Proteins and Glasses
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HANS FRAUENFELDER Center for Nonlinear Studies, MS B258, Los Alamos National Laboratory, Los Alamos, NM 87545, [email protected]
ABSTRACT The structure, the energy landscape, and the dynamics of proteins and glasses are similar. Both types of systems display characteristic nonexponential time dependencies of relaxation phenomena. Experiments suggest that both, proteins and glasses, are heterogeneous and that this fact causes the observed time dependence. This result is discussed in terms of the rough energy landscape characteristic of complex systems. INTRODUCTION At first look, proteins and glasses are dissimilar. Proteins are built from 20 different building blocks, amino acids.' Of the order of a hundred amino acids are covalently linked together to form a linear polypeptide chain. If the sequence satisfies some not fully understood conditions, the linear polypeptide chain folds into an often globular structure, the working protein. Textbooks picture the folded protein as a unique ordered structure. Glasses (amorphous or noncrystalline solids), on the other hand, are in essence thermally arrested ("frozen") liquids, without crystalline order. 2 Nevertheless, proteins and glasses display similarities that distinguish both from crystalline solids.3 Two, in particular, are conspicuous. The first concerns the time dependence of relaxation phenomena. These are usually nonexponential in time, and can often be described by a stretched exponential function, (D(t) = exp[- {k(T)t }13,(1 where 4D(t) describes the relaxing observable and is often normalized to (D(0) = 1. The exponent 13 is essentially temperature independent over a broad range of T, is less than 1, and can be as small as 0.1.45 6 7 The nonexponential time dependence can also be characterized by the expansion 1(t) = f f(k) exp[-k(T)t] dk,
(2)
where f(k) is the probability density for having a rate coefficient between k(T) and k(T) + dk. In a simple system, f(k) is a delta function. In glasses and proteins, however, f(k) can extend over a broad range of rate coefficients and can often be approximated by a Gaussian. The second observation concerns the temperature dependence of the rate coefficient k(T). In glasses and proteins, k(T) usually does not follow an Arrhenius law, but can be approximated by a Tamann-Vogel- Fulcher or a Ferry equation. Experiments thus show that proteins and glasses share two properties, non-exponential time dependence and non-Arrhenius temperature dependence. These properties can be traced 343 Mat. Res. Soc. Symp. Proc. Vol. 455 ©1997 Materials Research Society
back to the fact that both, proteins and glasses, have an aperiodic and frustrated structure. Aperiodicity and frustration, in turn, lead to the existence of conformational substates and of a rough energy or conformation landscape. CONFORMATIONAL SUBSTATES AND THE ENERGY LANDSCAPE The concept is simple. Neither glasses nor proteins have a unique structure. In the process of being arrested ("frozen"), a glass can assume a very large number of nearly isoenergetic struct
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