The contribution of heme propionate groups to the conformational dynamics associated with CO photodissociation from horse heart myoglobin

Photoacoustic calorimetry and transient absorption spectroscopy were used to study conformational dynamics associated with CO photodissociation from horse heart myoglobin (Mb) reconstituted with either Fe protoporphyrin IX dimethylester (FePPDME), Fe octaethylporphyrin (FeOEP), or with native Fe protoporphyrin IX (FePPIX). The volume and enthalpy changes associated with the Fe-CO bond dissociation and formation of a transient deoxyMb intermediate for the reconstituted Mbs were found to be similar to those determined for native Mb (DeltaV1 = -2.5+/-0.6 ml mol(-1) and DeltaH1 = 8.1+/-3.0 kcal mol(-1)). The replacement of FePPIX by FeOEP significantly alters the conformational dynamics associated with CO release from protein. Ligand escape from FeOEP reconstituted Mb was determined to be roughly a factor of two faster (tau=330 ns) relative to native protein (tau=700 ns) and accompanying reaction volume and enthalpy changes were also found to be smaller (DeltaV2 = 5.4+/-2.5 ml mol(-1) and DeltaH2 = 0.7+/-2.2 kcal mol(-1)) than those for native Mb (DeltaV2 = 14.3+/-0.8 ml mol(-1) and DeltaH2 = 7.8+/-3.5 kcal mol(-1)). On the other hand, volume and enthalpy changes for CO release from FePPIX or FePPDME reconstituted Mb were nearly identical to those of the native protein. These results suggest that the hydrogen bonding network between heme propionate groups and nearby amino acid residues likely play an important role in regulating ligand diffusion through protein matrix. Disruption of this network leads to a partially open conformation of protein with less restricted ligand access to the heme binding pocket.     

Volume and enthalpy profiles of CO binding to Fe(II) tetrakis-(4-sulfonatophenyl)porphyrin.

The focus of this study is to examine volume and enthalpy profiles of ligand binding associated with CO-Fe(II) tetrakis-(4-sulfonato phenyl)-porphyrin (COFe(II)4SP) in aqueous solution. Temperature dependent photothermal beam deflection was employed to probe the overall enthalpy and volume changes associated with CO-photolysis and recombination. The analysis demonstrates that ligand recombination occurs with a pseudo first order rate constant of (2.5+/-0.2)x10(4) s(-1) (at 25 degrees C) with a corresponding volume decrease of 6+/-1 ml/mol. The activation enthalpy (DeltaH(double dagger)) and volume (DeltaV(double dagger)) change for CO recombination (determined from temperature/pressure dependent transient absorption spectroscopy) are found to be 3.9 kcal/mol and 8.2 ml/mol, respectively. These data are consistent with a mechanism in which photolysis yields a five-coordinate high spin (H(2)O)Fe(II)4SP complex that recombines in a single step to form the low spin (CO)(H(2)O)Fe(II)4SP complex. Base elimination, often associated with CO photolysis from hemes, is not observed in this system. The overall volume changes suggest a transition state with significant high spin character. Furthermore, these results demonstrate the utility of coupling photothermal techniques with variable pressure/temperature transient absorption spectroscopy to probe heme reaction dynamics.     

Conformational dynamics associated with photodissociation of CO from dehaloperoxidase studied using photoacoustic calorimetry

Herein, we present photoacoustic calorimetry and transient absorption studies of the dynamics and energetics associated with dissociation of a ligand from Fe(2+) dehaloperoxidase (DHP) from Amphitrite ornata. Our data show that CO photodissociation is associated with an endothermic (DeltaH = 8 +/- 3 kcal mol(-1)) volume expansion (DeltaV = 9.4 +/- 0.6 mL mol(-1)) that occurs within 50 ns upon photodissociation. No additional thermodynamics were detected on slower time scales (up to 10 micros), suggesting that the dissociated ligand rapidly escapes from the heme-binding pocket into the surrounding solvent. Similar volume and enthalpy changes were observed for CO photodissociation in the presence of the substrate, 2,4-dichlorophenol or 4-bromophenol, indicating that either the substrate does not bind in the protein distal cavity at ambient temperature or its presence does not impact the thermodynamic profile associated with ligand dissociation. We attribute a fast ligand exchange between the protein active site and the surrounding solvent to the high flexibility of the distal histidine residue, His55, that provides a direct pathway between the heme-binding pocket and the protein exterior. The dynamics and energetics of conformational changes observed for dissociation of a ligand from DHP differ significantly from those measured previously for photodissociation of CO from the structural homologue myoglobin, suggesting that structural dynamics in DHP are fine-tuned to enhance the peroxidase function of this protein.     

