Modeling Protein Evolution - Computational Modeling of Biological Systems - page 320

mutant to test, and then efficiently accept or reject it based on this probability. While
the use of the Kimura formulation results in faster simulations, it eliminates the
possibility of observing interesting phenomena that arise from interactions among
mutations that are polymorphic in a population. For example, a favorable mutant
might not be fixed if, before it does, another mutant happens to arise that is more
favorable. Also, in a selective sweep , an extremely fit mutation that becomes fixed
rapidly can cause linked variants to become fixed as well, even if these other
variants are neutral or even deleterious. These additional variants are said to have
hitchhiked on the fixation of the favorable mutation. Finally, if the mutation rate
is especially rapid, then the fitness of a variant may depend partly on how often it
spawns deleterious mutations [ 29 , 30 ]. This can lead to emergent properties such as
robustness that would be overlooked when using the Kimura formulation.

3 The Distribution of Observed Protein Structures

As we accumulate an increasing number of protein structures, it is clear that the
distribution of proteins among the diverse folds is extremely uneven, with some
folds greatly over-represented and other possible folds that have not yet been
observed [ 31 - 35 ]. Three classes of explanations for this observation have emerged
[ 36 ]: (1) Some folds may be more “designable,” that is, they can be formed by
more sequences, and are therefore more likely to arise in evolution. (2) Some folds
are better suited to important or common functionalities, or a greater range of
functionalities. For instance, the cleft found in the common TIM Barrel fold might
be extremely well suited for catalyzing reactions. (3) Evolutionary dynamics, as
modeled as birth-death processes, may naturally lead to uneven distributions of
proteins as proteins with common folds are more likely to increase their number
through gene duplication events than proteins with rare folds. The first explanation,
involving the “sequence entropy” of various structures, has focused the most on the
nature of the genotype (sequence)-phenotype (structure) map, and the consequences
of this mapping for evolutionary processes.
Parallel to this effort has been the attempt to delineate more specifically the
processes that are involved in the creation of new protein folds [ 37 ]. It is clear, both
experimentally [ 38 , 39 ] and theoretically [ 14 , 40 ], that changes in protein structure
are extremely slow compared with the rate of change of protein sequences, with
many highly divergent pairs of proteins having extremely similar structures. For
proteins, investigations with simple models have shown that the neutral network
is clustered around a prototype sequence [ 41 ]. These neutral networks are isolated
from each other [ 42 ], manifested by the slow rate of change of structure. This is in
striking contrast to the case of RNA, where it is relatively easy to make changes
in structure with single changes in sequence [ 43 - 45 ]. (One possible explanation
for this difference may lie in how these different systems are modeled. Often
an RNA molecule is considered viable as long as it has a nondegenerate ground
state, resulting in the vast majority of sequences being viable. In contrast, proteins