13780
J. Phys. Chem. 1994,98, 13780-13790
The Protein-Glass Analogy: Some Insights from Homopeptide Comparisons J. L. Green, J. Fan, and C. A. Angell” Department of Chemistry, Arizona State University, Tempe, Arizona 85287-1604 Received: December 6, 1993; In Final Form: October 5, 1994@
The question of the “glassiness” of hydrated protein systems is examined by comparing reported observations on proteins with the characteristic features, both long time and very short time aspects, of the liquid-to-glass transition in liquid and polymer systems. In an attempt to reconcile conflicting features, the calorimetric behavior of the much-studied hydrophilic proteins, myoglobin and cytochrome c, has been determined by differential scanning calorimetry and compared with that of a model system, the hydrated monopeptide polyL-asparagine of comparable molecular weight. The results are analyzed in terms of the three canonical features of relaxation in glass-forming systems: non-Arrhenius character (fragility), nonexponentiality, and nonlinearity. The homopeptide has a nonfreezing water range comparable to the ice-saturated proteins, both native and denatured. Studies of the scan rate dependence of Tgfor a range of water contents from 14 to 29 wt % imply that the hydrated homopeptide system behaves as a “strong” liquid at all water contents. We show that this is consistent with the behavior of native proteins according to earlier studies. However, anneal and scan studies, particularly on hydrated cytochrome c, confirm the existence of an extremely broad distribution of relaxation times in the proteins. From these observations, and from comparison with data on related systems, we conclude that hydrated proteins indeed may be classed among glass-forming systems, but due to their special structural features and to the disposition of the bound water, they show great departures from thermorheological simplicity. This seems to be partly a consequence of a special strengthening, in fully hydrated proteins, of the secondary @) relaxations which are not calorically important in most glass-forming systems. We suggest that this may have developed to take advantage of the fast side chain dynamics typical of polymer systems and thereby to reduce the ambient temperature response times of biologically important processes. In the solution systems of this study, this feature smears out the glass transition almost beyond recognition. An analogy between the weakly first-order strong-to-fragile liquid transition in low-temperature water and the denaturing transition in proteins is briefly discussed.
Introduction
may have features in common with processes dominated by the motion of the water molecules which reside primarily There has been much recent interest in the relation between on the exterior of the protein and may even correlate with the the kinetics of processes in individual protein molecules and viscosity of the solution in which the protein is s u ~ p e n d e d . ~ , ~ ~ those in other complex systems such as viscous liquids and Such demonstrations indeed suggest that hydrated proteins, as glasses (both structural and spin) and neural In individual molecules, may possess the complexity necessary to all these cases, isothermal relaxation processes (as opposed to exhibit cooperative dynamics comparable with those of the diffusion-controlled chemical processes) show nonexponential simpler glass-forming liquid and polymer systems (although they character. The case of myoglobin has been studied in particular detaiL3-19 The nonexponential processes can u ~ u a l l y 4 - ~ , ~ ~ - ’ are ~ much smaller than the smallest microemulsion droplets so far known to preserve the glass transition signatures of the bulk be described by the stretched exponential, or Kohlrauschglassy materialsz0). This would explain why the key aspects Williams-Watts (KWW), function of their behavior seem to be independent of whether the proteins are studied as crystals, amorphous hydrated powders, or homogeneous liquid solutions.21 At the same time, there is need for caution since some criteria though a power law has been shown to give a marginally better for “glassiness” are frequently not, according to the best description in some cases.6*11,12In a parallel development information currently available, being met. For instance, a key carrying the same implications, Doster and colleagues15 have characteristic of the normal glass-forming system, which is not shown that inelastic neutron scattering processes in proteins seen in proteins, is its “glass transition temperature” T,. This follow certain key predictions of mode coupling theory which is usually defined by reference to the rather sharp decrease in has recently been found to account rather well for the behavior heat capacity which occurs when the system falls out of of liquid and polymer systems in the high-temperature (shortequilibrium during cooling and the even sharper increase in heat time) part of their approach to the glassy state. capacity which occurs when equilibrium is regained on wanning. It is a striking finding that the dynamics of relaxation in the The C, jump is generally believed to be a consequence of the interior of a protein (such as the Fe transition rate in heme crossing of experimental and system time scales and, for the judged from the Mossbauer line width in myoglobin,l6-l8 the common scan speed of 10 Wmin, seems to occur when the equilibration among tier 0 substates & and A1 in MbC0,6 the relaxation time for the structure reaches some 200 s.z2 Only in protein fluctuations responsible for opening pathways for CO the unusual cases of certain network liquids, like liquid Si02 or 0 2 binding to heme,12 and the CO-heme recombination (“strong” liquidsz3), does this signature of the glass transition fail to appear, and such behavior would not be expected from @Abstractpublished in Advance ACS Abstracts, November 15, 1994. 0022-3654/94/2098-13780$04.50/0
0 1994 American Chemical Society
The Protein-Glass Analogy systems which conform to mode coupling theory predictionsZ4 (usually reserved for very “fragile” liquid systemsZ4). It is unsettling, therefore, that precise adiabatic calorimetry studies of common proteins such as collagen, both moist and dry,25 and keratinZ5do not at any temperature show C, jumps at all comparable to those seen in ordinary liquid and polymer systems and even show little change in C, on d e n a t u r a t i ~ n . ~With ~,~~ myoglobin solutions, on which so many kinetic studies have been performed, 1-18 well-defined C, jumps had, until recently (see below), only been seen when glass-forming cosolvents such as glycerol were added to render excess water (Le., water in excess of the “unfreezable” water at the protein surface) glassforming.27 Most of the C, jump is associated with the glycerolwater solution. On the other hand, the gradual buildup of excess heat capacity of hydrated over dehydrated collagen in the temperature range 140-30026 or 180-230 K in hydrated myoglobinZ1 or methemy~globin~~ could be regarded as analogous to the excess heat capacity of liquid over glass in ordinary glass formers even though it is acquired over such a large range of temperatures. Recent scanning calorimetry results by Tseratli and Smirnova?8 in contrast to the earlier studies,25show the development of a C, jump on rescans after denaturation of collagen (though the plots presented seem to be idealized versions of the originals). Furthermore, definite though generally smeared-out increases in C, in certain food protein systems have been observed near ambient temperature and interpreted as glass transitions by other investigators.16-18 A rationalization of these observations in terms of waterplasticized polymer phenomenology was given a decade ago by Batzer and K r e i b i ~ h ?Slade,30 ~ and Hoseney et alS3land was later developed in detail by Slade, Levine, and F i n l e ~ .This ~~ effectively extended the original Kuntz-Kauzmann polymer interpretation of protein solutions33to the glassy state extreme found at low solvent contents. Also, recent works by Sochava, Smimova, and c o - ~ o r k e r sshow ~ ~ that, in selected globular proteins at low water contents, a distinct C, jump may occur and, further, that the magnitude of C, increases markedly on denaturation. Finally, two very recent studies on native proteins have appeared, with conflicting observations. One, conducted on myoglobin crystals carefully buffered with NaH2PO4 and KH2PO4 (28 and 29 wt %, respectively), showed both smeared and sharp glass transitions at 172-216 K depending on water content and thermal history.35 This behavior is rather different from that seen for salt-free homogeneous solutions studied in the present work and previously?1 and the role of the phosphatewater matrix in the crystal interstices needs to be clarified before the results can confidently be attributed to the water-protein system alone. The other conducted by Sartor et al.27 on unbuffered as-received proteins gave results more in keeping with earlier work. However, Sartor et al. demonstrated, by annealing experiments of a type not performed by earlier calorimetrists,that the smeared-out form of the C, increase could be interpreted in terms of the presence of the same continuous distribution of relaxation processes (extending over the range 170-300 K) that was earlier identified by Pissis et al.36using a “thermal sampling” variation of their thermally stimulated depolarization measurement^.^^ Sartor et aL2’ demonstrated that the behavior was similar to that found in an interpenetrating network polymer containing no water and modeled the behavior with an adaptation of the Tool-Narayanaswamy -Moynihan phenomenological model.22 While the comparison was impressive, the analogy is difficult to accept in toto as network polymers cannot unfold due to the covalent cross-links. We will examine the merits of an
J. Phys. Chem., Vol. 98, No. 51, 1994 13781
