Modeling Proteins at the Interface of Structure, Evolution, and Population Genetics - Computational Modeling of Biological Systems - page 353

[ 26 ] in a simulation context rather than for comparative purposes. Adopting existing
protein structure prediction protocols to model the large effect of insertions and
deletions on backbone structure would also be of interest.
In another trajectory, evolutionary systems biology is an emerging field. Sim-
ulations with more than one protein can enable evaluation of the interactome,
with pathway-level selective pressures rather than selective pressures on individual
binding interactions. Ultimately, this would sum up to simulation of a cellular
network on an evolutionary timescale. The logical endpoint in that direction is a
marriage of sequence-structure simulation to the metabolic and transcriptional rate
simulations common in systems biology today. A second goal in this trajectory is
the simulation of cross-species interactions, such as those involved in a viral or
bacterial infection or in the molecular interactions between organisms that co-exist
in an ecosystem. The more interconnections between layers of simulation that are
taken into consideration, the richer our description of evolution becomes and the
questions that can be asked multiply in both significance and number.

3 Phylogeny and Thermodynamics

Phylogenetic inference is another problem where structural models can enable a
greater level of understanding of the evolutionary process. Phylogenetic analysis
is a retrospective problem that enables complementary inference of evolutionary
processes. Models of phylogeny are generally formulated as continuous time
Markov chains, in which branch lengths are a function of the probability of
substitutions. As the probability of a mutation being accepted is impacted by the
disturbances which it may cause the protein energetically, there has been an effort
to incorporate biophysical reality into phylogenetic models in order to improve
their accuracy. These efforts have drawn upon the same classes of models as used
in the evolutionary simulation field. Using models which consider the constraints
of structure [ 17 ], one can evaluate the probability of fixing a mutation, resulting
in a particular evolutionary history, in the context of thermodynamic stability.
This approach lends itself naturally to incorporation in maximum likelihood (ML)
or Bayesian methods for phylogenetic tree construction. For instance, Parisi and
Echave [ 27 ] apply these considerations to phylogenetic inference. They make use
of a model, in which sequences are allowed to mutate and then are selected upon
based on structural constraints. The selection criterion is based on the difference in
contact potential between the position mutated and the nonmutated sequence. This
selection criterion can then be scaled by a parameter which is related to the selection
pressure. To apply this model in a phylogenetic context, site-specific replacement
matrices are calculated based on the contact potential score, amino acid equilibrium
frequencies, and a count matrix. The replacement matrices produced by this method
are then used to calculate the maximum likelihood of a data set based on a given
topology.