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Proportion of actual protein structures within the total structural space

Determine the proportion of physically possible protein structural patterns (including evolutionarily non-viable configurations) that are realized by actual evolved protein structures, and thereby assess whether the observed stepwise reduction in the number of two-dimensional 6×6 lattice protein structures as the environmental robustness κ_R/β increases—where κ_R := χ − χ_R is the difference between the joint and structure-conditioned hydrophobic susceptibilities—accurately explains phenotypic dimensional reduction under natural selection.

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Background

The paper defines an environmental robustness measure κ_R for a given lattice protein structure R, where κ_R is the difference between hydrophobic susceptibilities computed under the joint distribution over structures and sequences and under the posterior distribution conditioned on R. An analysis of 6×6 two-dimensional lattice proteins shows a steep, stepwise reduction in the number of structures as κ_R/β increases.

However, connecting this model-based reduction in structural space to biological evolution requires knowing what fraction of the total physically possible structural patterns (including those that are evolutionarily non-viable) are actually realized by real proteins. Without this proportion, it remains uncertain whether the model’s dimensional reduction reflects natural selection acting on actual protein structures.

References

It is unclear what proportion of the total structural space, including evolutionary non-viable protein structure patterns, is occupied by actual protein structures, so whether the results from Fig.\ref{6_by_6_changes_of_num_of_struct_with_chi} accurately explain the dimensional reduction of phenotypes from the perspective of natural selection remains uncertain.

— Alpha helices are more evolutionarily robust to environmental perturbations than beta sheets: Bayesian learning and statistical mechanics for protein evolution (2409.03297 - Takahashi et al., 5 Sep 2024) in Section DISCUSSION (paragraph referencing Fig. \ref{6_by_6_changes_of_num_of_struct_with_chi})