alternative concept which retains the chain polymer structural basis and emphasizes the role of dynamics within and between the side chains. Strong side chain interactions can act like thermally disruptive cross-links and hence can also provide a hierarchy of enthalpy-absorbing processes. As we will detail later, one gains thereby some insight into the strategy that Nature has developed to produce fast processes in proteins at ambient temperature. Evidence for a continuity of relaxation processes in hydrated proteins and protein crystals has also been provided by mechanical relaxation studies. According to studies of crystalline lysozyme by Gorelov and M o r o z ~ vthese , ~ ~ become active as low as 155 K and were regarded by them as manifestations of glasslike relaxation behavior. In dielectric and mechanical relaxation spectroscopy, secondary (or p) relaxations, which are normally almost undetectable by calorimetry, are easily observed.39 These processes, which are very fast in normal glass formers at their Tg’s and only “freeze out” at much lower temperatures, are due to local rearrangements involving low energy barriers. They usually lack the cooperative character of the primary (or a ) relaxation; hence, their characteristic times usually obey an Arrhenius law although the process is very nonexponential. In polymers they are strongly influenced by side chain structure, and it might be expected therefore that they may have a special role to play in protein dynamics. Finally, in this introduction we should discuss a phenomenon which has often been referred to as a “transition” (implicitly or explicitly a glass transition) in protein~,~-~~’~~’~-’8~21~23-25~39-42 which we think is of great This is the departure, with increasing temperature, of the mean-squared displacement of the atoms from the low-temperature harmonic T dependence, as determined by X - r a ~ fscattering ~ ~ ~ l and neutron scattering,21 Mossbauer s p e c t r o s ~ o p yand , ~ ~molecular ~~~ dynamics computer simulation studies (MD).@This phenomenon itself cannot be what is normally understood by relaxation phenomenologists as the glass transition (although it may well be the triggering mechanism, see below) because it can be observed in extremely short (picosecond) time scale studies, e.g., MD. The molecular diffusion or reorientation, which is necessary for the configuration space exploration responsible for the normal (100 s time scale) glass transition p h e n o m e n ~ n ~in~ liquid , ~ ~ or plastic crystals, cannot possibly occur on such short time scales at the temperature where the departure is observed. Neutron scattering studies of the same phenomenon in molecular glasses (e.g., tria-naphthylbenzene4) have estimated a time scale of 4 x 10-l2 s for the molecular motions involved. Notwithstanding the 14 orders of magnitude difference in their time scales, these two phenomena could be related at a fundamental level in either of two ways (and the distinction between the two may be smaller than it appears at first sight). The fust relation is through mode coupling theory,24according to which the fast process detected by neutron scattering should be the “fast” component of the response functi0n.4~ The slow component of the function, in the “idealized” theory, diverges at a dynamical singularity located at a critical temperature T,, which lies well above the calorimetric Tgbut is where, ideally, the - glass transition should occur. According to the theory, (r2)should diverge at T,,24,25and the near coincidence of the onset temperature with the calorimetric Tg seen in numerous (notably model fragile liquid o - t e r p h e n ~ land ~ ~ the elemental glass selenium46)must in this view be regarded as fortuitous. The second and alternative view sees the fast process as a sort of trigger for the barrier-crossing processes involved in those molecular rearrangements which come into the experimental time window at the calorimetric Tg. Computer simulation
13782 J. Phys. Chem., Vol. 98, No. 51, 1994 studies currently being reported51show that the onset of a slope change in the Debye-Waller factor near the calorimetric Tg can be seen on the time scale of the fastest modes in the system, i.e., as a true anharmonic displacement, preceding any a-relaxation or even the faster molecular /? or &processes. Furthermore, the effect can be seen, albeit weakly, in inorganic network glasses near the limit of the stronghagile liquid clas~ification~~ where mode coupling theory is not expected to apply.” Thus, although it can be said that mode coupling theory also sees the fast process as the necessary precursor of the slow, the connection may better be made through the soft mode approach of Buchenau and Z O ~ The . ~latter ~ has much in common, conceptually, with the early52proposal of a “phononconfiguron” equilibration through anharmonic coupling (according to which a connection was predicted between T, and To, the Debye temperature, near which anharmonic effects usually become prominent in crystals53). Clearly, vibrational modes in a rearranging group of molecules, Le., at the top of a barrier, are extremely, indeed terminally, anharmonic. Thus, the temperature where short wavelength vibrational modes go soft is the temperature where structural rearrangements become possible. Neutron scattering studies show that the slope change in the Debye-Waller factor is strongly q-dependent; it is more pronounced, and starts lower in temperature, the larger the q value. Thus, 57FeMossbauer spectroscopy with a characteristic q value of 7.29 A-l is very sensitive to these motions, detecting them at very small (3)values. In glycerol (an intermediate 57FeMossbauer spectroscopy detects the onset of the Debye-Waller factor slope change at 200 K,17,18 not far above the T, of 192 K. The behavior of 57Fein hydrated metmyoglobin proves to be very similar to that in glycerol, Le., the onset of the slope change in the Debye-Waller factor is observed at about 200 K.17 In neutron scattering data on D20 hydrated myoglobin, a departure from harmonic behavior is noted at 180 K and becomes strong above 220 K.21 Again, the behavior seems almost independent of whether the protein is studied in crystalline or hydrated powder form. An onset temperature of 180 K is also consistent with the results of the pioneering X-ray study of myoglobin by Parak et al.‘’l Finally, in X-ray scattering studies of ribon~clease,’~ the onset is reported at -220 K,14athe temperature at which biological activity becomes measurable, but the data scatter also allows an onset at 170 K.14b Thus, despite the absence of the usual sharp calorimetric signatures of the glass transition, there is much evidence for the onset of motional freedom in hydrated proteins in the range 160-200 K. In an attempt to understand how these many, and sometimes apparently conflicting observations, can be reconciled, we have undertaken a study by differential scanning calorimetry of solutions of two water-soluble proteins, cytochrome c and myoglobin, and have compared results for both native and denatured samples of differing moisture contents with results for a simplified analog system. As an analog system we chose the homopeptide polymer poly-L-asparagine (PO~Y-L-ASN), which is very hydrophilic and exhibits a wide range of glassforming aqueous solutions. We examine the results in relation to the three canonical characteristics of relaxation in glassforming systems, namely, non-Arrhenius behavior (quantified by the “strength” or “fragility”23), nonexponential relaxation (quantified by /3 in eq l), and nonlinearity of the relaxation (quantified as discussed later), and to the correlations between these characteristics seen in various model glass-forming systems. To keep the studies of proteins and homopeptides close in character to those of “normal” glass-forming systems,
Green et al. we have carried out the studies as far as possible on homogeneous solutions, using fast cooling where necessary to avoid or minimize the crystallization of ice. We believe these comparisons may help clarify some of the issues which are currently sources of some confusion in the developing understanding of protein dynamics and may thereby increase the interest content of the problem. In particular, the findings, analyzed in terms of the “fragility” of moist polypeptides relative to other liquid and polymer systems, offer some surprises.
Experimental Section Lyophilized cytochrome c (4.8 wt % H2O; Type I11 from horse heart), myoglobin (4.5 wt % H20; Type III from horse heart), and poly-L-asparagine (MW 10 400) were obtained from Sigma Chemical Co. Samples were prepared by adding to the protein (or polymer) the minimum amounts of distilled water needed to obtain a clear solution at -277 K. The samples were then evaporated slowly to reduce the water content to as low a value as possible before inhomogeneities in the sample wouid appear. A similar procedure was described by Sochava and Smimova.20 This stage corresponded to removal of almost all of the “freezable” water, i.e., that water not involved in the protein interior and in surface-bound layer. Composition was judged by weighing on an Analytical and Precision Balance Co. microbalance (&0.0002 g). In reporting compositions, we made allowance for the 4.5-4.8 wt % water contained in the lyophilized material. A comparable procedure was followed for the preparation of PO~Y-L-ASN samples. Some samples were studied almost immediately after preparation; others were allowed to stand and slowly lose water over a period of weeks before examination. Quantities (10-20 mg) of the clear viscous liquids obtained by these procedures were transferred to aluminum or stainless steel sample pans and hermetically sealed. A Perkin-Elmer Model DSC-4 differential scanning calorimeter, running at scan rates of 2.5, 10, 20, and 40 Wmin, was employed to observe the various thermal effects in the majority of samples. For some quantitative studies of heat capacity and enthalpy relaxation, a Setaram Model 121 DSC was used. The accuracy of this instrument was first confirmed by reproducing the heat capacity of pure A1203 to within 0.5% over the temperature range 180300 K. Unfortunately, the temperature range of this instrument is limited, and C, could not be determined below 173 K.
Results DSC scans, showing the heat flow J in mcal/s needed to maintain the sample at the same temperature as the reference pan, are given in Figure 1 for myoglobin containing considerable freezable water (without which homogeneous samples could not be obtained) and for concentrated cytochrome c containing very little freezable water. These scans are for samples studied immediately after preparation. The myoglobin sample, which is less easily dehydrated, had been quenched at 320 “C to minimize the precipitated ice content, and some crystallization of ice during the upscan is visible. A separate sample of cytochrome c, in which the water was allowed to equilibrate over a longer period and which has a somewhat more rapid increase in C, above Tgat -170 K, is shown in Figure 2. Figure 2 compares the scans for this sample both before and after thermally induced denaturation seen as an endotherm at 6070 “C in curve a. Figure 2 also contains two scan of poly-LASN sample, with 15 and 29 wt % water (0.18 and 0.40 g/g), after scaling to the same sample mass as the cytochrome c sample. In Figure 3 we show more quantitative data obtained
The Protein-Glass Analogy
J. Phys. Chem., Vol. 98, No. 51, I994 13783
temperature/K 220
100
140
260
I
A . !
i
1.5
1
denatured legumin, legumin. SW/. waMRef.34
t
1
/
"
'
"
'
'
"
'
200
'
"
"
'
'
"
'
"
'
"
'
300
250
o ! .
