Mapping the Pathways for O2 Entry Into and Exit from Myoglobin*

The effects of mutagenesis on geminate and bimolecular O2 rebinding to 90 mutants at 27 different positions were used to map pathways for ligand movement into and out of sperm whale myoglobin. By analogy to a baseball glove, the protein “catches” and then “holds” incoming ligand molecules long enough to allow bond formation with the iron atom. Opening of the glove occurs by outward movements of the distal histidine (His64), and the ligands are trapped in the interior “webbing” of the distal pocket, in the space surrounded by Ile28, Leu29, Leu32, Val68, and Ile107. The size of this pocket is a major determinant of the rate of ligand entry into the protein. Immediately after photo- or thermal dissociation, O2 moves away from the iron into this interior pocket. The majority of the dissociated ligands return to the active site and either rebind to the iron atom or escape through the His64 gate. A fraction of the ligands migrate further away from the heme group into cavities that have been defined as Xe binding sites 4 and 1; however, most of these ligands also return to the distal pocket, and net escape through the interior of wild-type myoglobin is <20–25%.

Thirty years ago, Perutz and Matthews (1) proposed that the pathway for ligand entry and exit into mammalian hemoglobins and myoglobins (Mb) 1 involves rotation of the distal histidine to form a short and direct channel between the heme pocket and solvent. The experimental evidence in favor of this histidine gate mechanism includes: (a) crystal structures with large bound ligands that force upward and outward rotation of the His 64 side chain (2)(3)(4); (b) significant increases in O 2 association rate constants at low pH, where the imidazole side chain becomes protonated and moves out into the solvent (5, 6); (c) large increases in the rates of ligand binding when the distal histidine is mutated to smaller apolar residues (7)(8)(9)(10)(11); and (d) increases in the rate constants for O 2 association and dissociation when residue Phe 46 (CD4) is replaced with Ala or Val, allowing greater mobility and outward movement of the distal histidine (12).
Several groups have argued that the histidine gate may not be the primary pathway for ligand movement into and out of myoglobin. Instead, they have proposed that ligands may escape through the interior of myoglobin by multiple transiently formed hydrophobic channels that eventually lead to the solvent phase. In 1984, Tilton et al. (13) suggested that the hydrophobic Xe binding cavities observed in myoglobin crystal structures are important components of these escape routes (orange spheres in Fig. 1). Molecular dynamics simulations have provided additional support for indirect pathways involving Xe sites (14,15). More recently, Huang and Boxer (16) suggested the existence of multiple entry and exit routes based on changes in the kinetics of geminate and overall O 2 and CO rebinding to random point mutants of myoglobin expressed in crude Escherichia coli lysates. Significant effects were observed for amino acid replacements at locations far removed from the distal and proximal histidines. Scott and Gibson (17,18) presented more direct kinetic evidence that dissociated ligands can access the Xe4 and Xe1 cavities. Filling these sites with xenon gas eliminates the slow phases observed for geminate rebinding on nanosecond and microsecond time scales but causes little change in the total amount of geminate recombination. Three groups have now reported low temperature crystal structures of wild-type and mutant myoglobins in which electron density attributed to photodissociated CO and O 2 is present in the Xe1 or Xe4 sites (19 -22). These studies demonstrate that ligands do migrate into these internal cavities and that population of the two Xe sites is associated with protein relaxation that occurs after photolysis (19,20).
These new crystallographic results prompted us to re-examine the question of how ligands move into and out of myoglobin and whether or not O 2 can escape directly from the Xe cavities through the interior of the protein. We have mapped entry and escape routes in myoglobin by measuring geminate and overall O 2 binding parameters for 90 myoglobin mutants at 27 different positions in the primary sequence. The locations of these residues are shown in Fig. 1, and the wild-type and mutant amino acids are listed in Tables I-V. Replacements were made at virtually all positions in or near the heme pocket and at locations near the Xe binding sites and along the escape routes proposed by Tilton et al. (13,14), Elber and Karplus (15), and Huang and Boxer (16). Additional residues were chosen on the basis of ligand movements observed in molecular dynamics simulations by Gibson and co-workers over the past 6 years (17,(23)(24)(25)(26). The remaining mutants were made for other studies dealing with the fluorescence and unfolding of apomyoglobin (residues 7, 8, 14, 79, and 131; see Refs. 18 and 27).

MATERIALS AND METHODS
Overall Association and Dissociation Rate Constants-Oxygen association time courses were measured by photolysis of MbO 2 samples using a 300-ns excitation pulse from a Phase-R model 2100B dye laser, and the results were analyzed using Equation 1 as described by Rohlfs et al. (8).
O 2 dissociation rate constants, k O 2 , were determined independently by analyzing stop-flow, rapid mixing time courses in which bound oxygen was displaced by carbon monoxide. All reaction conditions were 20°C, 0.1 M potassium phosphate, 0.3 mM EDTA, pH 7.0. Most of the association rate constants for NO binding to various Mb mutants were taken from Eich et al. (10,11). The remainder were determined using the same 300-ns dye laser photolysis apparatus used to measure bimolecular O 2 binding (23).
