Binding of Imidazole to the Heme of Cytochrome c1 and Inhibition of the bc1 Complex from Rhodobacter sphaeroides

The kinetics of imidazole (Im) and N-methylimidazole (MeIm) binding to oxidized cytochrome (cyt) c1 of detergent-solubilized bc1 complex from Rhodobacter sphaeroides are described. The rate of formation of the cyt c1-Im complex exhibited three separated regions of dependence on the concentration of imidazole: (i) below 8 mm Im, the rate increased with concentration in a parabolic manner; (ii) above 20 mm, the rate leveled off, indicating a rate-limiting conformational step with lifetime ∼1 s; and (iii) at Im concentrations above 100 mm, the rate substantially increased again, also parabolically. In contrast, binding of MeIm followed a simple hyperbolic concentration dependence. The temperature dependences of the binding and release kinetics of Im and MeIm were also measured and revealed very large activation parameters for all reactions. The complex concentration dependence of the Im binding rate is not consistent with the popular model for soluble c-type cytochromes in which exogenous ligand binding is preceded by spontaneous opening of the heme cleft, which becomes rate-limiting at high ligand concentrations. Instead, binding of ligand to the heme is explained by a model in which an initial and superficial binding facilitates access to the heme by disruption of hydrogen-bonded structures in the heme domain. For imidazole, two separate pathways of heme access are indicated by the distinct kinetics at low and high concentration. The structural basis for ligand entry to the heme cleft is discussed.

The binding of small molecules to c-type hemes has been widely studied in type I cytochromes c and is known to result in displacement of the native methionine ligand and to cause significant conformational changes in the heme binding domain (1)(2)(3)(4). The affinities and kinetics of binding reflect the interactions among the exogenous ligand, the heme, and the protein and provide a window into the static and dynamic properties of the heme domain.
In cytochromes (cyts) 2 c and c 2 , the methionine ligand of the heme is located in the middle of a 12-18-residue linker con-necting two ␣-helices of the conserved cytochrome c fold. Structural studies of cyts c and c 2 with exogenous ligands bound (1,2,5) show that part of the linker sequence (termed the "hinge" by Dumortier et al. (3)) is rotated to create a slight opening or loosening of the heme binding cavity. The initial and final states are generally referred to as closed and open. However, there is no direct evidence that ligand binding is preceded by a spontaneous conformation change that closely resembles the open state seen in ligand-bound structures or that the heme-methionine linkage is actually broken in any intermediate state. Indeed, the mechanism of ligand entry and access to the heme is still unknown.
Here we report on the kinetics of binding of imidazole and N-methylimidazole to cytochrome c 1 in isolated cyt bc 1 complex from Rhodobacter sphaeroides. Cytochrome c 1 is an integral component of the bc 1 complex, playing the role of electron carrier between the iron-sulfur protein and water-soluble cyt c (6). Little is known about ligand interactions with the heme of cyt c 1 , although mutational studies have shown that changing the endogenous distal axial ligand (methionine) significantly modifies the midpoint potential of cyt c 1 (7)(8)(9). Even less has been reported for exogenous ligand interactions with the c 1 heme. Osyzcka et al. (10) reported that cyanide partially inhibits cyt bc 1 from Rhodobacter capsulatus by binding to ferric cyt c 1 , with K d Ϸ 25 M. Inhibition of R. sphaeroides His-tagged bc 1 complex, when isolated with imidazole, was described by Guergova-Kuras et al. (11). This was attributed to lowering of the E m7 of cyt c 1 by binding Im on the basis of its known interaction with cyt c.
The very unusual kinetics of imidazole binding to cyt c 1 lead us to propose a novel mechanism for ligand binding to the heme, in which an initial and superficial binding near the heme cleft facilitates the subsequent entry into the heme pocket. The model is developed in the context of known structural and dynamic features of the heme domain, with general applicability to cyt c heme ligand binding.

EXPERIMENTAL PROCEDURES
Growth of R. sphaeroides strains, preparative procedures for the His-tagged cytochrome bc 1 complex, and methods of assaying ligand binding are described in the accompanying paper (43).
The imidazole and N-methylimidazole release rates were determined by adding 1 mM sodium ascorbate and 10 M DAD to bc 1 complex fully saturated with ligand and measuring the slow recovery of the ␣-band of cyt c 1 , at 552 minus 541 nm. Because of the lability of oxidized c 1 at room temperature, saturation with Im involved preincubation of stock bc 1 with 10 mM Im for at least 2 h on ice. After dilution into the assay medium (at room temperature), the residual concentration of ligand was low enough (ϳ0.1 mM) that the rate of reduction of free c 1 by ascorbate/DAD was much greater than the rate of ligand binding. Thus, after release, the rebinding of ligand was negligible compared with the reduction of the c 1 heme.
Imidazole and N-methylimidazole have essentially identical pK a ϭ 7.00 Ϯ 0.05 (12), and both are close to 90% deprotonated at pH 8, as used in this work. Concentrations and concentrationdependent parameters (e.g. K d , K B , k obs (on), etc.) are given in terms of total concentration of Im or MeIm without correction.
Kinetic measurements of reactions with rate constants slower than 0.5 s Ϫ1 were performed on a diode array Agilent 8453 spectrophotometer (integration time 100 ms) equipped with a UV-blocking filter (Corning Glass, CS 0 -52, cut-off wavelength 320 nm) to prevent a light-induced reduction of cyt c 1 . All reactions faster than 1 s Ϫ1 were studied using an Applied Photophysics SX-17MV stopped-flow spectrophotometer, with mixing time less than 2 ms and integration time 2.5 ms. Reactions with rate constants in the 0.5-1 s Ϫ1 range were typically studied using both instruments to provide overlap of the measurement ranges.