1
-140
-120
I
.
.
-100
.
,
-60
, . , . , -60
-20
-40
temperature
.
(O
,
. I
0
20
C)
Figure 1. DSC scans of vitrified freshly prepared concentrated aqueous solutions of cytochrome c (curve B: water content -49 wt %) and myoglobin (curve A: water content 50 wt %; the composition of the unfrozen component is uncertain in view of large melting endotherm), showing gradual increases in heat capacity above 170 and -150 K, respectively. Myoglobin shows a weak crystallization endotherm at -213 K because of initial quenching (at 320 Wmin). Cytochrome c shows same behavior if annealed at 150 K before upscan. Comparison is made with a scan of the conventional glass former glycerol for a sample of the same mass: the arrow shows where T, is located.
10
1
.
220 I
260
300
I
included for comparison. The small endothermic anomaly just above T, in the 29 wt % HzO case is believed to be due to successive crystallization and redissolution of ice.
u,
400
c " 300
ice
legumin denat 0 collagendenat 0 cytochromec
.....*..........WO
1
denaturation
melting
0
200
340
I
+
Figure 3. Heat capacity scans of poly-L-asparagine water solutions of four differing water contents in wt %, as in legend. Data for denatured globulin 11s (legumin) with 6 wt % water, from ref 34, are
temperature/K 180
140
I " " ,
0
0.2
.
I
0.4
.
20
0.7 I
W/W '
40
It
" I
.
60
wt %H20
-- 'c
+
e - -
AJ
I
80
100
+
Figure 4. Glass transition temperatures for poly-L-asparagine water homogeneous solutions, and a denatured cytochrome c sample of 14 wt % H2O from this work, compared with values reported for various denatured proteins and wheat glu and with the classical polymer diluent system polystyrene styrene. Data ref 34 (legumin), ref 29 (collagen), and ref 31 (wheat gluten). Ins& compares scan of PO~Y-L-ASN sample with 14% HzO (solid line) with scans of denatured legumin (6 wt % H20, dotted line) and collagen (10 wt % H20, dashed line).
crystall-
A
400
350
TemperatureK
--*.:
\
WP/OH20 -150
-110
-70
-30
temperature/
50
10 O
90
C
F g v e 2. DSC scans of aged cytochrome c solution. (The composition is close to the maximum H20 content retainable in glass on quenching at 320 Wmin, viz., -40 wt % H20.) Curve A, showing a crystallization exotherm at 213 K, is behavior before denaturation, and curve B (displaced down for clarity) and also curve B' (undisplaced) are behavior after denaturation. Note the absence of a crystallization exotherm during heating in the denatured case and the concomitant reduction in area of the ice melting peak. The temperature of the glass transition is assigned as 163 K and is unchanged on denaturation, while the heat capacity appears to have decreased slightly at the lower temperatures and is unaffected at the higher temperatures (see curve B'). Curves C and D are DSC scans for poly-L-asparagine of different water contents (14 and 29 wt % H2O) adjusted for small sample weight difference and displaced downward for clarity. Note the higher Tgvalues and sharpened appearances of the homopeptide phenomenon as well as absence of any ice crystallization. The strength of the transition is measured by AJ, defined as shown.
with the Setaram DSC for a series of homogeneous poly+ ASN solutions of water contents ranging from 14% to 29% H2O (0.16 to 0.41 g/g). Values of T, at the scan rate 10 Wmin, the
width of the glass transition AT,, the change in heat capacity at Tgdefined as shown in Figure 3, and the ratio Cp(Z)/Cp(g) at T, are collected in Table 1 along with other quantities to be described and discussed later. The values of T, are plotted against water content in Figure 4 where they are compared with the values for related systems to be discussed below. A value obtained by us for a strongly dehydrated denatured cytochrome c sample (with 15 wt % H20: not confirmed to be a homogeneous solution phase) is included and is seen to coincide with the values for the polyL-ASN and denatured legumin samples. The native state in this cytochrome c case had a much weaker calorimetric anomaly at this temperature, consistent with the findings of Sochava e t al.34 The horizontal dashed line passes through the points obtained from the ambient temperature homogeneous cytochrome c and myoglobin solutions (whose vitreous compositions are uncertain because of ice crystallization) and through the values given by Sartor et al." for hydrated myoglobin of water contents between 28 and 41 wt % (0.4-0.7 g/g). In Figure 5 are seen the results of scanning the PO~Y-L-ASN samples through T, at different rates Q in Wmin after cooling below Tg at the same rate. An Amhenius plot, log Q vs UTg,is
13784 J. Phys. Chem., Vol. 98, No. 51, 1994
Green et al.
TABLE 1: ProDerties of Water-Plasticized Poly-L-ASNand Other Systems wt % HzO h (g/g) T, (K) ATg (K) ATg/Tg C,(l) (J/gK) AC, at T, 13.6 0.16 279.8 18.7 0.07 2.15 0.57 15.7 0.19 264.8 16 0.06 2.27 0.65 21.4 0.27 236.2 20.9 0.09 2.32 0.60 0.41 219.4 21 0.10 2.60 0.68 29 191 8.0 0.042 1.84 0.84 glycerol OTPb 246.6 5.2 0.02 1.44 0.454 203 5.0 0.025 PPO 4000‘ GeAsSe ((r) = 2.4)d 430 34 0.08
Cp(l)/C,(g) at Tg 1.36 1.40 1.37 -1.35 1.84 1.46
EH od/mol) 230 194 183 (95)”
43 38 40.5 (23)”
D 23 28 25 98.3
524
110
6.3
m
-1.2 30 45 Parentheses indicate large uncertainties. o-Terphenyl. Polypropylene oxide, a well-characterized water,absorbing chain polymer of molecular weight 4000. Ge-As-Se is a model covalently bonded glass-forming system which displays a wide range of behaviors and has therefore played an important role in revealing correlations between the different characteristic^.^^ ( r ) is the mean coordination number or covalent bond density, and 2.4 is the value at which the system shows its maximum strength and hence broadest T,.
temperaturelK 10
.
140
180
220
260
300
340
n c
1000/T ( K ) . ’
Figure 5. Scan rate, Q, dependence of T, for the four PO~Y-L-ASN + water solutions of Figure 3, plotted in Arrhenius form so that slopes give activation energies for enthalpy relaxation. Comparison is made with behavior of a model fragile liquid, o-terphenyl (large circles). For calibration of the latter case literature viscosity data are included (filled squares,right-hand axis; vertical position of scale has been adjusted to permit easy comparison of slopes). Activation energies, EH, and fragilities, m, obtained from the slopes of these plots via eq 6 are collected in Table 1. temperature/K 220
260
300
A
0 Q v)
L
a
-E u
0 1
-90
.
.
.
, .50
.
.
.
,
.
; , . !
.
-1 0
temperature/
30
-150
-110
-70
-30
50
10
temperature/
90
C Figure 7. DSC scans of cytochrome c 50 wt % water before and after annealing treatments at annealing temperatures TA(,)(both below and above the initial T, of -170 K) which were carried out prior to the respective scans. Note that small “prepeaks” appear in the cytochrome c case even when annealed above the initial T,,establishing the existence of relaxation processes which are very slow compared with those responsible for the initial “glass transition”. See Figure 3 in ref 28b for similar behavior over extended Trange in methemoglobin. O
+
temperature TAand held for 30 min before cooling to 77 K and then upscanning. This was repeated for a number of annealing temperatures at different intervals below T, as defined from the initial scan for the unannealed sample. Three cases are shown in Figure 6. The presence of subsidiary “bumps” (or in the case of the highest annealing temperature, a peak) at approximately equal temperature intervals above the respective annealing temperatures is noted here and interpreted below. Smaller bumps, close to but above the electron limit, were observed for lower annealing temperatures. Finally, in Figure 7 we show the results of equivalent annealing experiments on hydrated cytochrome c. These weak effects are comparable with those reported by Sartor et aLZ7for hydrated myoglobin samples.