Measurement and Analysis of Geminate Recombination Time Courses-Time courses for geminate recombination were observed after excitation with a 9-ns YAG laser. These internal, first order processes were recorded on multiple time scales ranging from 0 -500 ns to 0 -5.0 s (Fig. 2). The results were analyzed in terms of the three-step, side path model shown in Scheme 1, which was first proposed by Chatfield et al. (28) and then elaborated by Scott and Gibson (17). The rate constants for intramolecular rebinding, escape, and movement through the protein (k 1 through k 4 ) were obtained by fitting sets of time courses to this model. The algorithms for numerically integrating the appropriate sets of rate equations, which account for recombination during the excitation pulse and incorporate corrections for bimolecular rebinding, are described in detail by Scott and Gibson (17). Sets of fitted geminate rate constants are given in Tables I-V. The geminate rebinding time courses can be fitted by the sum of two exponential processes and an offset reflecting the amount of escape to solvent. Any scheme that reduces to two exponential decays can represent the data. The side path scheme was chosen by Scott and Gibson (17) based on the effects of Xe binding and mutagenesis. The total fraction of photolyzed ligands that rebind intramolecularly, F geminate , can be measured directly or calculated as k 1 /(k 1 ϩ k 2 ) based on Scheme 1. The fraction of ligands that take the side path to state C and rebind more slowly, F secondary , can be calculated as k 3 /(k 1 ϩ k 2 ϩ k 3 ).
Determination  Tables I-V. The values of kЈ entry are defined experimentally. If a sequential binding scheme (Scheme 2) is used to analyze the geminate time courses, the bimolecular rate constant for ligand entry into the protein will still be defined as the ratio of the overall association rate constant and the total fraction of internal rebinding.
The steady state expression for kЈ O 2 using this linear scheme is still kЈ entry ⅐F geminate . In this case, F geminate ϭ k 1 k 4 /(k 1 k 4 ϩ k 3 k 2 ϩ k 1 k 2 ), and the fitted values of k 1 through k 4 will be significantly different from those obtained using a side path scheme. However, the computed value of F geminate will be the same as that calculated from the side path parameters since both schemes can accurately represent the observed data, and F geminate is the experimentally defined total amplitude of geminate rebinding (17). In the linear scheme, kЈ entry represents the bimolecular rate of formation of state C, and the fitted rate parameters for the formation and decay of this secondary state will affect the overall association rate constant (29,30). In contrast, the rate parameters for the formation and decay of C state in the side path scheme have no influence on the steady state expressions for the overall association and dissociation rate constants.
The overall association rate constant for NO binding, kЈ NO , serves an independent check of the calculated value of kЈ entry . Nitric oxide is the most reactive of the physiological gases, has the lowest quantum yield for complete photodissociation from the native myoglobin (Q Յ 0.01), and shows the largest amount of geminate recombination, F geminate Ն 0.99 (9,29,30). In effect, every time a NO molecule enters the distal pocket, it binds to the iron atom, and thus the rate-limiting step for the overall NO binding reaction is ligand entry. Since O 2 and NO have effectively the same size and polarity, the calculated value of kЈ entry for O 2 binding should be approximately equal to kЈ NO , which can be measured independently in conventional photolysis experiments.
Myoglobin Mutants-All mutants were constructed and expressed using the sperm whale myoglobin gene first synthesized by Springer and Sligar (31). The wild-type control protein has an extra N-terminal Met residue and an Asp 122 to Asn substitution. This double mutant shows identical ligand binding properties to authentic native SW Mb and recombinant proteins with and without the D122N replacement and the N-terminal methionine residue (32). Most of the mutations at residues between positions 60 and 75 were constructed using cassette mutagenesis and a pUC19 expression vector (7,33). The other mutants were made using a variety of oligonucleotide-directed techniques and a pEMBL19 expression vector (see Ref. 34). The basic expression and purification procedure was developed by Springer and Sligar (31) and used with minor modification (34).

Determination of the Individual Rate Parameters for O 2
Binding-Typical nanosecond time courses for intramolecular O 2 rebinding to wild-type and mutant myoglobins are shown in Fig. 2. Geminate data for all 90 different mutants were analyzed in terms of the side path scheme shown in Scheme 1, and the fitted parameters, k 1 to k 4 , are listed in Tables I-IV. Overall association and dissociation rate constants for each mutant were either taken from the literature or determined in new experiments. The errors in the latter rate parameters have been shown to be ϳϮ10 -20% based on measurements with wild-type myoglobin controls (32). The errors for the fitted geminate parameters are more difficult to define because they are correlated with each other and the observed fraction of recombination. Based on repeated experiments with wild-type oxymyoglobin, the errors in k 1 , k 2 , and F geminate were estimated to be ϳϮ20% (see also Ref. 25). The rate parameters for the secondary rebinding process are less well defined than the amplitude of this phase (17). Since the rate constant for ligand entry was calculated from the ratio of kЈ O 2 and F geminate , the estimated error for kЈ entry is ϳϮ30% based on the errors of  The results are organized in terms of the three-dimensional position of the mutated amino acid: Table I, the first shell of amino acids that are directly adjacent to bound O 2 (Leu 29 (B10), Phe 43 (CD1), His 64 (E7), Val 68 (E11)); Table II, the second shell of amino acids on the distal side of the heme group located toward the solvent interface (Arg 45 (CD3), Phe 46 (CD4), Leu 61 (E4), Gly 65 (E8), Val 66 (E9)), Thr 67 (E10)) and toward the protein interior (Ile 28 (B9), Leu 32 (B13), Ile 107 (G8), Ile 111 (G12)); Table III Table V.
