J. Phys. Chem. B 2005, 109, 19523-19528
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Determination of Microscopic Rate Constants for CO Binding and Migration in Myoglobin Encapsulated in Silica Gels Silvia Sottini,†,§ Stefania Abbruzzetti,†,§ Cristiano Viappiani,*,†,§ Luca Ronda,§,| and Andrea Mozzarelli§,| Dipartimento di Fisica, UniVersita` degli Studi di Parma, Parco Area delle Scienze 7/A, Dipartimento di Biochimica e Biologia Molecolare, UniVersita` degli Studi di Parma, Parco Area delle Scienze 23/A, 43100 Parma, Italy, and CNR-INFM, Parco Area delle Scienze 7/A, 43100 Parma, Italy ReceiVed: July 25, 2005; In Final Form: August 24, 2005
CO rebinding kinetics after nanosecond photolysis of myoglobin encapsulated in wet silica gels exhibits an enhanced geminate phase that allows the determination of the microscopic rate constants and the activation barriers for distinct ligand docking sites inside the protein matrix. Using a maximum entropy method, we demonstrate that the geminate phase can be well-described by a biphasic lifetime distribution, reflecting rebinding from the distal and proximal sites. Microscopic rates and activation barriers were estimated using a four-state model.
Introduction One of the cases in which the complexity of protein dynamics and function has been thoroughly investigated is that of carbon monoxide (CO) binding to myoglobin (Mb). Despite the impressive number of experimental works that have characterized the binding process under a variety of experimental conditions,1-14 new insights into protein function have recently been obtained. Ligand rebinding kinetics for different Mb mutants and under Xe pressures15-17 suggest that the dissociated ligand may migrate to a hydrophobic cavity, called the Xe1 cavity,18 on the proximal side of the heme, possibly via the Xe4 cavity on the distal side.19 Low-temperature X-ray crystallography studies20-22 have located the dissociated CO in these cavities, whereas time-resolved X-ray crystallography studies have followed, in real time, the ligand rebinding, ligand migration, and associated protein structural changes.23-25 Molecular dynamics simulations mapping the ligand escape pathways also proposed the involvement of the Xe cavities in CO escape.26 The kinetics of CO rebinding is complicated by overlapping structural relaxations, which, in many cases, have been described by a stretched exponential function.6,8,27-29 More recently,30,31 Agmon proposed a model merging ligand migration and structural relaxation. Because the population of the Xe cavities is low at room temperature, the characterization of these sites has been carried out at low temperatures and high glycerol concentrations in order to increase the geminate yield. 17 Recent reports on ligand rebinding kinetics after photolysis of MbCO trehalose glasses at room temperature showed that the geminate phase reflects rebinding from two different sites, likely located in the proximal and distal pockets.32-34 Encapsulation of Mb in wet silica gels has been recently shown to dramatically enhance geminate CO recombination, i.e., rebinding from the heme pocket,35,36 although not as much as * Corresponding author. † Dipartimento di Fisica, Universita ` degli Studi di Parma. § CNR-INFM. | Dipartimento di Biochimica e Biologia Molecolare, Universita ` degli Studi di Parma.
