The physical basis for the magnetic field dependence of proton spin-lattice relaxation rates in proteins

Abstract

The magnetic field dependence of the proton spin-lattice relaxation rate in polymeric materials and biological macromolecules may report important dynamical information. In the case where the system is dynamically heterogeneous as in plasticized polymeric systems or hydrated biopolymers, the spin-lattice relaxation of the liquid-proton population is generally coupled to the spin-relaxation behavior of the solid spins that often dominate the observable response of the liquid. In many of these systems the magnetic field dependence of the proton spin-lattice relaxation rate may be represented as a power law: 1/T1(ω)=Aω−b where a is a constant and b is usually found to be in the range of 0.5 to 0.8. We have shown that this power law may arise naturally from localized structural fluctuations along the backbone of chain molecules that modulate the proton dipole–dipole couplings, which form a network described by a fractal dimension that may be less than the Euclidean dimension. When the model for the solid spin-lattice relaxation rate constant is incorporated into the relaxation equations that couple the liquid and solid spin population responses, the composite model accounts quantitatively for proton spin-lattice relaxation rates measured in immobilized and hydrated protein systems and provides a fundamental basis for understanding the parametric dependence of proton spin-lattice relaxation rates in dynamically heterogeneous systems such as hydrated biopolymers, proteins, and biological tissues.