Ligand Migration in the Apolar Tunnel of Cerebratulus lacteus Mini-Hemoglobin*

The large apolar tunnel traversing the mini-hemoglobin from Cerebratulus lacteus (CerHb) has been examined by x-ray crystallography, ligand binding kinetics, and molecular dynamic simulations. The addition of 10 atm of xenon causes loss of diffraction in wild-type (wt) CerHbO2 crystals, but Leu-86(G12)Ala CerHbO2, which has an increased tunnel volume, stably accommodates two discrete xenon atoms: one adjacent to Leu-86(G12) and another near Ala-55(E18). Molecular dynamics simulations of ligand migration in wt CerHb show a low energy pathway through the apolar tunnel when Leu or Ala, but not Phe or Trp, is present at the 86(G12) position. The addition of 10–15 atm of xenon to solutions of wt CerHbCO and L86A CerHbCO causes 2–3-fold increases in the fraction of geminate ligand recombination, indicating that the bound xenon blocks CO escape. This idea was confirmed by L86F and L86W mutations, which cause even larger increases in the fraction of geminate CO rebinding, 2–5-fold decreases in the bimolecular rate constants for ligand entry, and large increases in the computed energy barriers for ligand movement through the apolar tunnel. Both the addition of xenon to the L86A mutant and oxidation of wt CerHb heme iron cause the appearance of an out Gln-44(E7) conformer, in which the amide side chain points out toward the solvent and appears to lower the barrier for ligand escape through the E7 gate. However, the observed kinetics suggest little entry and escape (≤25%) through the E7 pathway, presumably because the in Gln-44(E7) conformer is thermodynamically favored.

The large apolar tunnel traversing the mini-hemoglobin from Cerebratulus lacteus (CerHb) has been examined by xray crystallography, ligand binding kinetics, and molecular dynamic simulations. The addition of 10 atm of xenon causes loss of diffraction in wild-type (wt) CerHbO 2 crystals, but Leu-86(G12)Ala CerHbO 2 , which has an increased tunnel volume, stably accommodates two discrete xenon atoms: one adjacent to Leu-86(G12) and another near Ala-55(E18). Molecular dynamics simulations of ligand migration in wt CerHb show a low energy pathway through the apolar tunnel when Leu or Ala, but not Phe or Trp, is present at the 86(G12) position. The addition of 10 -15 atm of xenon to solutions of wt CerHbCO and L86A CerHbCO causes 2-3-fold increases in the fraction of geminate ligand recombination, indicating that the bound xenon blocks CO escape. This idea was confirmed by L86F and L86W mutations, which cause even larger increases in the fraction of geminate CO rebinding, 2-5-fold decreases in the bimolecular rate constants for ligand entry, and large increases in the computed energy barriers for ligand movement through the apolar tunnel. Both the addition of xenon to the L86A mutant and oxidation of wt CerHb heme iron cause the appearance of an out Gln-44(E7) conformer, in which the amide side chain points out toward the solvent and appears to lower the barrier for ligand escape through the E7 gate. However, the observed kinetics suggest little entry and escape (<25%) through the E7 pathway, presumably because the in Gln-44(E7) conformer is thermodynamically favored.
Although molecular dynamics (MD) 7 simulations suggest multiple interior pathways for O 2 entry into and exit from globins, most experiments with mammalian myoglobins (Mbs) and hemoglobins (Hbs) suggest a well defined single pathway involving a short channel between the heme propionates and the heme iron atom that is gated by the distal E7 histidine (1). To search for and define an interior ligand migration trajectory, we chose to use the neuronal mini-hemoglobin from Cerebratulus lacteus as a model globin system to examine its long apolar tunnel that leads from the distal portion of the heme pocket to an exit point between the C-terminal regions of the E and H helices of the tertiary fold, a pathway that is roughly 180°opposite the E7 channel and appears to be a major route for ligand entry (2). This model globin provides a well defined system to examine both experimentally and theoretically the effects of xenon binding, mutagenesis, and conformational heterogeneity on the competition between movement through the E7 gate versus an internal apolar pathway.
