Atomic Scale Fractal Dimensionality in Proteins

TL;DR

This study measures the fractal dimensionality of proton positions in Azurin proteins across temperature regimes, revealing a biologically relevant fractal dimension that may relate to protein function.

Contribution

It provides the first measurement of the fractal dimension of atomic paths in proteins under biologically relevant conditions using neutron scattering.

Findings

Fractal dimension of proton sets in Azurin is approximately 0.65.

A dynamical transition occurs at intermediate temperatures under hydration.

Fractal dimensionality may be linked to biological function.

Abstract

The soft condensed matter of biological organisms exhibits atomic motions whose properties depend strongly on temperature and hydration conditions. Due to the superposition of rapidly fluctuating alternative motions at both very low temperatures (quantum effects) and very high temperatures (classical Brownian motion regime), the dimension of an atomic ``path'' is in reality different from unity. In the intermediate temperature regime and under environmental conditions which sustain active biological functions, the fractal dimension of the sets upon which atoms reside is an open question. Measured values of the fractal dimension of the sets on which the Hydrogen atoms reside within the Azurin protein macromolecule are reported. The distribution of proton positions was measured employing thermal neutron elastic scattering from Azurin protein targets. As the temperature was raised from low to intermediate values, a previously known and biologically relevant dynamical transition was verified for the Azurin protein only under hydrated conditions. The measured fractal dimension of the geometrical sets on which protons reside in the biologically relevant temperature regime is given by $D=0.65 \pm 0.1$. The relationship between fractal dimensionality and biological function is qualitatively discussed.