  We propose to develop mean field theory in combination with Glauber
algorithm, to model and interpret protein dynamics and structure formation in
small to wide angle x-ray scattering (S/WAXS) experiments. We develop the
methodology by analysing the Engrailed homeodomain protein as an example. We
demonstrate how to interpret S/WAXS data with a good precision and over an
extended temperature range. We explain experimentally observed phenomena in
terms of protein phase structure, and we make predictions for future
experiments how the scattering data behaves at different ambient temperature
values. We conclude that a combination of mean field theory with Glauber
algorithm has the potential to develop into a highly accurate, computationally
effective and predictive tool for analysing S/WAXS data. Finally, we compare
our results with those obtained previously in an all-atom molecular dynamics
simulation.