in the case of trehalose glasses, for which no escape of the photodissociated ligand to the solvent phase is observed. The extent of the geminate phase is strongly affected by several parameters, including gelification protocols, temperature, and the presence of cosolutes that modulate the viscosity of the medium, e.g., glycerol.34,36,37 Furthermore, it was shown that distinct tertiary states were trapped, depending on whether Mb was encapsulated in the deoxy or carboxy state.36 The kinetics of CO rebinding to Mb in the gel was satisfactorily described by stretched exponential decays35,37 in which the stretching exponents for the geminate phase were found to be affected by temperature and glycerol concentration. The corresponding parameter for the bimolecular phase was much less sensitive to temperature and glycerol concentration. The description of the kinetics using stretched exponentials is not easily interpreted by a molecular mechanism, and was often justified by overlapping between conformational relaxation and ligand rebinding. In this paper we propose a different approach to the analysis of the kinetics, using the maximum entropy method (MEM), which allows us to retrieve a model-independent estimate of the lifetime distribution generating the observed kinetics. We analyzed the recombination kinetics for gel-embedded MbCO in the presence of glycerol as a function of temperature and glycerol concentration. The resulting lifetime distributions are exploited to retrieve microscopic rate constants and activation parameters for a four-state model that comprises the explicit indication of a docking site acting as a trap for the photodissociated ligand. Materials and Methods Encapsulation of MbCO. A solution containing 10 mM HEPES and 1 mM EDTA (pH 6) was added to an equal volume of tetramethyl orthosilicate (TMOS), and vortexed for 2 min at 4 °C. The mixture was then deoxygenated by bubbling He for 90 min. An equal volume of a solution containing 1% (w/v) Mb (horse heart, Sigma), 10 mM HEPES, 1 mM EDTA, and 30 mM sodium dithionite, at pH 6 and saturated with CO, was added. The resulting mixture was layered on a quartz slide in
10.1021/jp054098l CCC: $30.25 © 2005 American Chemical Society Published on Web 09/24/2005
19524 J. Phys. Chem. B, Vol. 109, No. 41, 2005 an oxygen-free atmosphere. The gelation occurred in 10-20 min at room temperature. When the gel was formed, a solution containing 100 mM HEPES, 1 mM EDTA, and 30 mM sodium dithionite, at pH 7 and saturated with CO, was layered on it. The sample thickness was approximately 1 mm. Bathing solutions containing glycerol concentrations ranging from 10 to 80% (w/w) were employed. We stored the samples at 5 °C for 3 days before performing the kinetic experiments to allow for equilibration of the system with CO in the gas phase. At all stages of the experiments, samples were kept in gastight vials to prevent leakage of O2 into the sample compartment. Absorbance spectra were routinely measured to ensure that the COprotein complex was fully formed.38,39 Photolysis Setup. The sample was held in a 1 × 1 cm2 gastight cuvette mounted in a homemade sample holder. The bathing solution was in equilibrium with a 1 atm CO atmosphere. Temperature was controlled by a Peltier element with a feedback control mounted below the cuvette holder. This allowed us to achieve temperature stability better than 0.1 °C in the investigated temperature range (10-50 °C). Dry gas flowing on the sample holder prevented the condensation of humidity on the cuvette walls. In the flash photolysis setup, photoexcitation was achieved using the second harmonic (532 nm) of a nanosecond Qswitched Nd:YAG laser (Handy Yag HYL-101 Quanta System). Transient absorbance was monitored using a multiline, continuous-wave argon ion laser (2013, Uniphase). The 488 nm line was selected by a Pellin Broca prism and an iris diaphragm. The power on the sample never exceeded 10 mW. Pump and probe beams hit the sample from the same side, at approximately a right angle to the gel surface. The pump beam hit a relatively large sample area (7 mm diameter) containing the spot illuminated by the probe beam (1 mm diameter). Part of the excitation laser output was directed to an energy meter (Laser precision RJ-7620) equipped with a pyroelectric energy probe (Laser precision RJP-735). Experiments were conducted with laser pulse energies of approximately 5 mJ. This energy corresponds to the photolysis of ∼30% of the CO-hemes, resulting in deoxy heme concentrations of about 100 µM at the end of the laser pulse. To minimize undesired photolysis of the samples, caused by the intense probe beam, we used a fast mechanical shutter (Uniblitz). The MbCO samples were exposed for 600 ms, and the repetition rate of exposure cycles was about 1 Hz. The synchronization of the experiment (laser triggering and shutter opening) was performed using homebuilt electronics.40 The probe beam was passed through a pinhole and a monochromator (Jobin Yvon H25) to remove the stray light from the pump laser. The intensity of the transmitted light was measured by a Si avalanche photodiode (Hamamatsu S2382) coupled with a transimpedance amplifier (Avtech AV149). The voltage output was then recorded by a digital sampling oscilloscope (Lecroy LT374). Typically, 100 traces were averaged to yield a transient absorbance signal. Three time scales were used, 1 µs, 100 µs, and 1 ms per division, and 10 000 points were acquired for each trace. Data Analysis After preprocessing (baseline subtraction and pulse energy normalization), the transmitted intensity signal, V(t), was converted to the absorbance change, ∆A(t), with respect to the prepulse value (V0) using the equation ∆A(t) ) log (V0/V(t)). The absorbance-change signals, corresponding to the different
Sottini et al.