THEORY
The binding of small molecules to c-type hemes has generally been described by minimal two-step mechanisms. Two previously presented versions differ according to whether the second order process of ligand binding precedes or follows the rate-limiting step (3,4,(13)(14)(15)(16). Most authors have adopted a scheme in which cyt c undergoes a ratelimiting but spontaneous structural change that ruptures the relatively weak Fe III -Met bond, forming a five-coordinate heme in an "open" conformation of the protein that permits second order binding of ligand, L.
The "open" conformation is considered to have a short lifetime at neutral pH, but it allows a number of small molecules (imidazole, cyanide, nitric oxide, azide, pyridine, etc.) to penetrate the heme binding pocket and occupy the position of the sixth ligand of the heme, effectively locking the cytochrome in the open conformation. Applying the steady state approximation (k close Ͼ Ͼ k open ϩ k off ), Scheme 1 yields the following, where k obs is the observed, pseudo-first order rate constant for ligand binding to heme.  Ϫ1 , where K bind ϭ k on /k off , and the kinetic "Michaelis constant" is given by K m ϭ k close /k on .
An alternative scheme has the ligand binding prior to breakage of the Fe III -Met bond, followed by a first order rearrangement (ligand exchange) to yield the final product (16,17).
If the initial binding establishes a fast equilibrium (K B ϭ k B /k ϪB , and k ϪB Ͼ Ͼ k R ), Scheme 2 gives the following.
At low ligand concentration, k obs ϭ k R K B [L] ϩ k ϪR , and the apparent second order rate constant is k obs (on) ϭ k R K B . At high ligand concentration, the limiting rate is Both mechanisms predict similar behaviors for the rate of product (cyt c Ϫ L) formation: first order in ligand at low ligand concentration (second order overall) and zeroth order at high concentration of ligand, as is observed. In either case, the rate-limiting event, characterized by either k open or k R , corresponds to a substantial structural rearrangement of the heme environment.
As originally proposed (14,15), the initial binding in Scheme 2 was in the heme pocket, at the Fe-S bond, and the ligand exchange process was by an S N 2 mechanism. Formally, however, it describes any mechanism in which the ligand preassociates with the protein in some way that facilitates the subsequent displacement of the Fe-S bond. This view will be developed further below.

RESULTS
Kinetics of Imidazole Binding to Cyt c 1 -We previously found equilibrium binding of imidazole to cyt c 1 to be quite tight, with K d Ϸ 0.33 mM at 25°C, pH 8 (43). The rate of binding shows a complex dependence on Im concentration and is very temperature-dependent. The kinetic parameters for Im binding are summarized in Table 1, with error estimates.
The initial rate of binding was proportional to the concentration of Im over the range 0.1-2 mM (Fig. 1), with an apparent second order rate constant, k obs (on) Ϸ 27 M Ϫ1 s Ϫ1 , at 25°C. However, at Im concentrations between 2 and 10 mM, the rate increased faster than expected for a second order reaction, indicating a roughly quadratic or parabolic dependence. The apparent second order rate constant increased to a value of 55 M Ϫ1 s Ϫ1 at about 8 mM imidazole before decreasing at higher concentrations, giving the profile a distinctly sigmoidal shape.
In the low concentration limit, as [Im] 3 0, the apparent rate constant provides a first approximation of the unbinding rate constant, k obs (off) Ϸ 0.014 s Ϫ1 .
At Im concentrations between 20 and 100 mM, the rate leveled off. A hyperbolic fit to the data at 10 -50 mM imidazole gave K m ϭ 15 mM and V max Ϸ 1.1. s Ϫ1 (corresponding to k obs (lim1) in the discussion below). The apparent second order binding constant was ϳ75 M Ϫ1 s Ϫ1 . This is significantly higher than that indicated by the initial slope and reflects the sigmoidicity that is evident at low concentrations. A much better fit ( Fig. 2) is given by assuming that Im binding is a self-activating process (see "Discussion").
At Im concentrations above 100 mM, it is clear that a novel process appears, and the rate increases steeply (Fig. 2). The slope of the increase in log(Rate) versus log[Im] indicates a parabolic dependence (i.e. an n value of about 2). The apparent second order rate constant recovers to a value (50 -70 M Ϫ1 s Ϫ1 ) similar to that observed at low concentrations, and the net rate continues to increase at 1 M imidazole. Almost identical behavior was seen in the presence of 900 mM NaCl. The slope of the increase in log(Rate) versus log[Im] at high concentration is slightly less steep, but it also corresponds to an n value near 2 with some indication of saturation at 1 M (Fig. 2, open circles).
At lower temperatures, the kinetics of Im binding showed a qualitatively similar concentration dependence (initially second order, with partial saturation at intermediate concentrations, followed by further acceleration at high concentrations).
At 15°C, the rate of binding in the low concentration (linear) range gave a second order rate constant of k obs (on) ϭ 5.5 Ϯ 0.3 M Ϫ1 s Ϫ1 . The plateau was indistinct, but the rate clearly accelerated again at Im concentrations above 200 mM, and the data were reasonably well fit by a simple model (see "Discussion") with a plateau rate of k obs (lim) ϭ 0.35 Ϯ 0.1 s Ϫ1 .
