Analysis of the kinetic barriers for ligand binding to sperm whale myoglobin using site-directed mutagenesis and laser photolysis techniques.

Time courses for NO, O2, CO, methyl and ethyl isocyanide rebinding to native and mutant sperm whale myoglobins were measured at 20 degrees C following 17-ns and 35-ps laser excitation pulses. His64 (E7) was replaced with Gly, Val, Leu, Phe, and Gln, and Val68 (E11) was replaced with Ala, Ile, and Phe. For both NO and O2, the effective picosecond quantum yield of unliganded geminate intermediates was roughly 0.2 and independent of the amino acids at positions 64 and 68. Geminate recombination of NO was very rapid; 90% rebinding occurred within 0.5-1.0 ns for all of the myoglobins examined; and except for the Gly64 and Ile68 mutants, the fitted recombination rate parameters were little influenced by the size and polarity of the amino acid at position 64 and the size of the residue at position 68. The rates of NO recombination and ligand movement away from the iron atom in the Gly64 mutant increased 3-4-fold relative to native myoglobin. For Ile68 myoglobin, the first geminate rate constant for NO rebinding decreased approximately 6-fold, from 2.3 x 10(10) s-1 for native myoglobin to 3.8 x 10(9) s-1 for the mutant. No picosecond rebinding processes were observed for O2, CO, and isocyanide rebinding to native and mutant myoglobins; all of the observed geminate rate constants were less than or equal to 3 x 10(8) s-1. The rebinding time courses for these ligands were analyzed in terms of a two-step consecutive reaction scheme, with an outer kinetic barrier representing ligand movement into and out of the protein and an inner barrier representing binding to the heme iron atom by ligand occupying the distal portion of the heme pocket. Substitution of apolar amino acids for His64 decreased the absolute free energies of the outer and inner kinetic barriers and the well for non-covalently bound O2 and CO by 1 to 1.5 kcal/mol, regardless of size. In contrast, the His64 to Gln mutation caused little change in the barrier heights for all ligands, showing that the polar nature of His64 inhibits both the bimolecular rate of ligand entry into myoglobin and the unimolecular rate of binding to the iron atom from within the protein. Increasing the size of the position 68(E11) residue in the series Ala to Val (native) to Ile caused little change in the rate of O2 migration into myoglobin or the equilibrium constant for noncovalent binding but did decrease the unimolecular rate for iron-O2 bond formation.(ABSTRACT TRUNCATED AT 400 WORDS)

. Similar studies of these residues in the cr and @ subunits of R-state human hemoglobin have been completed Mathews et al., 1989). The effects of site-directed mutagenesis on the equilibrium constants for Oe, CO, and alkyl isocyanide binding are readily interpreted in terms of the crystal structures of deoxymyoglobin and its corresponding liganded complexes. Hisa stabilizes bound Or by at least -1.4 kcal/mol through hydrogen bonding between the e-amino nitrogen of the imidazole side chain and the second bound oxygen atom (Phillips, 1981). Bound CO is destabilized by +l.O kcal/mol due to steric hindrance by His64. This is expressed structurally by a bent Fe=C=O geometry and movement of the E7 imidazole size chain away from the iron atom (Kuriyan et al., 1986). Valm does not appear to hinder Or binding, may serve to orient the bound ligand for more efficient hydrogen bonding to His64, but does inhibit CO binding, although the extent is significantly smaller than that due to His64. Bound methyl and ethyl isocyanide are markedly hindered by both Hisa and Valm, and these steric interactions are observed structurally as disorder in the position of His64 and a highly distorted iron-isocyanide geometry (Johnson et al., 1989). A quantitative summary of these results is presented in Egeberg et al. (1990).
Interpretation of the overall association and dissociation rate constants for ligand binding to the position 64 and 68 mutants is more difficult since these parameters are determined by at least two kinetically distinct processes: 1) migration into and out of the protein and 2) binding to or dissociation from the iron atom within the distal portion of the heme pocket. Frauenfelder's group was the first to resolve these processes experimentally and to attempt to explain them in terms of specific structural features within the sperm whale myoglobin molecule (Austin et al., 1975). In their early work, unimolecular rebinding from within the distal pocket was measured directly by photochemically dissociating CO-myoglobin in glycerol/water mixtures at low temperatures, conditions which prevent the ligand from leaving the protein matrix. Over the intervening 15 years, these processes have been resolved at room temperature in ordinary aqueous solutions by using short excitation pulses (see Ansari et al., 1986;Gibson et al., 1986;Henry et al., 1983;Cornelius et al., 1981;Jongeward et al., 1988;Petrich et al., 1988). Most ligandprotein complexes exhibit at least one unimolecular rebinding phase which can be assigned to bond formation between the iron atom and photodissociated ligand present within the protein. In combination with the overall association and dissociation rate constants, the observed geminate rate constants can be used to define most if not all of the kinetic parameters for a linear, consecutive reaction scheme (Henry et al., 1983;Gibson et al., 1986).