Plots of kЈ entry versus kЈ NO show a roughly linear correlation (Fig. 3). In general, the rate constant for O 2 entry should be greater than the measured association rate constant for NO binding because the calculated value of kЈ entry takes into ac-  The fraction of total geminate recombination, F geminate , was calculated as k 1 /(k 1 ϩ k 2 ). The fraction of slow, secondary geminate recombination, F secondary , was calculated as k 3 /(k 1 ϩ k 2 ϩ k 3 ). The bimolecular rate constant for ligand entry, kЈ entry , was calculated as kЈ O2 /F geminate . Values of k 1 through k 4 were obtained from fitting sets of geminate recombination time course and the values of kЈ O2 , k O2 , K O2 , and kЈ NO were measured independently or taken from the literature. The errors for wild-type (WT) myoglobin were estimated from averages of multiple geminate analyses (Ն10) and previous measurements of the overall binding parameters (32). ND, not determined; UD, undefined.

Mutant
Geminate rebinding parameters Bimolecular binding parameters Ligand entry rates Ͻ0    count all ligand movements into the protein, regardless of eventual location, orientation, and escape. The value of kЈ NO reflects only those movements that lead to bond formation with the iron atom and concomitant absorbance changes. Equality between kЈ NO and kЈ entry also assumes F geminate ϭ 1.0 for NO binding to all of the proteins examined, which may not be the case for those mutants with very high quantum yields (i.e. F43V, F46A, H64A, and V68I). In our view, the correspondence between kЈ entry and kЈ NO is remarkably good, considering the errors and difficulties in the measurements, particularly with those MbO 2 mutants that autooxidize rapidly. The results in Fig. 3 serve to validate experimentally the use of kЈ entry in mapping the location of pathways for ligand entry. Primary Site for Non-covalent Binding, State B-A structural interpretation of the side path scheme of Scott and Gibson (17,18) is shown in Fig. 4. This mechanism attempts to take into account the effects of added Xe gas, all of the mutagenesis data in Tables I-V, and the previous ideas of Olson, Phillips, Gibson, and co-workers (9, 23, 35). In the wild-type protein, transient outward movements of the distal histidine allow distal pocket water molecules to leave the protein and apolar ligands to enter through the His 64 (E7) gate. Dioxygen molecules are then captured in the space above pyrrole rings B and C that is circumscribed by Leu 29 , Leu 32 , Val 68 , and Ile 107 . Ligands in this location are designated as being in state "B," which is the location of the initial nanosecond photoproduct. This state has been well defined by mutagenesis experiments, IR spectroscopy, and molecular dynamics simulations (for a review, see Ref. 35 and references therein) and by time-resolved x-ray crystallography (19,20,22,36,37). Ligands can then move further into the protein, bind to the heme iron atom, or exit the protein back through the histidine gate. The observed movement depends on the accessibility of internal cavities, the reactivity of the iron atom, and the position of the His 64 side chain.
Secondary Sites (State C) on the Distal Side of the Heme-The most obvious path for secondary ligand movement is into the Xe4 cavity. This site is continuous with the primary pho-    todissociated site, making its exact boundaries difficult to define (orange sphere, Fig. 1; upper gray sphere, Fig. 4; inner cavity, Fig. 9). As described by Scott and Gibson (17,18), the geminate rebinding of O 2 to wild-type and 24 different myoglobin mutants is biphasic. The slower secondary phase accounts, on average, for about 25% of the observed absorbance change (Tables I and V; Ref. 17). When these proteins are equilibrated with 12 atm of Xe, the secondary phase is much reduced, and the primary phase becomes larger and significantly more rapid (Fig. 7C). In most cases, the total fraction of geminate recombination does not change significantly with Xe addition, and the overall second order rate constant for O 2 binding, kЈ O 2 , is little affected (Table V; Ref. 17). All these observations suggest that ligands do not enter or leave the protein through the Xe pockets, which instead appear to be on side paths (Scheme 1 and Fig. 4).
Building on the initial work of Scott and Gibson (17), we have now increased and decreased the size of most of the residues adjacent to the Xe4 pocket, including Ile 28 , Leu 32 , Ile 107 , and Ile 111 . Decreasing the size of residues 28, 32, and 107 to Ala increases the amplitude of the slow, secondary phase of gemi-nate recombination, whereas increasing the size to Trp almost completely abolishes it (Fig. 2C, Tables II and V). The effects of these mutations on the total amount of geminate recombination were more variable. For example, the I107W and I28W mutations cause F geminate to increase from 0.47 to 0.67 and 0.79, respectively, whereas the I107A and I28A substitutions cause only slight decreases to 0.38. Mutation of Ile 111 , which is located at the interior edge of the Xe4 pocket, had little effect on any of the kinetic parameters for O 2 binding (Table II).
Little or no effect on the total amount of recombination is observed for amino acid replacements at positions farther away from the iron atom, which include residues in the middle of the D helix (Met 55 ), at the end of the E helix (Ala 71 , Leu 72 ), at the EF (Lys 79 ) and FG (His 97 ) corners, and in the A (Trp 7 , Gln 8 , Trp 14 ) and H helices (Met 131 , Ala 144 ) (Table IV). Huang and Boxer (16) reported that the A144V mutation had significant effects on CO and O 2 recombination in crude lysates of E. coli containing recombinant myoglobin. In contrast, the purified A144V mutant has geminate recombination properties very similar to the wild-type protein (Table IV). The Q8V, M131L, and A144V mutations do cause 2-, 3-, and 1.5-fold, respectively, increases in the O 2 dissociation rate constant and therefore measurable decreases in oxygen affinity. The origin of these latter effects is unclear and may somehow be related to the overall stability of the globin molecule. However, these mutations cause little change in the rate constants for ligand entry and exit.