At 5°C, Im binding was so slow that the kinetics could not be directly measured at concentrations less than 5 mM. The rate was linear up to 25 mM imidazole, with an apparent second order rate constant k obs (on) ϭ 1.2 M Ϫ1 s Ϫ1 , decreasing to 0.5 M Ϫ1 s Ϫ1 over the range 50 -350 mM imidazole. At high concentrations (Ն400 mM), the apparent binding rate constant increased again, to at least 1.6 M Ϫ1 s Ϫ1 , and the rate accelerated with no sign of saturation up to 800 mM. The data could be crudely fit with a plateau rate of 0.09 Ϯ 0.03 s Ϫ1 .
The temperature dependence of the second order rate constants in the low concentration range indicates a very substan-    Table 3. Conditions were as follows. 1 M oxidized bc 1 complex in 50 mM Tris, pH 8.0, 100 or 900 mM NaCl, 20 mM cholate was mixed with various amounts of Im or MeIm at 25°C. tial activation energy for Im binding, E a Ϸ 110 kJ/mol, and a large preexponential factor, logA ϭ 20.6. Comparison of the fitted plateau rates yields E a Ϸ 80 kJ/mol and logA Ϸ 14 for this limiting process.
Kinetics of N-Methylimidazole Binding to Cytochrome c 1 -In contrast to Im, the rate of MeIm binding increased monotonically with concentration, with the exception of a slight decline at the highest concentrations (Fig. 2). A simple hyperbola fit the data well up to 600 mM, with K m Ϸ 1 M and V max Ϸ 72 s Ϫ1 . This is much faster than the plateau value for Im but comparable with the extrapolated maximum rate for Im (see below). The kinetic parameters for MeIm binding are summarized in Table  1, with error estimates.
The second order rate constant for N-methylimidazole binding (k obs (on) ϭ 71 M Ϫ1 s Ϫ1 at 25°C, pH 8) was similar to that for imidazole binding calculated from the hyperbolic fit to the 10 -50 mM data range. The apparent rate constant as [MeIm] 3 0 yields the unbinding rate constant, k obs (off) Ϸ 1.4 s Ϫ1 .
At 15°C, the MeIm binding rate was linear with concentration, with a second order rate constant of 7.5 Ϯ 0.2 M Ϫ1 s Ϫ1 . From the binding rate constants at 15 and 25°C, we estimate an activation energy for MeIm binding at 160 kJ/mol with a preexponential factor of logA ϭ 30.0 (see Table 2).
Unbinding from the Cyt c 1 -Ligand Complex-The Im and MeIm release rates from cytochrome c 1 were determined from the recovery of ascorbate reducibility (Fig. 3). The observed reduction is the net result of at least three reactions in sequence: release of ligand from cyt c 1 , rebinding of methionine to the heme to yield the high redox potential form, and reduction by ascorbate/DAD. From the plateau rate, we estimated the limiting step in methionine displacement and Im binding to the heme, k obs (lim) Ϸ 1 s Ϫ1 at 25°C. Because the cyt c 1 heme is predominantly ligated to Met in the native state, the rate of conformational recovery and Met rebinding must be much faster than 1 s Ϫ1 . Also, the rate of reduction of uninhibited cyt c 1 with ascorbate/DAD exceeds 10 s Ϫ1 at the concentrations used. Finally, the residual concentration of Im after dilution was 0.1 mM, which, together with the above estimate of k obs (on) ϭ 27 M Ϫ1 s Ϫ1 , gives a rate of 3 ϫ 10 Ϫ3 s Ϫ1 for rebinding of ligand to cyt c 1 at 25°C, at least 3 orders of magnitude slower than the rate of native cyt c 1 reduction by ascorbate/DAD. Therefore, the net rate of reduction, which was less than 0.1 s Ϫ1 at all temperatures, is equal to the rate of Im unbinding from the c 1 heme, including any associated conformational changes.
For N-methylimidazole, the same argument applies. The observed rate of reduction by ascorbate/DAD, which was less than 1 s Ϫ1 at all temperatures, is clearly indicative of MeIm release rather than the conformational recovery.
The observed rates of reduction at 25°C were 0.012 and 0.79 s Ϫ1 for Im and MeIm, respectively, indicating release rates, k obs (off), that differ by about 65-fold. The off rate for Im agrees well with the estimate obtained by extrapolating the binding rate to zero ligand concentration (0.014 s Ϫ1 ; see Fig. 2). However, for MeIm, the off rate measured in this fashion is roughly half the value (1.4 s Ϫ1 ) determined by extrapolation of the binding rate (Fig. 2). The release rates for both Im and MeIm show very strong temperature dependence (Fig. 3), with apparent activation energies of E a ϭ 161 kJ/mol for Im and 110 kJ/mol for MeIm. The preexponential factors, determined by extrapolation to 1/T ϭ 0, were also very large: log A ϭ 26.4 and 19.2 for Im and MeIm, respectively. The measured kinetic parameters for Im and MeIm release are summarized in Tables 1 and 2.

