Stability Diagram and Unfolding of a Modified Cytochrome
c
: WhatHappens in the Transformation Regime?
Harald Lesch,* Hans Stadlbauer,* Josef Friedrich,* and Jane M. Vanderkooi
†
*Technische Universita¨t Mu¨nchen, Lehrstuhl fu¨r Physik Weihenstephan, 85350 Freising, Germany and
†
Department of Biochemistry andBiophysics, School of Medicine, The University of Pennsylvania, Philadelphia, Pennsylvania 19104 USA
ABSTRACT We determined the stability diagram of a modified cytochrome
c
protein in a glycerol water mixture bymeasuring the first and the second moment of the fluorescence from the chromophore as a function of temperature andpressure. Temperature and pressure were varied between 273 and 363 K and 0.0001 and 1 GPa, respectively. The shift ofthe fluorescence maximum showed a characteristic sigmoidlike pattern from which information on the microscopic processes during unfolding is obtained: as the transformation regime is entered, the fluorescence shows a significant blue shift.The conclusion is that water molecules get into contact with the chromophore. They lead to strong electrostatic contributionsin the solvent shift, which counteract the red shifting dispersion interactions. Assuming that there are just two relevant statesthat determine the stability diagram, the complete set of thermodynamic parameters can be determined from the data.However, under certain pressure–temperature conditions the fluorescence pattern is more complicated, pointing towardreentrant transitions and, possibly, to consecutive steps in the unfolding process.
INTRODUCTION
The folding of proteins into a rather welldefined stablestructure is one of the most important biomolecular processes. Its details, especially the respective kinetic aspects,are still not very well understood. However, also as to thethermodynamic aspects, there are more questions than answers. Because folding and unfolding under pressure andtemperature variations are, for many proteins, especially forsmall ones, reversible processes, the unfolding process mayshed light on what happens during the folding process. Thepresent paper is aimed at unraveling some of the problemsconnected with the unfolding process of a modified cytochrome
c
(Cc) protein in a glycerol water mixture underquasistatic pressure and temperature variations.An important aspect in this context concerns the socalledstability diagram of proteins, whose contour line separatesthe native state
N
from the denatured state
D
(Hawley,1971; Zipp and Kauzmann, 1973; Heremans and Smeller,1998). The shape of the diagram is ellipselike, as firstshown by Hawley. Strictly speaking, an elliptic shape isonly obtained within the frame of a twostate model(
N
,
D
) and under the assumption that the second derivatives of the respective free enthalpies
G
are pressure andtemperatureindependent quantities. This latter restrictionimplies that a protein is characterized by welldefined material parameters, namely a temperature and pressureindependent specific heat, compressibility, and thermal expansion. Hence, the stability diagram contains the completethermodynamics of the unfolding process of the proteinunder investigation, i.e., the differences
C
p
,
,
,
S
,and
V
where the
denote the differences of the respective quantities in the native and the denatured state, respectively. However, to extract absolute numbers, one of thethermodynamic quantities should be known on an absolutescale. In our case, this additional information is obtainedfrom a determination of the equilibrium constant as a function of pressure and temperature.A thorough experimental validation of the quadratic approximation (elliptic shape) would imply the determinationof the thermodynamic material parameters over a sufficiently large temperature and pressure range. From a practical point of view, this is not feasible because a nonlinearextrapolation into the respective unstable regions of thephase diagram would be necessary. Nevertheless, Makhatadze and Privalov (1995) performed such extrapolationstudies for
C
p
. Their results show that this quantity isfairly constant, say between 278 and 335 K, but may decayto zero far beyond the denaturation transition. Smeller andHeremans (1997) discussed in detail how a pressure andtemperature dependence of the various parameters wouldchange the shape of the diagram. The quadratic approximation seems to hold perfectly for liquid crystals (Clark,1979). As to proteins, however, many experimental datashow distortions of the elliptic shape. We stress that thisdoes not necessarily reflect a failure of the approximations.Distortions may arise from a deviation from equilibrium dueto the sometimes very long relaxation times. Another sourceof errors may be due to the very broad transformationranges that lead to uncertainties in the determination of therespective thresholds. Despite these shortcomings, the dataevaluation based on the quadratic approximation hasyielded very reasonable values for the parameters involved.As we will show, this is true in our case as well.An interesting problem concerns the transformation regime itself, namely the question as to what happens on a
Submitted July 18, 2001 and accepted for publication December 17, 2001.