Previous structural, theoretical, and kinetic work have suggested that ligands enter the distal pocket of myoglobin through a channel between the distal histidine and valine which is created by rotation of the imidazole side chain of His64 about its C,-CB bond (Bolognesi et al., 1982;Ringe et 1 The alphanumeric codes (e.g. E7 and Eli) refer to the position of the residue within the helices and loops of the myoglobin folding pattern (Dickerson and Geis, 1983). In the case of native sperm whale myoglobin, E7 and El1 correspond to positions 64 and 68, respectively, in the amino acid sequence. The amino acids at the distal His(E7) and Val(E11) positions in the site-directed mutants are referred to as 64 and 68 for comparison with the native protein even though the recombinant myoglobins have an additional Met at the NH;! terminus. Kottalam and Case, 1988;Johnson et al., 1989;Rohlfs et al., 1990). We have attempted to resolve the individual contributions of Hi@ and Va16' to the kinetic barriers involved in ligand binding by analyzing geminate recombination time courses for a series of site-directed mutants of sperm whale myoglobin.
His@ was replaced by Gly, Val, Leu, Phe, and Gln to determine the importance of the size and polarity of the side chain at the E7 position; Valm was replaced with Ala, Ile, and Phe to determine the effect of size at the El1 position. By using ligands which differ in size and chemical reactivity, we were able to examine intramolecular rebinding over a wide range of time scales. The geminate recombination reactions for the NO derivatives were dominated by large, extremely rapid picosecond phases (tlh = 40 ps), whereas only nanosecond geminate intermediates were observed for the corresponding 02, methyl isocyanide, and ethyl isocyanide complexes. CO recombination reactions were also examined, but in most cases, the extent of rebinding from within the protein was too small (~5%) to allow accurate measurements.

MATERIALS AND METHODS
Preparation of Mutants-Wild-type and mutant sperm whale myoglobins were expressed in Escherichia coli using the synthetic gene of Springer and Sligar (1987). Construction and purification of the position 64 and 68 mutants were described by Springer et al. (1989) and Egeberg et al. (1990), respectively. Native sperm whale myoglobin (type II) was obtained from Sigma prior to the United States ban on whale products, stored at -20 "C, and used without further purification. Preparation of ligand solutions for kinetic measurements was described by Rohlfs et al. (1990) and Gibson et al. (1986). In our initial photolysis experiments, we found no differences between the geminate recombination time courses for native and wild-type myoglobin expressed in E. coli. Rohlfs et al. (1990) showed previously that native (Sigma) and synthetic wild-type myoglobin have identical overall association and dissociation rate constants for eight different ligands. Phillips et al. (1990) reported that the three-dimensional structure of wild-type metmyoglobin expressed in E. coli is identical to that of native metmyoglobin except in the immediate vicinity of the NH,-terminal methionine. In view of these controls, we combined and averaged the results for Sigma and wild-type myoglobin and listed the parameters as applying to native protein (Tables I-IV).
Measurement of the O2 recombination reactions for Gly", Vale4, Leu", and PheM myoglobin were complicated by high rates of autooxidation which made quantum yield determinations difficult. The oxygen complexes of these proteins were prepared at pH 9 in 0.1 M borate buffer under 1 atm of 02, and the flash photolysis experiments were carried out as auicklv as nossible (see Rohlfs et al. 1990). The geminate recombination reactions of native myoglobin were examined in 0.1 M phosphate at pH 7 and in 0.001, 0.010, 0.050, and 0.1 M borate at pH 9. No differences were found among the five conditions. Conventional rapid mixing and flash photolysis experiments were carried out to measure the overall association rate constants for 02, CO, and methyl isocyanide binding to native and mutant myoglobins at pH 7 and 9, and again no pH dependence was observed. Consequently, we assume that the O2 geminate recombination parameters for the position 64 mutants apply at both pH 7 and 9.

Laser Photolysis
Experiments-For the NO, 02, and CO reactions, protein samples were prepared in tonometers equipped with l-mm pathlength cuvettes. Isocyanide complexes were injected into thin cells capped with a serum stopper as described by Gibson et al. (1986). The heme concentrations were 20-100 pM. Overall quantum yields for the CO and isocyanide complexes, Qoverall, were measured using a conventional photolysis apparatus equipped with two photographic strobes containing thyristor quenching devices. The excitation flash was set to be a rectangular pulse with a width of -0.5 ms and rise and decay times ~0.1 ms. The extent of deoxymyoglobin formation produced by the pulse was measured as a function of relative light intensity, and the value of Qoverall was obtained as described by Gibson et al. (1986, Miniprint). Overall quantum yields for 02 were measured using either a 300-ns pulsed dye laser (Phase-R 2100B, see  or the 17-ns pulse system described below.  (Jongeward et al., 1988). However, Petrich et al. (1988) have shown that the initial photochemical behavior of heme proteins is much more complex and that the effective picosecond quantum yield is considerably less than 1 for O2 and NO heme complexes.