Photothermal studies of CO photodissociation from mixed valence Escherichia coli cytochrome bo3

Here, we report the volume and enthalpy changes accompanying CO photodissociation from the mixed valence form of cytochrome bo3 oxidase from Escherichia coli. The results of photoacoustic calorimetry indicate two kinetic phases with distinct volume and enthalpy changes accompanying CO photodissociation from heme o3 and its transfer to CuB. The first phase occurring on a timescale of <50 ns is characterized by a volume decrease of -1.3+/-0.3 mL mol-1 and enthalpy change of 32+/-1.6 kcal mol-1. Subsequently, a volume increase of 2.9 mL mol-1 with an enthalpy change of -5.3+/-2.5 kcal mol-1 is observed with the lifetime of approximately 250 ns (this phase has not been detected in previous optical studies). These volume and enthalpy changes differ from the volume and enthalpy changes observed for CO dissociation from fully reduced cytochrome bo3 oxidase indicating that the heme o3/CuB active site dynamics are affected by the redox state of heme b.     

A time-resolved photoacoustic calorimetry study of the dynamics of enthalpy and volume changes produced in the photodissociation of carbon monoxide from sperm whale carboxymyoglobin

The dynamics of the enthalpy and volume changes produced in the photodissociation of carbon monoxide from sperm whale myoglobin is investigated by time-resolved photoacoustic calorimetry. The enthalpy and volume changes for the formation of the geminate pair, which occurs within 50 ns of photolysis, are delta H = -2.2 +/- 2.8 kcal/mol and delta V = -10.0 +/- 1.0 mL/mol relative to carboxymyoglobin. The enthalpy and volume changes associated with formation of deoxymyoglobin and solvated carbon monoxide, formed with a half-life of 702 +/- 31 ns at 20 degrees C, are delta H = 14.6 +/- 3.4 kcal/mol and delta V = 5.8 +/- 1.0 mL/mol relative to carboxymyoglobin.     

Time-resolved thermodynamic profiles for CO photolsysis from the mixed valence form of bovine heart cytochrome c oxidase.

Photoacoustic calorimetry has been utilized to probe the thermodynamics accompanying photodissociation of the CO mixed valence form of bovine heart cytochrome c oxidase (COMV CcO). At pH's below 9 photolysis of the COMV CcO results in three kinetic phases with the first phase occurring faster than the time resolution of the instrument (i.e., < approximately 50 ns), a second phase occurring with a lifetime of approximately 100 ns and a third phase occurring with a lifetime of approximately 2 micros. The corresponding volume and enthalpy changes for these processes are: DeltaH1, DeltaV1 = +79 +/- 10 kcal mol(-1), +9 +/- 1 mL mol(-1); DeltaH2, DeltaV2 = -79 +/- 5 kcal mol(-1), -9 +/- 2 mL mol(-1); DeltaH3, DeltaV3 = +54 +/- 7 kcal mol(-1), +8 +/- 1 mL mol(-1). At pH's above 9 only one phase is observed, a prompt phase occurring in < 50 ns. The overall volume change is negligible above pH 9 and the enthalpy change is +29 +/- 5 kcal mol(-1). The data are consistent with the prompt phase being associated with CO-Fe(a3) bond cleavage, CO-CuB+ bond formation, Fe(a3) low-spin to high-spin transition and fast electron transfer (ET) from heme a3 to heme a followed by proton transfer from Glu242 to Arg38 on an approximately 100 ns timescale. The slow phase is likely a combination of CO thermal dissociation from CuB and additional ET between heme a3 to heme a. Interestingly, this phase is not evident above pH 9 suggesting linkage between CO dissociation/ET and the protonation state of a group or groups near the binuclear center.     

