  Diffusion of proteins on length scales of their own diameter in highly
concentrated solutions is essential for understanding the cellular machinery of
living cells, but its experimental characterization remains a challenge. While
X-ray photon correlation spectroscopy (XPCS) is currently the only technique
that in principle allows for a measurement of long-time collective diffusion on
these length scales for such systems, its application to protein solutions is
seriously hampered by radiation damage caused by the highly intense X-ray beams
required for such experiments. Here we apply an experimental design and an
analysis strategy that allow us to successfully use XPCS experiments in order
to measure collective long-time cage relaxation in highly crowded solutions of
the eye lens protein {\alpha}-crystallin close to and beyond dynamical arrest.
We also address the problem of radiation-induced damage in such experiments. We
demonstrate that radiation effects depend both on the total dose as well as the
dose rate of the absorbed radiation, and discuss possible processes and
mechanism responsible for the observed radiation effects as well as their
consequences for future applications of XPCS in biological systems.