Kinetic Barriers in Myoglobin
Our results for NO and O2 rebinding to myoglobins and hemoglobins using the 35-ps pulse system agree with their conclusions (Bellelli et al., 1990; Tables  I and II Tables  I-IV. k'xc, kcx, Kxc, kca, kac, and KM were calculated from these averages using the expressions in Equation 6. 1986). At present, it is difficult to distinguish between these possibilities experimentally, and thus, the fitted parameters in Table I (Henry et al., 1983;Gibson et al., 1986): When the excitation pulse was short compared with the relaxation time of the geminate reaction, the time courses were fitted to a single exponential expression with a constant absorbance offset: AA, = L4, + AA, exp (-k&) AA, is defined as the absorbance at time t after the pulse is over minus the absorbance of the sample before the pulse, AA, is the absorbance change which remains at the end of the geminate recombination phase and represents the extent of escape from the protein, AA, is the total absorbance change associated with geminate recombination, and kp is the observed geminate recombination rate constant, which is equal to kca + kcx. The fractional amount of geminate recombination, c3,, is defined experimentally as AAJ(AA, + AA& and is equivalent to k,J(kca + k&. kg, Ca,, and the overall kinetic parameters (Equation 4) can then be used to compute the individual rate constants for the two-step reaction mechanism given in Equation 2 (Henry et al., 1983;Gibson et al., 1986).
When the light pulse was longer and its duration approached the relaxation time of the geminate rebinding process, the differential equations prescribed by the reaction mechanism in Equation 3 must be numerically integrated, both during and after the light pulse, and the time constant of the recording system applied to the solutions (Gibson et al., 1986). This was done for all experiments using 17-ns excitation pulses. The value of khu was obtained using MbCO as a standard, and kc.+ kcx, and Q.. were fitted to the observed data using non-linear least squares algorithms. Two separate sets of experiments were carried out for most of the 02, CO, and isocyanide-myoglobin complexes listed in Tables  I-IV; one using a short 35-ps pulse and exponential analysis, and another using a 17-ns pulse and numerical integration techniques to fit the observed time courses. The agreement between the two sets of exper-As footnoted in Tables  II-IV,  certain  and movement away from the initial photodissociated contact pair. Replacing Va16' with Ile caused a 6-fold decrease in the first order rate constant for the geminate rebinding of nitric oxide, presumably because the larger El1 side chain limits access to the iron atom even in the contact pair (Table I).
O2 Rebinding-Sample time courses for the photolysis of oxymyoglobin are shown in Fig. 2 yield is that longer excitation pulses are required to obtain complete photolysis, and the best analyses of 02 recombination from state C were obtained using a 17-ns pulse (Fig. 2).
Only small changes were observed when comparing the nanosecond geminate recombination rate parameters for native oxymyoglobin with those for the position 64 mutants ( Fig. 2A and Table II). kg varied from 2 X lo7 to 4 X lo7 s-l, and c3, was in the range 0.3-0.6. As a result, the rate of rebinding from within the distal pocket, kca, was roughly equal to the rate of ligand escape from the protein, kcx, and neither changed more than 3-fold. In contrast, the overall association and dissociation rate constants and the corresponding rate parameters describing 0, migration into the protein, Larger changes in the geminate recombination rate parameters were observed for the position 68 mutations. Although the rates of O2 escape from the protein were roughly the same, the rate of binding to the iron atom from within the distal pocket decreased from 2.5 X lo7 to 7 X lo6 to 3 X lo6 s-' for the series Ala6' to Valm (native) to IleG myoglobin. This trend was reversed for Phe" myoglobin which showed a kca value equal to 1.5 X ~O'S-~.  (Table II). Increasing the polarity and size of the position 64 amino acid and the size of the position 68 residue inhibited non-covalent binding, and these trends were observed for all of the ligand molecules examined (Kxc values in Tables II-IV). due to the high rates of autooxidation of the Gly'j4, ValG4, Leu'j4, and PheG4 mutants. Even with this variation, it is clear that the low overall quantum yield of oxymyoglobin is due primarily to the A-M* reaction in Equation 1. In most cases, geminate recombination of O2 from state C further reduces the quantum yield by only a factor of 2 or less (Table II). Another consequence of the low picosecond photophysical CO Rebinding-Geminate rate parameters are reported for only those CO-myoglobin complexes which exhibited overall quantum yields SO.9 and 8, 2 0.1. The rate parameters for native sperm whale myoglobin were taken from Henry et al. (1983). In agreement with the results of Petrich et al. (1988), Qns appears to be -1.0 for all of the CO complexes examined. The rate of escape from the protein, kcx, was at least 2-fold less than that observed for O2 when direct comparisons were made (native, Leu64, and Phe6' myoglobin). Similar small differences were observed between kcx values for 0, and CO escape from the distal pockets of isolated LY and p subunits of human hemoglobin (Olson et al., 1987 Reactions were monitored at 436 nm during and after an attenuated 17-ns light pulse. Conditions: 0.1 M borate, pH 9.1, 20 "C for the position 64(E7) mutants