Nerve tissue Hbs occur in both vertebrates and invertebrates (3). Among these, the nerve Hb from the nemertean worm C. lacteus (CerHb) is the smallest functional globin known, being composed of 109 amino acids instead of the ϳ140 -160 residues typical of most monomeric globins (4,5). Analysis of the three-dimensional structure of CerHb has shown a markedly edited 3-over-3-globin fold with deletion of the N-terminal A-helix, extension of the GH region, and reduction of the C-terminal H-helix (6). Both sequence and fold comparisons indicate that CerHb is equally distant from all known globins, suggesting a specific mini-Hb family within the Hb superfamily. The affinity of CerHb for O 2 is very similar to that of mammalian Mbs, and its function appears to be O 2 storage and then release to axons and brain tissue during periods of burrowing under anoxic conditions (5). The evolution of a storage function in a highly altered globin structure has made CerHb an excellent model for testing biophysical mechanisms involved in the regulation of O 2 affinity and reaction rates (2,(7)(8)(9)(10).
Several distinct structural features make CerHb of interest for understanding structure-function relationships. First, the distal portion of the heme pocket contains Tyr-11(B10) and Gln-44(E7), which stabilize heme-bound O 2 by hydrogen bonding in many invertebrate globins with high O 2 affinity (11). However, unlike most of the globins containing this Tyr-Gln motif, CerHb also contains a polar Thr-48 residue at the E11 position, which in most globins is Val, Leu, Ile, or Phe. In CerHb, the non-bonded electrons of the Thr-48(E11) O␥ atom "pull" the proton on the Tyr-11(B10) hydroxyl group away from heme-bound O 2 , causing marked 1000-to 100-fold increases in the rate and equilibrium constants for O 2 dissociation, respectively (6,9). The net result is a P 50 for O 2 binding of ϳ0.6 torr (K d ϳ 1 M) for CerHb, which is similar to that of mammalian Mbs (10).
The second unusual structural feature of CerHb is a long apolar tunnel that connects the heme pocket to solvent through an exit pore between the C-terminal ends of the E and H helices. This tunnel is correlated with an unusually large association rate constant for O 2 binding to CerHb (kЈ O 2 ϭ 230 M Ϫ1 s Ϫ1 ) when compared with those of other invertebrate globins containing the Tyr-Gln active site motif, which normally show bimolecular association rate constants on the order of 1-5 M Ϫ1 s Ϫ1 (11). The rate constant for O 2 binding to CerHb is 10 times larger than that for sperm whale Mb and is similar to those for His(E7)Gly 8 mutants of Mbs and Hbs and to unhindered pentacoordinate model hemes (12)(13)(14). The cause of these high rates appears to be a wide, ϳ10 Å long channel that traverses the interior of the globin matrix, allowing relatively unhindered access to the heme pocket.
The CerHb tunnel has roughly the shape of an hourglass, is located between the E-and H-helices, is directed from the solvent to the heme pocket, and terminates at the active site as an aperture, which is circumscribed by the side chains of Val-7(B6), Phe-10(B9), and Thr-48(E11). This channel is lined by small hydrophobic residues and has a diameter that varies from 6.9 to 5.5 Å at the narrowest segment, which is close to residue Leu-86(G12) (6). Diatomic ligands are thought to enter and exit the tunnel through an opening between the E and H helix, which appears to have evolved by the complete loss of the N-terminal A-helix that is found in almost all other globins. Obstructing the tunnel entrance by increasing the size of Ala-55(E18) to Phe or Trp causes an ϳ4-fold decrease of both kЈ O 2 and k O 2 and a 5-fold increase in the fraction of geminate recombination due to restriction of both entry into and escape from the apolar channel (2). In contrast, mutagenesis of Gln-44(E7) to either smaller or larger amino acids has little effect on internal rebinding after photolysis or bimolecular binding from solvent, suggesting strongly that the E7 gate for ligand entry/exit found in mammalian Hbs and Mbs (13,14) is not a significant pathway in CerHb (2).
Apolar cavities and tunnel systems that could support ligand diffusion to and from the heme have been observed in selected globin families, although relative to CerHb, some of these channels are structurally and topologically distinct within the overall tertiary fold (15)(16)(17). However, in most cases there has been little experimental proof that these tunnels are used by diatomic ligands. Cavities large enough to accommodate xenon atoms have been found in most globins, including sperm whale Mb and Scapharca inaequivalvis HbI; however, in both of the latter cases, xenon binding has little effect on either the fraction of geminate recombination or on overall rates of ligand binding or release (13,18,19), implying that these internal spaces are not part of the route for ligand entry and escape.
