Abstract
Protein structure is invariably connected to protein function. There are two important secondary structure elements: alpha-helices and beta-sheets (which sometimes come in a shape of beta-barrels). The actual shapes of these structures can be complicated, but in the first approximation, they are usually approximated by, correspondingly, cylindrical spirals and planes (and cylinders, for beta-barrels). In this paper, following the ideas pioneered by a renowned mathematician M. Gromov, we use natural symmetries to show that, under reasonable assumptions, these geometric shapes are indeed the best approximating families for secondary structures.
Highlights
Symmetries explain why the secondary protein structures consists of alpha-helices and beta-sheets
In [4], we showed that symmetries can explain some resulting shapes of beta-sheets
A protein usually consists of several alpha-helices and beta-sheets
Summary
Symmetries explain why the secondary protein structures consists of alpha-helices and beta-sheets. We will add, to the basic approximate shapes of a circular helix and a planes, one more shape This shape is observed when, due to tertiary structure effects, a beta-sheet “folds” on itself, becoming what is called a beta-barrel. A protein usually consists of several alpha-helices and beta-sheets In some cases, these combinations of basic secondary structure elements have their own interesting shapes: e.g., coils (alpha-helices) sometimes form a coiled coil. We use symmetries to describe the basic geometric shape of secondary structure elements; we hope that similar symmetry ideas can be used to describe the shape of their combinations as well
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