(stretched, P- â, ) that may be related to nonequilibrium relaxation of the distal pocket. A two-pulse photolysis experiment, which probes a kinetically selected ...
VOLUME
P H YSICAL REV I E%
68, NUMBER 3
LETTERS
20 JAWUARV 1992
Relaxation Dynamics of Myoglobin in Solution
%. D. Tian, J. T. Sage, Departntent
of Physics,
V. Srajer, and P. M. Champion
IVortheastern Unit ersity, Boston. Massachusetts (Received 2 July l99l)
02I I5
The geminate rebinding kinetics of MbCO in solution at high temperature (260-300 K) shows nonex—, ) relaxation of the distal that may be related to nonequilibrium ponential behavior (stretched, pocket. A two-pulse photolysis experiment, which probes a kinetically selected subpopulation, demonstrates that the nonexponential behavior arises from a fluctuationally averaged system and also reveals slow interconversion times for large-scale protein motions. Measurements as a function of temperature lead to a direct determination of the Arrhenius barrier at the heme (18+' 2 kJ/mole).
P-
PACS numbers:
87. 15.He, 36.20. Ey, 64.70.Pf, 82. 20. Mj
Myoglobin (Mb) reversibly binds molecular oxygen in muscle cells and is one of the simplest of the heme proteins. The heme group is embedded in the globular protein matrix and covalently linked to an amino acid, the proximal histidine. In the deoxygenated state, the ferrous iron atom is high spin (S=2) and is displaced by ao-0. 45 A from the berne plane. A major electronic state change takes place when a diatomic ligand binds to the iron atom and the d electrons become paired in a In addition to the electronic low-spin configuration. nuclear reorganization energy changes, a significant (-. Itat& 10 kJ/mole) is associated with moving the iron into the heme plane [1 (a)]. The optical properties of the berne [1 (b)] provide a convenient probe of these structural changes and can be used to monitor the dynamics, subsequent to pulsed laser photolysis, as the ligand either rebinds to the heme or escapes to the solvent through the protein matrix [2]. The tightly packed x-ray structure suggests that dynamical fluctuations of the protein conformation must play a significant role in the process of ligand migration between the heme pocket and the solution [3(a)]. lt has also been suggested that protein Auctuations can lead to modulations of the heme geometry that affect its reactivity [1(a)]. Experiments that probe the existence of functionally different protein conformations have been carried out at low temperature [2] where the Auctuation time scales are drastically reduced or frozen out (quenched disorder). The ligand remains trapped in the heme pocket at low temperature (T 180 K) and nonexponential geminate rebinding to the heme is observed [2]. Other experiments have revealed a glasslike behavior of the protein with a Tg-l85 K, ~here protein motransition temperature, tions begin to unquench and ligand escape to the solvent occurs [4, 5]. Below this temperature the photolysis of the diatomic ligand leads to a low-temperature photoproduct state (Mb*), where partial relaxation of the heme moves out-of-plane position (ao the iron to an intermediate --0.2 A) [5(b)]. The nonexponential rebinding kinetics [2] of Mb* have been linked with structural disorder (cr„— O. I A) and spectroscopic properties of the heme group [1,5-7]. A schematic overvie~ of the reaction sequence for CO
—
(
photolysis as
(y), escape, and rebinding to the heme
~::
is given
T)185K
MbCO
~
(Mb', CO)
Mb
+
CO,