Secondary Sites (State C) on the Proximal Side of the Heme-Scott and Gibson (17) postulated that photodissociated O 2 migrates into or near the high affinity Xe1 binding site because even low pressures of Xe have a significant effect on the time course of geminate recombination. More recently, Ostermann et al. (19) and Chu et al. (20) observed photodissociated CO in this pocket using time-resolved x-ray crystallographic techniques, and Vojtechovsky et al. (21) reported O 2 in this pocket when native crystals were equilibrated with 100 atm of pure oxygen.
The Xe1 pocket is located underneath the porphyrin ring in a cavity circumscribed by Leu 89 , Phe 138 , and Leu 104 . Ala replacements at positions 104 and 138 increase and Trp replacements decrease, respectively, the fractional amount of slow secondary phases. However, these mutations have little effect on the total amount of geminate recombination, the fitted rate parameter for ligand escape, and the calculated rate constant for ligand entry (Tables IV and V). Surprisingly, the amplitude of the secondary geminate phase decreases when Leu 89 is replaced with either glycine or tryptophan. This apparent anomaly was resolved when Liong et al. (38,39) found that the L89G mutation allows several water molecules to enter the Xe1  pocket through the "hole" created by this substitution. Thus, both mutations cause the Xe1 cavity to be filled, with water in the case of Gly 89 myoglobin and an indole ring in the Trp 89 mutant. The effects of mutations at Ile 99 are more complex and difficult to interpret because there are significant changes in the conformation of the porphyrin ring (Table III; Refs. 38 and 39).
Decreasing the size of residue 99 to an alanine causes an increase, not a decrease, in the extent of geminate rebinding. Similar results are observed for the isosteric L99N mutation, and both substitutions cause 2-fold increases in overall O 2 affinity, suggesting changes in reactivity of the iron atom due to puckering of the porphyrin ring (38,39).
The Distal Histidine Gate-The most compelling evidence in FIG. 5. Maps of the effects of mutagenesis on the fraction of secondary geminate rebinding, the total fraction of geminate recombination, and the rate constants for ligand entry and escape. The side view (left panels) and top view (right panels) correspond to those shown in Fig. 1, where the Xe pockets and helices are labeled. Top panels, map of amino acids, which, when mutated from small to large residues, cause marked decreases in the extent of secondary geminate rebinding. Phe 43 , Phe 46 , and His 64 side chains were removed since mutating these residues to alanine or valine causes the total fraction of geminate recombination to decrease to Յ0.15, making it difficult to define the secondary phase. Arg 45 was removed from the side view to allow visualization of other residues in the CD corner and D helix but was placed in the top view. Positions where mutations cause Ն100% changes in the fraction of secondary phase are green. Positions where mutations cause Ͻ100% but Ն50% changes in F secondary are yellow. Positions where mutations cause less than 50% changes in F secondary are marked in white, if a complete size series (Ala or Val to Phe or Trp) was examined, or in dark gray, if only a limited set of mutations was examined. The Xe binding sites are orange spheres. Middle panels, map of mutations that affect the total fraction of geminate recombination, F geminate . Positions were marked in red when mutation from a small to large or wild-type residue causes Ն100% changes in the fraction of total geminate recombination. Positions are marked in orange when mutations cause changes in F geminate Ͻ100% but Ն67%; and positions are marked in yellow where mutations cause changes in F geminate Ͻ67% but Ն33%. The remaining residues are highlighted in white or dark gray as in the upper panels. Bottom panels, map of amino acids that affect the rate constants for ligand entry and exit. Residues were marked in red (Phe 43 , His 64 , and Val 68 ) when the product kЈ entry(small) / kЈ entry(large) ϫ k escape(small) /k escape(large) was Ͼ30 and as high as 500. Phe 46 was marked in orange and has a value of kЈ entry(small) /kЈ entry(large) ϫ k escape(small) /k escape(large) between 30 and 10. Residues were marked in yellow (Leu 29 and Leu 32 ) when their product ratios were between 10 and 3. The remaining residues show little or no effects and are marked in white or gray as described for the top and middle panels.
favor of ligands entering myoglobin through the distal histidine gate is shown in Fig. 3C. Most mutations that cause kЈ entry to be Ն 100 M Ϫ1 s Ϫ1 involve insertions of smaller residues at position 64, and there is a inverse correlation between the size of residue 64 and both the calculated value of kЈ entry and the measured value of kЈ NO (Table I). Karplus, Elber, and others have argued that these mutations "poke" a hole in an inner tube, allow gas to enter and escape rapidly, and do not identify the location of the naturally occurring "valve" for ligand entry (15). This criticism is valid but may be addressed by examining the effects of the H64W mutation. If ligand entry does occur primarily through the distal histidine gate, blocking this route with a large Trp residue should decrease the bimolecular rate constant for ligand entry.
The calculated value of kЈ entry for the Trp 64 mutant is 9 M Ϫ1 s Ϫ1 , which is substantially smaller than that for either the Phe 64 mutant (130 M Ϫ1 s Ϫ1 ) or the wild-type His 64 protein (34 M Ϫ1 s Ϫ1 ). Thus, the large indole side chain does appear to "plug," although not completely, the valve for ligand entry. This conclusion is supported by the laser photolysis results shown in Fig. 2A. When the distal histidine is replaced with alanine, the rate constant for O 2 entry increases ϳ20-fold (Table I), and bimolecular rebinding can be seen in the 2-s geminate time courses measured at 1 atm O 2 (Fig. 2A). The H64A mutation also decreases the fraction of true geminate rebinding to almost zero, presumably because ligands can escape directly to solvent. The H64W mutation produces the opposite effect, an increase in F geminate to ϳ0.7.
