and used to calculate the charges on the reacting proteins (see "Discussion").
To further investigate the relationship between log k1 and I"', the reaction of CDNP-lysine 13 cytochrome c with cytochrome oxidase was examined over a wider range of ionic strengths. The low activity of the CDNP-lysine 13 cytochrome   mM, there is a large positive deviation from linearity, indicating that extrapolation to zero ionic strength from rate constants determined over an intermediate ionic strength (Fig. 4) is likely to lead to underestimation of kIo (34).
The decrease in reactivity brought about by derivatization TO determine which parameters are influenced, the temperature dependence of the reaction of cytochrome oxidase with Some of the cytochrome c derivatives was determined. The results of this study are depicted in an Arrhenius plot (Fig. 6). The enthalpies and entropies of activation were determined from this plot and are listed in Table 1. At temperatures below 20 "c, the enthalpy of activation was calculated to be 16.6 f 0.5 kcal mol". Within the estimated experimental error, the values for AH$ were indistinguishable for all the cytochromes c examined. From these results, it appears that the activation enthalpy of the rate-limiting step of the presteady state reaction is not altered by modification of a single lysine residue on cytochrome c, and hence, the observed differences in rate constants are manifested only in the entropy of activation, ASS. At temperatures above 25 "C, the value of AH$ is between l and 4 kcal mol", in line with the results of Yoshida et al. (35) on the steady state reaction of cytochrome c with cytochrome oxidase. The biphasic nature of the Arrhenius plot cannot be ascribed to denaturation of cytochrome oxidase at the higher temperatures, since incubation at 30 " c for over 1 h did not result in any loss in activity. The large value of AH$ at temperatures below 20 "C indicates that, at least in this temperature range, the reaction is not diffusion limited. For diffusion-limited reactions, one expects a much lower value of approximately 3.5 kcal mol", representing essentially the temperature dependence of the viscosity of the solvent (36). This conclusion is confirmed by the observation that when the viscosity was increased by the addition of sucrose up to 30% (w/v), the rate constants in the temperature range between 4 and 30 "C were not affected (data not shown).

The Presteady State Reaction of Cytochrome c Derivatives with Cytochrome Oxidase and with the Native Cytochrome c . Cytochrome Oxidase
Complex-The steady state reaction of singly substituted cytochrome c derivatives with cytochrome oxidase has generally been investigated under low ionic strength conditions (12-16). Monophasic kinetics were observed for the steady state oxidation of the most inhibited ferrocytochrome c derivatives (CDNP-lysines 13, 72, 86, and 87), suggesting that a distinction between the high and the low affinity reactions depends on the properties of the cytochrome c derivative employed and that the high affinity reaction is more strongly inhibited than the low affinity reaction by modification of lysyl residues on cytochrome e.
In comparing the presteady state with the steady state kinetics of these cytochrome c derivatives (see Table I), one finds that, although the relative order of the activities of the CDNP-lysine-modified proteins is the same for the high and the low affmity reactions in the presteady state reactions, and compares well with their relative order in steady state kinetics (15, X), these modified cytochromes c appear to be much more inhibited in their low affinity reactions in the presteady state as opposed to the steady state system, For example, the K , for the reaction of CDNP-lysine 13 cytochrome c2 is only 1 order of magnitude larger than the K, for the low affinity reaction of native cytochrome c, whereas the corresponding "on" constants ( k l ) differ by 2 orders of magnitude. Similar discrepancies exist for the low affinity reactions of other CDNP-modified cytochromes c, and are not apparent for the high affhity reactions (Table I). It is likely that these differences reflect the fact that, in the analysis of the low affinity lysine 13 cytochrome c (16). only monophasic kinetics was observed for the reaction of CDNP-phase by the presteady state system, the modified proteins react with the high affinity native cytochrome c.cytochrome oxidase complex, whereas the steady state reaction is with a modified cytochrome C . cytochrome oxidase complex. Since it has been shown that the low affinity reaction is not independent of the nature of the cytochrome c at the high affinity site (g), it is not surprising that a CDNP-cytochrome c bound to the high affinity site will have a smaller influence on the low affinity reaction than the native protein.
Notwithstanding the above discrepancies, an important result of the presteady state kinetics is that the high and low affinity interaction domains on the surface of cytochrome c appear to be indistinguishable, imposing restrictions on possible models for the cytochrome c e cytochrome oxidase reaction.