where MbCO is the bound state, (Mb*, CO) is the lowtemperature photoproduct state with CO trapped in the heme pocket, and Mb+CO is the state where the ligand has reached the solution and both the protein and heme The dashed lines in the have fully relaxed to equilibrium. schematic diagram represent the possibility of additional states on the kinetic pathway. For example, at 293 K we expect the relatively rapid [3(b)] ( + ps) formation of a species, (Mb, CO), with a relaxed heme but with CO still trapped in the pocket of the unrelaxed protein. An early model [7] for ligand binding in Mb utilizes systwo coordinates to describe the protein-heme-ligand tem and, when the system is quenched below Tg no energetically significant heme relaxation is allowed subseThis model simulates the quent to ligand photolysis. low-temperature kinetics, but it forces all of the proteinheme relaxation to take place above Tg and predicts a significantly larger Arrhenius barrier at the heme (E.,t model [1 (a), 33 k J/mole) than a three-coordinate 5(b)] that allows partial relaxation of the berne in Mb*
—
(F,,
—
16 kJ/mole). t Above Tg, the rebinding barrier can be time dependent ao) and its and the relaxation of the heme (e.g. , ao occur on time fluctuations structural protein-induced scales that depend on temperature [6,7]. At 293 K, heme relaxation takes place on a ps time scale [3(b),6], but it is not clear whether the heme structural fluctuations and the protein relaxation time scales are rapid compared t(~ the CO rebinding and escape rates ( 10' s '), or are slo~ed by the complex and interconnected nature of' the protein. These issues, and the measurement of the Arrhenius barrier height at the heme, are the motivations for the present study. The experiment utilizes Nd-doped yttrium-aluminumgarnet laser pulses (10 ns, 532 nm) to photolyze liquid samples of MbCO or Mb02 ( 10 It M) in either aqueous (0. 1M KPi) mixtures. The kinetic or glycerol-buffer response is monitored by probing the strong heme absor-
1992 The American Physical Society
—
—
VOLUME
PHYSICAL REVIEW LETTERS
68, NUMBER 3
bance at 423 nm, which is a characteristic of MbCO, with an attenuated (20 pW) cw dye laser. The sample I K) using a circulating temperature is controlled bath arrangement, and sealed optical cuvettes maintain diatomic ligand pressure at 1 atm. The optical signal current) is averaged at 10 Hz, with a (photomultiplier 350-MHz digital oscilloscope, and converted into the normalized surviving population of Mb molecules, N(t), that have not yet rebound ligand. Nonlinearities in the detection circuitry (e.g. , photomultiplier tube saturation) must be reduced below the 1% level and this, rather than ligand photolysis, is what limits the probe power. Dibeam chroic filters and mirrors and a counterpropagating geometry ensure optical homogeneity and overlap in the pulse and probe light paths. Care is taken to adjust the photolyzing pulse energy and beam diameters so that the complete interaction volume is photolyzed (&98%). Polarization scramblers are used to remove the linear dichroism contribution to the signal that arises from the relatively slow (& 100 ns) rotational difl'usion of the protein in glycerol solutions. In the double-pulse experiments, an optically (dt 100 ns) or electronically (ht & 100 ns) delayed laser pulse is adjusted to photolyze the portion of the sample that has rebound ligand during the delay time. The kinetic response with the second pulse blocked is subtracted from the double-pulse experiment to yield the response of the rebound fraction. The single-pulse, double-pulse, and the difl'erence kinetics (shifted by ht and normalized) are then displayed for comparison. In Fig. 1 we display the kinetic response of MbCO monitored at 423 nm and at the isosbestic point (-430 nm) in both aqueous buffer and 75% glycerol mixtures. At 293 K, the aqueous MbCO data agree well with the early pioneering report of Henry et al. [8]. However, the geminate rebinding at short times is distinctly nonexponential for both MbCO and MbOz (not shown). In aqueous solution at 293 K, the geminate phase can be fitted adequately with either a single stretched exponential or with a biexponential form. At 273 K the biexponential is no longer adequate and a stretched exponential (P=0.5~0. 1) leads to clearly superior fits. In 75% glycerol solution a second geminate phase is clearly evident below 285 K and the data are fitted with the following function:
(~
(
N(1) = l ie
'
+I qe
'
+1,
e.