Figure 1. Top, temperature dependence of the lifetime distribution for a MbCO solution in 75% glycerol. Bottom, lifetime distributions at 10 °C (black curve) and 50 °C (red curve). τ is expressed in seconds.
time scales, were merged into a single curve covering several time decades. Time courses were subsequently logarithmically down-sampled to obtain 200 data points. ∆A(t) values were scaled to 1 to give the fraction of deoxy species, N(t), as a function of time. The lifetime distributions associated with the observed kinetics were evaluated using the program MemExp (version 2.0), written by P. J. Steinbach.41,42 The program MemExp uses the MEM and either nonlinear least-squares (NLS) or maximumlikelihood (ML) fitting to analyze a general time-dependent signal in terms of distributed and discrete lifetimes. One distribution of effective log lifetimes, g(log(τ)), was extracted from the data. 3
ζi ) D0
∫-∞+∞g(log τ)e-t /τ d(log τ) + ∑(bk - ck)(ti/tmax)k i
k)0
(1)
The polynomial describes the baseline. The g distribution is obtained numerically from the data, and is not restricted to any functional form. MemExp automatically recommends one distributed description of the kinetics as optimal. Baselines were always flat and of very small amplitude. Results and Discussion CO rebinding kinetics after photolysis of a MbCO solution containing 75% glycerol is characterized by an appreciable geminate yield with a remarkable temperature dependence. Figure 1 shows the results of the MEM analysis of the rebinding kinetics carried out between 10 and 50 °C. The peaks at the shortest times are due to geminate rebinding, whereas the single peak at the long time range is due to the bimolecular rebinding from solvent. At temperatures below 20 °C, the lifetime distribution for the geminate phase shows two peaks, suggesting heme binding of CO molecules docked at two distinct sites. This finding is in agreement with previously observed bimodal lifetime distributions in the geminate phase for MbCO solutions
CO Rebinding Kinetics to Myoglobin Gels
J. Phys. Chem. B, Vol. 109, No. 41, 2005 19525
Figure 2. Lifetime distributions for gel-encapsulated MbCO at 10 °C in the absence (black curve) and presence (red curve) of 80% glycerol. τ is expressed in seconds.
containing 79% glycerol. This distribution was interpreted as arising from CO molecules docked at the Xe1 and Xe4 sites.17 We have previously observed that encapsulation in silica gels enhances geminate rebinding with respect to solution.30,31,33 We found that the geminate rebinding kinetics for MbCO gels become biphasic at low temperature and high glycerol concentration (Figure 2). The additional constraints imposed on the protein by glycerol decrease the fraction of CO molecules escaping to solvent. This fraction accounts for ∼50% of the photodissociated ligands at 80% glycerol and 10 °C. The recovered lifetime distribution for the geminate phase shows a progressive splitting in two peaks as the glycerol concentration is increased. The distributions in the absence (black curve) and presence (red curve) of 80% glycerol, at 10 °C, are compared in Figure 2. The single peak at log(τ) ) -6.64 splits into two well-separated peaks at log(τ) ) -6.58 and -5.44. The peak attributed to the bimolecular rebinding shifts from log(τ) ) -3.1 to -2.8. Since the observed geminate lifetime distribution becomes bimodal at glycerol concentrations above ∼50%, the splitting is very likely related to protein dynamics rather than to static heterogeneity. The shoulder in the geminate peak is not consistently found in the distributions and is likely due to numerical artifacts.43 The lifetime distribution was found to be influenced by temperature (Figure 3). As observed for MbCO solutions containing 75% glycerol, the lifetime distribution progressively splits into two peaks as temperature decreases (top panel). The presence of two peaks is evident in the bottom panel of Figure 3, where the distribution at 10 °C (red curve) is compared with the distribution at 50 °C (black curve). A visual inspection of Figures 2 and 3 reveals that the lifetime distribution for the gel-encapsulated sample is much broader than that for the sample in solution (Figure 1). Overall, these data strongly indicate that a description of CO rebinding kinetics with a three-state model is not appropriate under conditions in which the high viscosity leads to the efficient population of slower rebinding sites within the protein matrix. To extract kinetic parameters to be used in a mechanistic model, we have described data by a sum of three Gaussian curves, two for the geminate phase and one for the bimolecular rebinding. Although this is probably a drastic simplification, this method has proven to be useful in previous analyses of similar CO rebinding kinetics to Mb in viscous solutions.17 The peak positions of the three Gaussian bands (τi,app) were used to estimate the average apparent rate constants for the processes (ki ) 1/τi,app). In this analysis, bands arising from shoulders of the peaks (as those in bottom panel of Figure 2) were neglected, because they simply reflect the noise of the experimental rebinding curves and the lack of sampling at short time scales.43
Figure 3. Top, contour plot for g(log(τ)) at 75% glycerol as a function of temperature. Bottom, lifetime distributions at 10 °C (red curve) and 50 °C (black curve) for CO rebinding kinetics to MbCO in silica gels at 75% glycerol.