and 0.1 M phosphate, pH 7.0, 20 "C for the position 68(Ell) mutants. Panels A and B show normalized time courses for 0, rebinding to E7 and El1 mutants of myoglobin. The observed absorbance changes were represented as open circles connected by thin lines. Panels C and D show time courses and fitted curves for O2 rebinding to native and Phe" myoglobins. The open circles represent observed data; the solid lines are fitted curves obtained by numerical integration of the differential equations describing Equation 3. The rightmost time course in panel C represents data collected in 160 ns (% of the n axis scale) and was fitted simultaneously with the data collected in 400 ns. The inset in panel D represents data collected on a longer time scale and, again, this time course was fitted simultaneously with the others. Relative laser light intensities for the traces in C and D were from top to bottom C, l/a, %6, KU, %4; D, 1, 'A, '/a, %6, and '/a for the inset. ences between O2 and CO were observed for the rates of binding from within the distal pocket: kca for O2 rebinding was 5-30-fold greater than that observed for CO. Braunstein et al. (1988) examined the low temperature recombination kinetics of Gly6* CO-myoglobin. Extrapolation to 300 K suggested that the ksa values for CO rebinding to Gly6" and His? (native) myoglobin are similar. The relative insensitivity of the NO picosecond rebinding process to mutations at position 64 is consistent with this observation. Braunstein et al. (1988) reported a l&fold increase in the pocket occupancy factor for CO binding when Hiss4 was replaced with Gly, in agreement with the increases in Kxc which we observed for O2 and CO binding to mutants containing Gly or apolar amino acids at residue 64 (Tables II and  III). A direct comparison is not possible since the pocket occupancy factor corresponds to KxcKcs in Equation 1 and cannot be measured experimentally at room temperature (Doster et al., 1982;Henry et al., 1983;Gibson et al., 1986).
Isocyanide Rebinding and the Importance of Pocket Size- The geminate recombination time courses for methyl isocyanide showed a greater dependence on protein structure than those for O2 rebinding, particularly for the position 64 mu-tants (Fig. 3, Table IV). The extent of intramolecular rebinding (0,) increased with increasing size of the Ei' residue for the series Va164, Leu64, and Phe64. The Va16' to Ile mutation increased the extent of methyl isocyanide escape from the distal pocket, whereas the Val@ to Phe mutation effectively prevented ligand movement out of the protein (Qoverall I 0.01). Kxc for non-covalent methyl isocyanide binding depended markedly on the size of both the position 64 and 68 amino acids, decreasing from 3.8 M-' for Gly64 to 0.0094 Me1 for Phe@ myoglobin (Table IV). The ethyl and methyl isocyanide rebinding parameters exhibited similar dependences on the position 64 and 68 amino acids (Table IV). The major difference was that the rate and extent of geminate recombination were uniformly greater for the larger ligand (Fig. 4A). We previously interpreted this result in terms of the limited size of the distal pocket (Gibson et al., 1986). Large translations or rotations away from the iron atom after photodissociation cannot occur for ethyl isocyanide without substantial steric interactions with surrounding amino acid side chains. Although less stable in state C, as judged by a 3-fold lower value of Kxc for noncovalent ethyl isocyanide binding compared with that for the methyl compound, the larger ligand is held in place for more rapid rebinding. This idea is supported by three independent observations. First, little or no nanosecond geminate recombination was observed for the methyl and ethyl isocyanide complexes of soybean leghemoglobin, which is known to have a large, sterically unhindered active site . Second, the x-ray crystallographic structure of ethyl isocyanide-myoglobin shows tight packing of Leu", Phe33, Phe43, Hi@', Va16', and Ile'07 around the bound ligand molecule (Johnson et al., 1989; Fig. 6B). Third, an extreme example of this behavior is observed for the tert-butyl isocyanide complex of native myoglobin. A large picosecond geminate rebinding phase is observed for this ligand, presumably because the bulky tert-butyl group prevents movement of the isocyano group away from the iron atom (Gibson et al., 1986;Jongeward et al., 1988). These data and observations also suggest strongly that state C can be assigned to non-covalently bound ligand molecules located in the distal cavity. Further evidence for the importance of the size of the distal pocket is provided by the results for the ValGs to Phe substitution. X-ray crystallographic data for Phe6' metmyoglobin have shown that the phenyl group is pointed away from the heme iron atom, filling the gap between Leu7* and Ilelo7 (see Fig. 6; . The net result is a decrease in the size of the distal cavity adjacent to the ligand-binding site. As shown in Figs. lC, 2B and D, 4B and Tables II-IV, this mutation caused marked increases in the rates and extents of geminate recombination for all ligands, including CO. Kxc decreased 15-30-fold for CO and O2 binding and 3-fold for methyl and ethyl isocyanide binding. The similarities between the effects of increasing the size of the ligand molecule for a given protein and those of the Va16* to Phe mutation for a given ligand are striking and argue for a similar underlying cause, a decrease in the ratio of the size of the distal pocket to the size of the ligand molecule (Fig. 4).