%'hen the geminate yield is small, the time course of the geminate phase is usually thought [8] to reflect ligand escape from the pocket rather than rebinding. However, it has recently been suggested [6] that an inhomogeneous distribution of heme rebinding barriers is maintained up to 290 K and contributes to the geminate decay. In general, the nonexponential geminate character can result from two primary possibilities: (i) The protein fluctuation time scales at these temperatures could be relatively
20 JANUARY 1992
1.0:
1.0: .98
. 50
0.8— 0.6—
0.4— . 94
0.2—
. 92
0.0
1.0
I
I
I
IIIIIII
I I
IIIIIJ
I
I
IIIIIII
I
I
IIIIIII
I
I
IIIIII'
I
I
jlllU
I
—4% . 95— . 90—
—2%
. 85
. 80
10
,
—3%
50
rol
—1% 10
10
0%
10
10
10
FIG. 1. The kinetic response of MbCO in aqueous and 75% glycerol solutions. The solid lines are least-squares fits using Eq. (1). P is set to 0.5 in (d) but is free to vary in (a), (b), and (c). The other parameters for (a), (b), and (c) respectively are li (3.21,7.05, 28. 2)%, kl =(9.03, 1.41, 2.74)x106 s ', Iq (0,0, 13.6)%, kq-(0, 0, 4.48) x10 s ', and k, (6.76, 3.01, 3.04)&10' s '. The % absorbance change at the isosbestic point near 430 nm is measured at reduced CO concentration and plotted in (d). The fits in (d) lead to li =88.5%, ki 4.45& 10 s ', Ip 11.5%, and k~ 1.42~ 10 s slow, leading to an ensemble with a quasistatic distribution of rebinding and escape rates (inhomogeneous ensemble), or (ii) the protein fluctuations may be fast enough for averaging, but the relaxation toward equilibrium of key regions (e.g. , the distal pocket or heme) within each protein may occur on a time scale that affects the ligand binding and escape rates (homogeneous ensemble). In considering these possibilities, we should keep in mind that proteins are complex systems and that some regions (involving small groups of atoms and small length scales) might fluctuate rapidly, while other regions (involving larger groups of atoms and larger length scales) might undergo relatively slow interconversions. Double-pulse experiments, which probe only the fraction of the ensemble that has rebound CO after a time h, t, should distinguish between these possibilities. If ht is less than the fluctuation (averaging) time scale as in (i), the experiment probes only those proteins having large rebinding rates and the geminate phase of the rebound fraction should have an increased amplitude and rates that are faster than Ar . In (ii), the averaging is com-
409
VOLUME
PH
68, NUMBER 3
YSICAL REVIEW LETTERS
piete and, so long as the full distribution of initial conditions develops within ht, the geminate yield and stretched exponential response of the rebound fraction should remain fixed. Such experiments with delays as short as 80 ns are shown in Fig. 2. The increased geminate amplitudes associated with the kinetics of the rebound fraction reveal characterthat a slowly interconverting subpopulation, ized by more rapid geminate rebinding, is being selected The more rapidly rebindin the double-pulse experiment. ing Ao state [9(a)], which has an increased population at low pH [10], is a likely candidate for this role (see below). More importantly, the geminate decay of the kinetically selected subpopulation extends well beyond the 80-ns delay time. In fact, the rescaled geminate decay of this subpopulation is identical to that of the full ensemble error [Fig. 2(d)]. Thus, the within the experimental nonexponential decay at T& 260 K cannot be attributed to possibility (i) or to an incomplete fluctuational averaging of the heme rebinding barrier distribution as previously suggested [6]. Evidently, as in (ii) the stretched exresults priponential time course at high temperature marily from ligand escape that is coupled to slow (~ 100 ns) components of protein relaxation. Possibility (ii) is also suggested by absorbance changes 1.0
0.8 0.6
O, Z ~
I
0.0
I
10
10
10
I
I I I I I I I I II
I I
I
I
I I
I I
II
I
10
I