DISCUSSION
Ligand Binding to c-type Hemes-For cyts c and c 2 , the equilibrium binding properties are well known for many exogenous ligands, but the mechanism of binding is still under debate. Many ligands to the ferric heme exhibit saturation kinetics, indicating an internal step that is rate-limiting at high concentrations (4, 16 -18). Two versions of a minimal two-step model are described by Schemes 1 and 2 (see "Theory"), which, with steady state and rapid equilibrium constraints applied, yield formally identical kinetic behavior-hyperbolic dependence on ligand concentration, reaching a maximum rate determined by an internal event (Equations 1 and 2). Without additional information, the two models cannot be distinguished, although previous reports have generally favored Scheme 1 (3,4,13,16). We observed similar behavior for cyt c 1 with many ligands, including MeIm described here. However, for Im, the concentration dependence of the rate of binding is complex and necessitates the introduction of an initial ("superficial") binding interaction   (43).
prior to the conformational and bond formation events that yield the heme liganded state. We first compare the kinetics of MeIm and Im binding to cyts c 1 , c, and c 2 before developing a new model of ligand binding that accommodates the unusual behavior of Im binding to cyt c 1 . N-Methylimidazole Binding and Release-The kinetics of binding N-methylimidazole to cyt c 1 are well fit by a hyperbolic concentration dependence (up to 0.6 M). The associated parameters (Table 1) are similar in value to those reported for binding of many nitrogenous ligands to cyts c and c 2 (k obs (on) ϭ 30 -130 M Ϫ1 s Ϫ1 (4,16,19); k obs (lim) ϭ 25-60 s Ϫ1 (3,4,16,18)). The value of k obs (off) Ϸ 1.4 s Ϫ1 obtained by extrapolating k obs to zero concentration is almost twice as large as the value (0.79 s Ϫ1 ) measured by assaying heme reducibility after preincubation with MeIm. No such discrepancy was seen for k obs (off) for Im. The smaller value yielded k obs (off)/k obs (on) Ϸ 11.1 mM for MeIm, in good agreement with the measured K d ϭ 9.3 mM (43). It is possible that the difference between the two assays of k obs (off) for MeIm indicates a slow conformational or configurational change in the heme-bound state of MeIm that is not complete on the time scale (Յ1 s) of the initial rate of binding.
Imidazole Binding and Release-The concentration dependence of the kinetics of Im binding to cyt c 1 is markedly different from that of MeIm or that reported for any previously described ligand or cyt c combination. Two regimes were apparent, at 0 -100 mM and Ͼ100 mM imidazole. In both regions, the rate increased with concentration in an approximately parabolic manner before approaching a saturation level. Preliminary studies show qualitatively similar dependences for 2-methyl-and 4-methylimidazole (not shown), and so far it is unique to imidazoles with both nitrogens free.
Because of the sigmoidicity of the concentration dependence, estimates of the second order rate constants for Im binding varied from 25 to 70 M Ϫ1 s Ϫ1 . This range is in good agreement with values for horse heart cyt c and R. sphaeroides and R. capsulatus cyt c 2 (50, 125, and 90 M Ϫ1 s Ϫ1 , respectively) (4,16).
Two limiting rates are evident in the concentration dependence. Above 30 mM, the rate of Im binding approached a limiting value, k obs (lim1), of about 1 s Ϫ1 , indicating an implicit conformational step as seen in cyt c and c 2 but with a much longer transition time (1 s versus 30 ms). After reaching an intermediate plateau at 50 -100 mM, the rate of binding increased again at higher concentrations, with a parabolic dependence (n Ϸ 2 in the log(Rate) versus log[Im] plot). Saturation was not reached at 1 M imidazole, but the negative curvature indicated a limiting rate (i.e. k obs (lim2)) of about 100 s Ϫ1 . This is similar to the limiting rates seen for cyts c and c 2 (3,4,16,18).
The steep acceleration at high concentrations is not an ionic strength effect. The contribution to ionic strength from the imidazole is small because only 10% is charged at pH 8, and raising the ionic strength from 100 to 900 mM NaCl had only minor effects on the kinetics and concentration dependence. Furthermore, in high salt, the increase in rate at high Im concentration was still indicative of n Ϸ 2.
Temperature Dependence of Ligand Binding and Release Kinetics-The temperature dependences of the observed rates for Im and MeIm binding and release by cyt c 1 were studied in the low concentration region (i.e. k obs (on), k obs (off), and k obs (lim1)), and the activation parameters, E a and logA, are summarized in Table 1. The temperature dependences of the high concentration limit rate for Im, k obs (lim2), and MeIm were not accessible due to lack of saturation at the lower temperatures.
The activation parameters for the on and off rates are consistent with the independently determined thermodynamic factors of equilibrium binding (43). Applying a simple transition state analysis to the temperature dependence of the kinetics, we can compare E a and RlnA for the on and off rate constants with the enthalpy (⌬H 0 ) and entropy (⌬S 0 ) of the equilibrium binding constant. 3 For the non-enthalpic components, the intercept at 1/T ϭ 0 in transition state theory is given by the equation, lnA ϭ lnk TST ϩ ⌬S TST ‡ /R ϩ ln. Assuming that k TST and the adiabaticity factor, , are the same for on and off reactions, R(lnA on Ϫ lnA off ) ϭ ⌬⌬S TST ‡ , which equates with ⌬S 0 . These comparisons are summarized in Table 2 and demonstrate the equivalence of the kinetic activation and equilibrium terms, within reasonable expectations of the data.
The magnitudes of the activation parameters associated with all of the rate processes are very large but are comparable with those reported for Im and MeIm binding to cyt c (20 -22) and cyt c 2 (4) ( Table 1). In particular, Dumortier et al. (4) analyzed Im binding to cyt c 2 according to the mechanism of Scheme 1. They decomposed the overall reaction into two steps, the closed-open transition and Im binding to the open state, and reported separate parameters for k open and k off . Their temperature data yield 4 values of E a and logA for k off , which agree well with those for the unbinding rate constant, k obs (off), for cyt c 1 -Im. Their results for the rate-limiting step in Scheme 1, which is identified with the closed-open transition, k open , are comparable with our estimate of E a for the plateau rate, k obs (lim1), for Im binding to cyt c 1 . However, a more suitable comparison might be with the maximum rate, k obs (lim2), for which we have no temperature dependence data.