The effects of the F46A, F46V, and F43V mutations provide additional support for the histidine gate hypothesis. These replacements cause large increases in kЈ entry and decreases in the extent of geminate recombination ( Figs. 2A and 3C). The distal histidine in the crystal structures of these mutants is highly disordered (12,40). In the case of F46V MbCO, the imidazole side chain is rotated upward and outward, creating a direct channel from the bound ligand to the solvent interface. This conformation accounts for the marked increase in the rate and fraction of ligand escape from the mutant protein (12,41). Unlike the H64W mutation, tryptophan replacements at positions 46 and 43 do not appear to block ligand entry. The F46W mutation causes no change in kЈ entry , and the F43W mutation results in an increase in this rate constant (Tables I and II). In the latter case, the large indole ring appears to push against the distal histidine causing it to be more disordered (40).

Maps for Ligand Movement in Myoglobin-
We have created three-dimensional maps to summarize the effects of mutagenesis on the individual rate parameters for geminate and overall bimolecular O 2 binding (Fig. 5). The design of these maps follows the presentation made by Huang and Boxer (16) for the effects of point mutations on CO and O 2 rebinding to recombinant myoglobin in bacterial lysates. In their work, an automated procedure was used to screen the effects of large numbers of random single mutations. In our study, mutations from small to large residues were made rationally, the proteins were expressed and purified, and complete sets of overall and geminate O 2 binding rate parameters were determined. With one or two exceptions, there is good agreement between the two approaches in terms of identifying amino acid side chains that regulate the kinetics of ligand binding.
Secondary sites for photodissociated ligands were defined by highlighting those positions which, when mutated from a large to a small amino acid, cause marked increases in the fraction of slow geminate rebinding, F secondary . The results of this analysis are shown in the upper two panels in Fig. 5. Positions where mutations cause large, moderate, and very little change in F secondary are marked in green, yellow, and white or gray, respectively. All the mutations that affect the slow phase of geminate recombination cluster around the Xe4 and Xe1 sites. These results support the low temperature, time-resolved x-ray crystallographic results (19,20,22). Small amounts of photodissociated ligands are able to move into these cavities under physiological conditions.
Ligands in state C are almost certainly not in one specific location but dispersed throughout the region marked by the green and yellow residues and the two orange spheres representing the Xe4(distal) and Xe1(proximal) cavities (Fig. 5, upper panels). Residues further removed from the heme group, in the area between the A, G, and H helices, including Xe sites 2 and 3, do not appear to be accessible to dissociated ligands. The latter region of the protein remains intact in the molten globule intermediate that is observed during either acid, urea, or guanidinium chloride-induced denaturation of apomyoglobin (42)(43)(44)(45)(46). Thus, this portion of the intact myoglobin structure may be too rigid to allow rapid penetration by ligand molecules.
Determinants of the Amount of Internal Rebinding-In an attempt to define the pathways for ligand escape, we have mapped the effects of mutations from large to small amino acids on the total fraction of geminate recombination, F geminate . The results are shown in the middle panels of Fig. 5 6. Effects of mutagenesis on the rate constants for ligand entry and exit as a function of residue position. Panel A, the logarithm of the ratio of kЈ entry for the mutant with the smallest amino acid divided by kЈ entry for the mutant with the largest amino acid was calculated for each position along the primary sequence. In cases where the wild-type protein showed the smallest or largest rate constant, the ratio was calculated using kЈ entry for wild-type myoglobin in the denominator. All the parameters are listed individually in Tables I-IV. The filled bars represent the ratios for kЈ entry and the open bars, k escape , which is equal to the fitted value of k 2 for the side path scheme in Scheme 1 and Fig. 4. Panel B, equilibrium constants for the formation of state B were calculated as K entry ϭ kЈ entry /k escape . Then, as in panel A, the logarithm of the ratio of K entry(small) /K entry(large) was calculated and plotted versus sequence position. The large increases in the latter ratio for Ala mutations at positions 28, 29, 32, 64, 68, and 107 define the position of ligands in the major non-covalent binding site (state B in Fig. 4). are marked in color, and only one proximal residue, Ile 99 , is highlighted (yellow). The positions showing the largest effects occur at His 64 (red), Val 68 (red), Ile 28 (orange), Leu 29 (orange), Phe 43 (orange), and Phe 46 (orange). These positions are at the solvent interface and in or near the major non-covalent binding site (state B) for dissociated or entering ligands.
The middle panels in Fig. 5 suggest that only a few ligands exit myoglobin by migrating from one Xe site to another and then out through the interior of the protein. If those pathways were dominant, Ala substitutions at interior positions near Xe sites 1, 2, and 3 should have decreased to a greater extent the total amount of geminate recombination by allowing more rapid escape, and Trp mutations should have prevented escape, causing larger increases in F geminate . These types of changes are observed to a greater extent for mutations in the regions near His 64 or the major non-covalent binding site (state B).
Pathways for Ligand Entry and Exit and Non-covalent Binding-The effects of changing from a large (Phe, Trp) to a small amino acid (Ala, Val) on the rates of entry and exit are plotted versus position along the primary sequence in Fig. 6A. If the position being examined is located along a pathway for ligand movement into the protein, such mutations should increase both kЈ entry and k escape significantly. The largest effects are observed for mutations at positions 28, 29, 32, 43, 46, 64, 68, and 107 (Fig. 6A). In general, the variation in k escape is much smaller, Յ5-fold, than the 200-fold range of values for kЈ entry . The effects of changing the native residue to a small amino acid differ significantly, depending on whether the residue is internal or located near the solvent interface. The external F43V, F46A, and H64A mutations cause both kЈ entry and k escape to increase significantly (Tables I and II), demonstrating that the naturally occurring residues at these positions must form significant parts of the barrier to ligand movement into and out of myoglobin.