I I I I I II
$
I
I I
I
I
I I I I II
I
I
I
I
I 1tl I
i
I
I
I
I
I III
10
10
1.0
(a)— ( —l )
O. B
MbCO
264K
0.6
' pH7. 0 . pH63
t
o
pH4. 9
o. o 10
10
10
10
10
()
—6
20 JANUARY 1992
at the isosbestic point [11] [Fig. 1(d)], which are consistent with a redshift ( I nm) of the deoxy Soret band at short times [12]. This shift is similar to that observed [5(b)] between the "closed" (A ~) and "open" (Ao) states [9(a), 10] of MbCO and may reflect alterations in the heme environment as the protein structure evolves toward the unbound conformation. The enhanced geminate yield of the subpopulat ion selected in the double-pulse experiment arises from an increased relative population of the more rapidly rebinding minority Ao state [9(a)]. As the delay time At is extended, the ensemble is allowed more time to average the Ao and A] states. For glycerol solutions at 293 K and pH 5.0, we find that the kinetics of the rebound fraction overlay the kinetics of the full ensemble when hI is 50 ps [Fig. 2(b)]. We suggest that this time scale is a direct measure of the rate for averaging the large-scale protein interconversions associated with transitions between the open (Ao) and closed (A~) conformations of the distal pocket [10]. The rebinding kinetics at lower pH [Fig. 2(c)l show the effect of increasing the Ao population and are consistent with an enhanced Ao fraction in the double-pulse experiment [solid dots in 2(a) and 2(b)]. Note that only the geminate amplitudes are affected as the pH is varied and that the nonexponential geminate decay kinetics, when rescaled, are not significantly altered by the fraction of the Ao state present in the ensemble. Since the rescaled geminate decay is the same for both the A[) and A ] states at these temperatures, an inhomogeneous distribution of these states cannot lead to the nonexponential behavior. The relative increase of the geminate amplitudes in the double-pulse experiments can be quantitatively analyzed as a function of pH using the known [10] populations of Ao and A]. This leads to a rebinding rate for Ao that is times larger than for A] at 264 K and is consistent with the view that the geminate amplitude probes the ligand rebinding while the time course of the decay probes the ligand escape. To be more specific about ligand escape, we consider the time evolution associated with the rearrangement of the distal pocket as the ligand moves away from the heme and the protein relaxes toward the unbound conformation. One approach, used to treat diffusive and/or hierarchically constrained complex systems [13], suggests that the rate of escape from the metastable state 8 =(Mb, CO) can be written as ' /3 —]
—
-3
~BF
&0&~ &
~BF
&0 s
FIG. 2. Single- and double-pulse
kinetics and their difI'erence, shifted by Ar and rescaled [solid points (a) and (b)]. All samples are in 75% glycerol. The changes in geminate amplitude as a function of pH (c). The rescaled geminate decay (d) is independent of pH (open symbols) or kinetic selection (solid points).
410
&max
~
(2)
is-
which leads to the stretched exponential behavior described by Eq. (I) with 1~k ~ka~, so long as Pl;kaz ro fixed to a value much less than unity and ~ „.„+k~ '. The final states F correspond to the bound state (F=A) or a state where the ligand has escaped from the pocket and the protein has relaxed (F=C). The quantity k8. ~
&
VOLUME
PHYSICAL REVIEW LETTERS
68, NUMBER 3
] 0
I
I
I
I
I
Ills
I
l
I
Ills
I
I
I
I
IIII[
I
I
I
I
I
Ills
I
I
I
I
0.8
0.6
14.6
14.4 14.2
0.4
140
&
13.8
0.2
13.6
o.o 1O-9
10-~
10
1O-6
1O-5
1O-4
10 ~
10
t. (s)
FIG. 3. The temperature dependence of the kinetic response. The solid curves are fits using Eq. (I) with P=0. 5. Inset: The Arrhenius
plot of
I]k] =ka.~.
corresponds to the rate of CO rebinding to the relaxed heme, prior to distal-pocket relaxation, and can be approximated by the product I]k even if a fourth state is added [5(a)] to account for the three phases observed in ~
Fig.
l
(c).