Thermodynamics of phosphopeptide binding to the human peptidyl prolyl cis/trans isomerase Pin1

Proteins containing phosphorylated Ser/Thr-Pro motifs play key roles in numerous regulatory processes in the cell. The peptidyl prolyl cis/trans isomerase Pin1 specifically catalyzes the conformational transition of phosphorylated Ser/Thr-Pro motifs. Here we report the direct analysis of the thermodynamic properties of the interaction of the PPIase Pin1 with its substrate-analogue inhibitor Ac-Phe-D-Thr(PO3H2)-Pip-Nal-Gln-NH2 specifically targeted to the PPIase active site based on the combination of isothermal titration calorimetry and studies on inhibition of enzymatic activity of wt Pin1 and active site variants. Determination of the thermodynamic parameters revealed an enthalpically and entropically favored interaction characterized by binding enthalpy deltaH(ITC) of -6.3 +/- 0.1 kcal mol(-1) and a TdeltaS(ITC) of 4.1 +/- 0.1 kcal mol(-1). The resulting dissociation constant KD for binding of the peptidic inhibitor with 1.8 x 10(-8) M resembles the dissociation constant of a Pin1 substrate in the transition state, suggesting a transition state analogue conformation of the bound inhibitor. The strongly decreased affinity of Pin1 for ligand at increasing ionic strength implicates that the potential of bidentate binding of a substrate protein by the PPIase and the WW domain of Pin1 may be required to deploy improved efficiency and specificity of Pin1 under conditions of physiological ionic strength.     

Entropy drives integrin alphaIIbbeta3:echistatin binding--evidence from surface plasmon resonance spectroscopy.

This investigation examined the molecular mechanisms that enable the alphaIIbbeta3 integrin to bind efficiently, tightly, and selectively to echistatin, an RGD disintegrin. We used surface plasmon resonance spectroscopy to measure the rate, extent, and stability of complexes formed between micellar alphaIIbbeta3 and recombinant echistatin (rEch) mutants, immobilized on the surface of a biosensor chip. alphaIIbbeta3 bound readily and tightly to wild-type RGD-rEch and RGDF-rEch but not to RGA-rEch or AGD-rEch, demonstrating that both of those charged moieties contribute to integrin recognition. van't Hoff analysis of the temperature dependence of the RGD-rEch K d data yielded an unfavorable enthalpy change, Delta H degrees = 14 +/- 3 kcal/mol, offset by a favorable entropy term, TDelta S degrees = 23 +/- 3 kcal/mol. Eyring analysis of the temperature dependence of the kinetic parameters yielded Delta H a degrees (++) = 9 +/- 2 kcal/mol and TDelta S a degrees (++) = -4 +/- 2 kcal/mol, indicating that a substantial activation enthalpy barrier and a smaller activation entropy hinder assembly of the encounter complex. Thus, equilibrium thermodynamic data demonstrate that entropy is the dominant factor stabilizing integrin:echistatin binding, while transition-state thermodynamic parameters indicate that the rate of complex formation is enthalpy-limited. When electrostatic contacts are the major source of receptor:ligand stability, theory and experiment indicate that entropy-favorable ion-pair desolvation often provides the driving force for molecular recognition.     

Thermodynamics of carbon monoxide binding to monomeric cytochrome c'

The thermodynamic parameters for carbon binding to monomeric Rhodopseudomonas palustris cytochrome c' are determined. An enthalpy change for CO(aq) binding to the cytochrome is measured directly by titration calorimetry as -6.7 +/- 0.2 kcal/mol of heme, the CO binding equilibrium constant is measured at 35 degrees C as (1.96 +/- 0.05) X 10(5) M-1, and the binding equilibrium constant at 25 degrees C is calculated from the van't Hoff equation as (2.8 +/- 0.1) X 10(5) M-1. Comparison of the results to the known energetics of CO binding to dimeric cytochrome c', where the CO binding site is buried in the protein interior, indicates that the heme binding site on the monomer form is, in contrast, more exposed.     

Activation volumes for intramolecular electron transfer in Escherichia coli cytochrome bo(3)

In this report we describe the activation volumes associated with the heme-heme electron transfer (ET) and CO rebinding to the binuclear center subsequent to photolysis of the CO-mixed-valence derivative of Escherichia coli cytochrome bo(3) (Cbo). The activation volumes associated with the heme-heme ET (k=1.2 x 10(5) s(-1)), and CO rebinding (k=57 s(-1)) are found to be +27.4 ml/mol and -2.6 ml/mol, respectively. The activation volume associated with the rebinding of CO is consistent with previous Cu X-ray absorption studies of Cbo where a structural change was observed at the Cu(B) site (loss of a histidine ligand) due to a change in the redox state of the binuclear center. In addition, the volume of activation for the heme-heme ET was found to be quite distinct from the activation volumes obtained for heme-heme ET in bovine heart Cytochrome c oxidase. Differences in mechanisms/pathways for heme b/heme o(3) and heme a/heme a(3) ET are suggested based on the associated activation volumes and previously obtained Marcus parameters.     

