Mathematical Modeling and Optimization Methods for De Novo Protein Design - Systems Biology: Networks, Models, and Applications - page 42

Monte Carlo sampling. This is the approach adopted by both Desjarlais
and Handel [20] and Kraemer-Pecore et al. [21]. Under this approach
an ensemble of related backbone conformations close to the template
are generated at random. Then a sequence will be designed for each of
them under the rigid backbone assumption, and finally the backbone
sequence combination with the lowest energy will be selected. For
symmetric proteins, backbone structure can actually be modeled by
parametric fitting, and this should improve computational efficiency.
However, the vast majority of protein structures are nonsymmetric,
which make this parametric approach infeasible. Su and Mayo [17]
overcame this difficulty by treating a-helices and b-sheets as rigid
bodies and designing sequences for several template variations of the
protein Gb1. Farinas and Regan [22] considered a discrete set of
templates when they designed the metal binding sites in Gb1, and they
identified varied residue positions that would have been missed if
average three-dimensional coordinates had been used for calculations.
Harbury et al. [23] incorporated template flexibility through an alge-
braic parameterization of the backbone, when they designed a family
of a-helical bundle proteins with right-handed superhelical twist.
They were able to achieve a root mean square coordinate deviation
between the predicted structure and the actual structure of the de novo
designed protein of around 0.2 Å.
One natural approach to incorporate backbone flexibility is to allow
for variability in each position in the template. The deterministic in silico
sequence selection method, recently proposed by Klepeis et al. [24,25]
using the integer linear optimization technique, takes into account tem-
plate flexibility via the introduction of a distance-dependent force field
in the sequence selection stage. Pairwise amino acid interaction potential,
which depends on both the types of the two amino acids and the dis-
tance between them, was used to calculate the total energy of a sequence.
Instead of being a continuous function, the dependence of the interaction
potential on distance is discretized into bins. With typical bin sizes of 0.5
to 1 Å, the overall protein design model that Klepeis et al. [24,25] devel-
oped implicitly incorporated backbone movements of roughly the same
order of magnitude.
MATHEMATICAL MODELING AND OPTIMIZATION METHODS
Once an energy function has been defined, sequence selection is
accomplished through an optimization-based search designed to mini-
mize the energy objective. Both stochastic and deterministic methods
have been applied to the computational protein design problem. The
Self-Consistent Mean Field (SCMF) [26] and dead-end elimination
(DEE) [27] are both good examples of deterministic methods.