Mathematical Modeling and Optimization Methods for De Novo Protein Design - Systems Biology: Networks, Models, and Applications - page 47

discrete set of backbones, which does not allow for the true flexibility
that would afford more optimal sequences and more robust predictions
of stability. Moreover, several models that attempt to incorporate back-
bone flexibility highlight a second difficulty, namely, inadequacies
inherent to energy modeling [20]. The need for empirically derived
weighting factors, and the dependence on specific heuristics, limit the
generic nature of these computational protein design methods. Such
modeling-based assumptions also raise issues regarding the appropri-
ateness of the optimization method and underscore the question of
whether it is sufficient to merely identify the globally optimal sequence
or, more likely, a subset of low-lying energy sequences. An even more
difficult problem relevant to both flexibility and energy modeling is to
correctly model the interactions that control the functionality and activity
of the designed sequences.
DE NOVO PROTEIN DESIGN FRAMEWORK
In Klepeis et al. [24,25], a novel two-stage computational peptide and
protein design method is presented, not only to select and rank
sequences for a particular fold, but also to validate the stability and
specificity of the fold for these selected sequences. The sequence selec-
tion phase relies on a novel integer linear programming (ILP) model
with several important constraint modifications that improve both the
tractability of the problem and its deterministic convergence to the
global minimum. In addition, a rank-ordered list of low-lying energy
sequences is identified along with the global minimum energy
sequence. Once such a subset of sequences has been identified, the fold
validation stage is used to verify the stabilities and specificities of the
designed sequences through a deterministic global optimization
approach that allows for backbone flexibility. The selection of the
best designed sequences is based on rigorous quantification of energy-
based probabilities. In the following, we will discuss the two stages
in detail.
In Silico Sequence Selection
To correctly select a sequence compatible with a given backbone template,
an appropriate energy function must first be identified. Desirable prop-
erties of energy models for protein design include both accuracy and
rapid evaluation. Moreover, the functions should not be overly sensi-
tive to fixed backbone approximations. In certain cases, additional
requirements, such as the pairwise decomposition of the potential for
application of the dead-end elimination algorithm [27], may be necessary.
Instead of employing a detailed atomistic level model, which
requires the empirical reweighting of energetic terms, the proposed