DISCUSSION
Structural Interpretations-Ortep drawings of the heme pockets of the O2 and ethyl isocyanide complexes of sperm whale myoglobin are shown in Fig. 5. The view is from the back of the distal pocket, looking out toward the solvent through the proposed channel between Val@ and His64. In the ethyl isocyanide complex, the Hisa imidazole side chain was drawn in the open conformation ( Fig. 5B; Johnson et al., 1989). In Fig. 6, top views of the distal pockets are presented using space filling models. The iron atom and porphyrin ring (dark blue atoms) are located underneath the distal residues and in the plane of the photograph, and Leu"(BlO), which forms the top of the ligand-binding site, has been removed to reveal the sides and back of the distal pocket. The first two atoms of the ligand molecules (red) are located underneath His64 (H64, light blue atoms) and directly adjacent to the y2-CH3 group of Va16'( V68, light blue).
The picosecond intermediates observed in laser photolysis experiments are thought to represent ligand molecules in the  (Jongeward et al., 1988;Petrich et al., 1988). These contact pair intermediates should resemble closely the original ground state. During the very rapid NO rebinding reactions, there is little time for ligand movement and distal structural features to influence the observed geminate rate constants. As shown in Table  I, the rate of NO rebinding from state B is little affected by the size and polarity of the position 64 residue. Only in the case of Gly64 were the rates of rebinding and escape from the first geminate intermediate increased. The largest effect was observed for the Va16' to Ile mutation which caused a B-fold decrease in kBla. This substitution also markedly restricts equilibrium binding (K values in Tables IIA, IIIA, IVA, and  IVC), and this inhibition appears to be due to steric hindrance of the bound ligand since molecular graphics suggests that the 6-CH3 group of Ile6' should be located directly over the iron atom. The relative uniformity of the NO recombination parameters also indicates that the mutations are fairly conservative and do not cause large changes in the reactivity of the iron atom due to global alterations in protein folding. In our view, the nanosecond intermediates observed for 02, CO, and isocyanide rebinding represent ligand molecules noncovalently bound in the distal cavity circumscribed by Leu"'(BlO), Phe43(CD1), His64(E7), Vala(Ell), and Ile'07(G8) (Fig. 6) Kottalam and Case, 1988). As shown in Fig. 6B, the alkyl side chain of covalently bound ethyl isocyanide is also located in this cavity. Kottalam and Case (1988)   All experiments with the mutants were carried out at least twice. The overall association and dissociation rate constants were taken from Rohlfs et al. (1990) and Egeberg et al. (1990  Reactions were monitored at 445 nm following a 35-ps light pulse under conditions described in Fig. 3. Open circles represent observed absorbance changes. Solid lines are fitted curves generated from single exponential fits to Equation 5. A shows normalized time courses for methyl and ethyl isocyanide rebinding to native sperm whale myoglobin. B shows normalized time courses for methyl isocyanide rebinding to myoglobin with either a valine (native) or a phenylalanine at position 68.
preparation of free energy level diagrams based on Equation 3. This is probably the best empirical approach until molecular dynamics calculations can be used routinely to simulate kinetic phenomena on nanosecond time scales. Traditional cliagrams for 02 and CO binding to native sperm whale myoglobin are shown in Fig. 7A. The free energy of the Mb+X state was defined as 0, and those for wells C and A were computed as: Gc = -RTlnKxc and Ga = -RThK, where K is the overall association equilibrium constant.4 The observed geminate rate constants were defined as kca = Acaexp(-AG#c.JRT) and kcx = Ac+xp(-AG$cx/RT). Both pre-exponential factors were set equal to lOlo s-l. Although somewhat arbitrary, this value is roughly equal to the largest picosecond rate constants observed for NO rebinding from contact pairs (B states in Equation 1) and also approximates the largest possible rate constant for ligand escape from the protein (i.e. Acx = 3D,/R2, where R is the radius of the distal pocket and DX is the ligand diffusion constant in water). The absolute values of Acx and Aca do not affect the differences  have shown that the partition constants for taking 02, CO and ethyl isocyanide from aqueous solutions into an apolar phase are all 4.0, and thus these ligands do have the same chemical potential in water. Methyl isocyanide is more soluble in water, has a partition constant which is -2-fold smaller, 1.8, and thus has a lower chemical potential in aqueous solvents than the other ligands. This small difference (RT ln(1.8/4.0) = -0.46 kcal/mol) was added to all of the barrier heights and wells for methyl isocyanide binding to correct for hydrophobic effects when comparing the four ligands (see Reisberg andOlson, 1980 or Mims et al., 1983). The coordinates for the upper panel were taken from the structure of MbO, determined by Phillips (1980). The coordinates for the lower panel were taken from the "open" conformation of the MbENC structure determined by Johnson et al. (1989). The ORTEP drawings were generated from a view starting at a position near the back of the pocket looking out toward the solvent through the proposed channel between His"' and Vale'.