C
Figure 6. DSC scans of PO~Y-L-ASN + 15% HzO before and after ) T, annealing treatments at various annealing temperatures T A ( ~below prior to scan.
used in order to obtain the “activation energies” for enthalpy relaxation. Also included are data for the well-characterized fragile liquid o-terphenyl to serve as an accuracy check. T, is defined by the onset temperature as usual. The activation energies EH are collected in Table 1. In Figure 6 we show the results of some annealing studies on PO~Y-L-ASN.Samples were cooled from well above Tgto a
Discussion
1. Glass Transition Manifestations and TgValues. First we note how, in the case of the freshly prepared myoglobin and cytochrome c solution in Figure 1, there is no discemible jump in J (4,) at all, though there is a broad increase in J in the range 160-260 K interrupted by a shallow dip starting at 200 K in the case of myoglobin. This latter is attributed to crystallization of ice additional to that which formed during the quench, since it does not appear in an immediate rescan or in the scan of the same sample after denaturation. This crystal-
J. Phys. Chem., Vol. 98, No. 51, 1994 13785
The Protein-Glass Analogy lization (seen also in the native cytochrome c case in Figure 2) will leave ice in contact with a residual glassy phase. At 260 K the total ice formed during cooldown and upscan commences to melt. According to studies on food proteins and aqueous sugar systems,32this occurs at a special point called T i , which is a sort of fixed point for those binary systems in which only one component can crystallize. It is the Tgof the noncrystallizer (here protein) when saturated with water. The T i effect is better seen in the curve for cytochrome c probably because of the smaller ice content. This feature merits further study for the present systems, since it implies the presence at higher temperatures of residual glassy material from which ice cannot crystallize, with T . very similar to those of the hydrated homopeptide polymers discussed below. In the case of the aged cytochrome c sample, shown in Figure 2, there is a regime of comparatively rapid increase in J , starting at -160 K, and a glasslike transition with a substantial increase in C, can be defined. This phenomenon has little to do with the fact that the protein has tertiary structure, since it is almost unchanged (except for some loss of abruptness) on denaturation (see Figure 2, curve b [displaced for clarity] and dashed trace [not displaced]). The only obvious effect of denaturation is to inhibit the crystallization of the water which froze out during warm-up of the native sample. Comparable observations were made on freshly prepared samples (in which the ice content was larger). While similar behavior is seen in ovalbumin33the weak dependence of C, on folding state contrasts with the observations on globular proteins, e.g., IIS globulin in which substantial increases in C,, up to 20%, have been noted on d e n a t ~ r a t i o n .The ~ ~ latter difference may be due partly to the lower water content of the samples as well as to the different character (stronger denaturation peak) of the proteins. The values of Tg that we observe, 160-170 K, are close to the value of 170 K found in methemyoglobin by Sartor et al.,27 who noted that it was independent of vitrified water content in the range 28-41 Wt % (0.4-0.7 g/g). The comparison of the protein behavior with the homopeptide solution behavior at different water contents is instructive though the comparison is limited by the ranges of homogeneous solutions which could be prepared. At the highest homopeptide water content, 29 wt % (0.41 g/g), the abrupt (normal polymerlike) jump in C, has started to smear out, though an onset transition at lower temperature, e.g., the 170 K as seen in proteins, was not obvious in Perkin-Elmer DSC-4 scans of these solutions (not shown). On the other hand, annealing studies of the homopeptide (see Figure 6 discussed below) showed the presence of significant enthalpy relaxation at temperatures well below the primary glass transformation range. At lower water contents the homopeptide T,’s are comparable in magnitude (and also water content dependence) to those of denatured globular proteins and of proteins with little tertiary structure, e.g., wheat gluten.31 The temperature of the T, onset seen in the icesaturated proteins is comparable to the glass transition in a number of simple hydroxylated molecular systems containing water at the ice-saturated glass-forming limit, e.g., propylene glycol 55 wt % water53and glucose water;54see Figure 4. Among polymer systems, only the very hydrophilic cases, such as poly(hydroxyethy1 methacrylate), have such low T,’s, and these only become prominent at water contents of 30 wt % and higher.55 To understand these observations, we propose that the low Tg seen in the proteins studied here and by others, all of whom report onset values in the range 160-170 K,21,27is actually the onset of a strong water-sensitized /?-relaxation like that recently noted in a somewhat complex organic salt system which
+
+
exhibited a calorimetrically strong secondary relaxation due to side chain rotation.28 The “real”, Le., the primary or a-process, glass transition involving the chain segmental motions is, in this view, not realized until a considerably higher temperature is reached, e.g., the glass transition temperature of the homopeptide polymer at comparable water contents. However, this a-process in proteins is not obvious because of the continuing buildup of sub-T, j3-like processes which merge the two together. In the native state the a-glass transition may be repressed (reduced in magnitude) and/or pushed to higher temperat u r e ~ ,and ~ ~this , ~ ~is more true the lower the water content. According to Sartor et al.,27the a degrees of freedom may not be completely accessed before the denaturing transition intercedes. However the observation that, in fully hydrated states, native and denatured samples behave so similarly argues that water plasticization of native proteins is very effective at relaxing the configurational restrictions imposed by the folding process. The reason that the increased d($)/dT in the Debye-Waller factor for interior components of the protein (such as the heme of the myoglobin molecule) are seen at about 200 K is, then, a combination of (i) a-T, lowering by water increase, to the nonfreezing water limit of -30 wt % (0.42 g/g), where T, is 220 K for the PO~Y-L-ASN, and (ii) the involvement of the faster @-relaxationof side chain dynamics. The involvement of side chain dynamics in biologically important processes seems appropriate: the same strategy is used by materials scientists designing fast-responding liquid crystal displays, when they put the active elements into the side chains of the polymeric display materials. The wide temperature range over which the full configurational heat capacity is established is consistent with the findings of noncalorimetric studies of relaxation in proteins, e.g., the low-frequency mechanical relaxation study of crystaltine lysozyme by Gorelov and Morozov3*and the dielectric measurements of Pissis et al.36,37Gorelov and Morozov found that, at a frequency of 20 kHz, mechanical losses by the protein commences rather sharply at 190 K. However, rather than decreasing at some higher temperature as in a normal relaxing system, the losses remain high up to 300 K. This implies the presence of a continuing sequence of longer time scale, higher activation energy processes. From the frequency dependence of the initial loss increase, an activation energy of 75 kJ/mol was obtained by Gorelov and Morozov. From this, we may calculate the onset temperature at the frequency Hz, which is characteristic of the glass transition. [The value Hz is obtained both from (2n x lo2 s)-l, where lo2 s is the structural relaxation time deduced for the glass transition when measured at 10 K/min,22 and also from direct measurements of dielectric relaxation near Tg.]The value obtained for Tonset (at Hz) is 157 K. The assumption of Arrhenius behavior would be unsound for an a-relaxation process but appropriate if we are actually dealing with secondary relaxations. Onset values of 157 K would clearly be compatible with our calorimetric results and with those of Doster et al.21and of Sartor et aLZ7 Both are consistent with the results of the longer time scale thermally stimulated depolarization studies of Pissis and c o - ~ o r k e r s ~ ~ . ~ ~ on lysozyme with 22.4 wt % H20. These measurements, conducted at 1 Wmin, showed rapid depolarization setting in at about 150 K (and peaking at 176 K). (This study also detected a weak process at the much lower temperature of 120 K.) In all studies of native proteins, mechanical, dielectric, and calorimetric, the loss (e”, etc.) at the onset of relaxation becomes weaker as water content decreases, and most authors suggest therefore that the relaxation strength derives from relaxation
-
13786 J. Phys. Chem., Vol. 98, No. 51, 1994
Green et al.