All net binding mechanisms under consideration involve significant structural reorganization to make room for the exogenous ligand and to stow the released methionine side chain. The very large Arrhenius preexponentials and enthalpies are consistent with the kinetic barrier arising from highly cooperative events akin to protein folding or, more generally, structural changes in a complex, fluctuating matrix (23).
A Four-site Binding Model for Imidazole-The dependence of imidazole binding in both low and high concentration regions is parabolic, suggestive of a substrate activation process (24). Within each concentration region, this can be accounted for by an initial or "superficial" binding of two Ims that precedes 3 The correction to the activation energy to yield the activation enthalpy, ⌬H TST ‡ ϭ E a Ϫ RT, cancels in the difference between on and off rate values and in any case is well within the error of the data (RT Ϸ 2.5 kJ/mol). 4 Calculated from Table III  heme cleft access ("opening" and "closing"), followed by ligand exchange. We first consider the low concentration regime, with two binding sites, 1 and 2, and apply ordered addition because it gives somewhat better fits than random addition unless significant cooperativity is included. It is also simpler (see supplemental material for full description).
In Scheme 3, the association constants, K B1 and K B2 , describe fast, superficial binding equilibria that precede the conformational change (open/close) and heme ligand bond formation necessary for the complete ligand exchange. At the present time, however, the kinetic data provide few guidelines for partitioning the postbinding events between the conformational and bond formation steps. These will be considered later, but we first combine them in a "reaction step." The non-zero value of the second order rate constant for Im binding at low concentrations indicates that the substrate activation is "non-essential" (i.e. the single ligand state, (L)c, has finite reactivity, but the double ligand state, (L)c(L), is more active (24)). This yields Scheme 4, with k R1 Ͻ k R2 . The inclusion of the binding equilibria after reaction, K B1 P and K B2 P , is necessary for a complete thermodynamic description that meets the requirements of microscopic reversibility. However, it has little impact on the concentration dependence of the kinetics unless the pre-and postreaction equilibria are dramatically different.
Scheme 4 leads to an observed rate of ligand binding (see supplemental material) as follows, where k ϪR includes k ϪR1 and k ϪR2 and is weakly concentrationdependent due to K B1 P and K B2 P . However, at [L] 3 0, it resolves to k ϪR1 . Analytical expressions are obtained for the second order binding rate constant, k obs (on) ϭ k R1 K B1 ϩ k ϪR2 K B2 P , the off rate constant, k obs (off) ϭ k ϪR1 , and the dissociation constant, K d ϭ (K B1 K R1 ) Ϫ1 , all at low Im concentration, and a lim-iting rate constant, k obs (lim1) ϭ k R2 , at intermediate concentrations. This describes very well the kinetics of Im binding in the 0 -50 mM concentration range. However, the rate of Im binding increased again at higher concentrations, also with a parabolic dependence as seen at low concentration.
Because of the clear separation between the low and high concentration regimes, the full range of the Im binding kinetic data can be well accounted for as the sum of two independent reaction paths, both exhibiting substrate activation at a pair of binding sites, sites 1 and 2, with relatively high affinity (K B1 and K B2 ), as described above, and sites 3 and 4 with much weaker affinity (K B3 and K B4 ). Each path is described by Equation 3, with distinct parameter sets for the low and high concentration regions (subscripts 1 and 2 and subscripts 3 and 4, respectively). This full description provides an additional limiting case of Implications of the Four-site Model for Imidazole Binding-The resulting fit to the imidazole data, using two Equations 3, is shown in Fig. 2. Both sets of Im data at 25°C, at low and high ionic strength, are well fit by similar parameters, and the compensation between rates and affinities does not warrant refinement beyond the range of values given in Table 3. 5 The effective second order rate constant for each state is approximately given by k Rn K Bn (n ϭ 1-4). In the lowest concentration range, the inverse relation provided an initial estimate of k R1 using the measured value of k obs (on) ϭ 27 M Ϫ1 s Ϫ1 . In the intermediate plateau region, we can still largely ignore the low affinity sites, and there is one dominant state with both high affinity sites occupied and k R2 ϭ 0.85 s Ϫ1 . The apparent association constant is approximately 6 K B app ϭ 75 M Ϫ1 , giving an on-rate constant of ϳ65 M Ϫ1 s Ϫ1 . This is in good agreement with the maximum slope of 55 M Ϫ1 s Ϫ1 observed in the range of 3-10 mM imidazole. For occupation of low affinity site 3, which appears with K B3 Ϸ 0.5 M Ϫ1 , a significant reaction rate would obliterate the plateau. The observed dependence requires that single occupancy of low affinity site 3 exhibits only low reactivity, with k R3 Ͻ 5 s Ϫ1 . However, with both low affinity sites occupied, the reactivity is greatly enhanced, with k R4 ϭ 110 s Ϫ1 .
When high affinity binding sites 1 and 2 are both occupied, the maximum rate (k R2 ϭ 0.85 s Ϫ1 ) is 2-3 times faster than for 5 Reasonable fits were obtained using single values for K B1 ϭ K B2 ϭ 100 Ϯ 10 M Ϫ1 and K B3 ϭ K B4 ϭ 1 Ϯ 0.1 M Ϫ1 , but better fits were obtained using separate values for all. In the case of a model with random addition, best fits required a significant amount of cooperativity in binding (␣ Ͼ 2). Both of these improvements are consistent with the second imidazole of each pair interacting with the first. shows the fully occupied state to be more than 100-fold more reactive than when only the high affinity sites are filled and 300 times faster than for singly occupied high affinity site 1.
