Principles of Protein Structure - H. Schulz 1982

Thermodynamics and Kinetics of Polypeptide Chain Folding
Thermodynamic Aspects
Thermal Fluctuations in Protein Structures

Isolated protein molecules undergo significant structural fluctuations. In any thermodynamic description of Cell/13.html">Protein Structure, it must be borne in mind that an individual protein molecule together with its surrounding solvent constitutes a very small system [419]. At a given Temperature, the ROOT-mean-square value of the energy fluctuations δH of the system is given by [420]:

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For macroscopic systems, these fluctuations are indeed very small compared to the internal energy. However, for a single protein molecule with a mass m of about 5 ∙ 10^-20 g and a specific heat capacity c = 0.32 cal ∙ grad^-1 ∙ g^-1 [421, 422] at 37°C, the fluctuations amount to 7 ∙ 10^-20 cal (k is the Boltzmann constant), which corresponds to approximately 40 kcal/mol on a molar basis. Such fluctuations significantly exceed the value of ΔG_total. Nevertheless, the relaxation times are only on the order of nanoseconds, which is insufficient to induce significant unfolding of the native structure.

Nevertheless, such fluctuations can be observed experimentally. One example is the dynamic behavior of Tyr side chains in the pancreatic Trypsin inhibitor. According to X-Ray Diffraction data, these side chains are tightly packed; however, nuclear magnetic Resonance spectra indicate that these side chains oscillate between two states differing by a 180° rotation around the C_β — C_y bond >1423, 424]. The same technique has been used to prove the conformational lability of seemingly rigid residues in Lysozyme [425], Ribonuclease [426], and Myoglobin [427]. Furthermore, it has been established that the fluorescence of Trp buried within ribonuclease can be quenched by the action of O₂ [428, 429], indicating the ability of O₂ to penetrate into the interior of the molecule. Similar Conclusions follow from experiments on fluorescence relaxation [430], phosphorescence [431], and hydrogen exchange [414]. All these data, as well as some others [432], demonstrate that the protein molecule is quite flexible. Atoms can displace relative to their average positions determined by X-ray Diffraction Analysis. It should be noted that Oligomeric Proteins (and protein crystals, from which most of the data have been obtained) have a larger mass m than monomeric ones. Therefore, the fluctuations per unit mass are smaller in them.