modes involving the water hydration shell of the Water at the protein surface was emphasized in our introduction.) A at boundaries of globular molecules, like the “tissue” material large heat capacity in the /3-relaxation regime would in this case of cluster models of glasses,57 would certainly be expected to be consistent with the idea that /?-relaxations are actively contribute to the secondary relaxation manifold, but water involved in the protein function: this suggests one reason why incorporated in between-chain sites away from the surface and function is usually lost as water content decreases. acting as a plasticizer would also enhance the /3-relaxation In the phenomenology of viscous liquids, the magnitude of contributions from the side chains. Because of the greater the heat capacity change at the glass transition and the thermal motion in the side chains, it has not been possible from temperature dependence of the various relaxation times freX-ray studies so far to assign unambiguous water molecule quently prove to be ~ o r r e l a t e d .It~ ~would therefore be interestpositions in the side chain regionss8 Ambient temperature ing to measure the activation energy for the structural relaxation process in cytochrome c by DSC techniques,22,61 analysis of the dependence of the dielectric constant of lysozyme for comparison on water contentsg suggests that water molecules in excess of with the heat capacity change and with the activation energy 50 per molecule (-15 wt %) are rotationally quite free (on measured by mechanical spectroscopy where available, e.g., for kilohertz time scales) and hence could be involved with the side lysozyme by Gorelov and M o r o z ~ v .However, ~~ the smearing of the glass transition in the protein solutions, in combination chains. The variation with water content of Tgof the a-process can with the problem of variable recrystallization of excess water, be judged from early studies on the protein wheat g l ~ t e n , ~ ~ . ~ ’makes the determination of the enthalpy relaxation temperature dependence by variable scan rate DSC studies impractical. On for which a wide glass-forming composition range is available and the glass transitions are almost as well-defined as in our the other hand, neither of these problems exists with the simpler homopeptide- water system. Similar behavior has now been hydrated homopeptide system. Thus, the “activation energy” seen for IIS globulin ( l e g ~ m i n ) particularly , ~ ~ ? ~ ~ when denatured. for enthalpy relaxation in poly-~-ASN-H20, which will be that In fact, the IIs globulin water data of Sochava and S m i r n ~ v a ~ ~ for the a-process, can be determined. The results for several provide a smooth continuation of PO~Y-L-ASN data to 0% water. water contents have been shown in Figure 5 . Figure 5 also The dependences of Tg on water content in these systems are makes a comparison of the homopeptide result with the behavior compared with each other in Figure 4 and also compared with of the model fragile glass former o-terphenyl determined with the same instrument. Since the scan dowdscan up procedure data for a classical polymer-plasticizer system, polystyrene styrene. described by Debolt et aL61 was followed, the slope of each Taken together, these data in Figure 4 give strong support to plot gives correctly the activation energy at Tg,as defined by the picture of hydrated proteins as water-plasticized polymer EH = R d In Q/d( UTg) systems27-32,34to which we add the notion that anomalous (4) smearing to low temperatures occurs because of incorporation where Q is the coolingheating rate. Because of the relatively of calorimetrically strong /?-relaxations as water content is broad glass transitions and the absence of the overshoots seen increased. The manner in which the dynamics of certain interior motions in the protein are influenced by the solvent dynamics6*21b in simpler systems, only the Tg onset definition of T.. (see Figure 3) has been used in the analysis. Note in Figure 5 that the EH (the so-called “ slaved glass transitions”6) is, however, not values for all of the polypeptide water solutions are much clarified by our study: the key question here is whether the smaller than for the fragile liquid o-terphenyl, studied in the solvent couples to the a - or the /?-components of the total same measurement series. The EH value obtained from the relaxation spectrum and whether the decoupling observed at Figure 5 data for OTP, 524 kJ/mol, is in good agreement with lower temperatures by Dosler and colleagues21b(analogous to those determined from viscosity6* and structural relaxatiod3 the decoupling of conductivity from viscosity in fast ion glasses) studies. is related to this distinction. These data may be used to make tentative comparisons of 2. Heat Capacity and Fragility of Hydrated Polypeptide the dynamical characteristics of the a-process in hydrated Systems. If hydrated proteins are indeed glass-former systems, proteins with those of other polymer and liquid systems and then it is important to consider further the thermodynamic thus to provide a broad backdrop against which much of the strengths of their transitions (whether of a- or /3-relaxation detailed information available on kinetic processes in proteins origin) and also their “fragilitie~”:~since these must be relevant can be discussed. A useful basis for comparison of different to biological function. liquids is the stronglfragileclassification scheme which classifies The magnitude of the heat capacity in any stationary system liquids according to their deviations from Arrhenius relaxation is determined by the mean square entropy fluctuation (AS’), kinetic^.'^ The “strength” of a liquid may then be quantified and in a classical glass former, the magnitude of the conjiguby means of the D parameter in the modified Vogelrational heat capacity AC, is directly proportional to the Tammann-Fulcher equation for the relaxation time increase in mean-square entropy fluctuation at T,,according to the relations60 z = zo exp[DTd(T - To)]
+
+
+
(3) where k~ is the Boltzmann constant. Since the conformational changes involved in protein functions like the passage of 0 2 to a heme group form part of this spectrum of entropy fluctuations, their probability should be enhanced in a structure which has a large excess C, provided the configurational degrees of freedom of the system are properly coupled together. (The remarkable coupling of the vital interior relaxation processes to the dynamics
Graphically, the behavior of different systems may profitably be compared using a Tg-scaled Arrhenius plot, of which an example containing data for a range of chain polymer systems@ is shown in Figure 8. Many chain polymer systems are found to be extremely fragile, D < 5 . The strongest behavior so far recorded for a chain polymer is that of polyisobutylene [-CC(CH3)2-ln. When a wide range of relaxation time data are not available, the “strength” D, or its inverse, the “fragility”, can be assessed from the slope of the scaled Arrhenius plot at Tg,Le., from the activation energy measured at Tg.For instance, the “fragility”
The Protein-Glass Analogy
0.0
0.2
J. Phys. Chem., Vol. 98, No. 51, 1994 13787
0.4
0.6
0.8
1 .o
T g IT
+
Figure 8. Values of relaxation times for PO~Y-L-ASN15.5% H20
(thick solid line) calculated over a range of temperatures from the VTF equation with parameters determined by fragility obtained from DSC scan rate dependence studies of Figure 5 . Comparison is made with longitudinal relaxation time data for several types of chain polymers of differing fragility identified in legend (from ref 40). Solid lines are plots of the VTF equation for different strength parameters D (encircled) while dashed lines are lines of different fragility m defined from Arrhenius slope at T, by eq 6. m of a liquid has been defined65by the relation
m = d log t(T,)ld(llT,)= EH/2.303RTg
(6)
and this is related to the strength parameter D of eq 5 by65
m = 17
+ 59OlD
(7)
which asserts that z changes by 17 orders of magnitude between a phonon-like high-temperature limit and the value of -100 s at the glass transition temperature (Tgdetermined at 10 K/min).22 The values of EH and m for the polypeptide-water solutions and the molecular liquid OTP are collected in Table 1. The important finding from Figure 5 and Table 1 is the “strength’ exhibited by the variably hydrated polyhomopeptides implied by the small (and apparently composition independent) values of in. We have included a VTF plot of the relaxation times characteristic of a liquid with m = 40 ( D = 26) in Figure 8 (thick dashed curve) and note that the behavior implied is even stronger than that of polyisobutylene. Strong liquid behavior is also indicated by the relatively small increase of C, at Tg for the homopeptide (see Figure 3 and Table l), compared with the intermediate hydrogen-bonded liquid glycerol, and by the broad glass transition ATg/Tgrelative to those of more fragile liquids (see Table 1). However, this conclusion will need to be confirmed by more reliable methods, such as transient mechanical elastometry. The question then provoked by the comparisons in Figure 4 is whether the relaxation behavior of natural proteins, or at least the backbone-dominated component thereof, is also strong liquidlike. The enthalpy relaxation time-temperature dependence at Tgreported for myoglobin crystals by Miyazaki et al.35 certainly implies very strong liquid behavior, m = 28-32, by eq 7. Comparable values are implied by the small “effective” Arrhenius activation energies for slowed-down processes influenced by solvent viscosity in myoglobin near 160 K,lz>@ where eq 7 yields fragility in values of -30. However, the temperature ranges in question here suggest these processes occur in the p-like water-dominated subsystem. Such subsystems could owe their equally low fragilities to something akin to the open network hydrogen-bonding scheme similar to that which makes water near its T, a strong liquid. This would
be consistent with the fact that the activation volume for CO rebinding processes is either very small or negative,66characteristic of water and other open networks (though other explanations are also available66). It is also consistent with the discussion of hydrated myoglobin structure given by Doster et al.?l who identified the aqueous component as “amorphous solid water”. Strong liquid character is also consistent with the finding from neutron scattering studiesz1that hydrated proteins exhibit a well-defined Boson peak which persists far above any suggested T, (indeed up to denaturation) as in strong glass formers.68 To see whether the time scale assigned to the fastest process identified in blood proteins, which is related to equilibration among the hydrated protein substates, could be consistent with strong liquid behavior, we compare its time scale with the thick dashed line in Figure 8 for the homopeptide. For instance, we take the inverse of the rate constant K* in Figure 10 of ref 12 for Mb* Mb barrier relaxation in myoglobin, which is 2.5 x s at 240 K, and check the value of Tg with which it is consistent. We find T.Tfor this time would be 0.70 from which Tg = 168 K. This is indeed consistent with the calorimetric onset temperature but not with the onset temperature, -200 K,15 of the Debye-Waller factor slope change discussed in the Introduction of this paper. Likewise, the average heme relaxation time in the T range 260-280 K measured by Mossbauer spectroscopy in metmyoglobin is 3 x low6s,16,69which would require T, = 170 K, rather lower than the 200 K suggested by the onset of the 57Fe Debye-Waller factor slope change. If we assign a Tg of ~ 2 0 0 - 2 2 0 K to backbone relaxation at these hydrations, then both of the observations imply either (i) a decoupling from polypeptide backbone kinetics, as discussed earlier, or (ii) a temperature dependence more fragile than that of PO~Y-L-ASN. Either of these would be consistent with the highly nonexponential relaxation found by recent analysis of the metmyoglobin Mossbauer s p e ~ t r a , ’as~ *well ~ ~ as of a variety of other molecular processes in pr0teins.6-l~ Nonexponentiality, Le., the need to introduce a broad distribution of relaxation times in order to describe the relaxation of a system after a perturbation, is the second canonical characteristic of glass-forming liquids (applying to both primary and secondary relaxations), and we discuss it in the context of protein behavior in the next section. 4. Nonexponentiality and Nonlinearity of Relaxation. The typical glass formerpolymeric or otherwise-exhibits not only a non-Arrhenius temperature dependence but also (i) nonexponential relaxation, which means eq 1 is needed, and (ii) nonlinear relaxation, which means that when a relaxational process is studied in the nonergodic (out-of-equilibrium) state, its relaxation time depends on how far from equilibrium the system is. These are the three canonical features of the a-relaxation in glass formers, and recent studies by Hodge70 and BOhmer7l have suggested that all three characteristics are c~rrelated.~ A~ fragile liquid usually exhibits more highly nonexponential relaxation kinetics and a strong nonlinearity. This is why physical aging in polymers, which are usually fragile in character, is such a problem. Most conventional glass formers, particularly chain polymers, also exhibit what is called “time-temperature superposability” (also called “thermorheological simplicity”), meaning that the departure from exponentiality, p of eq 1, is independent of temperature. In this section we comment briefly on what we say about polypeptides and proteins in respect to the latter two characteristics. Because of the emphasis we are giving to secondary relaxations in our interpretation of protein dynamics, we will note where connections between primary and secondary relaxations can be made.