Alanine replacements at the internal Ile 28 , Leu 29 , Leu 32 , Val 68 , and Ile 107 positions cause either no effect or only small increases (Յ2-fold) in the rates of ligand entry and escape (Tables I and II). In contrast, tryptophan mutations at these positions inhibit both the rate and extent of non-covalent ligand binding, as seen by decreases in kЈ entry , increases in k escape , and concomitant decreases in the equilibrium constant for non-covalent binding (entry) into the protein (i.e. K entry ϭ kЈ entry /k escape ; Tables I and II; Fig. 6B). These results confirm experimentally that residues 28, 29, 32, 68, and 107 surround the primary non-covalent binding site (state B in Fig. 4, see also Fig. 9).
In order to emphasize the kinetic barrier, the ratios kЈ entry(small) /kЈ entry(large) and k escape(small) /k escape(large) were multiplied together, which is equivalent to adding the logarithmic values for the filled and empty bars shown in Fig. 6A. The resultant product was used to generate the three-dimensional map shown in the bottom panels of Fig. 5. Those residues that show large, intermediate, small, and no effects on the rates of both entry and escape are marked in red (Phe 43 , His 64 , and Val 68 ), orange (Phe 46 ), yellow (Leu 29 and Leu 32 ), and white or gray, respectively. This map argues strongly that ligands enter and exit myoglobin primarily through the channel created by outward movement of the distal histidine. Mutations in the interior of the protein have little effect on the rate constants for ligand entry and escape, even though these replacements often have significant effects on the rates and amplitudes of geminate recombination. The latter changes in internal rebinding were seen for many of the interior random mutants screened by Huang and Boxer (16). Small numbers of ligands do reach these positions; however, the majority of them appear to return to the distal pocket and escape through the histidine gate.
The Problem of Water Barriers-Most of the distal histidine mutants also alter the apparent equilibrium constant for the formation of state B. In wild-type deoxymyoglobin, a water molecule is present in the distal pocket and stabilized by hydrogen bonding to the distal histidine. This water molecule inhibits the entry of all ligands, regardless of the pathway taken (47). Replacement of the distal histidine with apolar amino acid acids results in the loss of internal water. This effect accounts in part for the large increases in kЈ entry and K entry observed for the formation of state B in Gly 64 , Ala 64 , Val 64 , Leu 64 , and Phe 64 mutants (9,35,48).
Perhaps the most remarkable result in Tables I-V is the relative invariance of the fitted rate constant for ligand escape. The value of k escape ranges from 5 to Յ30 s Ϫ1 , with an average value of ϳ10 s Ϫ1 . In contrast, the rate constant for internal bond formation, k bond , ranges from Յ0.05 to Ͼ200 s Ϫ1 , and the bimolecular rate constant for ligand entry, kЈ entry , ranges from 0.2 to 540 M Ϫ1 s Ϫ1 . The large variance in kЈ entry is clearly a reflection of the importance of the size of the internal pocket available for capturing entering ligand molecules. The rate of entry can be increased if internal water is lost by replacing His 64 with an apolar amino acid or decreased if the size of the distal pocket is reduced further by insertion of large aromatic residues at positions 28, 29, 32, 68, and 107. The invariance of k escape may be the result of a more general "ice-like" water barrier to ligand escape from the protein. Clathrate structures are found on the surface of all proteins and may limit outward movement of both the distal histidine and the ligand molecules.  Tables I and II for apolar mutations at positions  Ile 28 , Leu 32 , Val 68 , Leu 89 , Leu 104 , Ile 107 , Ile 111 , and Phe 138 . Panel A, correlations between log (kЈ entry ) and F geminate and F slow . F slow is defined as the absolute amplitude of the slow geminate rebinding phase and is given by F geminate ϫ F secondary . The solid line for F geminate is a fit to a polynomial of degree 2 with r ϭ 0.897; the solid line for F slow is a fit to power function with r ϭ 0.61. Panel B, correlations between log (kЈ entry ) and log(k bond ). The solid line represents a linear fit with r ϭ 0.862. Panel C, correlations between log (kЈ entry ) and log(k escape ). The solid line represents a linear fit with r ϭ 0.198.
Multiple Pathways-An alternative interpretation of the invariance of k escape is that there are multiple pathways with roughly equal resistance to ligand escape (15,16). For this situation, it would be difficult to slow the observed rate of escape by a single point mutation. For example, if there are four pathways with equal rates of ligand movement, blocking one of them would only decrease the net rate of entry or exit by ϳ25%. This argument could account for the lack of effect of interior tryptophan substitutions near the Xe4 and Xe1 sites. However, if one of these pathways were opened up by an alanine substitution, the values of kЈ entry and k escape should increase markedly. Elber and Karplus (15) and Huang and Boxer (16) used the latter argument to rationalize the results observed for the H64G, H64A, and H64V mutations. They argued that the 10-fold increases in kЈ entry for these replacements are due to creation of a "hole," which allows rapid ligand entry and escape. However, if the multiple pathway interpretation were true, then valine and alanine substitutions in the internal escape pathways should also cause large increases in kЈ entry and k escape . In contrast to these predictions, large effects are not observed for Ala mutations located in the interior of the distal and proximal heme pockets.