In this work we have focused our attention on providing both direct experimental and theoretical evidence for ligand access to the heme pocket through the tunnel in CerHb and estimates of what fraction of the ligands use this route versus the E7 gate pathway, which dominates in mammalian Mbs and Hbs that contain a distal histidine. We have shown that xenon atoms can be accommodated within the CerHb tunnel by x-ray crystallography, examined the effects of xenon binding on CO geminate recombination, measured the effects of changing the width of the channel with Leu-86(G12) to Ala, Phe, and Trp mutations, and complemented these experiments with molecular dynamics simulations of how Leu-86 mutations modulate the tunnel shape, size, and energy barriers to ligand migration. Our results demonstrate that there is a strong correlation between tunnel size and observed rates of ligand binding to CerHb. More importantly, CerHb is the first example of a globin in which xenon binding markedly increases geminate recombination and slows bimolecular ligand entry.

EXPERIMENTAL PROCEDURES
Sample Preparation-Wild-type (wt) and mutant recombinant CerHbs were expressed and purified as described previously using a synthetic gene with codon usage optimized for expression in Escherichia coli (6,10). Most recombinant CerHb samples were isolated in the reduced state and used directly. When necessary, the unstable mutants were pre-reduced with dithionite, quickly passed through a Sephadex G-25 column, and eluted with buffer equilibrated with 1 atm of CO. All reactions were measured in 0.1 M phosphate buffer, pH 7.0, 1.0 mM EDTA, 20°C.
Measurement of Overall Rates of Ligand Association and Dissociation-CO association time courses were measured after complete laser photolysis of 50 M CerHbCO samples containing various CO concentrations under pseudo first order conditions, and CO dissociation was measured by mixing CerHbCO with high concentrations of NO (2). Time courses for O 2 association and dissociation were measured after complete laser photolysis of CerHbCO samples containing various mixtures of O 2 /CO (2), and association rate constants for NO binding to deoxy-CerHb were measured using a flow-flash multi-mixing apparatus and the 500-ns dye laser system (2).
Measurement of Geminate Recombination-Time courses for internal rebinding within CerHb were measured at 436 nm after excitation with a 9-ns excitation pulse from a Lumonics YAG-laser system using a Tektronix TDS3052 digitizing oscilloscope and Hamamatsu high speed PM tube with a 2-ns rise time. Experimental procedures and fitting routines were performed as previously described (2). For experiments with xenon, a 0.3-ml sample of CerHbCO was transferred to a stainless steel pressure cell with a gas volume of ϳ4 ml. The cell was equipped with anti-reflection-coated sapphire windows and had a path length of 1 mm as previously described (19). Data were first collected with 1 atm CO over the sample, and then the required pressure of xenon was introduced through a three-way valve attached to the top of the cuvette. The sample was then equilibrated with the CO-xenon mixture for several minutes by shaking the cuvette to expose the solution to the gas space. The fraction of geminate recombination (F gem ) and the rate of geminate recombination (k gem ) were determined as previously described (2).
Crystallization, Data Collection, and Refinement-The oxygenated derivative of the Leu-86(G12)Ala (L86A) CerHb mutant was crystallized by vapor diffusion techniques (protein concentration 27 mg/ml) under conditions matching those for the wt protein (20). Elongated prismatic crystals (about 0.05 ϫ 0.05 ϫ 0.2 mm 3 ) grew within 1 week. The crystals were transferred to 2.8 M ammonium sulfate, 50 mM sodium acetate, pH 6.0, and 15% glycerol (v/v) (cryoprotectant solution) immediately before data collection at 100 K. L86A Cer-HbO 2 crystals are isomorphous with those of the wt protein.
High resolution data (1.60 Å) on the L86A CerHb mutant crystals were collected at the European Synchrotron Radiation Facility (beam line ID14-1, Grenoble, France) ( Table 1). To promote xenon diffusion within the protein matrix, selected L86A CerHbO 2 crystals in their cryoprotectant solution were exposed to 10 bar xenon for 5 min in a high pressure chamber (Xcell, Oxford Cryo-system). The x-ray diffraction data sets for the xenon-bound oxygenated derivative of the L86A CerHb mutant were collected at 100 K using a MAR-Research 345 imaging plate detector coupled to a Rigaku RU-H3R rotating anode generator (copper K␣ radiation; resolution 2.3 Å) ( Table 1).
High resolution data (1.3 Å) for the aquomet form of the wt CerHb protein crystals were collected at the European Synchrotron Radiation Facility (beam line ID14-1, Table 1). The aquomet form of CerHb was obtained by soaking the oxygenated wt protein crystals (20) with 10 mM K 3 Fe(CN) 6 . Crystals were then transferred to the cryoprotectant solution supplemented with the same amount of K 3 Fe(CN) 6 before data collection at 100 K.
