Nanosecond structural dynamics of intrinsically disordered β-casein micelles by neutron spectroscopy

β-casein undergoes a reversible endothermic self-association, forming protein micelles of limited size. In its functional state, a single β-casein monomer is unfolded, which creates a high structural flexibility, which is supposed to play a major role in preventing the precipitation of calcium phosphate particles. We characterize the structural flexibility in terms of nanosecond molecular motions, depending on the temperature by quasielastic neutron scattering. Our major questions are: Does the self-association reduce the chain flexibility? How does the dynamic spectrum of disordered caseins differ from a compactly globular protein? How does the dynamic spectrum of β-casein in solution differ from that of a protein in hydrated powder states? We report on two relaxation processes on a nanosecond and a sub-nanosecond timescale for β-casein in solution. Both processes are analyzed by Brownian oscillator model, by which the spring constant can be defined in the isotropic parabolic potential. The slower process, which is analyzed by neutron spin echo, seems a characteristic feature of the unfolded structure. It requires bulk solvent and is not seen in hydrated protein powders. The faster process, which is analyzed by neutron backscattering, has a smaller amplitude and requires hydration water, which is also observed with folded proteins in the hydrated state. The self-association had no significant influence on internal relaxation, and thus, a β-casein protein monomer flexibility is preserved in the micelle. We derive spring constants of the faster and slower motions of β-caseins in solution and compared them with those of some proteins in various states (folded or hydrated powder).