-
Green et al.
13788 J. Phys. Chem., Vol. 98, No. 51, 1994 It is possible to use calorimetry to test for the presence of a broad distribution of relaxation times. This is by use of the anneal-and-scan studies of the type illustrated in Figures 6 and 7, which we now discuss. The phenomenology of enthalpy relaxation in glass-forming systems has been examined by a number of a ~ t h o r s . ~Hodge ~ - ~ ~and B e r e n ~in~particular ~ have drawn attention to the complex behavior which is found when the relaxation is very nonexponential. For systems with weakly nonexponential behavior, annealing below Tg (e.g., at TA,3 in Figure 6) leads, on reheating, to strong C, “overshoots” which are larger the lower the TA, provided that the glass has been annealed to equilibrium. However, for strongly nonexponential systems the tendency is to develop “annealing p r e p e a k ~ ”This .~~ is because only a small fraction of the total of relaxing elements is able to relax in the time allowed during annealing at TA, so only this component of the enthalpy can be reabsorbed on the upscan. The finding in Figure 6 that, for the homopeptide, most annealing steps (e.g., at TAJ and T A , ~give ) prepeaks rather than overshoots testifies to the breadth of its relaxation spectrum. Thus, we find a contradiction to the normal correlation between liquid strength and e~ponentiality~~-unless, of course, the extra components relaxing come from an additional class of enthalpy absorbing processes, beyond the a-relaxation. In an attempt to quantify the nonexponentiality of the homopeptide relaxation, dielectric relaxation studies (to be reported in detail later) were carried out. Although these were frustrated by the presence of a large proton conductivity, the corresponding electric modulus spectra78c o n f i i e d the presence of a very broad distribution of relaxation times. On the other hand, the modulus relaxation time found in this work was much shorter than the enthalpy relaxation time, suggesting that the protodwater molecule rotations are somewhat decoupled from the primary relaxation and hence are to be regarded as ,&like processes, which are characteristically broad. The involvement of P-processes thus appears already, though weakly so, in the heat capacity behavior of the model homopeptide system, even at lower water contents (see Figure 6 and discussion thereof). Thus, it is uncertain whether the small values of p @m @ c D ) ~of ~ )eq 1 commonly found for dynamical processes in proteins, PKWW = 0.2-0.44,11,12,15,1g.66 (cf. the values 0.4-0.7 commonly found for liquids and polymers near their TgZ3), should be regarded as further support for the importance of ,%like processes in proteins or as evidence for exceptional nonexponentiality of the a-relaxation in proteins. The microheterogeneous nature of the chains in the protein case would certainly lead to the latter expectation, and the truth is probably somewhat in between. The annealing studies on the cytochrome c case illustrated in Figure 7 and ref 27 show how, in a protein, the somewhat unusual behavior of the homopeptide system can be carried out to an extreme in which very little enthalpy can be relaxed out by any single choice of annealing temperature. Even an annealing treatment carried out at 183 K, i.e., well above the onset Tgof 160 K, causes a peak to appear on rescan (peak 2 after TA,2). This sort of behavior is unknown in calorimetric studies of the glass transition in molecular liquids and shows that a large part of the configurational heat capacity remains inaccessible at 183 K even on long time scales-as expected if this is a B-relaxation region. Such behavior was illustrated in greater detail in recent paper by Sartor et al.,27who showed by the same technique that the presence of a hierarchy of separable relaxation elements, extending up to ambient temperatures, was a general feature of proteins. They demonstrated that similar behavior could be observed in an interpenetrating network polymer and interpreted it using the Debolt-Moynihan ap-
proach22s61in which the relaxation time z is written in a manner which allows nonergodicity to be taken into account via a structural state or “fictive temperature” Tfdependence. This deals with the nonlinear aspect of relaxation by allowing z to depend on the fictive temperature Tf as well as the real temperature T by writing z as the sum of two terms weighted by the nonlinearity parameter x (0 < x < 1) according t022,61.74-?7
z = To ex
%$+ [l -
XI-
3
Note that equilibrium is defined by the condition Tf= T, since Tfis defined as the temperature at which the existing structure is the equilibrium structure. Sartor et al.27 obtained an impressive simulation of the observed behavior by using an exceptionally broad distribution of relaxation times @ = 0.07) and a large nonlinearity parameter, x = 0.7. Both of these are characteristic of extremely fragile systems, the p value in particular being reminiscent of spin glass b e h a ~ i o r . ’Con~~~~~ sistent with such assignments, the value of AH obtained from the fit, 300 kJ/mol, leads to a large fragility parameter m according to eq 6, m = 92 if Tg= 170 K. However, this is in conflict with the evidence from the homopeptide behavior and other observations12*66,80 that the polypeptides are rather strong in their temperature dependences. A resolution of this conflict may be found in the results of an earlier study by Pissis and c o - w ~ r k e r s , who ~ ~ , ~used ~ a dielectric analog of the calorimetric anneal-and-scan technique. Just as we observed a heat absorption on the upscan depending on our annealing temperature (even above the ‘‘Ti’),so do they detect a current flow at a temperature depending on the temperature of polarization. The additional feature obtained by Pissis et al. is a measure of the temperature dependence of the selected element of the relaxation spectrum. Rather than observing a single large value of the activation energy at each temperature, Pissis et al. showed that each of the elements has a different activation energy which is higher the higher the temperature at which it is observed. Similar behavior has been seen in hydrogel systems and a chain polymer polarized below Tg.As noted above, the latter usually exhibit “thermorheological simplicity”; Le., their relaxation spectra exhibit a constant (nonDebye) form over a wide range of temperatures.81*82This can only be true if all components of the non-Debye spectrum of relaxation times have the same activation energy. On this basis it would seem that the proteins either are behaving in a thermorheologically complex manner or are being studied below their “real” T,. However, repetition of these measurements on systems of known thermorheological character is needed before the implications can be confidently accepted. Certainly, in the presence of thermorheological complexity if becomes difficult separately to assess the degree of nonlinearity of the relaxational response and indeed also the fragility, and a new approach to the modeling of this behavior may be required. It will first be important to clarify whether or not the denatured state is thermorheologically more simple as suggested by our preliminary dielectric study of the hydrated homopeptide. An implication of the existence of thermorheological complexity is the existence of elements in the spectrum of relaxation processes which have large eq 7 m values. This would be consistent with Frauenfelder’s remarkg3that “proteins are both strong and fragile” depending on which process, i.e. which component of the total spectrum, one is examining. The possibility of a division of the system’s total configurational degrees of freedom into subsystems with not only
The Protein-Glass Analogy different activation energies but also differing fragilities is intriguing and is utilized in the next segment of our discussion. 5. Denaturation and Fragility. Here we consider how denaturation might relate to the properties we have discussed thus far. Denaturation, the sudden loss of tertiary protein structure, occurs at the upper (high r ) end of the configurational excitation process for native proteins, about which our measurements have not had much to say. While it is probably best seen as an entirely unrelated phenomenon, the following idea may merit some examination. In view of the very wide range of fragilities exhibited by simple chain polymer systems (see Figure 8), it is reasonable to ask what could be found at the extreme of high fragility. Extreme fragility corresponds to the case where all the entropy of disordering (and all the changes in relaxation time associated with it) occur in a very narrow range of temperature near Tg (see Figure 8). But this extreme would then constitute a first-order transition from glass to fluid. Behavior close in character to this has recently been suggested for water itself near 228 K where the inverse transition is seen on hyperquenching-as a transition from fragile liquid to strong l i q ~ i d . The ~ ~ ,transition ~~ is to a strong liquid rather than to a glass transition because only a fraction of the liquid degrees of freedom are lost in the first-order transition. The closest well-studied example of this sort of transition is the transition between mesophases in liquid crystal systems, in which the order parameter is orientational in nature (and changes discontinuously at the phase transition) rather than hydrogen bond driven short-range order, as in the water case. Now if a specific order of cross-linking of polymer chain units constitutes the folded state of proteins, then a discontinuous change in this order parameter constitutes the denaturing transition. It is known that this is associated with a sudden and reversibles5 change in the local segmental mobility,s6 so it has much in common with the strong fragile liquid transition (the molten globule being the equivalent of the higher entropy fragile liquid state). The transformation from a strong to a fragile liquid via a weak first-order transition has recently been described using a simple thermodynamic model appropriate to systems with a subsidiary minimum in the internal energy due to favorable packing at a volume different from that of van der Waals packing,87and it is believed to account for the behavior of water at low temperatures and moderate pressures (if not ambient).s7 The model predicts that, on heating, the first-order transition should be preceded by anomalies anticipating an absolute mechanical instability (a spinodal) at a temperature slightly above that of the first-order transition. This is exactly the implication of Morozov and Morozova’s studies of mechanical softening of protein crystals as the temperature of the unfolding transition is approached.ss They argue forcefully that the instability in the crystal, implied by their data to lie a few degrees above the unfolding temperature, is directly consequent on an equally imminent instability in the folded molecules themselves. The scenario for protein relaxation outlined in this paper, incorporating fast p-relaxations, slower a-relaxations, and thermorheological complexity, couched in the language of relaxing strong and fragile liquids, complements the n-tier description of proteins of F r a ~ e n f e l d e and r ~ ~W~ o~ l~y~n e ~ but *~~~ adds a new upper tier, with just two statesg0(two megabasins of probability on the potential energy hypersurface, in Stillinger’s language,91see also ref 92), for the liquid polymorphs. Indeed, the line separating the folded from unfolded states in Figure 6 of ref 89, in which the transition occurs at a temperature
-
J. Phys. Chem., Vol. 98, No. 51, 1994 13789 which is lower the larger the energy landscape roughness parameter, seems to bear a close relation to our notion of change from fragile (high density of energy minima on the hypers u r f a ~ e ~to~ ~strong , ~ ~ (low ) density of minima), across the folding transition. The fact that some proteins, when less hydrated than those we examined here, show a substantial increase in configurational heat capacity on d e n a t u r a t i ~ n ~ ~ indicates that in these cases a relatively larger fraction of the system’s configurational degrees of freedom are involved in the “strong-to-fragile” transition. It would be expected that such proteins (apparently some globular proteins like 11s globulin (legumin) would be those with the larger denaturation entropies, and this seems to be the case.34
Concluding Remarks In view of Figure 4,we believe it should be possible to go considerably further with the imitation of some features of protein phenomenology, using simple homo and dipeptide polymers with hydrophilicities exceeding that of the present PO~Y-L-ASN system. Hopefully such imitations will eventually include some aspects of the folding transition. In the meantime it seems important to explore further the phenomenology of bulk homopeptide polymers and other polymers with hydrogen bond cross-linking, as a class of chain polymer melts about which not much is currently written.
