Glass Transitions In Proteins

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The idea that water acts as a plasticizer of the protein conformation is not new; it was suggested many years ago by Bone and Pethig [102] on the basis of dielectric relaxation studies (see Chapter 4). In recent years, several studies of fully hydrated proteins and protein crystals also have indicated the existence of a glasslike dynamical transition at about 200 K in proteins. It is well known that glass transition temperatures for synthetic polymers decrease with increases in plasticizer content, yet the possibility that the transition at 200 K in fully hydrated proteins and the transition observed at 298 K at low hydrations are related has been established only recently. In this section, we describe the 200 K transition as well as work on the hydration dependence of the transition temperature. We begin by briefly describing some basic properties of glass transitions in synthetic polymers. Further details can be found in Refs. 103-105 or other standard texts on synthetic polymers.

A. Glass Transition Behavior in Polymers

At sufficiently low temperatures, all amorphous polymers enter a rigid, glassy state in which large-scale segmental motions of the polymer chain no longer occur. Those motions which do occur in the glassy state are local and are restricted to side-chain motions and small-amplitude motions of a few chain atoms. On heating, polymers become flexible in a characteristic temperature range, called the glass-rubber transition region, where atoms of the polymer chain gain sufficient thermal energy for coordinated long-range molecular motions to become possible. The glass transition region in which large changes in mechanical properties occur is usually quite broad (20-30°C), and glass transition temperatures (7"g) vary widely with chemical structure, polymer molecular weight, degree of cross-linking, and sample crystallinity. For example, the glass transition temperature of polyethylene is 140 K, while Tg values for polymers such as polyisoprene and polyisobutylene are about 200 K and those for polystyrene, poly(vinyl chloride) and poly(methyl methacrylate) are about 350-380 K. Glass transition temperatures for amorphous polyamides such as Nylon 6, Nylon 6,6, and Nylon 6,4 are about 330-350 K.

Polymers may undergo a number of transitions as various modes of motion are excited with increases in temperature. By convention, the glass transition is usually designated the a-transition and other transitions associated with side-chain rotations as well as small-amplitude chain motions are designated (3-, 7-, 8-, etc. transitions in order of decreasing transition temperature. For example, polyamides show two transitions in addition to the glass transition: the (3-relaxation process assigned to motions of the amide groups (Fp = 190-210 K), and the 7-relaxation process associated with motions of individual methylene groups along the main chain (Ty = 130 K).

Many thermodynamic and mechanical properties undergo readily observable changes in the glass transition region, and so a variety of techniques are available to characterize the transition. Both dilatometric and calorimetric measurements may be used to define the glass transition temperature [103]. In addition, dilatometric methods provide information about free volume changes in the transition region. The variations in specific volume and enthalpy with temperature through the glass transition region are shown in Fig. 8a. Both show a change in

Figure 8 The temperature dependence of (a) the specific volume and enthalpy of an amorphous polymer through the glass transition region and (b) the corresponding changes in the thermal expansivity and heat capacity.

slope characteristic of second-order transitions. Under normal conditions of measurement, the glass transition is not a true thermodynamic transition but represents a relaxation process. In the limit of long measurement times, however, the glass transition approaches the behavior expected of a true second-order transition [106,107]. The corresponding changes in the heat capacity (Cp) and the characteristic increase in thermal expansivity (a) above the glass transition, attributed to the expansion of free volume in the flexible state, are shown in Fig. 8b. A number of static and dynamic mechanical methods are available to characterize the visco-elastic properties of polymers through the glass transition region, including the determination of Young's modulus and its component storage and loss moduli. Dielectric relaxation and broad-line proton NMR methods have also been used to characterize the transition.

The estimate of the glass transition temperature depends on the time scale of the experiment. Slower measurements give lower values for Tg. In dynamic methods, a 10-fold decrease in frequency can be expected to produce about 5-8°C decrease in the estimate of Tg, although the exact size of the effect will depend on the activation energy for the relaxation process.

The glass transition temperature is greatly influenced by the presence of small molecule "plasticizers." For example, water is a plasticizer of polyamides and causes a dramatic decrease in their glass transition temperatures, as shown in Fig. 9. At hydration levels above 0.10 g water/g polymer, Ts values for Nylon 6, Nylon 6,6 and Nylon 6,4 are about 240 K. This represents a decrease of about 80-100°C relative to Tg in the dry state [100], In polyamides, water provides al-

Hydration g water / g polymer

Figure 9 The glass transition temperature for the polyamides, Nylon 6 (squares), Nylon 6,6 (triangles), and Nylon 4,6 (circles) as a function of hydration (plasticizer content). Data from Welander and Maurer [100].

