VOLUME 62, NUMBER 16 PHYSICAL REVIEW LETTERS 17 APRIL 1989 Glassy Behavior of a Protein I. E. T. Iben, ' ' D. Braunstein, ' W. Doster, H. Frauenfelder, ' M. K. Hong, ' J. B. Johnson, ' S. Luck, ' P. Ormos, ' A. Schulte, ' ' P. J. Steinbach, ' A. H. Xie, ' and R. D. Young ' "'Department of Physics, University of Illinois, 1110 West Green Street, Urbana, Illinois 61801 t"Physik Department, Technische Universitiit Munchen, D 8046 G-raching, Federal Republic of Germany Department of Physics, Illinois State University, Normal, Illinois 61761 (Received 16 June 1988) Quasistatic and kinetic studies of the infrared CO stretch bands of carbonmonoxymyoglobin show that proteins and glasses share essential characteristics, in particular metastability below a transition temper- ature and relaxation processes that are nonexponential in time and non-Arrhenius in temperature. PACS numbers: 87. 15.Da, 64. 70.Pf, 78. 30. Jw, 82. 20.Rp Proteins and glasses may appear to have little in com- mon. Proteins are macromolecules with well defined structures ', glasses are frozen liquids. Despite this diA'erence, proteins and glasses share one fundamental property: Both can assume a very large number of near- ly isoenergetic conformational substates (CS), valleys in the conformational energy landscape. For proteins, the existence of CS followed from the nonexponential time dependence of the binding of small molecules (Oq and CO) to myoglobin at low temperatures. Supporting evi- dence came from other experiments and from theory. For glasses, a potential-energy surface with a large num- ber of minima was postulated by Goldstein; for spin glasses, the evidence came from theory. The existence of CS in proteins and glasses raises the question as to whether these systems share other properties. We now describe some attributes of glasses and later show that these are also found in proteins. Glasses are formed when, on cooling, a liquid becomes a structurally disordered solid. The temperature at which the viscosity reaches 10' poise is called the glass temperature Tg The specific heat below 1 K is approxi- mately proportional to the temperature. Glass proper- ties well below Tg depend on history; glasses are in a metastable (nonequilibrium) state. Near and above Ts the response of a glass to a mechanical or electrical per- turbation is dominated by the a relaxation. Its relaxa- tion function &„(t) is usually nonexponential in time and can be parametrized by a stretched exponential, @„(t) =exp[ — (kt) ~], or by a power law, The average rate at temperature T is (k) =nk, (T). The temperature dependence of k„(T) follows the Arrhenius relation, k„(T) =4 exp[ — E/kttT], only over small tem- perature intervals. Typical values near Tg, E = 1. 6 eV, A =10 s ', also imply that the Arrhenius relation is inappropriate for glasses. However, k„(T) can be de- scribed over more than 10 orders of magnitude either by the Vogel- Tammann-Fulcher equation, k, (T) =AvTt;exp[ — E/ka(T Tp)] or by the relation' " k„(T) = k o exp [ — (To/T ) ]. (3) Both relations fit the data for glycerol (T~ = 185 K) from 190 to 260 K. ' ' We now examine the proteins for glasslike properties. Two are well known: Each individual protein is disor- dered (aperiodic) and the specific heat of proteins below 1 K is glasslike. ' The other attributes, however, have been less well explored. Here we report experiments that verify the metastability at low temperatures, and the nonexponential time and the non-Arrhenius temperature dependence of the protein relaxations near 200 K in car- bonmonoxymyoglobin (MbCO). The folded polypeptide chain of the oxygen-storage protein myoglobin (Mb) embeds a heme group with a central iron atom which reversibly binds ligands such as Oq and CO. ' Our experiments focus on the stretch bands of CO bound to Mb which are very sensitive to external parameters such as solvent, pH, temperature (T), and pressure (P). ' ' We measure the stretch bands with a Mattson Fourier transform infrared spec- trometer. Figure 1 shows that MbCO displays at least three diff'erent CO stretch bands, Ao, A], and A3. Fits to Voigtian line shapes' yield the areas (A;), center fre- quencies (v;), and linewidths (I;) of the A bands. We also observe the rate of heat absorption via diff'erential scanning calorimetry (DSC). The experiments fall into two classes, quasistatic and kinetic. Quasistatic indicates that the glasslike behavior of MbCO below a transition temperature T g prevents attainment of thermodynamic equilibrium. Quasistatic measurements determine the band parameters as functions of solvent, pH, T, and P. In the kinetic studies we observe the relaxation of the protein after a pressure release. Quasistatic experiments Figure 1 shows . — the ir spec- tra from 1910 to 1990 cm ' in a 75% glycerol-water sol- vent (3:1 by volume) at pH 6.8 with potassium phos- phate buA'er. The sample was brought to a pressure P at 300 K. Data were then taken under constant pressure at successively lower temperatures. The cooling rate of 0.01 K/s and waiting time of about 600 s at each temper- 1916 1989 The American Physical Society