Acknowledgment. This work was supported by the NSFDMR under Solid State Chemistry Grant DMR 9108028. We thank Professor Gregory Petsko and Dr. Dagmar Ringe for very helpful discussions and for their suggestions of appropriate homopeptides for this study, Professor Hans Frauenfelder for stimulating our original interest in this problem and for helpful comments on the manuscript, Dr. Harry Levine for reminding us about the T i point, and many other colleagues, particularly Walter Kauzmann and Uli Nienhaus, for their criticism and their tolerance of our ignorance while this paper was being written. References and Notes (1) Fisher, D. S.; Grinstein, G. M.; Khurana, A. Phys. Today 1988, 14, 56. (2) (a) Frauenfelder, H.; Sligar, S. G.; Wolynes, P. C. Science 1991, 254, 1598. (b) Wolynes, P. G. In Proceedings of the International Symposium on Frontiers in Science; Chan, S . S.,Debrunner, P. G., E&; AIP Conf. Proc. 1988, 180. (3) Austin, R. H.; Beeson, K. W.; Eisenstein, L.; Frauenfelder, H.; Gunsalus, I. Biochemistry 1975, 14, 5355. (4) Austin, R. H. Spin Glasses in Biology. In Directions in Condensed Matter Physics; Stein, D. L., Ed.; World Scientific: Singapore; Vol. 6, p 179. (5) Goldanskii, V. I.; Krupyanskii, Yu. F.; Fleurov, V. N. Dokl. Akad. Nauk SSSR 1983, 272, 978. (6) Iben, I. E. T.; Braunstein, D.; Doster, W.; Frauenfelder, H.; Hong, M. K.; Johnson, J. B.; Luck, S.; Ormos, P.; Schulte, A,; Steinbach, P. J.; Xie, A. H.; Young, R. D. Phys. Rev. Lett. 1989, 62, 1916-1919. (7) Austin, R. H.; Beeson, K. W.; Frauenfelder, H.; Gunsalus, I. Biochemistry 1975, 14, 5355. (8) Frauenfelder, H.; Petsko, G. A,; Tsemoglou, D. Nature (London) 1979, 280, 558. (9) Hartmann, H. F.; Parak, F.; Steigemann, Petsko, G. A.; RingerPonzi, D.; Frauenfelder, H. Proc. Natl. Acad. Sci. U S A . 1982, 79, 4967497 1. (10) Frauenfelder, H.; Parak, F.; Young, R. D. Annu. Rev. Biophys. Biophys. Chem. 1988, 17, 451. (11) Young, R. D.; Frauenfelder, H.; Johnson, J. B.; Lamb, D. C.; Nienhaus, G.U.; Philipp, R.; Scholl, R. Chem. Phys. 1991,158,315-327. (12) Steinbach, P. J.; Ansari, A.; Berendzen, J.; Braunstein, D.; Chu, K.; Cowen, B. R.; Ehrenstein, D.; Frauenfelder, H.; Johnson, J. B.; Lamb, D. C.; Luck, S.; Mourant, J. R.; Nienhaus, G. U.; Ormos, P.; Philipp, R.; Xie, A.; Young, R. D. Biochemistry 1991, 30, 3988-4001.
Green et al.
13790 J. Phys. Chem., Vol. 98, No. 51, 1994 (13) Hong, M. K.; Berendzen, J.; Braunstein, D.; Cowen, B. R.; Frauenfelder, H.; Iben, I. E. T.; Mourant, J. R.; Ormos, P.; Scholl, R.; Schulte, A.; Steinbach, P. J.; Xie, A.; Young, R. D. Biophys. J . 1990, 58, 429. (14) (a) Rasmussen, B. F.; Stock, A. M.; Ringe, D.; Petsko, G. A. Nature 1992, 357, 423. (b) Tilton, R. F., Jr.; Dewan, J. C.; Petsko, G. A. Biochemistry 1992, 31, 2469. (15) (a) Doster, W.; Cusack, S.; Petry, W. Nature (London) 1989,337, 754. (b) Phys. Rev. Lett. 1990, 65, 1080. (16) Singh, G. P.; Parak, F.; Hunklinger, S.; Dransfield, K. Phys. Rev. Lett. 1981, 47, 685. (17) Parak, F.; Heidemeier, J.; Nienhaus, G. U. Hyperfine Interact. 1988, 40, 147. (18) (a) Parak, F.; Nienhaus, G. U. J . Non-Cryst. Solids 1991, 131133, 362. (b) Nienhaus, G. U.; Frauenfelder, H.; Parak, F. Phys. Rev. B 1991, 43, 3345. (19) Ansari, A.; Jones, C. M.; Henry, E. R.; Hofrichter, J.; Eaton, W. A. Science 1992, 256, 1796. (20) Dubochet, J.; Adrian, M.; Teixeira, J.; Kadiyala, R. K.; Alba, C. M.; MacFarlane, D. R.; Angell, C. A. J . Phys. Chem. 1984, 88, 6727. (21) (a) Doster, W.; Bachleitner, A.; Dunau, R.; Hiebi, M.; Luscher, E. Biophys. J. 1986,50,213-219. (b) Settles, M.; Post, F.; Muller, D.; Schulte, A.; Doster, W. Biophys. Chem. 1992, 43, 107. (22) Moynihan, C. T.; Macedo, P. B.; Montrose, C. J.; Gupta, P. K.; Debolt,M.A.;Dill,J.F.;Dom,B.E.;Drake,P.W.;Easteal,A.J.;Elte~, P. B.; Moeller, R. P.; Sasabe, H. A.; Wilder, J. A. Ann. N.Y. Acad. Sci. 1976, 279, 15. (23) (a) Angell, C. A. In Relaxations in Complex Systems; Ngai, K., Wright, G. B., Eds.; National Technical Information Service, U.S. Department of Commerce: Springfield, VA, 1985; p 1. (b) Angell, C. A. J . NonCryst. Solids 1991, 131-133, 13. (24) Gotze, W. In Liquids, Freezing, and the Glass Transition; Hansen, J. P., Levesque, D., Eds.; NATO-AS1 Series; Plenum: New York, 1989. (25) (a) Haly, A. R.; Snaith, J. W. Biopolymers 1971, IO, 1681-1699. (b) Haly, A. R.; Snaith, J. W. Biopolymers 1968, 6, 1355-1377. (26) Andronikashvili, E. L.; Mrevlishvili, G. M.; Japaridze, G. Sh.; Sokhadze, V. M.; Kvavadze, K. A. Biopolymers 1976, 15, 1991-2004. (27) (a) Sartor, G.; Hallbrucker, A.; Hofer, K.; Mayer, E. J . Phys. Chem. 1992, 96, 5133. (b) Sartor, G.; Mayer, E.; Johari, G. P. Biophys. J. 1994, 66, 249-258. (28) Tsereteli, G. I.; Smimova, 0. I. Biophysics 1989, 34 ( 5 ) , 984984. (29) Batzer, H.; Kreibich, U. T. Polym. Bull. 1981, 5, 585. (30) Slade, L. American Association of Cereal Chemists 69th Annual Meeting, Minneapolis, 1984; abstract 112. (31) Hoseney, R. C.; Zeleznak, K.; Lai, C. S. Cereal Chem. 1986, 63, 285-286. (32) Slade, L.; Levine, H.; Finley, J. W. In Protein Quality and Eflects of Processing; Phillips, R. D., Finley, J. W., Eds.; Marcel Dekker: New York, 1989. (33) Kuntz, I. D.; Kauzmann, W. Adv. Protein Chem. 1974, 28, 239345. (34) (a) Sochava, I. V.; Tseretoli, G. I.; Smirnova, 0. I. Biojizika 1991, 36. (b) Sochava, I. V.; Smirnova, 0. I. In Food Hydrocolloids 1993,6 (6), 513-524. (35) Miyazaki, Y.; Matsuo, T.; Suga, H. Chem. Phys. Lett. (in press). (36) (a) Pissis, P. J . Mol. Liq. 1989,41, 271. (b) In Proton Transfer in Hydrogen Bonded Systems; Bountis, T., Ed.; Plenum Press: New York, 1992; p 207. (37) Pissis, P.; Anagnostopoulou-Konsta, A.; Apekis, L.; DaoukakiDiamanti, D.; Christodoulides, C. J. Non-Cryst. Solids 1991, 131-133, 1174-1181. (38) (a) Gorelov, A. V.; Morozov, V. N. Biophys. Chem. 1987,28, 199. (b) Morozov, V. N. Presentation at USSR-USA Workshop on Proteins, Chemogolovska, U.S.S.R., July 1991. (c) Morozov, V. N.; Gevorkian, S. G. Biopolymer 1985, 24, 1785. (39) (a) McCrum, M. G.; Reid, B. E.; Williams, G. Anelastic and Dielectric Effects in Polymeric Solids; Wiley: London, New York, 1967. (b) Johari, G. P.; Goldstein, M. J . Chem. Phys. 1970, 53, 2372. (40) (a) Kuczera, K.; Smith, J.; Karplus, M. Proc. Natl. Acad. Sci. U.SA. 1990, 87, 1601. (b) Kuriyan, J.; Karplus, M. J . Mol. Biol. 1990, 213, 351. (41) Par& F.; Hartmann, H.; Aumann, K. D.; Reuscher, H.; Rennekamp, G.; Bartunik, H.; Steigemann, W. Eur. Biophys. J . 1987, 15, 237-249. (42) Frauenfelder, H. Int. J . Quanhtm Chem. 1989, 35, 711. (43) Goldstein, M. J . Chem. Phys. 1969, 51, 3728. (44) Fujara, F.; Petry, W. Europhys. Lett. 1987, 4, 921. (45) Petry, A.; Bartsch, E.; Fujara, F.; Kiebel, M.; Sillescu, H.; Farrago, B. Z . Phys. B: Condens. Mater. 1991, 83, 175. (46) Buchenau, U.; Zom, R. Europhys. Lett. 1992, 18, 523.