SCHEME 1: Relevant Chemical Equilibria for CO Rebinding in a Four-State Model
The minimal model necessary in order to include the observed additional kinetics in the geminate phase is a four-state model, described in Scheme 1. We assume that photolysis of bound state A leads to a geminate photoproduct C with CO in the distal pocket. CO can either escape to the solvent, forming state S, or be trapped in a docking site, state B, that is not solvent-accessible.19,30,34 For simplicity, we do not explicitly include any structural relaxation, which is likely hidden in the retrieved lifetime distributions. Suggestions for this model also come from recent timeresolved crystallography data on a Mb mutant, for which the photodissociated ligand was located in Xe4 after photolysis, and whose disappearance from this site was found concomitant with its appearance in the Xe1 pocket.24 It is difficult to distinguish a fine structure in the fast rebinding kinetics. Therefore, we do not treat rebinding separately from the Xe4 site and the rest of the distal pocket. The ligand can diffuse from the distal pocket to the proximal side and be trapped into state B, which may be identified as the Xe1 site but likely contains subpopulations. The differential equations corresponding to Scheme 1 can be solved analytically, and microscopic rates can be obtained, as reported below. The overall rebinding rate kCG for the geminate phase is
Ag1kg12 + Ag2kg22 kCG ) kCB + kCA + kCS ) kCA where
(2)
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kCA ) Ag1kg1 + Ag2kg2
(3)
kBC ) kg1 + kg2 - kCG
(4)
kCB ) kCG - kCA - kCS
(5)
kCS )
AbkCA 1 - Ab
(6)
Ag1, Ag2, and Ab represent the normalized areas corresponding to the two geminate peaks and Ab is the normalized area corresponding to the bimolecular rebinding. kg1 ) 1/τg1,app and kg2 ) 1/τg2,app are the average rates corresponding to the two geminate peaks, whereas kb ) 1/τb,app is the average rate for the bimolecular distribution. The concentrations of CO were obtained using the solubility of CO as a function of temperature and glycerol concentration.37 We assumed that the contribution to Ag1 and Ag2 resulting from CO molecules entering the heme pocket from solution can be neglected. The rebinding rate from solution can be estimated in the steady-state approximation 4 as
kSC[CO] )
kbkBC(kCG - kCB) - kb2kCG -(kCG - kCS)kb + kBCkCA
(7)
In the steady-state approximation, the concentration of the protein in state C is assumed to be independent of time.4 At [CO] ) 1 mM, the relative values of the rate constants justify the steady-state approximation, and show that during ligand rebinding there is a pre-equilibrium with respect to the CO entering and exiting a noncovalent binding site in the protein.4 In the limit of vanishing kBC and kCB, eqs 2-7 reduce to those already reported for a three-state model. 37 Figure 4 shows the Arrhenius plot for the microscopic rates derived from Scheme 1 for CO rebinding kinetics to Mb in silica gel at 80% glycerol as a function of temperature. The population of state B is substantial only at low temperatures (