Address reprint requests to Dr. Josef Friedrich, Technische Universita¨tMu¨nchen, Lehrstuhl fu¨r Physik Weihenstephan, Vo¨ttinger Str. 40, D85350Freising, Germany. Tel:
498161713294; Fax:
498161714517; Email: j.friedrich@lrz.tumuenchen.de.© 2002 by the Biophysical Society00063495/02/03/1644/10 $2.00
1644 Biophysical Journal Volume 82 March 2002 1644–1653
microscopic level at the boundary of the stability diagram.As to the thermal stability of proteins, this question wasdiscussed by Baldwin (Baldwin, 1986; Baldwin and Muller,1992). It was assumed that heat denaturation occurs underconditions where it becomes favorable for the protein toexpose its hydrophobic core to the surrounding water solvent similar to how an oil droplet is dissolved in water.However, as Kauzmann (1987) pointed out, pressure denaturation of a protein does not fit into the concept of the oildroplet model, because the respective changes in volumehave opposite signs. Recently, this discrepancy was solvedby Hummer et al. (1998a,b). These authors suggested that,during pressure denaturation, quite in contrast to heat denaturation, water is pressed into the core of the protein whereit fills the voids. During this process, the structure changesbut only in a way that keeps the protein in its compactshape.In this paper, we use fluorescence spectroscopy to shedsome light on this problem. The quantity on which we focusis the center (
max
) and the width (
w
) of the 00transition of a chromophore within a protein. The chromophore used is afluorescent derivative of the hemeprotein Cc. Fluorescencetechniques are very useful in this context because, on theone hand, the band center and the width of a fluorescenceline are very sensitive to changes in the molecular environment of the chromophore and, on the other hand, the interactions of a chromophore with its environment, which causethe changes in these quantities, are known in great detail sothat information on what is happening on a microscopiclevel can be readily extracted from the respective experimental patterns.
EXPERIMENTALMaterials aspects
Lyophilized substituted cytochrome
c
(ZnCc), in which zinc replaces theiron, was prepared from horse Cc (Sigma Chemical Co., St. Louis, MO) aspreviously described (Vanderkooi et al., 1976). It was dissolved in amixture of KH
2
PO
4
buffer at pH 7 and glycerol at a ratio of 1:2.5 (v/v).The protein concentration was 3.7
10
4
mol/l.
Spectroscopy
The solution (
25 nl) was filled into a diamond anvil cell. Pressure wasvaried between atmospheric pressure and
1 GPa. Its magnitude wasdetermined from the pressure shift of the ruby fluorescence whose reference values were taken from the literature (Eremets, 1996). The accuracywas
100 MPa. The sample was excited with light from a pulsed dye laserpumped by an excimer laser. Excitation was carried out into the Soret bandat 420 nm. The fluorescence light was collected in a collinear arrangement,dispersed in a spectrometer and detected via a CCDcamera. The resolutionlimit of the setup was
0.06 nm. The line center
max
and the line width
w
(fullwidth halfmaximum [FWHM]) of the 00fluorescence band, thetwo quantities that we used for investigating protein stability, could bedetermined within an accuracy range of
0.1 nm, respectively. Thisaccuracy level amounts to
3% of the total changes in these quantities.The experiments were carried out in a way that a certain temperature waskept constant and the pressure was varied or vice versa. The temperaturecould be controlled within an accuracy of
0.5–2 K in a range covering273 to 363 K.A problem in the experiment concerns the establishing of thermalequilibrium. For some of the points in the stability diagram, we measuredthe respective kinetics, i.e., pressure and temperature in the transformationrange were kept fixed, and the relaxation of the maximum of the fluorescence was measured. The respective relaxation times were in the range of 20 min. Hence, we adjusted the waiting times in the transformation rangeaccordingly. Nevertheless, we stress that the establishing of thermal equilibrium may strongly depend on the thermodynamic conditions, and, because the transformation range is rather broad the question of how close toequilibrium the actual experiment was carried out is a serious one and notalways easy to answer.For the determination of the line shift and the line width, we proceededin the following way. The main constituent of the chromophore is a ratherrigid aromatic ring whose
electron system determines the respectiveoscillator strength. Because this ring is not likely to be changed during thetransformation, it is reasonable to assume that the oscillator strength of thetransition considered does not change. In addition, the scale of the respective changes of the center and the width of the band is rather small ascompared to the respective inhomogeneous width, e.g., a few nanometerscompared to 15 nm, so that the total band could be reasonably well fittedby a Gaussian. Maximum and width of this Gaussian fit curve are thequantities that are plotted in the figures.