All diffraction data were processed using MOSFLM and SCALA programs (21,22) and phased by molecular replacement methods with the program MOLREP (23), as implemented in the CCP4 program package (CCP4, 1994), using the wt CerHbO 2 structure as the starting model (PDB accession code 1kr7) (6). Crystallographic refinement was performed using the program REFMAC (24), and the program COOT (25) was used for model building/inspection. Xenon atoms were initially refined at 100% occupancy together with the protein structure. At the end of refinement, inspection of difference Fourier maps indicated that the xenon occupancies were overestimated. To obtain better values, the fractional occupancies were systematically decreased until no residual difference signal was detected. The relevant data collection and refinement statistics are reported in Table 1. The programs Procheck (26) and Surfnet (27) were used to assess the stereochemical quality of the protein structures and to explore the protein matrix cavities. Atomic coordinates and structure factors for the L86A CerHbO 2 , xenon-bound L86A CerHbO 2 , and wt aquomet CerHb have been deposited with PDB accession codes 2xkg, 2xkh, and 2xki, respectively (28).
Computational Methods-MD simulations were performed starting from the crystal structure of wt CerHbO 2 (PDB accession code 1kr7 (6)), and in some cases the out conformation of Gln-44(E7) observed in the structure of the wt aquomet CerHb derivative was used in the model. All systems were solvated with water molecules leaving 10 Å between the protein surface and the system limit. Histidine protonation was assigned to favor H-bond formation. All simulations were performed with the parmm99 force field (29) using Amber8 (30). The equilibration process was performed by slowly heating the system to a final temperature of 298 K. The oxygenated and deoxygenated heme model system charges were determined by using restrained electrostatic potential charges (31) and HF/6 -31G(d) wave functions according to the Amber standard protocol. This set of partial charges has been successfully used in similar systems (32).
To study the properties of the wt CerHb tunnel cavity system, the diffusion free energy profiles for O 2 along the tunnels were calculated by performing constant velocity MSMD simulations using the Jarzynski inequality (33), which relates equilibrium free energy values with the irreversible work performed over the system and proceeds along a reaction coordinate from reactants to products. In the present study the reaction coordinate was chosen as the iron to O 2 distance. Calculations were performed using a force constant of 200 kcal mol Ϫ1 Å Ϫ1 and a pulling velocity of 0.05 Å ps Ϫ1 . To reconstruct the free energy profile of ligand migration along the tunnel, a set of MSMD runs was performed starting from equilibrated MD structures with the ligand (i) in the distal pocket, (ii) in the crystallographic xenon-binding sites, and (iii) outside the tunnel. Ten MSMD simulations were performed in each direction (forward/exit and backward/entry). In cases in which two overlapping profiles were obtained (from entry and exit sets), we confirmed that they matched.
The free energy profiles for the transition between the in and out conformations of Gln-44(E7) were obtained with Umbrella Sampling techniques (34). In this method the potential function is modified so that the unfavorable states are sampled sufficiently. The modification of the potential function can be written by adding a bias harmonic potential according to EЈ(r) ϭ E(r) ϩ k(r Ϫ ) 2 , where E(r) is the potential energy of the protein for a given configuration r (i.e. the force field equation), and k is the force constant. The harmonic potential is centered at some point along the reaction coordinate (). The corresponding profile was computed using the Gln-44(E7) N⑀2-iron distance as the selected reaction coordinate, and 12 different 2-ns runs were performed varying the center of the harmonic potential along the reaction coordinate.
In-silico L86A, L86F, and L86W mutant structures were generated using the Modeler program (35). The generated structures were equilibrated by slowly heating the system to a final temperature of 298 K. MD simulations for the in silicogenerated mutants were performed for 10 ns using the specifications described above. From these simulations we obtained plots representing the interaction energy between the O 2 molecule and the protein determined from classical molecular interaction potential calculations.

Crystal Structures of L86A CerHbO 2 and Its Xenon
Derivative-To examine the accessibility of the apolar tunnel, wt CerHbO 2 crystals were equilibrated with high pressures of pure xenon gas. This gas has been used successfully to identify cavities in a variety of Mbs and Hbs (15, 16, 18, 36 -40). Unfortunately, wt CerHbO 2 crystals quickly lose diffraction power after exposure to xenon, even at low pressure and short times. This effect could be due to xenon binding at intermo-lecular crystal contacts, causing disruption of the crystal lattice, or to xenon binding within the apolar channel, expanding the protein and indirectly disrupting intermolecular contacts.
