  We investigate conductance and conductance fluctuations of two transmembrane
proteins, bacteriorhodopsin and proteorhodopsin, belonging to the family of
protein light receptors. These proteins are widely diffused in aqueous
environments, are sensitive to visible light and are promising biomaterials for
the realization of novel photodevices. The conductance exhibits a rapid
increase at increasing applied voltages, over a threshold value. Around the
threshold value the variance of conductance fluctuations shows a dramatic jump
of about 5 orders of magnitude: conductance and variance behaviours trace a
second order phase transition. Furthermore, the conductance fluctuations
evidence a non-Gaussian behaviour with a probability density function (PDF)
which follows a generalized Gumbel distribution, typical of extreme-value
statistics. The theoretical model is validated on existing current-voltage
measurements and the interpretation of the PDF of conductance fluctuations is
proven to be in line with the microscopic mechanisms responsible of charge
transport.
