  We refine a protein model that reproduces fundamental aspects of protein
thermodynamics. The model exhibits two transitions, hot and cold unfolding. The
number of relevant parameters is reduced to three: 1) binding energy of folding
relative to the orientational energy of bound water, 2) ratio of degrees of
freedom between the folded and unfolded protein chain and 3) the number of
water molecules that can access the hydrophobic parts of the protein interior.
By increasing the number of water molecules in the model, the separation
between the two peaks in the heat capacity curve decreases, which is more
consistent with experimental data. We also show that if we, as a speculative
assumption, assign effectively only two distinct energy levels for the bound
water molecules, the hot peak in the heat capacity curve will be larger than
the cold peak, in accordance with experimental observations.