The reaction equilibrium constants for each state are given by K Rn ϭ k Rn /k ϪRn or K Rn ϭ (K Bn K d ) Ϫ1 . The measured and fitted kinetic data sets are incomplete for this purpose, but we can obtain a likely range of values by assuming either that k ϪRn Ϸ k ϪR1 (except for k ϪR3 , which must be less) or that K d is roughly constant. Although K d can vary, microscopic reversibility requires it to be the same for both binding pathways with single occupancy (i.e.
The resulting reaction equilibrium constants are summarized in Table 4. Despite the range of values obtained for each, using the two relationships, it is clear that that there are two distinct classes of postbinding reaction equilibrium: for the high affinity binding sites K Rn Ͻ 100 and for the low affinity binding sites K Rn Ͼ 1000. Also, for K R3 Ϸ 5000, the limit value of k R3 Ͻ 5 s Ϫ1 requires k ϪR3 Յ 0.001 s Ϫ1 . This is substantially smaller than k ϪR1 . These differences in kinetic and equilibrium constants between the high and low affinity binding sites probably originate in the open/close and ligand exchange contributions to the "reaction step," which we discuss next.
The Constituent Events of the Reaction Steps-Although the underlying events comprising the "reaction step" are unknown in detail, they must include conformational and liganding components. To provide insight into the nature of the initial binding events and their influence on heme ligand formation, we consider a two-step expansion of the reaction step in Scheme 3, where c* represents a state of cyt c 1 with the heme accessible to the exogenous ligand. Scheme 5 identifies open/close and ligand exchange processes, such that K R ϭ K O K L . Assuming that k C Ͼ Ͼ k O (i.e. K O Ͻ Ͻ 1), we have the following.
These reduce to distinct limits, depending on whether k C Ͼ Ͼ k L or k C Ͻ Ͻ k L . The slow reaction rates (k R1 , k R2 ) and relatively small reaction equilibria (K R1 , K R2 ) associated with the high affinity bind-ing sites suggest the influence of a very small value of the open/ close equilibrium, K O . We suggest that this is due, in part, to a fast rate of closure, such that k C Ͼ k L . This yields k R Ϸ K O k L and k ϪR Ϸ k ϪL from Equations 4 and 5. Thus, k ϪR (MeIm) and k ϪR1 (Im) (i.e. k obs (off)) provide measures of the rate of ligand unbinding from the heme, k ϪL . The modest 2-3-fold activation of k R2 that occurs upon binding a second imidazole at site 2 can act through an increase in K O while maintaining the same rate relationship (k C Ͼ k L ).
In the high concentration/low affinity regime, the standout features are the small values of k R3 and k ϪR3 and the substantial acceleration upon binding a second Im (k R4 ). We suggest that for single occupation of site 3, the conformational change is slow, and in particular, the rate of closure is slow so that k C Ͻ k L . This leads to k R Ϸ k O and k ϪR Ϸ k C /K L . Thus, as surmised above, the values of k R3 and k ϪR3 reflect quite different processes from k R1 and k ϪR1 , etc. Activation of the low affinity path upon binding a second Im to site 4 would probably occur through acceleration of both k O and k C , possibly changing the rate-determining condition to k C Ͼ k L , so that k R Ϸ K O k L and k ϪR Ϸ k ϪL at high concentrations.
This description implies that singly bound Im at site 3 leads to a kinetically sluggish response of the heme cleft. As discussed below, we propose that this is due to its ability to form two hydrogen bonds that limit the conformational flexibility of the protein. Binding the second Im releases the kinetic constraint, greatly enhancing k O and k C and possibly revealing an increased value of K O .
Comparison of Imidazole and N-Methylimidazole Binding-The simple hyperbolic concentration dependence seen for MeIm appears to be quite distinct from the complex behavior of Im. However, the adequacy of a hyperbolic fit for MeIm is not evidence for the absence of multiple binding sites, whereas the behavior seen for Im requires the minimal assumption of two pairs of sites. Thus, MeIm could exhibit a multiplicity of binding sites, but it is possible to eliminate the kinetic significance of high affinity sites. The measured on and off rate constants are fully consistent with the measured dissociation constant, K d Ϸ 10 mM. Because K d ϭ (K B K R ) Ϫ1 , if K R Ͼ Ͼ 1, as reasonably expected, then (K B ) Ϫ1 Ͼ Ͼ 10 mM for all sites. If sites existed with (K B ) Ϫ1 Ͻ 10 mM, which is even tighter than Im, then K R would be Յ1, and the maximum extent of heme ligation would be small, contrary to observation (43). Here we compare the characteristics of Im and MeIm binding at the low and high concentration limits, assuming a single binding site for MeIm.
The determinations of k obs (on) and k obs (off) at low concentration yield dissociation constants for Im (0.44 mM) and MeIm (11.1 mM) that differ by a factor of 25, in excellent agreement with our equilibrium measurements (43). The kinetic affinity constant (K B ) for Im (in the low concentration range) and MeIm exhibit even greater disparity (ϳ100 versus 1 M Ϫ1 ). Because K d ϭ (K B K R ) Ϫ1 , these evaluations yield the net reaction equilibrium K R Ϸ 90 for MeIm. Alternatively, the kinetic fit yields K R ϭ k R /k ϪR ϭ 70/1.4 ϭ 50. The equivalent parameter for Im is K R1 Ϸ 25-50 (Table 4).