To solve this problem we crystallized the L86A CerHbO 2 mutant, in which constriction near the center of the tunnel is relieved by removal of three side chain carbon atoms at the G12 helical position. When crystals of L86A CerHbO 2 were exposed to high pressures of xenon, diffraction persisted after incubation with ϳ10 atm of xenon, and a full diffraction data set was successfully collected at 2.3 Å resolution. The resulting structure was refined to a final R-factor of 19.4% and Rfree of 26.6% and compared with the independently determined structure of the xenon-free L86A CerHbO 2 mutant. For comparison, a full dataset was collected to 1.6 Å resolution for xenon-free L86A CerHbO 2 , and a model was refined to final R-factor and R-free values of 15.4 and 18.6%, respectively ( Table 1).
The backbone structure of xenon-free L86A CerHbO 2 is virtually identical to that of wt CerHbO 2 , with a r.m.s.d. of 0.15 Å calculated for all 109 C␣ atom pairs. The only significant structural differences between the mutant and wt structures are small rotations of the side chains of Leu-98(H9) and Ile-102(H13). The net result of these changes and the Ala replacement is an increase in the tunnel inner diameter by ϳ1.9 Å. This increase either promotes preferential xenon binding in the channel versus binding to external sites or facilitates internal xenon binding without requiring expansion of the protein structure and further alterations in intermolecular packing.
where F obs and F calc are the observed and calculated structure factor amplitudes, respectively. d Data were produced using the program PROCHECK (26).
The heme cavity of xenon-free L86A CerHbO 2 is identical to that of wt CerHbO 2 ( Table 2). Conservation of the heme distal-site structure in wt CerHbO 2 and the xenon-free L86A mutant is supported by their similar kinetic parameters for diatomic ligand binding (Tables 3-5), which ensures that this mutant is a reliable model for studying ligand diffusion through the apolar matrix tunnel. The structure of the L86A mutant containing bound xenon is also very similar to that of wt CerHbO 2 , with a r.m.s.d of 0.19 Å for all 109 C␣ atom pairs. Inspection of the residual difference electron density after the initial refinement of the xenon-bound mutant indicated the presence of two xenon atoms (Xe1 and Xe2) at refined occupancies of ϳ 65% and temperature factors of 36 and 22 Å 2 , respectively (Fig. 1). The Xe1 site is directly adjacent to Ala-86(G12) and surrounded by the heme ring B vinyl carbon atoms, the terminal side chains of Phe-10(B9) and Ile-52(E15). The Xe2 site is adjacent to the Xe1 site, surrounded by the heme ring B methyl group, Tyr-51(E14), Leu-98(H9), Ala-101(H12), and Ile-102(H13), and is near Ala-55(E18) and the exit to solvent. Together, the xenon atoms fill most of the tunnel located in the protein interior (transparent gray spaces in Fig. 1 In the outermost conformation of Gln-44(E7) (out) in xenon-bound L86A CerHbO 2 , the amide side chain has moved toward the solvent and away from the iron atom by a small ϳ56°rotation about the C␣-C␤ bond, has lost contact with the ligand, and instead is stabilized by a hydrogen bonding network, which links the N⑀ or O⑀ atom to the carbonyl O of Ala-40(E3) and the heme A propionate carboxyl groups through two well defined water molecules ( Table 2; Fig. 2A).
