Physics of Squeezed Helices (Vol. 44 No. 1)

When confined to a surface helical filaments form "squeelices". Two categories of squeelices exist, depending on the sign of the twist-kink self-energy (positive and negative for g >1 and g <1 respectively). (a,b) Typical filament-helices in 3-D before confinement. (a',b') When confined, (a) transforms into untwisted circularized shapes (g > 1) while (b) assumes twisted and wavy shapes (g<1).

Helically coiled filaments are everywhere in living nature. In experimental situations, filaments are often squeezed flat (or nearly flat) onto two-dimensional surfaces. Under such 2D confinement filament-helices form what we call "squeelices" - peculiar squeezed conformations often resembling looped waves, spirals or circles. Many such shapes have been observed and reported for a variety of biological and man-made filaments.

With filament-helices being such a ubiquitous structure, we asked the question: what happens when filament helices become confined? We found that the confinement produces some dramatic changes in filaments shape, giving rise to several notable and surprising effects. In particular “squeelices” can display an enhanced cyclisation probability, unusually strong end-to-end fluctuations and a conformational multistability. The conformational dynamics of confined helices is most naturally described in terms of discrete particle-like entities – which we call the "twist-kinks". These "twist-kinks" turn out to be analogous and are physically related to crystal dislocations in solids and Sine-Gordon-kinks from soliton physics. Twist-kinks move thermally along the confined helix and interact much like quasi-particles. Confined helices can further thermally switch between discrete twist-quantized states comprising different numbers of twist-kinks.

Doing simple things (confining) to simple objects (helical filaments) can give rise to complex physics.

G-M. Nam, N-K. Lee, H. Mohrbach, A. Johner and I. M. Kulíc, ‘Helices at interfaces’, EPL, 100, 28001 (2012)