Abstract
Long range interactions between nuclear spins and paramagnetic ions can serve as a sensitive monitor of internal motion of various parts of proteins, including functional loops and separate domains. In the case of interdomain motion, the interactions between the ion and NMR-observable nuclei are modulated in direction and magnitude mainly by a combination of overall and interdomain motions. The effects on observable parameters such as paramagnetic relaxation enhancement (PRE) and pseudocontact shift (PCS) can, in principle, be used to characterize motion. These parameters are frequently used for the purpose of structural refinements. However, their use to probe actual domain motions is less common and is lacking a proper theoretical treatment from a motional perspective. In this work, a suitable spin Hamiltonian is incorporated in a two body diffusion model to produce the time correlation function for the nuclear spin-paramagnetic ion interactions. Simulated observables for nuclei in different positions with respect to the paramagnetic ion are produced. Based on these simulations, it demonstrated that both the PRE and the PCS can be very sensitive probes of domain motion. Results for different nuclei within the protein sense different aspects of the motions. Some are more sensitive to the amplitude of the internal motion, others are more sensitive to overall diffusion rates, allowing separation of these contributions. Experimentally, the interaction strength can also be tuned by substitution of different paramagnetic ions or by varying magnetic field strength (in the case of lanthanides) to allow the use of more detailed diffusion models without reducing the reliability of data fitting.