(47) Frick, B.; Richter, D.; Petry, W.; Buchenau, U. Z. Phys. 1988, B70, 73. (48) Chahid, A.; Allegria, A.; Colmenero, J. Macromolecules, in press. (49) Frick, B.; Richter, D. Phys. Rev. B 1993, 47, 14795. (50) (a) Ngai, K. L.; Rendell, R. W.; Plazek, D. J. J . Chem. Phys. 1991, 94, 3018. (b) Ngai, K. L.; Rendell, R. W.; Rajopal, A. K.; Teitler, S. Ann. N.Y. Acad. Sci. 1986, 484, 150. (51) Shao, J.; Angell, C. A. J . Chem. Phys., submitted. (52) Angell, C. A. J . Am. Ceram. SOC. 1968, 51, 117. (53) Boehm, L.; Smith, D. L.; Angell, C. A. J. Mol. Liq. 1987.36, 153. (54) Green, J. L.; Angell, C. A. J . Phys. Chem. 1989, 93, 2880. (55) Hofer, K.; Mayer, E.; Johari, J. P. J . Phys. Chem. 1990, 94, 2689. (56) Fan, J.; Cooper, E. I.; Angell, C. A. J . Phys. Chem. 1994,98,9345. (57) Rao, C. N. R.; Rao, K. J. Mater. Res. Bull. 1982, 17, 1337. (58) Blake. C. C. F.: Pulford. W. C. A.: Artvmink. P. J. J. Mol. Biol. 1983,167, 693. (59) Bone. S.: Pethig. R. J . Mol. Biol. 1982. 157. 571. (60)Landau,L.; LifLhitz, E. M. Statistical Physics; Pergamon: London, 1958. (61) Debolt, M. A.; Easteal, A. J.; Macedo, P. B.; Moynihan, C. T. J . Am. Ceram. Soc. 1976, 59, 16. (62) Laughlin, W. T.; Uhlmann, D. R. J . Phys. Chem. 1972, 76, 2317. (63) Wang, C. H.; Fytas, G.; Lilge, D.; Dorfmiiller, Th. Macromolecules 1981, 14, 1363-1370. (64) Angell, C. A,; Monnerie, L.; Torell, L. M. Symp. Mater. Res. SOC. 1991, 215, 3. (65) Bohmer, R.; Angell, C. A. Phys. Rev. B 1992, 45, 10091. (66) Frauenfelder, H.; Alberding, N. A.; Ansari, A,; Barunstein, D.; Cowen, B. R.; Hong, M. K.; Iben,I. E. T.; Johnson, J. B.; Luck, S.; Marden, M. C.; Mouranti, J. R.; Onnos, P.; Reinisch, L.; Scholl, R.; Schulte, A.; Shyamsunder, E.; Sorensen, L. B.; Steinbach, P. J.; Xie, A.; Young, R. D.; Yue, K. T. J . Phys. Chem. 1990, 94, 1024-1037. (67) Angell, C. A. J . Phys. Chem. 1993, 97, 6339-6341. (68) Angell, C. A,; Cheeseman, P. A,; Tamaddon, S. Science 1982,218, 885. (69) Nienhaus, G. U.; Parak, F. Hyperfine Interact., in press. (70) Hodge, I. M. Symp. Mater. Res. Soc. 1991, 215, 3. (71) Bbhmer, R.; Angell, C. A. In Disorder Effects on Relaxational Processes; Blumen, A,, Richert, R., Eds.; Springer: Berlin, 1993. (72) Earlier studies by Ngai (Ngai, K. L.; Rendell, R. W.; Rajopal, A. K.; Teitler, S. Ann. N.Y. Acad. Sci. 1986, 484, 150; Ngai, K. L.; Rendell, R. W. J . Chem. Phys. 1991, 94, 3018) and Bohmer et al. (Bohmer, R.; Angell, C. A. Phys. Rev. B 1992, 45, 10091) had established connections between the f i t two. (73) Narayanaswamy, 0. S. J . Am. Ceram. SOC. 1971, 54, 491. (74) Moynihan, C. T.; Opalka, S. M.; Mossadegh, R.; Crichton, S. N.; Bruce, A. J. In Molecular Dynamics and Relaxation Phenomena in Glasses; Dorfmuller, Th., Williams, G., Eds.; Lecture Notes in Physics Vol. 277; Springer: Berlin, 1987; p 16. (75) Scherer, G. W. J . Am. Ceram. SOC. 1984, 67, 504. (76) Hodge, I. M. Macromolecules 1983, 16, 898. (77) Hodge, I. M.; Berens, A. R. Macromolecules 1982, 15, 756, 762. (78) Hodge, I. M.; Angell, C. A. J . Chem. Phys. 1977, 67, 4. (79) Ogielski, A. T. Phys. Rev. 1985, 32, 7384. (80) Young, R. D. J. Chem. Phys. 1993, 98, 2488. (81) Borjesson, L.; Stevens, J.; Torell, L. M. Polymer 1987, 28, 1803. (82) Kremer, F.; Boese, D.; Fetters, L. J . Non-Cryst. Solids 1991, 131133, 728. (83) Frauenfelder, H., private communication. (84) The inverse is the transition from strong liquid to fragile liquid on flash heating, as in the analogous case of “fiit-order melting” of (tetrahedral) amorphous silicon (Donovan et al. J . Appl. Phys. 1985, 57, 1795). The fast temperature change is needed to avoid the crystalline state, since the phenomenon, in both silicon and water cases, occurs in the metastable supercooled state. (85) Sochava, I. V.; Beloposkaya, T. V.; Smimova, 0. I. Biophys. Chem. 1985, 22, 323. (86) Kuwajima, K. Proteins Struct. Funct. Genet. 1973, 6, 87. (87) Poole, P. H.; Sciortino, F.; Grande, T.; Stanley, H. E.; Angell, C. A. Phys. Rev. Lett. 1994, 73, 1632. (88) Morosov, V. N.; Morosova, T. Ya. J . Biomol. Struct. Dyn. 1993, 11, 459. (89) Bryngelson, J. D.; Onuchic, J. N.; Socci, N. D.; Wolynes, P. G. J . Phys. Chem., in press. (90) (a) Shaklovitch, E. I.; Gutin, A. M. Nature 1990, 346, 773. (b) Privalov, P. L. Adv. Protein Chem. 1979, 33, 167. (91) Stillinger, F. H. Phys. Rev. B 1990, 41, 2409. (92) Angell, C. A. Proc. Natl. Acad. Sci. USA., in press. I
,
I