In Fig. 3 we display the kinetic response as a function of temperature. The inset shows an Arrhenius plot of the heme rebinding rate (ktt~-I~k~) that leads to Eq =18 2 k 3/mole. This result agrees with predictions kJ/mole) based on optical and kinetic holeburning studies [5(b),6]. The high-temperature intercept of the Arrhenius plot gives ko =3.2 & 10 s ', which is close to the prefactor used to fit the low-temperature ki-
+ (-l6-20
netics [I (a), 2]. In summary, we have found nonexponential ligand es' —. ) at relatively cape kinetics for Mb high temperatures, even in aqueous solution. The double-pulse experiments indicate the presence of multiple protein fluctuation time scales that rapidly average localized regions of the system, such as the iron out-of-plane displacernent [l (a)l, while the averaging of larger-scale protein conformations (e.g. , the open and closed states of the distal pocket) takes much longer. These experiments also demonstrate that the nonexponential kinetics observed above 260 K are homogeneous in nature and suggest that protein relaxation takes place on the same time scale as ligand escape ( IOO ns). Within this scenario, the rates
(P-
—
20 JANUARY 1992
for rebinding to the heme at 260-300 K lead to values for E~ and ko that are in good agreement with extrapolations of the low-temperature kinetics [2,61 and the predictions of a simple model [I (a), 5(b)]. Overall, these conclusions are consistent with the concept that tiers or hierarchies govern the underlying physics of biomolecules [9(b)] although they differ from a recent analysis [6] that uses a single fluctuation time scale and attributes the nonexponential rebinding at high temperature to a static distribution of heme rebinding barriers. This work is supported by NSF Grant No. 90-16860 and NIH Grant No. AM-35090.
[I] (a)
V. Srajer, L. Reinisch, and P. M. Champion, J. Am. Chem. Soc. Il0, 6656 (1988); (b) V. Srajer, K. Schomacker, and P. M. Champion, Phys. Rev. Lett. 57, 1267
(1986). [2] R. H. Austin et al. , Biochemistry l4, 5355 (1975). [3] (a) D. A. Case and M. Karplus, J. Mol. Biol. l32, 343 (1979); (b) J. Petrich et al. , Biochemistry 30, 3975
(1991). [4] I. E. T. Iben et al. , Phys. Rev. Lett. 62, 1916 (1989); W. Doster et al. , Phys. Rev. Lett. 65, 1080 (1990). [5] (a) V. Srajer, L. Reinisch, and P. M. Champion, Biochemistry 30, 4886 (1991); (b) V. Srajer and P. M. Champion, Biochemistry 30, 7390 (1991). [6] P. J. Steinbach et al. , Biochemistry 30, 3988 (1991). [7] N. Agmon and J. J. Hopfield, J. Chem. Phys. 79, 2042 (1983); N. Agmon, Biochemistry 27, 3507 (1988). [81 E. Henry et al. , J. Mol. Biol. l66, 443 (1983). [9] (a) A. Ansari et al. , Biophys. Chem. 26, 337 (1987); (b) A. Ansari et al. , Proc. Natl. Acad. Sci. U. S.A. 82, 5000
(1985). [10] D. Morikis et al. , Biochemistry 2$, 4791 (1989); L.
Zhu
et al. , J. Mol. Biol. (to be published). [I I] The isosbestic point is found by varying the probe wavelength to minimize the absorbance change (ttA) near the onset of the bimolecular phase where the deoxy Mb population is significant and hA is not trivially zero. Kinetic hole burning due to an inhomogeneous deoxy Soret band should lead to isosbestic changes with hA =0 at 10 ns, if berne relaxation is fast [3(b)] and its fluctuations are
—
slow
[6].
[12] (a) A. Ansari et al. , Biophys. J. 59, 286a (1991); (b) D. Lumbright et al. , Biophys. J. 59, 286a (1991). [13] R. G. Palmer et al. , Phys. Rev. Lett. 53, 958 (1984); J. Klafter and M. F. Shlesinger, Proc. Natl. Acad. Sci. U. S.A. $3, 848 (1986); K. L. Ngai el al. , J. Chem. Phys. $6, 4768 (1987); J. Non-Cryst. Solids l3l-l33 (1991), edited by K. L. Ngai and G. B. Wright.
411
