On the form of growing strings

TL;DR

This paper models growing strings similar to nascent proteins, revealing that non-equilibrium growth dynamics naturally lead to helical structures, which may have evolutionary significance.

Contribution

It introduces a model of growing self-interacting strings that explains the formation of helical structures during growth, linking non-equilibrium dynamics to biological evolution.

Findings

Growing strings develop pronounced helical structures at the end.

The growth ensemble mimics an equilibrium under effective stretching.

Evolution favors helical structures at the protein's C-terminus.

Abstract

Patterns and forms adopted by Nature, such as the shape of living cells, the geometry of shells and the branched structure of plants, are often the result of simple dynamical paradigms. Here we show that a growing self-interacting string attached to a tracking origin, modeled to resemble nascent polypeptides in vivo, develops helical structures which are more pronounced at the growing end. We also show that the dynamic growth ensemble shares several features of an equilibrium ensemble in which the growing end of the polymer is under an effective stretching force. A statistical analysis of native states of proteins shows that the signature of this non-equilibrium phenomenon has been fixed by evolution at the C-terminus, the growing end of a nascent protein. These findings suggest that a generic non-equilibrium growth process might have provided an additional evolutionary advantage for nascent proteins by favoring the preferential selection of helical structures.