Hydration g water / g polymer

Figure 9 The glass transition temperature for the polyamides, Nylon 6 (squares), Nylon 6,6 (triangles), and Nylon 4,6 (circles) as a function of hydration (plasticizer content). Data from Welander and Maurer [100].

ternative mobile hydrogen bond donors and acceptors for amide groups, facilitating segmental motions of the polymer chains.

B. Free Volume in Glass Transition Theory

The concept of free volume is central to theories of the glass transition. Segmental motion of polymer chains cannot take place without adjacent regions of free volume. Obviously, such molecular motions are always accompanied by rearrangements of free volume. The thermal expansivity above the glass transition temperature is greater than that below Te . Changes in the specific volume of an amorphous polymer are shown in Fig. 10. The specific volume of the polymer below rg (i.e., in the glassy state) may be expressed as [104],

At Ts the specific volume is

and above Ts (i.e., in the flexible or rubbery state), it is given by

Expansivity Glass
Figure 10 The specific volume of an amorphous polymer as a function of temperature, showing the changes in free volume in the glass transition region. The shaded region represents the free volume. See text for details. Taken from Hiemenz [104],

Vf and Vo refer to the free volume and the volume occupied by the polymer, respectively. The thermal expansivities of the rubbery and glassy states are d(V0 + Vf )/dT

V(T) and dVJdT

If expansion of the glassy state is assumed to occur at constant free volume, the free volume fraction (i.e.,flT) = V((T)/V(T)) above the glass transition temperature can be represented by [108,109]

where K is constant. Examination of volume data for a number of polymer systems by Simha and Boyer [110] suggested that the free volume fraction at Te was a constant equal to about 11%.

Considerations of polymer melt viscosities in terms of the free volume required for molecular motion leads to the well-known Williams-Landel-Ferry (WLF) equation [111]:

Tlo to f0 fJOLf + T ~ To which relates the viscosity, -q, or relaxation time for a process, t, at a temperature T above Tg to the corresponding quantities, or t0, measured at some reference temperature T0. Here/0 is the free volume fraction at T0, ar is the thermal expansivity of the free volume, and B is a constant usually assigned a value of unity, consistent with the analysis of viscosity data by Doolittle [112]. The free volume fraction at a temperature T is given by

Analysis of linear amorphous polymers assuming B = 1 and with T„ = Tg gives the following parameter estimates [103]:

The analysis thus assigns a value to the free volume fraction at the glass transition temperature of 2.5% for all linear amorphous polymers independent of their chem ical structure, which is considerably smaller than that suggested by Simha and Boyer [110]. The analysis of the glass transition by Hirai and Eyring [113,114] in terms of holes provides estimates of the free volume fraction at Tg that vary from about 4 to 12%.

C. The 200 K Transition in Fully Hydrated Proteins

There is now a considerable body of evidence that demonstrates hydrated proteins undergo a glasslike transition at 180-220 K. This includes studies of motions monitored by ESR spin labels [65,115-117], Mossbauer spectroscopy [115,117,118], phosphorescence [70,115], and neutron scattering [119] as well as by RSMR techniques [101] (see also Chapter 5). Frauenfelder and coworkers have also explored, in great detail, the hierarchy of conformational substates in myoglobin and the glasslike properties of myoglobin (see the review by Frauenfelder et al. [ 120]). The dynamical transition has also been reproduced in recent molecular dynamics simulations of myoglobin [121,122]. To this list must be added a remarkable x-ray crystallographic study of ribonuclease A by Tilton et al. [123] at nine temperatures over the range from 98 to 320 K that provides the temperature dependence of individual atomic Debye-Waller factors (B factors: B = 8tt2(x2)). Figure 11 shows the temperature dependence of the average mean square displacements, (x2), for all nonhydrogen protein atoms derived from the B factors for ribonuclease A, together with results from inelastic neutron scattering [119] and Mossbauer spectroscopic studies [118] of myoglobin. The values derived from

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  • Ville
    Do proteins have glass transition temperature?
    1 year ago

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