Some escape from the Xe sites cannot be ruled out. An upper limit for the bimolecular rate of entry through alternative pathways can be estimated from the calculated value of kЈ entry for the H64W mutant, which is 4-fold lower than that for wild-type myoglobin. Thus, as much as ϳ25% of the ligands could be entering the protein by routes through the protein interior. However, adding Xe to wild-type myoglobin has little or no effect on kЈ entry and F geminate (Fig. 2C and Table V). Small increases in kЈ entry are observed when alanine replacements are made at positions located in the Xe4 and Xe1 cavities. For example, the I28A, L104A, and F138A substitutions cause kЈ entry to increase ϳ40 -50%. However, these changes are only slightly greater than the estimated error for these parameters, Ϯ30% (see Fig. 6), and indicate that the amount of ligand entry through these alternative pathways is small even when the Xe cavities are made larger.
In some cases, tryptophan replacements at or near the Xe4 and Xe1 pockets do cause large decreases in kЈ entry and increases in F geminate , which might indicate the closing of a pathway for ligand entry and escape (Fig. 2, B and C). Correlations between these parameters and the fitted rate constants for bond formation and ligand escape are shown in Fig. 7 for mutations at internal positions near the Xe cavities. As the size of the amino acid side chain decreases from Trp to Ala, the rate of ligand entry increases, the total fraction of geminate recombination decreases and the amplitude of the slow geminate phase increases (Fig. 7A). If these changes were reflecting an opening up of interior pathways, the decrease in F geminate should be due to an increase in the rate of escape with no change in the rate of internal bond formation. However, the opposite effect is observed (Fig. 7, B and C); k bond decreases markedly as kЈ entry increases and k escape is either unchanged or decreases slightly.
Free Energy Diagrams-The origin of the strong inverse correlation between k bond and kЈ entry can be seen clearly by constructing free energy diagrams for O 2 binding (Fig. 8). The inner and outer barrier heights and the wells for covalent (state A) and non-covalent (state B) ligand binding were calculated using the analyses described originally by Carver et al. (9) and reviewed by Olson and Phillips (35). The most extreme case is seen for the V68W mutant, in which the tryptophan side chain fills the back portion of the distal pocket. This replacement causes large and roughly equal increases in the absolute free energy of state B and the outer barrier to ligand entry (Fig. 8A).
Thus, there is a direct correlation between the internal target size and the rate and extent of ligand entry into myoglobin. The absolute free energy of the inner barrier for bond formation is unaffected by the decrease in pocket volume. As a result, ⌬G ‡ B3A for internal rebinding in V68W myoglobin is very low, and k bond is markedly increased with respect to that for the wild-type protein. In contrast, ⌬G ‡ B3X for escape is still large, and the apparent rate constant for escape is unchanged or increases slightly. The net result is that photodissociated ligands almost always rebind and the total fraction of geminate recombination approaches 1 (Fig. 2B).
Similar, but less pronounced changes in the free energy diagram occur for I28W, I32W, and I107W mutations. In our view, the increases observed in the fractional amount of geminate recombination for these tryptophan mutations are due primarily to a decrease in the internal volume for dissociated ligands and not to blocking alternative pathways for entry and escape. Carver et al. (9) showed that increasing the size of the ligand molecule from O 2 to methyl and ethyl isocyanide also causes dramatic increases in F geminate and k bond , little change in k escape , and marked decreases in kЈ entry and K entry . The free energy diagram for ethyl isocyanide binding to wild-type myoglobin looks very similar to that for O 2 binding to the V68W mutant shown in Fig. 8A. Thus, the ratio of the size of the primary non-covalent binding pocket (state B) to that of the ligand is a major determinant of the rate constant for ligand entry.
The free energy diagram for O 2 binding to F46A myoglobin contrasts with that for the V68W mutant (Fig. 8B). This replacement causes a selective decrease in the absolute free energy of the outer barrier, with little change in the free energy of FIG. 8. Free energy barrier diagrams for O 2 binding to wildtype, V68W, F46A, and L29W sperm whale myoglobin. The free energy wells for states A and B and the absolute barrier heights were calculated as described by Carver et al. (9) and Olson and Phillips (35). The solid lines describe the barriers and wells for wild-type myoglobin, and the dashed lines represent the free energy diagrams for the mutants. state B and the inner barrier to bond formation. The decrease in the barrier to entry and escape is almost certainly a result of the greater flexibility of the distal histidine side chain in this and the F46V mutant (12).
Distal Pocket Size and the Rates of Ligand Entry and Escape- Fig. 8 (A and B) emphasizes the complex nature of the kinetic barrier to ligand entry and exit. The height of the barrier includes an entropic contribution due to sequestering the ligand in a small volume and a steric contribution requiring movement of the distal histidine and disruption of water structure at the solvent interface near the heme propionates. These effects also suggest multiple positions for ligands in state B. A three-dimensional representation of the spaces available to ligands in the distal pocket of myoglobin is shown in Fig. 9 along with the key amino acid side chains that determine the size and shape of the cavity. Some entering or dissociated O 2 molecules are located directly above the iron atom in an orientation perpendicular to the heme and poised for rapid bond formation. Some are oriented with the dioxygen bond parallel to the plane of porphyrin ring in a position that facilitates escape through the histidine gate. Others are more randomly positioned in the interior of the distal pocket and perhaps even in the Xe4 cavity. Interconversion between these positions occurs rapidly on nanosecond time scales at room temperature. As a result, the observed ns time courses for geminate rebinding of O 2 show simple one or two exponential behavior at room temperature. These results contrast with the complex behavior observed for O 2 and CO rebinding at low temperatures (49,50) or for NO rebinding on picosecond time scales (9,23,24,30,51).