The relative similarity of these values for Im (at low concentration) and MeIm is coincidental because K R is composite, including both conformational and heme bonding changes (i.e. K R ϭ K O K L (see Scheme 5)), and K L is expected to be significantly larger for Im than for MeIm. In molecular dynamics simulations of an in silico c 1 -Im complex (43), hydrogen bonds were formed between the N ␦ H of imidazole and the protein, both directly and via an intervening water. A similar arrangement is seen in the crystal structure of the cyt c 2 -Im complex and accounts for the observed high affinity of cyt c 2 compared with cyt c (1, 4). This is not possible for MeIm, and the Fe-N bond for MeIm may also be weaker due to steric clashes with the N-methyl group. A larger value of K L for Im points toward a substantially smaller value of K O for Im at low concentrations. As discussed below, binding of Im in the low concentration regime is probably via an access pathway different from that employed by MeIm, and a significant difference in K O is a reasonable expectation. At the same time, K O must be small (Ͻ Ͻ1) for any path, implying large, albeit different, values of K L (Ͼ ϾK R ) for both Im and MeIm, such that both very effectively exchange for methionine once in the heme site. This is fully consistent with the known affinities of ferric heme for thioethers and imidazoles (25).
In the high concentration regime, the maximum rates for Im and MeIm are similar (k obs (lim2) Ϸ 110 and 75 s Ϫ1 , respectively). This is consistent with Im (with all sites occupied) and MeIm entering by similar routes, rate-limited by a process that does not significantly distinguish between their hydrogen bonding capabilities. The superficial affinities of MeIm and Im are also similarly weak in this region (K B , K B4 Ϸ 1 M Ϫ1 ). At the same time, the parabolic dependence of k obs for Im shows that the reaction step, k R (see Equation 4), is modified by the superficial interactions represented by K B3 and K B4 to yield the high value observed for k R4 . The large difference in net ligand affinity (K d ) for Im and MeIm is fully accounted for by the difference in k ϪL , with little change in the ligand exchange reaction rate, k L . Thus, k O and K O are the prime candidates for the sensitivity of k R to surface binding interactions. We suggest that the superficial binding of a single Im limits the protein dynamics underlying the open/close process and that this is relieved by binding a second Im, yielding a heme cleft mobility similar to that achieved by a single MeIm. We now discuss the possible structural basis for this behavior.
The Structural Basis of Ligand Entry to Cyt c 1 -In cytochromes c and c 2 , the conformational changes necessary to accommodate the displaced methionine and the new heme ligand are centered on the short linker (12-18 residues) between helices ␣3 and ␣5 of the standard cyt c fold, in particular the 8 -14 residues that constitute the so-called "hinge" region that spans the methionine. Molecular dynamics modeling of the c 1 -Im complex shows a similar structural impact of ligand binding (43). However, the linker between the two helices in cyt c 1 is much larger (68 residues in R. sphaeroides), being the site of a major sequence expansion that distinguishes it from type I cyts c (27). The sequence variety and structural characteristics of the linker, which include helix ␣4 in type I cyts c, suggest that flexibility control in this region is important to function. In the longer linker of cyt c 1 , additional controlling elements include a pair of short, antiparallel ␤-strands, a proline-rich sequence, small ␣-helical segments, a ␤-branched amino acid two residues from the methionine (␤XM motif), and, unique to Rhodobacter, a disulfide bond.
The site of ligand entry is not known for any cytochrome c, but it is noteworthy that the heme of cyt c 1 is markedly solventexposed and is exposed on two sides, in contrast to cyts c and c 2 . It is particularly striking that the two propionate groups (on rings A and D) of the c 1 heme are fully exposed because these are completely concealed in cyts c and c 2 (see supplemental material). We suggest that the propionates are key elements of the high affinity sites of Im binding in cyt c 1 . This face of the cyt c 1 protein, which is quite polar, also constitutes the docking site for the iron sulfur protein (ISP) subunit of the bc 1 complex (28,29), so the heme is alternately exposed and occluded during the turnover cycle of the bc 1 complex.
The apparently unique ability of Im and methyl derivatives with both nitrogens free to access a high affinity path in cyt c 1 implicates the capacity to form two hydrogen bonds. Access and binding to the heme from these sites is slow, with a maximum rate of about 1 s Ϫ1 , reflecting a likely limitation in the structural dynamics along this edge of the heme cleft. The propionates are engaged in electrostatic interactions with residues on both sides of the cleft, which may restrict its movement. Interference with these interactions may be necessary to allow sufficient flexibility for ligand entry.
The parabolic dependence in the low concentration range implicates an activated process, as illustrated by Scheme 3. We suggest that a single Im binds at or near the propionates, forming two hydrogen bonds that either restrict its own mobility or may bridge the heme cleft, thereby restraining its movement. A second Im then substitutes as a hydrogen bond partner of the first, inducing greater flexibility and allowing Im to progress more readily toward the heme. This would be consistent with the superficial binding modes modifying k O and/or K O .
The heme is also exposed along the ring C-D edge. This face of the cyt c 1 protein is quite apolar, and backbone amides provide the only potential for hydrogen bond interactions around the cleft opening. Only this heme edge is exposed in cyts c and c 2 , which exhibit kinetically simple binding of Im and MeIm at high concentrations. It seems likely, therefore, that this edge provides a common site of entry for ligands of these cytochromes and for the low affinity pathway of Im entry to cyt c 1 . The parabolic dependence of Im binding to cyt c 1 in the high concentration regime indicates that the surface binding of a single imidazole is also not sufficient to facilitate the entry of imidazole into the heme pocket via the low affinity sites and that binding of a second imidazole is necessary for facile entry. The restriction of this behavior to Im again suggests that the formation of two hydrogen bonds may underlie this effect.