Similar in and out conformations for Gln-44(E7) occur in the structure of wt aquomet CerHb (Fig. 2B). The terminal amide side chain atoms in the in conformation appear to be interacting with the coordinated water molecule, whereas in the out conformation the amide side chain has moved away from the coordinated ligand and again is fixed in position by a hydrogen bonding network involving the carbonyl of Ala-40(E3). In both the in and out conformers of aquomet CerHb, there is an electrostatic interaction between Lys-47(E10) and the heme-7-propionate. In the out conformer of both xenonbound L86A CerHbO 2 and wt aquomet CerHb, the Gln-44(E7) amide side chain still blocks access to the iron atom by filling the outer portion of the channel between the N-terminal region of the E-helix and the heme propionates. This position contrasts with the truly open position of His(E7) in sperm

Distances between polar atoms in the distal pockets of L86A CerHbO 2 , wild-type CerHbO 2 , and wild-type aquomet CerHb
The in and out conformation of the Gln-44(E7) side chain are indicated by the superscript "i" and "o" letters.   8, and 9). The error in kЈ entry is very large because F gem is close to 0.0, poorly defined, and has an error of Ϯ60%. When F gem is Ն0.1, the error in kЈ entry diminishes greatly to ϳϮ20%. FEBRUARY 18, 2011 • VOLUME 286 • NUMBER 7

Ligand Migration in Cerebratulus Hb
whale MbCO when it is protonated at low pH or when Phe-46(CD4) is mutated to Val (41,42). Fig. 3 and Table 3, F gem for both wt and L86A CerHbCO increases almost linearly with increasing xenon pressure, from ϳ0.1 at 0 atm to ϳ0.35 at 15 atm (Table 3). Equilibration with 15 atm of N 2 has no effect on F gem for wt CerHbCO, ruling out a non-specific pressure effect. As observed previously for wt MbO 2 (13), there is no effect of 15 atm of xenon on the fraction of geminate CO rebinding in Mb, which remains close to 0 (expected value is 0.05, Fig. 3B). The linear dependence of F gem on xenon pressure indicates weak binding of the gas to CerHbCO in solution, with a P 50 Ͼ 15 atm. The fractional occupancy estimated from the crystal structure at 10 atm of xenon was ϳ0.65, indicating a somewhat higher affinity under the crystallization conditions. Assuming a lower estimate of 15 atm for the P 50 of both xenon sites, the extent of geminate recombination at full occupancy of sites 1 and 2 is predicted to be ϳ0.7 compared with Յ0.1 when the channel is completely open. Thus, xenon binding in the channel reduces the extent of CO escape at least 7-fold, strongly supporting the view that the apolar channel is the major pathway for ligand escape. It should be noted that the results in Fig. 3 are the first to show a large effect of xenon binding on the total fraction of geminate recombination in a globin.

Effects of Xenon Binding on Geminate CO Recombination-As shown in
Effects of L86A, L86F, and L86W Mutations-We have already examined the effects of increasing the size of the amino acid at the Ala-55(E18) position, which is adjacent to the Xe2 site, and found that Leu, Phe, and Trp substitutions trap CO in the tunnel after laser photolysis, increasing F gem to ϳ0.50, and decreasing the bimolecular rate constant for ligand entry roughly 4 -10-fold (Fig. 4). To examine the Xe1 site, we measured ligand binding to L86A, L86F, and L86W mutants (Figs. 4 and 5; Tables 4 and 5).
The L86F and L86W CerHbCO mutants show progressive increases in geminate recombination, with F gem for the L86W mutant being roughly the same as that for the A55W variant. However, for the 86(G12) mutants, the rates of geminate recombination remain very large, Ն100 s Ϫ1 compared with that for the A55W mutant, which is 10-fold smaller, ϳ10 s Ϫ1 (Fig. 4). The Trp-86(G12) side chain keeps the photodissociated ligand closer to the iron atom, facilitating its rebinding and lowering the entropic barrier to bond reformation. In the A55W mutant, the entire tunnel is available to dissociated ligands because only the exit to solvent is blocked, and as a result, rebinding to the heme iron is slower (2).
The rates of O 2 and CO binding to the 86 mutants are compared with those for wt and A55W CerHb in Table 4, and a summary of NO association and calculated bimolecular rates of ligand entry are presented in Fig. 5 and Table 5. Both the association and dissociation rate constants for O 2 binding decrease 2-3-fold when Leu-86 is replaced with Trp, demonstrating that the indole ring limits both diatomic gas escape and entry into the active site but has little effect on the overall affinity. A similar ϳ3-fold decrease in kЈ NO is observed. Because of the free-radical nature of NO, its reactivity with reduced iron is intrinsically very high, and virtually every NO molecule that enters the active site binds, causing ligand movement into the distal portion of the heme pocket to be the rate-limiting step. Thus, kЈ NO should equal the bimolecular rate of ligand entry, kЈ entry .
