Spontaneous curvature in chiral polar filaments near interfaces*

Chiral filaments (actin, DNA, alpha helical strands, $\ldots$) are ubiquitous in biology, and they frequently come into contact with interfaces or inhomogeneous environments, either in biology (e.g. actin on membranes) or use and processing of biomaterials (fibrils at solvent boundaries or nanoparticle surfaces). Recent experiments\footnote{S Jordens, \textit{et al.}, ``Adsorption at liquid interfaces induces amyloid fibril bending and ring formation'', \textit{ACS Nano} (2014) \texttt{http://pubs.acs.org/doi/pdf/10.1021/nn504249x}.} have shown that amyloid fibrils can develop unusual curvatures at the air-water interface. Here we show that spontaneous curvature follows, on symmetry grounds, for chiral polar filaments placed in inhomgeneous environments such as near surfaces. We demonstrate this for simple model surface-fibril interactions, and discuss some of the implications.