between the barrier heights for the mutant and native proteins. Setting Acx = AcA makes it easier to visualize the ratelimiting step in the overall reaction and to estimate the extent of geminate recombination by comparing the relative heights of the inner (C-A) and outer (C-X) kinetic barriers. Reduction of the observed values of kcA and kcx from 10" s-' was expressed by positive values of AG$ca and AG$cx, respectively. The free energies of the C-A and C-X kinetic barriers were calculated as [-RT ln(Kxc) + RTln(lO'"/kc~)] and [-RT ln(K& + RT ln( 101'/kcx)], respectively. Comparisons between the energy barriers and wells for the different ligandmyoglobin complexes are shown in Fig. 7B using a bar graph format and the reaction coordinates defined in Equation 3. The X+Mb state is not shown in the bar graphs since its free energy is defined as 0.
For CO binding, 95% of the ligand molecules escape from state C after photolysis and the overall quantum yield is approximately 1 (Table III). This experimental observation requires that the inner C-A barrier be roughly 2 kcal/mol FIG. 6. Top views of the distal pockets of the 0, and ethyl isocyanide (ENC) complexes of sperm whale myoglobin. Space filling images were generated by the program ANIMOL AED with coordinates from the structures cited in Fig. 5. The upperpanel shows the residues circumscribing the distal pocket of oxymyoglobin using single-letter abbreviations for the specific amino acids (i.e. His"' is labeled H64; Val"', V68, etc.). The porphyrin ring (dark Hue atoms) is below these distal residues in the plane of the paper, and the ligand atoms are shown in red and labeled 0. The lower panel shows the same view for the ethyl isocyanide complex.
The ethyl side chain of the ligand is also shown in red and labeled C. greater than t.he outer X-+C barrier. Thus, the rate-limiting step for bimolecular CO binding from the solvent phase is iron-ligand bond formation, and the overall association rate constant is given by k~~..J& (Doster et al., 1983;Gibson et al., 1986;Jongeward et al., 1988). For 0, binding, 40-50% of the ligand molecules in state C escape from the heme pocket, and thus, the heights of the inner and outer barriers must be roughly equal. This accounts in part for the low overall quantum yield of oxymyoglobin; however, the major cause is a low picosecond quantum yield of state C. Migration into the protein and bond formation from within the pocket limit the overall association rate constant to roughly the same extent so that k' for O? binding must be computed as k'XCkc.4/(kc.A + kc4 The bimolecular rate constant for OZ binding is greater than that for CO binding because the inner barrier for 0, is 2.3 kcal/mol smaller. This appears to be an intrinsic chemical effect since the association rate constants for O2 binding to sterically unhindered model hemes are consistently 10-20fold greater than those for CO binding (Traylor et al., 1985;Collman et al., 1983). Frauenfelder and Wolynes (1986) have interpreted these differences as due to the requirement of spin-forbidden electronic rearrangements for iron-CO bond formation.
The same arguments indicate that nitric oxide should show a large intrinsic reactivity with ferrous iron, and this explains why NO rebinds from the initial contact pair on the picosecond time scale.
In the case of methyl isocyanide binding, the outer kinetic barrier is 1 kcal/mol greater than the inner barrier. Although the free energy of methyl isocyanide in state C is roughly 2 kcal/mol greater than that of the diatomic gases, it is kinetically trapped in the distal pocket so that only 15% of the ligand molecules escape after photolysis.
Thus, even though the quantum yields of the O2 and methyl isocyanide complexes of native myoglobin are roughly the same, the underlying causes are quit,e different. The rate limiting step for methyl isocyanide binding is migration into the protein, and k' P k'xr (Table IV). The results presented in Tables II-IV show the power of  combining protein engineering with laser photolysis techniques. Equation 3 is clearly a simplification of the real mechanism which probably involves multiple protein conformations (C states), side chain motions, and ligand rotations and translations.
However, the empirical analysis in Figs. 8 and 9 has allowed us to resolve effects of size and polarity at the HiP(E7) and Val"'(E11) positions on the inner and outer kinetic barriers.