The lower reactivities of O 2 and CO cause them to enter and leave the active site many times before bond formation occurs, and for a two-step scheme the overall association rate constant is given by Equation 1 (2), where k bond and k escape are the first order rates for internal iron-ligand bond formation and ligand escape, respectively. Thus, kЈ entry can be estimated from the overall association rate constant and the corresponding fraction of geminate recombination. Unfortunately, geminate rebinding of O 2 to CerHb is very fast, and a significant amount occurs during the excitation pulse, making an accurate estimate of F gem,O 2 difficult (2). Estimates of kЈ entry based on bimolecular association rate constants and F gem values for CO binding are given in Tables 3 and 5. Equilibrating L86A CerHb with 15 atm of xenon causes an Ն2-fold decrease in the value of kЈ entry . Assuming that the two xenon sites are Յ50% occupied, this result suggests that filling the Xe1 and Xe2 pockets would decrease kЈ entry at Ͼ 4-fold. Similarly, the L86W mutation decreases the calculated kЈ entry value ϳ6-fold compared with the computed value for
L86A CerHb. The magnitude of this decrease is similar to that observed for the A55W mutation ( Table 5).

Dynamics of O 2 Entry/Exit for wt CerHb and the Leu-86(G12)
Mutants-To analyze the resistance to ligand migration through the xenon sites, we computed the free energy profile for O 2 movement through the apolar tunnel in wt Cer-HbO 2 (PDB accession code 1kr7 (6)). The free energy profile and positions of the O 2 molecule as it was moved along the tunnel are presented in Fig. 6. After entry into the channel, a small barrier was observed between 8 and 11 Å from the heme-iron atom, with two well-separated local minima (Fig.  6A). This barrier is the result of steric restriction of the tunnel diameter by the Leu-86(G12) side chain in wt CerHb. The O 2 positions in Fig. 6B show that the ligand can pass consecutively through both xenon sites, which tentatively correlate with the observed free energy minima. Much larger free energy barriers were calculated on the two ends of the broad free energy well of the tunnel. A barrier of ϳ5.5 kcal/mol was computed for O 2 movement from the distal pocket into the Xe1 binding site, and then a ϳ2 kcal/mol barrier was estimated for ligand movement out of the Xe2 site, past Ala-55(E18), and into solvent. The 5.5 kcal/mol barrier is due to steric restrictions of the side chains of Phe-10(B9), Tyr-11(B10), and Val-7(B6) (Fig. 6B).
To complement the kinetic results in Tables 4 and 5, we constructed the L86A, L86F, and L86W mutants in silico, performed 10-ns MD simulations, analyzed the tunnel structure for each of them, and displayed the results in Fig. 7. The L86A mutant displays a continuous tunnel with two secondary sites corresponding to the Xe1 and Xe2 positions. In contrast, the L86F and L86W mutants display a marked increase of the barrier between the Xe1 and Xe2 free energy wells shown in Fig. 6A and create spatial barriers that divide the tunnel into separate cavities as shown in Figs. 7, B and C. Blockage of the tunnel by these aromatic side chains is consistent with the 2-5-fold decreases in the rates of ligand binding and release and the increase in F gem,CO observed for these mutants (Fig. 5 and Tables 4 and 5). However, the kinetic results suggest that   (41,42). MD simulations of the free energy barriers for O 2 movement were performed using the wt aquomet CerHb in and out conformers. The in Gln-44(E7) conformation matches that observed in wt Cer-HbO 2 (6). In simulations of the out conformer, the amide side chain of Gln-44(E7) is stabilized by a strong interaction between its O⑀ atom and the N atom of Lys-47(E10), which occurs by an ϳ90°rotation of the Gln-44(E7) side chain about the C␦-C␥ bond relative to its position for the in conformer in the wt aquomet CerHb crystal structure (Fig. 8A). However, the amide side chain still blocks the outer portion of the E7 channel.
To estimate populations and interconversion of the in and the out Gln-44(E7) conformations in wt CerHb, we performed free energy calculations for the transition in both redox states using Umbrella sampling schemes and the distance from the heme-iron atom to the N⑀ atom of Gln-44(E7) as the reaction coordinate. The in form is most stable in the ferrous Cer-HbO 2 state (black line, Fig. 8B), as is observed in the x-ray  crystal structure (6). In the ferric state, the in and out conformations have similar free energy wells, explaining why both conformations are observed in the crystal structure of aquomet CerHb. When free energy profile calculations for O 2 migration from the heme-iron to the solvent were performed using the out Gln-44(E7) conformation, further movement of the Gln-44(E7) side chain away from the heme-iron and out of the E7 channel occurred (Fig. 9B). The N⑀ and O⑀ atoms of the amide side chain are in positions similar to those seen for N⑀ and C⑀ atoms of His-64(E7) in the open conformation of sperm whale MbCO at low pH or in the F46V MbCO mutant (41,42). When Gln-44(E7) is in this truly open conformation in CerHbCO, the calculations suggest only a small, ϳ1 kcal/mol, free energy barrier to ligand entry and exit through the open E7 channel (Fig. 9). These results show that the overall barrier to ligand movement through the E7 gate is governed primarily by the free energy difference between the in and completely open conformation. In the case of wt CerHbO 2 or CerHbCO, the in conformation of Gln-44(E7) is favored by at least a factor of 10, which probably explains why no out conformer is observed in the crystal structure (i.e. Յ10%). An additional barrier occurs for the rotation of the Gln-44(E7) side chain from the out conformer seen in the xenon-bound L86A CerHbO 2 and wt aquomet CerHb structures to the open conformer required in the simulations for O 2 exit through the E7 gate.