Determination of the equilibrium constant
For the following procedure, the assumption of thermal equilibrium for thewhole transformation range is essential. As can be seen (e.g., see Figs. 2,3, and 5), an increase of temperature and pressure results in a characteristicpattern of the shift of the band center. In the low range of these parameters,there is almost no shift or only a rather moderate red shift. The transformation range, in contrast, is characterized by a rather strong blue shift.After the transformation is completed, the blue shift levels off. As a rule,the transformation range is rather broad. This broad range may possibly bedue to a low cooperativity of the transformation process or to a dispersionof the parameters involved. Along these lines of reasoning, we interpret thepattern of the shift of the band center in the following way (for details seeDiscussion). In the low (
p
,
T
)parameter range, we just measure the pressure or temperature shift of the native state
N
. We denote the wavelength just before transformation to the denatured state occurs, as
N
. After thetransformation is completed, we measure the respective shifts of thedenatured state
D
. We denote the wavelength associated with the denatured state just after the transformation is completed, as
D
.
N
and
D
aredetermined from the intersections of the linearly extrapolated data ranges,as shown in Fig. 7. In the transformation range, the wavelength
max
of thefluorescence maximum is a superposition of
N
and
D
weighted by therespective occupation probabilities
p
N
and
p
D
of the respective states.Suppose that the total band
F
(
) can be written as a superposition of twoGaussians:
F
p
N
a
N
exp
N
2
2
N2
p
D
a
D
exp
D
2
2
D2
. (1)
Because, as argued above, the oscillator strengths
a
N
and
a
D
of the twostates are roughly the same and the relative changes in the peak wavelengthand the bandwidth are small, the exponentials are sufficiently similar, so
Stability Diagram of Cytochrome
c
1645Biophysical Journal 82(3) 1644–1653
that the wavelength of the band maximum is obtained from the firstderivative as
max
p
N
N
p
D
D
. (2)
Within the frame of the twostate model,
p
N
and
p
D
can be expressedthrough the equilibrium constant
K
(Hawley, 1971; Vidugiris and Royer,1998; Panick et al., 1999) as
p
N
11
K
,
p
D
K
1
K
, (3)
so that
K
(
p
) and
K
(
T
) can be determined from
N
,
D
, and the measuredvalues of
max
in the transformation range. Once
K
is known as a functionof temperature or pressure,
G
G
D
G
N
is determined from
G
RT
ln
K
. (4)
RESULTS
Figure 1 shows the fluorescence spectrum of ZnCc in theQband range at ambient temperature for a series of pressurelevels between 100 MPa and 1 GPa. The band at 585 nm isthe srcin followed by a superposition of several vibrationsaround 640 nm. The sharp line structure around 695 nm isthe fluorescence from a ruby crystal that is simultaneouslyrecorded to determine the actual pressure level. As is obvious from the data, the pressure shift and broadening in theinvestigated range is rather moderate. Nevertheless it isclearly discernable that the Q band undergoes a blue shift atelevated pressure levels.Figure 2 shows how band center
max
and bandwidth
w
(FWHM) of the Q transition behave under a pressure variation up to
1.5 GPa: The band center is almost insensitiveto pressure variations up to
600 MPa. Then, it undergoesa blue shift that covers a range of
3 nm. Beyond
1 GPa,the blue shift levels off again. The bandwidth increasessteadily with pressure and reaches a maximum around 0.9GPa. Then, it decreases again. The maximum of the broadening coincides with the midpoint of the range of the blueshift. The temperature of the experiment was 298 K.Figure 3 shows the behavior of
max
and
w
under atemperature variation at ambient pressure. The band centershifts moderately to the red up to temperatures of
315 K.
FIGURE 1 Fluorescence spectrum of ZnCc at ambient temperature. Theband around 588 nm represents the
Q
x

Q
y
00band region. The bandaround 640 nm is a superposition of several vibronic bands. The narrowband around 695 nm is the fluorescence from ruby. The pressure levels atwhich the various spectra were taken are listed in the insert .FIGURE 2 Center (
max
) of the
Q
x

Q
y
00band and the respective width(FWHM) as a function of pressure measured at a temperature of 298 K.The stability boundary is indicated by the vertical broken line.FIGURE 3 Center (
max
) of the
Q
x

Q
y
00band and the respective width(FWHM) as a function of temperature at ambient pressure. The broken linemarks the stability boundary.