Estimation of the Overall Net Charge of Purified Cytochrome Oxidase-It has long been known that the bimolecular association rate constants for the reactions of cytochrome c with its physiological redox partners are among the fastest protein-protein interactions measured (4,37, 38). As outlined under "Introduction," these reactions are aided by electrostatic interactions, and therefore, it should be possible to estimate the net charge of the reactants from the effect of ionic strength on the reaction rate. In discussing electrostatic contributions to the reaction rate constant, two effects must be taken into account. 1) The net charge on the proteins affects the reaction rate, because there are long range attractive and repulsive coulombic interactions. Classical Bronsted-Debye-Huckel theory, which describes the effects of ionic strength on reaction rate constants, refers to these types of forces (32). The maximum reaction rate of a diffusion-controlled reaction between proteins of zero net charge is approximately 10" M" s-' (11). Due to these long range electrostatic forces, the upper limit of the rate increases by a factor of about 4/unit charge (36). 2) The distribution of charges on the proteins may result in dipoles which will affect the orientation of the reactants in their respective electric fields, and may thereby enhance the reaction rate (19, 20). This and other short range interactions may be considered, as a first approximation, not to be affected by changes in ionic strength.
Various theoretical approaches have been used to relate the ionic strength dependence of reaction rate constants to the net charges of the reactants (34,(39)(40)(41)(42)(43). Quantitative relationships have been derived for reactions between small ions (32) and between a charged protein and a small ion (39). For a reaction between molecules A and B that is not diffusion controlled, the following expression is valid (44,45): in which kI0 is the rate constant at zero ionic strength, kR is the hypothetical rate constant for E + 00, namely at infinite ionic strength when A and B are uncharged, RAB+ is the radius of the transition complex, e is the electron charge, c is the dielectric constant of the solvent, k is the Boltzman constant, and T is the absolute temperature.
This expression may be applicable to the reaction between cytochrome c and cytochrome oxidase, as the temperaturedependence studies have indicated that it is not diffusion controlled under the assay conditions employed. Indeed, the activation enthalpy for the presteady state reaction below 20 "C ( Fig. 6 and Table I) is 16.6 kcal mol", much higher than the 3.5 kcal mol" expected for a diffusion-limited process (36).
For the calculation, the values of kl0 and kR were estimated from the ionic strength dependence of the reaction of CDNPlysine 13 horse cytochrome c, the only preparation for which the reaction with cytochrome oxidase was sufficiently slow to to the reaction between cytochrome c and cytochrome oxidase also depends on assuming that over the ionic strength range studied there is no change in the reaction mechanism, as well as no change in the conformation of the proteins or in specific ion binding that would affect their net charges.
In calculations of the interaction energies of charged molecules, the dielectric constant of the intervening medium (water) becomes very important. Ordinarily, water has a dielectric constant of about 78. In the presence of a free electric charge, such as occurs in the case of ionized groups on the surface of cytochrome e, the effective dielectric constant is decreased due to the strong orientation of the water dipoles in the field around the charge. A value of 50 was used for the dielectric constant a t small distances from the active site on cytochrome c, as estimated by Rees (46). The radius of the complex between cytochrome c and cytochrome oxidase was taken to be the radius of a sphere having a surface area equal to the sum of the surface area of the two proteins (34). Purified cytochrome oxidase can be approximated by a sphere with a radius of 40 8, (47,48) and cytochrome c can be taken as a sphere of radius 18 8, (3). This yields a value of 45 8, for RAH+ The values for kl" and h~? were estimated by extrapolation of the data shown in Fig. 5, and were found to be 5 X loR and 1.7 X lo3 M" s-', respectively.
Substitution of these values into Equation 2 yields a value of -48 for (zA -2)zu, in which ZA is the charge on native ferrocytochrome e, ZA is the charge on the purified cytochrome oxidase, and (ZA -2) is the expected charge of CDNP-lysine 13 cytochrome e. If ZA is taken to be in the range of +6.5 to +8 for native ferrocytochrome c at neutral pH (38, 46), the resulting value for zB will vary from -8 to -10.5.
Such values appear to be within the expected range, as estimations of the net charges of beef and human cytochrome oxidases from the amino acid sequences of their subunits, as determined directly (49)(50)(51)(52)(53)(54) and from the nucleotide sequences of the mitochondrial DNA (55), yield an overall net charge of about -12. However, this does not take into account any acidic phospholipids that may be closely associated with the purified beef oxidase employed and may contribute to the net charge. Furthermore, the abundance of histidyl residues, particularly in subunits I and 111, makes the calculation of the effective charge tenuous, since the pK, may vary considerably at neutral pH depending on the environment of each particular group.