Polarity
at Residue 64-The effects of substitutions at the E7 helical position on the free energy barriers for O2 binding are shown in Fig. 8A. A detailed discussion of the overall equilibrium changes has been presented in previous publications (Springer et al., 1989 andRohlfs et al., 1990). The inner and outer kinetic barriers and the free energy of state C for O2 binding were lowered by 1.0 to 1.5 kcal/mol when Hi@' was replaced with apolar amino acids, regardless of their size. In contrast, the His"" to Gln substitution produced only small decreases (~0.3 kcal/mol) in the free energies of the barriers going from left to right after the shaded bar in panels A, C, and D. Inpanel B, 0 represents Leufi4 (left) and Phe" (right) following the solid bar for native myoglobin. and well C. These results suggest that the polarity of His64 is more important than its size in inhibiting the kinetic processes and the non-covalent binding of oxygen. In previous work, the effects of polarity at the position 64 amino acid side chain were explained in terms of the stabilization of water molecules within the distal pocket of deoxymyoglobin . When comparing the properties of myoglobin and the LY and fl subunits of R-state hemoglobin, there appears to be an inverse relationship between the occupancy levels of distal pocket water molecules near His(E7) and the overall CO and O2 association constants . The results in Fig. 8 5 and 6). Both effects would increase the outer kinetic barrier and be reduced markedly by substitution of apolar amino acids for His64 if the main pathway for ligand entry into the protein is between the distal histidine and valine. Whatever the detailed mechanism, O2 movement into the distal pocket must cause the net displacement of water, and the equilibrium constant for this process, Kxc, should be reduced significantly if the HZ0 molecules are hydrogen-bonded to a polar amino acid side chain.
The marked inhibitory effect of HisG4 and Gln'j4 on the inner kinetic barrier for oxygen binding is more difficult to interpret. It is possible that water molecules rapidly enter the protein and become associated with HisG4 after the photolysed ligand moves to the back of the distal pocket. Assuming a k',~c rate for water equal to roughly 1 X lo8 Mm1 s-' and a concentration of 55 M, the half-time for water movement into the distal pocket would be ~130 ps, which is short enough to affect nanosecond-rebinding processes. Alternatively, rebinding of 0, from state C may require small net movements of Hise4 away from the iron atom, and these motions may be restricted by participation of the imidazole side chain in an extended hydrogen-bonding lattice. The effects of position 64 substitutions on the barriers to CO binding were similar to those observed for O2 binding, although data could only be obtained for those derivatives with overall quantum yields less than 0.9 (Fig. 8B, Table  IIIB). Again, both barrier heights were lowered by about 1 kcal/mol when His64 was replaced with an apolar side chain, and this is consistent with the roughly parallel effects of position 64 mutations on the overall association rate constants for CO and O2 binding (see Rohlfs et al., 1990).
The size of residue 64 plays a more dominant role in determining the rate of isocyanide entry into the protein and the stability of these ligands in the distal pocket (Fig. 8, C and D). Substantial increases in the free energy of the X+C barrier and well C were observed for the series Gly64 s Va164 c LeuG4 < PheG4 myoglobin.
The inner kinetic barrier for isocyanide binding is governed by more specific stereochemical interactions with the position 64 amino acid. The overall size of the side chain and freedom of rotation about the /3carbon appear to be the key factors since the lowest C-A barriers were observed for Glyc4 and Leu64 myoglobin and the highest were observed for HisG4, ValG4, and Phe64 myoglobin Kinetic Barriers in Myoglobin (Fig. 8, C and D). These relationships correlate roughly with the stabilities of the final equilibrium bound states in which the lowest free energies were observed for the LeuM and Gly@ myoglobin-isocyanide complexes.
Vu168 and the Inner Kinetic Barrier-The major effect of increasing the size of the El1 residue for O2 binding to Ala", ValM (native), and Ilea myoglobin is a selective increase in the C+A kinetic barrier (Fig. 9A). Little or no change was observed for the free energy of state C or the height of the outer kinetic barrier. Thus, for these substitutions, the El1 residue has almost no effect on the rate of O2 entry into the distal pocket, but does restrict access to the heme iron atom. This restriction is quite large for the IleM mutant, is manifested by a 1-kcal/mol increase in the C!+A barrier compared with native myoglobin, and is consistent with the g-fold decrease in the rate constant for geminate recombination of NO produced by the same amino acid change ( Table I). The lack of effect on the outer kinetic barrier suggests that O2 may enter the distal pocket by passing over Va16s; however, steric interaction with this residue does occur when the ligand approaches the iron atom for bond formation (Figs. 5 and 6).