Photoacoustic calorimetric study of the conversion of rhodopsin and isorhodopsin to lumirhodopsin

The enthalpy and volume changes for the conversion of rhodopsin and isorhodopsin to lumirhodopsin have been investigated by time-resolved photoacoustic calorimetry. The conversion of rhodopsin to lumirhodopsin is endothermic by 3.9 +/- 5.9 kcal/mol and is accompanied by an increase in volume of 29.1 +/- 0.8 mL/mol. The lumirhodopsins produced from rhodopsin and isorhodopsin are energetically equivalent.     

Fast events in protein folding: structural volume changes accompanying the early events in the N-->I transition of apomyoglobin induced by ultrafast pH jump

Ultrafast, laser-induced pH jump with time-resolved photoacoustic detection has been used to investigate the early protonation steps leading to the formation of the compact acid intermediate (I) of apomyoglobin (ApoMb). When ApoMb is in its native state (N) at pH 7.0, rapid acidification induced by a laser pulse leads to two parallel protonation processes. One reaction can be attributed to the binding of protons to the imidazole rings of His24 and His119. Reaction with imidazole leads to an unusually large contraction of -82 +/- 3 ml/mol, an enthalpy change of 8 +/- 1 kcal/mol, and an apparent bimolecular rate constant of (0.77 +/- 0.03) x 10(10) M(-1) s(-1). Our experiments evidence a rate-limiting step for this process at high ApoMb concentrations, characterized by a value of (0. 60 +/- 0.07) x 10(6) s(-1). The second protonation reaction at pH 7. 0 can be attributed to neutralization of carboxylate groups and is accompanied by an apparent expansion of 3.4 +/- 0.2 ml/mol, occurring with an apparent bimolecular rate constant of (1.25 +/- 0.02) x 10(11) M(-1) s(-1), and a reaction enthalpy of about 2 kcal/mol. The activation energy for the processes associated with the protonation of His24 and His119 is 16.2 +/- 0.9 kcal/mol, whereas that for the neutralization of carboxylates is 9.2 +/- 0.9 kcal/mol. At pH 4.5 ApoMb is in a partially unfolded state (I) and rapid acidification experiments evidence only the process assigned to carboxylate protonation. The unusually large contraction and the high energetic barrier observed at pH 7.0 for the protonation of the His residues suggests that the formation of the compact acid intermediate involves a rate-limiting step after protonation.     

Thermodynamic analysis of binding between mouse major urinary protein-I and the pheromone 2-sec-butyl-4,5-dihydrothiazole

The mouse pheromone 2-sec-butyl-4,5-dihydrothiazole (SBT) binds to an occluded, nonpolar cavity in the mouse major urinary protein-I (MUP-I). The thermodynamics of this interaction have been characterized using isothermal titration calorimetry (ITC). MUP-I-SBT binding is accompanied by a large favorable enthalpy change (DeltaH = -11.2 kcal/mol at 25 degrees C), an unfavorable entropy change (-TDeltaS = 2.8 kcal/mol at 25 degrees C), and a negative heat capacity change [DeltaC(p)() = -165 cal/(mol K)]. Thermodynamic analysis of binding between MUP-I and several 2-alkyl-4,5-dihydrothiazole ligands indicated that the alkyl chain contributes more favorably to the enthalpy and less favorably to the entropy of binding than would be expected on the basis of the hydrophobic desolvation of short-chain alcohols. However, solvent transfer experiments indicated that desolvation of SBT is accompanied by a net unfavorable change in enthalpy (DeltaH = +1.0 kcal/mol) and favorable change in entropy (-TDeltaS = -1.8 kcal/mol). These results are discussed in terms of the possible physical origins of the binding thermodynamics, including (1) hydrophobic desolvation of both the protein and the ligand, (2) formation of a buried water-mediated hydrogen bond network between the protein and ligand, (3) formation of strong van der Waals interactions, and (4) changes in the structure, dynamics, and/or hydration of the protein upon binding.     