The Temperature Dependence of the Presteady State Reaction-It is clear from the data presented in Table I that modification of a single lysine at any point on the surface of cytochrome c has little effect on the activation enthalpy of the presteady state reaction with cytochrome oxidase. Furthermore, for those cytochromes c modified outside the enzymic interaction domain there is also little change in the activation entropy, making it difficult to assess from the present data whether the changes in the rate constant for the reaction with cytochrome oxidase are to be attributed to AH* or AS* or both. Indeed, it should be noted that for this group of modified cytochromes c the changes in thermodynamic parameters required to account for the observed inhibitions are expected to be small, and likely to be within the error of the measurement (19). However, for the cytochromes c modified within the enzymic interaction domain, the degrees of inhibition correspond to much larger changes in the thermodynamic parameters, and from the Arrhenius analysis (Table   I) clearly result from the changes in AS*.
Since all CDNP-lysine cytochrome c derivatives have maintained the optical and structural properties, as well as the reduction potential of the native protein (15,16,22), their differences in reactivity most probably originate from an altered surface charge distribution on the protein, and in addition, for those derivatives modified within the enzymic interaction domain, from a disruption of the native enzymesubstrate complex. The latter is expected to have a marked effect on the activation entropy (56). This may be interpreted as a solvent effect (56), polarity changes which occur in the reactants during the course of the reaction resulting either in an increase or decrease in the amount of solvent molecules bound to the reactants. Also, if charges are neutralized during the reaction, there will be a release of solvent molecules.
It has been shown that AH* is independent of ionic strength for the reaction of cytochrome c with the oxidase (7). As a consequence, the value of AH* of this reaction is associated only with kR. It is possible to estimate k~ (the reaction rate constant under conditions in which there are no electrostatic interactions between the two proteins) by sustituting into Equation 2 the values determined for kl" and exp -(zAzee2/ kTRArt*). Using a value of 10" M" s-l for kl" (8) and estimating from the charge on cytochrome oxidase that Z A Z~ is in the range of -64 to -69 yields values from 1.35 X lo3 to 5 X lo3 M" spl for kR. This is very close to the value determined experimentally for the reaction of CDNP-lysine 13 cytochrome c with beef cytochrome oxidase at very high ionic strength (1.2 M), suggesting that the reactions of native and CDNP-lysine 13 cytochromes c may be indistinguishable under conditions in which all charges are screened ( i e . the effect of the chemical modification is strictly electrostatic without any steric effects). Substitution into Equation 3 yields The range of values calculated for kH and the experimentally determined value for AH* (16.5 kcal/mol) results in values from 14.2 to 16.8 cal/degree/mol for AS*. This represents the nonelectrostatic contribution to the entropy of activation.
Indeed, a large portion of the interaction domain on the front surface of cytochrome c is composed of hydrophobic side chains near the exposed heme edge, which are surrounded by a ring of lysyl residues. It is likely, therefore, that, in the formation of the productive electron transfer complex with cytochrome oxidase, structured water is released to the bulk phase, resulting in a gain in entropy.
The observed discontinuity in the Arrhenius plot at 21 "C may offer an interesting insight into the mode of interaction of cytochrome c with cytochrome oxidase. Purified cytochrome oxidase is capable of binding more than one molecule of cytochrome per cytochrome aa3 (15,16,57) and recent studies indicate that phospholipids may be involved in the low affinity phase of the enzymic reaction (58). That cytochrome c may bind to phospholipid and diffuse two-dimensionally onto the catalytic site or sites has been proposed by Roberts and Hess (59). Such reaction mechanisms may enhance reaction rates considerably as the reduction of dimensionality brought about by binding to a membrane will increase encounter efficiency (60, 61). It is possible that the diffusion rate of cytochrome c on the phospholipids changes at the transition temperature as it is likely that such diffusion is strongly dependent on membrane viscosity. This would relate the Arrhenius plot discontinuity directly to the mobility of cytochrome c in this system. It should be borne in mind that the purified cytochrome oxidase preparation employed contains a considerable amount of phospholipid (27) and may in part mimic the state of the enzyme in its original mitochondrial membrane environment. Alternatively, a phospholipid phase transition may lead to a conformational change in the oxidase altering the activation energy for the reaction with cytochrome c.