DISCUSSION
The Size and Accessibility of the Apolar Channel-The crystal structure of L86A CerHbO 2 equilibrated with ϳ10 atm of xenon demonstrates that the central cavity between the E and H helices is readily accessible to apolar gases (Fig. 1). The exact positions of Xe1 and Xe2 are near the free energy wells calculated for wt CerHbO 2 using dioxygen as a probe (Fig. 6). Xenon binding to both wt and L86A CerHbCO causes a significant increase of F gem (Fig. 3), experimentally demonstrating that occupancy of the apolar cavity blocks ligand escape. Even though xenon binding to animal Hbs and Mbs is well documented, the results for CerHb are the first to show a large effect on the fraction of geminate recombination and that the xenon cavities are on the pathway for ligand entry and escape. In contrast, xenon binding to sperm whale Mb and S. inaequivalvis Hb causes little or no change in F gem for either O 2 or CO rebinding (13,18,19).
The extent of geminate recombination also increases significantly, to ϳ50%, when the size of the Leu-86(G12) side chain is increased (Fig. 4). The L86F and L86W mutations cause marked decreases in both kЈ O 2 and k O 2 with little change in affinity as would be expected if the pathways for ligand entry and exit were blocked ( Table 4). The magnitude of the L86W effect is similar to that observed when exit from the tunnel into the solvent is blocked by the A55W mutation (Fig. 4, Table 4, and Ref. 2). The tunnel mutations also cause large decreases (4 -5-fold) of the rate constant for bimolecular NO binding, which is limited only by movement into the protein (Table 5). Similar decreases are obtained for the bimolecular rate constant for ligand entry calculated using kЈ CO , F gem , and Equation 1 (Table 5).
Pathway for Ligand Binding-As described above, filling the apolar cavity with either xenon atoms or large aromatic amino acids at position 86(G12) markedly inhibits ligand entry and exit and increases both the rate and extent of geminate recombination. The simplest interpretation of these results is shown in Scheme 1 (2, 7). The apolar tunnel containing the xenon binding sites is assumed to be the major pathway for ligand entry and escape. Laser excitation photodissociates the iron-ligand bond, generating an initial inter-mediate with ligand remaining in the distal pocket (state B). From there the ligand either rebinds rapidly or moves into the apolar tunnel. Once inside the tunnel, the ligand can occupy multiple locations in the large space between the distal pocket and the solvent aperture. This large space slows return to the heme-iron and geminate recombination, allowing most of the ligands to escape into solvent.
When xenon atoms or the indole ring of Trp-86(G12) block the initial portion of the tunnel, ligands are trapped in or very near to the distal pocket and rapidly rebind to the heme iron. As a result, large values of k gem and F gem are observed (Fig. 4, Tables 3 and 5). The ligand molecules that move past the bound xenon atoms or the Trp-86(G12) side chain rapidly escape because return to the distal heme pocket from the exterior portion of the tunnel is restricted. When the tunnel exit is blocked by the A55W mutation, F gem also increases. However, in this case, the rate of internal rebinding decreases markedly because the trapped ligand molecules can access the entire apolar tunnel, making return to the heme iron and net escape much slower ( Fig. 4 and Table 5). Scheme 1 is also supported strongly by the calculations shown in Fig. 6. Entry into the tunnel has a free energy barrier of ϳ5.5 kcal/mol due to steric restrictions by Phe-10(B9), Tyr-11(B10), Thr-48(E11), and Val-7(B6) (Scheme 1). The steric barrier between the two xenon sites (near Leu-86) is small (Յ1 kcal/ mol), and the exit to solvent is near Ala-55, with a barrier of ϳ2 kcal/mol. pletely open conformation, in which the amide side chain has rotated even further away from the heme-iron than in the out conformation shown in Fig. 8. to complete opening of the distal histidine or glutamine gate is significant.