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interpenetrating domains. This problem led to the introduction of the next two quantities
into the fitness function.
Domain distortion is a measure we devised to represent the degree to which domains 1
and 2 differed structurally from their conformations in the starting structure. As was
observed by Schlauderer et al[121] domain structure is typically conserved during
domain hinge bending motion, even across structures of substantially different sequence;
in fact the definition of domain hinge bending requires this[8,9]. This quantity is zero for
the starting structure and so cannot be used alone for prediction; the point is instead to
exclude from consideration generated structures with interpenetrating or otherwise
improbably deformed domains.
Free energy of folding, or stability, can be used to discriminate energetically feasible
conformers from those with unnatural orientation or excessively interpenetration of
domains. However since a wide variety of conformers, including both the holo and the
apo, are stable, this measure alone cannot find the holo structure in an ensemble. The
point is again to exclude unphysical structures.
These four terms together suggest a physical model of ligand binding in domain hinge
bending proteins. Binding energy is lowest in the apo structure because the former
stabilizes the latter. Radius of gyration is minimized as the solvent-filled volume of the
cleft diminishes during closure; this position is stabilized by inter-domain and domain-
ligand contacts, including many van der Waals interactions which are approximately
quadratic as we will discuss. Domain distortion is disfavored because by definition
structural domains are are already in their stable conformation[8,9,112]. Stability is high
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