In contrast to Im, monodentate MeIm binds more weakly but can still break up a hydrogen-bonded pair. However, it would be unable to restrain the heme cleft dynamics by forming a second hydrogen bond. Binding a single MeIm would therefore suffice to facilitate the first steps of entry into the heme pocket.
X-ray structures of cyt c 2 and its Im adduct show that there is remarkably little perturbation of the heme cleft at the propionate (ring A-D) edge, and the major change in the final structure occurs along the ring C-D and B-C edges of the heme cleft (1). In particular, the native ligand methionine (Met 100 in R. sphaeroides cyt c 2 ) is displaced to the heme edge and becomes almost fully solvent-exposed, and Phe 102 lifts up from the ring B-C edge to allow a clear view of the bound imidazole (see supplemental material).
The protein structural options for initial binding events in cyt c 2 are largely limited to backbone amides. In R. capsulatus cyt c 2 , mutation of Gly 95 causes substantial enhancement of the rate of ligand binding, although it does not move much itself (30). This residue, which is adjacent to the ligand methionine, is not at all conserved (it is Lys 99 in R. sphaeroides cyt c 2 ), but the peptide NH is in strong interaction with the D propionate of the heme in both the native and Im-bound states (1). Thus, despite its very similar placement in the initial and final states, the kinetic behavior of the Gly 95 mutants suggests a role in the transition.
In simulations of the R. sphaeroides cyt c 1 -Im adduct (43), the results were quite similar to cyt c 2 , despite the very different sequences. The conformational change displaces the methionine (Met 185 ) to the heme edge, and the major movement raises the first two of three consecutive prolines (Pro 186 -Pro 188 ) along the heme C-D edge (Fig. 4). In cyt c 1 , the residue immediately before the methionine (equivalent to Gly 95 in R. capsulatus cyt c 2 ), is Ala 184 in R. sphaeroides and Arg 182 in R. capsulatus. As for cyt c 2 , the backbone amide of these unconserved residues is well placed to hydrogen-bond to the D propionate. However, in contrast to cyt c 2 , the cyt c 1 -Im simulations showed a substantial displacement of this residue. On the other hand, there is much less perturbation along the B-C edge of the heme. Perhaps because of the rigidity of the triple proline sequence, the backbone movement necessary to accommodate the displaced methionine is exerted more on the preceding residues.
Stability of the Heme Binding Domain of Cyt c 1 -The significance of two of the features of the cyt c 1 "hinge" (the disulfide bond and the ␤XM motif, which is almost universal but notably absent in R. capsulatus) is substantiated by mutant studies in R. capsulatus and R. sphaeroides. In R. capsulatus, the disulfide bond is required to maintain cyt c 1 in the native high potential form. However, second site revertants were recovered in which an alanine located two residues away from the Met-ligand was replaced by a ␤-branched amino acid, defining the ␤XM motif (31,32).
In contrast, cyt c 1 of R. sphaeroides contains the disulfide bond but has isoleucine in the ␤XM motif. Mutants of R. sphaeroides lacking the disulfide bond between Cys 145 and Cys 169 were still able to grow phototrophically. Although the E m of cyt c 1 was substantially lowered, it was at least 100 mV more positive than in the equivalent R. capsulatus mutants (33). Thus, the ␤XM motif in R. sphaeroides appears to restrain the amplitude of the midpoint potential change associated with the removal of the S-S bond.
We suggest that hydrogen bond networks in and around the heme cleft are involved in stabilizing cyt c 1 in its compact, high potential form, in a manner qualitatively similar to the effect of the disulfide bond. The superficial binding of ligand initiates the disruption of these interactions, destabilizing the native form of cyt c 1 and lowering the energetic barrier for the conformational transition that opens the heme cleft for direct binding to the heme. The multiplicity of potential ligands in vivo emphasizes the need for stabilizing structures like the disulfide bond and the variety of secondary structures seen in the hinge regions of different c-type cytochromes.
For soluble cyt c, the stability of the heme distal pocket is affected by bulk phase influences, including the solution environment (34) and dielectric constant (35). Destabilization results in lowering of the apparent pK a of the so-called alkaline transition, a major conformational change that occurs at high pH and is accompanied by the displacement of the native methionine ligand by a variety of internal nitrogenous ligands, notably lysine amines (36 -38). The alkaline transition, itself, is too slow at pH Ͻ 9 (37,39) to contribute to the spontaneous conformational change required by Scheme 1, for example, but some exogenous ligands are known to promote the alkaline transition. However, the ability of small molecules to do this is not well correlated with their heme-liganding propensity (40,41). Furthermore, the necessary concentrations are high, in the molar range, and it has not been clear that this action is any more specific than a general chaotropic effect.
Here we have found that even at a few mM, the kinetics of Im binding imply rather specific surface interactions that can affect the structure and dynamics of the protein. The behavior at concentrations above 100 mM suggests similar influences upon specific binding at other sites. Additional, nonspecific interactions at high concentration cannot be ruled out and may be responsible for the fall off in activity at MeIm concentrations approaching 1 M, but they do not seem to play a significant role in the main range of this study.
We have proposed that the rate-limiting events in binding imidazole and N-methylimidazole to the heme of cyt c 1 include a conformational change that is facilitated by interactions with ligand superficially bound, in some cases at multiple sites. We also suggest that this picture may be extended to c-type cytochromes, generally, whereby exogenous ligand binds first to the protein in a superficial manner, disrupting existing hydrogen- Right images, imidazole bound (from MD simulation). Top, view along the exposed heme ring D-C edge. Bottom, view from above. Residues shown are Ala 184 -Pro 188 . The figure was prepared with VMD (42).