Modeling Proteins at the Interface of Structure, Evolution, and Population Genetics - Computational Modeling of Biological Systems - page 351

Fig. 2 The symmetrical
contact map excluding
contacts within four amino
acid positions derived from
the structure of the SAP
protein (PDB ID 1D4T) at a
distance of 4.5 ˚ Aisshown.
This enables the definition of
residues in contact with each
other for the use of
informational potentials
Although lattice models have provided a wealth of information on the rules that
govern proteins in general, they are not well suited to describing differences between
distinct protein folds with respect to either function or evolution. Simulating the
evolution of sequences in real protein conformations or folds requires a higher
level of detail. Currently, the most popular approach involves creating a native
contact map from an experimentally determined structure (see Fig. 2 ). This allows
one to specify the effect of backbone shape on which residues are near each
other, and hence how their proximity and its effect on the overall folding energy
constrains their mutual mutational opportunity. A pairwise residue interaction
energy is typically assumed [ 15 ](Fig. 1 b), although this may also be augmented
with a term representing the effects of solvation [ 16 ]. Since the contact map never
changes, one need only to evaluate the effects of a substitution on a relatively small
number of local interactions. Parisi and Echave [ 17 ] adopted this level of structural
description to simulate the evolution of a left-handed beta-helix domain with a
known and specific sequence pattern thought to be due to folding constraints. Using
a random walk simulation with an energy difference-based fitness criterion, they
demonstrated that it is possible to reproduce the specific pattern of sequences of this
fold. This suggests that particular folds exert quite specific evolutionary pressures
that constrain the variation of sequences within a protein family. Bastolla and co-
workers [ 18 ] showed that overdispersed substitution (deviation from the expected
Poisson distribution) can result from neutral evolution under structural constraint
rather than selection and that the rate of substitution can vary considerably between
populations for the same reason.
An interesting contrast to the contact map is presented by the coarse-grained
(CG) physics-based approach (Fig. 1 b). Instead of relying on pairwise interactions
between residues, which inherently ignores multiresidue effects, a variety of
descriptors of separate forces is applied to a protein model with a reduced level of