Tryptophan insertions at positions 28, 32, 68, and 107 sequester dissociated ligands closer to the iron atom. In most cases, confining the ligand near the heme group increases both k bond and k escape , and reduces the number of states required to fit the observed time courses from two to one (Tables I and II; Fig. 2, B and C). These effects are due to the increased probability of finding the ligand above the iron atom or poised to leave the pocket when the interior cavities are reduced in size and no longer available to the dissociated ligand (Fig. 9). The same interpretation explains why these Trp mutations cause even larger decreases in the rate constant for ligand entry.
In the case of non-covalent binding, the ligand must enter the distal pocket when the histidine gate is open and then remain inside long enough to be captured when the gate closes. If the cavities in the back of the distal pocket are open, entering ligands will spend more time moving around inside the protein before migrating back out into solvent. If these cavities are filled with large aromatic amino acid side chains, the entering ligands will be reflected back out at a higher frequency and have a much lower probability of being caught inside when the histidine gate closes. As a result, the net rate for ligand entry, kЈ entry , is much smaller when the distal pocket is reduced in size by Trp insertions.
Ligand Escape from Mutant Myoglobins-In contrast to the native protein, direct escape from the Xe4 and Xe1 pockets may be the dominant pathway in some mutants. The energy diagram for the L29W mutant (Fig. 8C) shows that both the absolute value of the internal barrier to bond formation and the bound state are increased dramatically by direct steric hindrance with the large indole side chain (52). Thus, photodissociated ligands are prevented from rebinding to the iron atom and probably also from escaping via the distal histidine gate due to the presence of the large indole side chain hanging directly over the center of the heme group. The amount of geminate recombination is effectively zero (Fig. 2B). Similarly, entering ligands are unable to reach the interior portion of the distal pocket (state B in Fig. 9) and are reflected back out into solvent at a high frequency, causing dramatic decreases in kЈ entry , kЈ NO , and kЈ O 2 (Table I).
Ostermann et al. (19) used crystals of L29W myoglobin to visualize photodissociated CO non-covalently bound in both the Xe4 and Xe1 sites, under conditions where complete escape from the protein was prevented by freezing. The large indole ring completely prevented rebinding to the iron atom under these conditions, maximizing the amount of electron density associated with photodissociated ligands. Large decreases in the extent of geminate recombination also occur when Leu 29 is mutated to Tyr (53-55), and Brunori et al. (22) used the triple L29Y/H64Q/T67R mutant to determine the crystal structure of photodissociated CO in the Xe4 pocket at low temperatures.
In an attempt to simulate escape from the Xe4 site, we placed ligand molecules in this cavity and then used the LES method (15) and the MOIL set of programs (56,57) to calculate ligand trajectories. Simulations were carried out in wild-type myoglobin for up to 100 ps. If no external water molecules were placed around the protein, ligands streamed out of the structure through gaps between the B and G helices near His 24 , Arg 118 , and His 119 , as was observed by Elber and Karplus (15). When crystallographic waters were incorporated into the structure, particularly those waters associated with His 24 , Arg 118 , and His 119 , or a box of water was built around the protein, no ligands migrated out of the Xe4 pocket on the time scales that were examined (Յ100 ps). When external water was present, FIG. 9. Space-filling model of the heme pocket of wild-type sperm whale oxymyoglobin. The structure was taken from PDB file 2MGM (48). Key amino acids in the distal pocket are shown as stick models and labeled in black. The heme group and the proximal histidine (His 93 ) are also presented as stick models. The rest of the protein is drawn as a space-filling model in yellow. The entire D helix and the CD corner were cut away to show the interior of the active site. The view is looking across the heme group toward the E helix and is rotated 180°from the orientation shown in Figs. 1 (left), 4, and 5 (left column) to allow better visualization of state B, the Xe1 and Xe4 cavities, and their interconnections. the entire protein structure was more compact, inhibiting ligand movement in any direction on picosecond time scales. These theoretical results emphasize the importance of surface water as a barrier to ligand escape, regardless of the pathway taken.
Conclusions-The side path scheme in Fig. 4 provides a simple and quantitative interpretation of the effects of mutagenesis and Xe addition on geminate and overall rate constants for O 2 binding to sperm whale myoglobin. In effect, the globin acts as a baseball glove to "catch" and then trap incoming ligand molecules long enough to allow bond formation with the iron atom. Opening of the glove occurs by upward and outward movements of the distal histidine, and the ligands are trapped in the interior "webbing" of the distal pocket. Following this analogy, it is more difficult to catch in-coming ligands if the pocket of the glove is already filled with water molecules or if it is reduced in size with tryptophan substitutions since many more of the entering ligands will bounce back out into solvent. Thus, the rate of ligand capture correlates directly with the size and depth of the internal pocket, whereas the rate of escape from this non-covalent binding site depends more on the frequency of gate opening.
The cavities in the interior of myoglobin are also important for ligand release. These spaces allow dissociated O 2 molecules to remain unattached to the iron atom long enough for net escape through the distal histidine gate. A three-dimensional picture of the non-covalent binding site (state B) is shown in Fig. 9. Filling the interior distal cavity with Trp residues at positions 28, 32, 68, or 107 causes 3-30-fold decreases in the overall rate constant for oxygen dissociation due to sequestering the ligand near the iron atom, which selectively enhances the rate of internal rebinding (k O 2 and k bond values in Tables I  and II). Without compensating mutations, such decreases would impair the physiological function of myoglobin, which is to release oxygen rapidly for mitochondrial respiration during muscle contraction when there is no blood flow and then to take up it quickly during muscle relaxation. Consequently, the cavity in the interior of the distal pocket is conserved in all mammalian myoglobins and is also present in the ␣ and ␤ subunits of vertebrate hemoglobins.