ABSTRACT
One can achieve a more uniform native-state structure and remove scattering concerns by using solution phase samples. To avoid strong background from bulk solvent, one can form thin (~100 μm) lms of solution and dry these in a controlled way, using, for example, a closed cell with humidity control. e hydration can be set high enough to achieve protein structural homogeneity in the lm, but suciently low so that bulk water is not present and cannot contribute to absorption. Terahertz measurement of such samples, however, still had glasslike absorption. While closer examination of the complex permittivity of the hydrated lms revealed that the response could not be entirely accounted for with just relaxational response, but also required at least one damped harmonic oscillator (Knab et al. 2006), it is clear that for fully hydrated proteins, we must consider multiple contributions to the dielectric response. By proper decomposition of the data, enhanced by systematic variation of temperature, solvent content, or protein functional state, one can isolate the component arising from the protein structural vibrations. We can write down an approximate decomposition for solution phase proteins using the following formula:
ε ε ε ε ε= + + +W bW p relax p vib, , , (11.1)
where the subscripts W, bW, p, relax, and p, vib refer to permittivity contributions from the bulk water, bound water, protein relaxational response, and protein long-range structural vibrational response, respectively. is decomposition is a vast simplication, ignoring any interaction between dierent components, but it expresses the various sources of dielectric response for the complex sample. e rst three components are modeled very well using dielectric relaxation, and the last component is a sum of damped harmonic oscillators. In this chapter, we will discuss the dierent relaxational contributions to the terahertz response for hydrated proteins and methods to remove these so that one can extract the contribution from protein structural motions. We will discuss general aspects of relaxational response, the permittivity of water, in all its various forms, present in biological samples, and the relaxational response from amino acid side chains. Finally, we will discuss, in light of all the various models for relaxational eects, how the current measurements for protein samples suggest that the long-range vibrations of proteins do contribute to the terahertz response.