Dynamics of carbon monoxide recombination to fully reduced cytochrome c oxidase in plant mitochondria after low-temperature flash photolysis.

Rebinding of CO to reduced cytochrome c oxidase in plant mitochondria has been monitored optically at 590-630 nm after flash photolysis at low temperature from 160 to 200 K. (1) Under 100%-CO saturation, CO rebinding exhibits a four-step mechanism. The thermodynamic parameters of the first phase have been determined; its activation energy, Ea1, is 38.9 kJ.mol-1 and its enthalpy, delta H+/-1, and entropy, delta S+/-1, of activation are respectively 37.5 kJ.mol-1 and -75.8J.mol-1.K-1. (2) When the CO concentration is decreased to 0.2%, rebinding still occurs according to a four-step mechanism. The rate constant of the first phase is CO-concentration-independent. Under non-saturating conditions there is only one CO molecule per occupied site. The rebinding mechanism does not require additional CO molecules to be present in the haem pocket. (3) Dual-wavelength scanning experiments failed to detect optical forms correlated with the resolved phases. (4) Results are discussed with respect to previous work related to CO rebinding to mammalian cytochrome c oxidase and myoglobin.     

Structure-based thermodynamic analysis of a coupled metal binding-protein folding reaction involving a zinc finger peptide

The thermodynamics of metal binding by the prototypical Cys(2)His(2) zinc finger peptide CP-1 has been examined through the use of isothermal titration calorimetry. In cholamine buffer at pH 7.0, the binding of zinc(II) to CP-1 shows an enthalpy change of DeltaH degrees (obs) = -33.7 +/- 0.8 kcal/mol. Between one and two protons appear to be released accompanying the metal binding process. The heat of protonation of the cholamine buffer used is quite large (-11.5 kcal/mol), indicating that a portion of the observed metal binding enthalpy is due to buffer protonation. Structure-based thermodynamic analysis including the effect of water release from zinc(II) appears to account for the entropy associated with the coupled metal binding-protein folding process semiquantitatively. The strongest driving force for the reaction is the enthalpy associated with the four bonds from zinc(II) to cysteinate and histidine residues, compared with the bonds from zinc(II) to water. The binding of cobalt(II) to CP-1 is less enthalpically driven than the binding of zinc(II) by -7.6 kcal/mol. This value is approximately equal to, but slightly larger than, the expectation based on considerations of ligand field stabilization energy.     

Temperature dependence of the dissociation rate constants for the nonactivated (molybdate-stabilized) and activated progesterone receptor-hormone complexes from the chick oviduct

Both the nonactivated and activated forms of the chick oviduct cytosol progesterone receptor-hormone complexes displayed first-order dissociation kinetics at temperatures between 0 and 25 degrees C. The rate constant was always 2-3-times greater for the nonactivated than for the activated complex. The thermodynamic parameters calculated from the Eyring plot for the nonactivated and activated forms, respectively, were: delta H+ = 28.6 +/- 0.2 and 29.9 +/- 1.5 kcal/mol; -T delta S+ = 7.4 +/- 0.6 and 7.7 +/- 1.6 kcal/mol; and delta G+ = 21.3 +/- 0.5 and 22.1 +/- 0.1 kcal/mol. These values suggest that activation results in an increase in enthalpy of the ligand-receptor interaction, thus stabilizing the complex. The dissociation rate constants for the native complex obtained by two different experimental approaches, namely, isotope dilution ('chase') and dissociation against charcoal, indicated the absence of cooperativity in the receptor-ligand binding.     

Activation Parameters for the Spontaneous and Pressure-Induced Phases of the Dissociation of Single-Ring GroEL (SR1) Chaperonin

We investigated the dissociation of single-ring heptameric GroEL (SR1) by high hydrostatic pressure in the range 0.5-3.0 kbar. The kinetics were studied as a function of temperature in the range 15-35 degrees C. The dissociation processes at each pressure and temperature showed biphasic behavior. The slower rate (k1,obs) was confirmed to be the self-dissociation of SR1 at any specific temperature at atmospheric pressure. This dissociation was pressure independent and followed concentration-dependent first-order kinetics. The self-dissociation rates followed normal Eyring plots (In k1,obs/T vs. 1/T) from which the free energy of activation (deltaG++ = 22 +/- 0.3 kcal mol(-1)), enthalpy of activation (deltaH++ = 18 +/- 0.5 kcal mol(-1)), and entropy of activation (deltaS++ = -15 +/- 1 kcal mol(-1)) were evaluated. The effect of pressure on the dissociation rates resulted in nonlinear behavior (ln k2,obs vs. pressure) at all the temperatures studied indicating that the activation volumes were pressure dependent. Activation volumes at zero pressure (V++o) and compressibility factors (beta++) for the dissociation rates at the specific temperatures were calculated. This is the first systematic study where the self-dissociation of an oligomeric chaperonin as well as its activation parameters are reported.     