1646 Lesch et al.Biophysical Journal 82(3) 1644–1653
The red shift is followed by a range with a pronounced blueshift, which levels off beyond 343 K.
w
steadily increaseswith temperature but, beyond the midpoint of the blueshiftrange, the respective increase/Kelvin flattens.Figure 4 serves as an example to demonstrate that thepatterns of
max
and
w
under pressure and temperaturevariations can be more complex. In this example, the temperature is varied at a pressure level of 700 MPa. The shiftof the band center and, somewhat less pronounced, also thechange of the bandwidth can be subdivided into three subranges. The range up to
298 K is characterized by a ratherpronounced red shift on the one hand and, somewhat unusual, a significant band narrowing, on the other hand. Therange between 298 and 338 K is characterized by a blueshift and a broadening. Beyond 338 K, another range with astrong blue shift follows, which is also accompanied by aband broadening. The midpoint of this range is around 350K. We attribute such a complex pattern to several, in thiscase two, consecutive steps in the denaturation process.Figure 5 summarizes most of the pressure (
A
) and temperature (
B
) denaturation experiments. The data are represented as a function of the respective deviations from thetransformation boundary
G
0, namely of
c
,
p
p
c
,and
T
T
c
, respectively. The index
c
characterizes thetransformation boundary.
p
c
and
T
c
were determined fromthe midpoints of the blueshift ranges and from the associated linebroadening patterns.Figure 6 shows the stability diagram of the protein investigated. As can be seen, the shape of the diagram isellipselike. Note that, in the fluorescence pattern of Fig. 4,only the midpoint around 350 K fits into the diagram.Figure 7 shows how we determined the edge values of thewavelengths
N
and
D
, which characterize the entrance toand the exit from the transformation range. We extrapolatedthe data of the respective ranges in a linear fashion. Therespective cross points determine
N
and
D
, as describedabove. The data in Fig. 7 correspond with those in Fig. 3.Figure 8 shows the difference
G
G
D
G
N
as afunction of pressure between 600 MPa and 1.1 GPa asdetermined from Eq. 4 and the measured wavelength of theband center (Eq. 2). The temperature is 298 K. The solidline represents a fit to a parabola whose first and secondderivative yield the changes of the volume
V
and theisothermal compressibility
, respectively.Figure 9 is similar to Fig. 8. It shows
G
as a function of temperature at ambient pressure. The first and second derivatives yield the changes in entropy and specific heat
FIGURE 4 Center (
max
) of the
Q
x

Q
y
00band and the respective width(FWHM) as a function of temperature at a pressure of 700 MPa.FIGURE 5 Summary of (
A
) pressure and (
B
) temperature denaturation data.
c
,
T
c
, and
p
c
represent the wavelength, temperature, and pressure,respectively, at the stability boundary.
Stability Diagram of Cytochrome
c
1647Biophysical Journal 82(3) 1644–1653
capacity,
S
and
C
p
, respectively. Values of the thermodynamic parameters are summarized in Table 1.
DISCUSSIONThe general pattern of the fluorescence andmicroscopic aspects of thetransformation process
The interactions of a dye probe with its respective environment have been intensively studied in the past and areknown in detail (for a review, see Israelachvili, 1994) sothat it seems possible to extract information from the behavior of the fluorescence under changes of temperature andpressure on what is happening on a microscopic level duringthe unfolding process. The general pattern that we observe,e.g., for
max
, is characterized by almost no changes or onlya moderate red shift in the low pressure or temperaturerange. This range is followed by a pronounced blueshiftrange, which again levels off at higher parameter values.We first consider the behavior of the pressure shift.Proteins are ordered structures. Nevertheless they are characterized by an unusually large mean square displacement
FIGURE 6 Stability diagram of ZnCc as obtained from the fluorescenceexperiments. The contour line represents a leastsquare fit of a secondorder curve to the data points. The protein is stable inside the ellipticlikeboundary. The outside range corresponds with the denatured state.FIGURE 7 Determination of the edge values of
N
and
D
.FIGURE 8 Difference of the Gibbs free energy
G
as a function of pressure at a temperature of 298 K. The fit curve is a parabola.FIGURE 9 Difference of the Gibbs free energy
G
as a function of temperature at ambient pressure. The fit curve is a parabola.
1648 Lesch et al.Biophysical Journal 82(3) 1644–1653