The results in Figs. 8 and 9 show that both His64 and Vala form part of the inner kinetic barrier to ligand binding. Our previous measurements with double mutants have shown that these contributions appear to be roughly additive . The overall association rate constants for O2 and CO binding decreased when the El1 residue was increased in size from Alam to ValM to Ile"(, even when His64 was replaced with Gly'j4. However, the effects of these El1 substitutions were significantly smaller than those observed for the His? to Gly mutation. The latter observation is also consistent with the pathway proposed in Figs. 5 and 6 since the size and polarity of His'j4 are postulated to regulate both the outer and the inner kinetic barriers. For methyl and ethyl isocyanide binding, both kinetic barriers and the free energy of state C depend significantly on the size of the El1 residue (Fig. 9, C and D). As was the case for the apolar position 64 residues (Fig. 8, C and D), the free energy of state C for isocyanide binding was roughly proportional to the size of the El1 side chain. The largest mutational effect was a l-l.5 kcal/mol increase in the C-A barrier when Val@ was replaced with Ile.
Pocket Size Effects and Ligand Pathways-The key role played by the volume of the distal pocket in regulating both the overall and geminate kinetic properties of myoglobin was first discussed in detail by Frauenfelder and co-workers (Doster et al., 1982 and references therein). The data in Figs. 4,7-9 emphasize the importance of this factor. For native myoglobin, increasing the size of the ligand from methyl to ethyl isocyanide raised the outer kinetic barrier and the free energy of state C by roughly the same amount, 1 kcal/mol, but had little or no effect on the inner barrier (Fig. 7B). The net result was a 4-fold increase in the nanosecond geminate recombination rate (Fig. 4A) and a 2-3-fold decrease in the overall quantum yield (Table IV). The larger ligand is less stable in state C because of its size, which limits the number of conformations and degrees of freedom in the distal pocket and which also causes unfavorable steric interactions with the surrounding amino acids (Fig. 6B).
Similar phenomenological changes were observed for each ligand when the size of the distal pocket was decreased by substituting Phe for Val=. As shown in Fig. 9, this mutation increased the free energy of state C and the outer X-& barrier by l-2 kcal/mol for all ligands but produced much smaller effects on the inner C-A barrier. The net results of these changes were 1) decreases in the overall association rate constants, 2) marked decreases in the overall quantum yields because the effective rate of rebinding from within the pocket increased relative to that for escape, and 3) decreases in the overall dissociation rate constants because thermally dissociated ligand molecules also rebind more rapidly from within the distal pocket (Tables II-IV). These effects may even extend to the initial contact pair since the rate for NO movement away from the iron atom in Phem myoglobin, &az, is roughly 6-fold smaller than that for native protein ( Table  I).
The simplest interpretation of the decrease in KXC for the Va168 to Phe substitution is that the volume of the noncovalent binding site is reduced when the space between Leu7', Ile"', and Ile'07 is filled by the phenyl side chain . Even if this space is not contiguous with the larger distal cavity, the presence of the Phe-side chain in this region of the protein should reduce the number of possible orientations of the ligand and the Leu3', Leu7*, and Ilelo7 side chains in the main pocket (Fig. 6). Only a small effect was observed on the inner kinetic barrier since the phenyl group is pointing away from the iron atom. The increase in the outer kinetic barrier is more difficult to interpret. It is possible that the phenyl side chain may serve to restrict motions of the E-helix, which in turn could prevent movement of His64 and/or other residues involved in creating a channel for ligand movement into the distal pocket. It is also possible that the space between Leu7* and Ilelo7 may represent an alternative channel for the entry of small ligands into the distal pocket, and filling this gap with the side chain of Phe6' blocks this route. This pathway cannot be ruled out by our experimental observations; however, entry into the cavity between Leu7' and Ilelo7 appears to be blocked by the E and G helices (Fig.  6). Further mutagenesis studies in this region of the protein, refinement of the structure of Phe'j8 myoglobin, and molecular dynamics calculations are needed to examine this point.
Conclusions-The functional roles of the distal histidine and valine are now well-defined. The polarity of the imidazole side chain inhibits the rate of entry into the distal pocket, decreases the equilibrium constant for the non-covalent binding of apolar ligands, and raises the inner kinetic barrier for bond formation with the heme iron atom. Although inhibitory for these kinetic processes, the polarity of His64 is required to stabilize bound 02 by hydrogen bonding. ValG8 does not significantly limit the rate of entry of small ligand molecules into the heme pocket; however, this residue does inhibit the final approach to the iron atom and equilibrium binding, particularly for CO and isocyanides, which prefer linear Fe-C-O or Fe-C-N-geometries. The nanosecond kinetic intermediate observed for 02, CO, and isocyanide rebinding to myoglobin, state C in our reaction scheme, can be associated with ligand located in the distal cavity (Fig. 6). The size and polarity of this non-covalent binding site is partly determined by His64 and Va16', and these distal pocket characteristics play an important role in determining the overall rate constants for ligand binding, even when no effect is observed on the equilibrium constant.