Reciprocal cooperative effects of multiple ligand binding to pyruvate kinase

The formation of multiple ligand complexes with muscle pyruvate kinase was measured in terms of dissociation constants and the standard free energies of formation were calculated. The binding of Mn2+ to the enzyme (KA = 55 +/- 5 X 10(-6) M; deltaF degrees = -5.75 +/- 0.05 kcal/mol) and to the enzyme saturated with phosphoenolpyruvate (conditional free energy) KA' = 0.8 +/- 0.4 X 10(-6) M; deltaF degrees = -8.22 +/- 0.34 kcal/mol) has been measured under identical conditions giving a free energy of coupling, delta(deltaF degrees) = -2.47 +/- 0.34 kcal/mol. Such a large negative free energy of coupling is diagnostic of a strong positively cooperative effect in ligand binding. The binding of the substrate phosphoenolpyruvate to free enzyme and the enzyme-Mn2+ complex was, by necessity, measured by different methods. The free energy of phosphoenolpyruvate binding to free enzyme (KS = 1.58 +/- 0.10 X 10(-4)M; deltaF degrees = -5.13 +/- 0.04 kcal/mol) and to the enzyme-Mn2+ complex (K3 = 0.75 +/- 0.10 X 10(-6)M; deltaF degrees = -8.26 +/- 0.07 kcal/mol) also gives a large negative free energy of coupling, delta(deltaF degrees) = -3.16 +/- 0.08 kcal/mol. Such a large negative value confirms reciprocal binding effects between the divalent cation and the substrate phosphoenolpyruvate. The binding of Mn2+ to the enzyme-ADP complex was also investigated and a free energy of coupling, delta(deltaF degrees) = -0.08 +/- 0.08 kcal/mol, was measured, indicative of little or no cooperativity in binding. The free energy of coupling with Mn2+ and pyruvate was measured as -1.52 +/- 0.14 kcal/mol, showing a significant amount of cooperativity in ligand binding but a substantially smaller effect than that observed for phosphoenolpyruvate binding. The magnitude of the coupling free energy may be related to the role of the divalent cation in the formation of the enzyme-substrate complexes. In the absence of the activating monovalent cation, the coupling free energies for phosphoenolpyruvate and pyruvate binding decrease by 40-60% and 25%, respectively, substantiating a role for the monovalent cation in the formation of enzyme-substrate complexes with phosphoenolpyruvate and with pyruvate.     

Unusual pressure effects on ligand rebinding to the human myoglobin Leucine 29 mutants

Using high pressure flash photolysis, we revealed that the side chain of Leu(29) controls the reaction volume of the ligand migration process in myoglobin, which is the primary factor for the unusual activation volume of ligand binding in some Leu(29) mutants. As we previously reported (Adachi, S., Sunohara, N., Ishimori, K., and Morishima, I. (1992) J. Biol. Chem. 267, 12614-12621), CO bimolecular rebinding in the L29A mutant was unexpectedly decelerated by pressurization, suggesting that the rate-determining step is switched to ligand migration. However, very slow CO bimolecular rebinding of the mutants implies that bond formation is still the rate-determining step. To gain further insights into effects of the side chain on ligand binding, we prepared some new Leu(29) mutants to measure the CO and O(2) rebinding reaction rates under high hydrostatic pressure. CO bimolecular rebinding in the mutants bearing Gly or Ser at position 29 was also decelerated upon pressurization, resulting in apparent positive activation volumes (DeltaV), as observed for O(2) binding. Based on the three-state model, we concluded that the increased space available to ligands in these mutants enhances the volume difference between the geminate and deoxy states (DeltaV(32)), which shifts the apparent activation volume to the positive side, and that the apparent positive activation volume is not due to contribution of the ligand migration process to the rate-determining step.