  The simplest approximation of interaction potential between amino-acids in
proteins is the contact potential, which defines the effective free energy of a
protein conformation by a set of amino acid contacts formed in this
conformation. Finding a contact potential capable of predicting free energies
of protein states across a variety of protein families will aid protein folding
and engineering in silico on a computationally tractable time-scale. We test
the ability of contact potentials to accurately and transferably (across
various protein families) predict stability changes of proteins upon mutations.
We develop a new methodology to determine the contact potentials in proteins
from experimental measurements of changes in protein thermodynamic stabilities
(ddG) upon mutations. We apply our methodology to derive sets of contact
interaction parameters for a hierarchy of interaction models including
solvation and multi-body contact parameters. We test how well our models
reproduce experimental measurements by statistical tests. We evaluate the
maximum accuracy of predictions obtained by using contact potentials and the
correlation between parameters derived from different data-sets of experimental
ddG values. We argue that it is impossible to reach experimental accuracy and
derive fully transferable contact parameters using the contact models of
potentials. However, contact parameters can yield reliable predictions of ddG
for datasets of mutations confined to specific amino-acid positions in the
sequence of a single protein.
