Functional State Dependence of Picosecond Protein Dynamics

We examine temperature dependent picosecond dynamics as a function of structure and function for lysozyme and cytochrome c using temperature dependent terahertz permittivity measurements. A double Arrhenius temperature dependence with activation energies E1 ~ 0.1 kJ/mol and E2 ~10 kJ/mol fits the native state response. The higher activation energy is consistent with the so-called protein dynamical transition associated with beta relaxations at the solvent-protein interface. The lower activation energy is consistent with correlated structural motions. When the structure is removed by denaturing the lower activation energy process is no longer present. Additionally the lower activation energy process is diminished with ligand binding, but not for changes in internal oxidation state. We suggest that the lower energy activation process is associated with collective structural motions that are no longer accessible with denaturing or binding. Critical to the function of proteins is both their three dimensional structure and the dynamics of this structure. On the picosecond timescale motions important for function include surface solvent, side chains and large scale correlated structural motions[1-3]. It has been suggested that the large scale correlated structural motions play a key role in the necessary structural reorganization that occurs during function [4, 5]. These correlated motions have recently been measured using coherent scattering techniques [6-8]. These exciting results raise the question of whether these correlated motions change with structure and function. Further, ref. 8 has suggested evidence of an optical mode at ~ 3 cm, suggesting that optical techniques may be used to characterize these motions. Previously THz spectroscopic techniques have been applied to proteins [9]. To date the most dominant impact of these measurements has been the characterization of the biological water [10], and the ability of the techniques to characterize correlated motions has been disappointing. This is largely due to the dominant contribution of the biological water that likely masks the underlying protein motions. The temperature dependence of material properties can reveal underlying processes that contribute to behavior at higher temperatures. For example, the role of conformational sub states in protein function was introduced as a result of temperature dependent measurements of ligand rebinding in myoglobin [11]. Here we find that the temperature dependent picosecond dielectric response reveals two dominant activated processes and one of these processes is removed when 3D structure is removed or constrained, suggesting that this process is associated with structural motions. The higher energy process does not significantly change with denaturing or ligand binding and is likely a beta relaxational response due to local solvent motions at the protein surface. The results demonstrate that terahertz optical measurements can access underlying correlated motions, and how these motions are effected with small ligand binding. Previously most temperature dependent measurements of picosecond protein dynamics have focused on the so called dynamical transition (DT) at ~ 220K [12-14]. While not a true transition, this term is given to a rapid change in the average atomic mean square displacement as a function of temperature. The DT requires both a minimum solvent concentration and peptide size. The effect has been ascribed to a variety of phenomena, the simplest of which is the temperature dependence of beta relaxations. In addition to these local motions, collective motions will be thermally populated and contribute to the picosecond response. In order to differentiate the nature of the picosecond motions we measured the temperature dependent THz dielectric response for different functional states of two proteins, hen egg white lysozyme (HEWL) and cytochrome c (CytC). Hen egg white lysozyme (HEWL) is a small protein, having 129 residues and a molecular weight (MW) of 14,400 Da. Lysozyme works as an antibacterial agent by hydrolysing the glycosidic bond between N-Acetyl-D-glucosamine (NAG) and N-Acetylmuramic acid (NAM) in cell walls [15]. However HEWL can stably bond with tri-N-Acetyl-Dglucosamine (3NAG) [16], and undergoes a conformational change similar to its functional state when cleaving the NAGNAM bond. Cytochrome c (CytC) is a small heme protein with 105 residues and MW of 11,700 Da. The primary role of CytC is to transfer an electron from cytochrome c reductase to cytochrome c oxidase which is embedded in the inner mitochondrial membrane, through the change in the oxidation state of the heme Fe. We find that the temperature dependence of the imaginary part of the permittivity in the 0.2 – 2.0 THz range for native state HEWL and CytC is best described by the sum of two Arrhenius terms with activation energies E1 ~ 0.1