Field-cycling nuclear magnetic resonance relaxometry of molecular dynamics at biological interfaces in eye lenses: The Lévy walk mechanism

Abstract

We have studied the water dynamics in whole rabbit lens and fragments using H1-field-cycling nuclear magnetic resonance relaxometry. We have measured the proton spin–lattice relaxation time T1 as a function of the Larmor frequency. The data can be interpreted well using the reorientation mediated by translational displacement model in combination with the mechanism of bulk-mediated surface diffusion, where individual water molecules perform Lévy walks with a Cauchy diffusion propagator. This gives evidence of anomalous water surface diffusion on proteins in the rabbit lens. We assume that the lens protein surface topology can be modeled by a polyhedral structure of randomly oriented faces with individual correlation lengths s0. For the whole lens we obtained the most frequent s0 value of 2.5 nm whereas for fragments from the rabbit cortex and the nucleus we obtained values of 3 and 0.3 nm, respectively. The correlation length values obtained for the lens can be attributed to the short-range order of the lens proteins necessary for maintaining lens transparency.