  Cohesive interactions between filamentous molecules have broad implications
for a range of biological and synthetic materials. While long-standing
theoretical approaches have addressed the problem of inter-filament forces from
the limit of infinitely rigid rods, the ability of flexible filaments to deform
intra-filament shape in response to changes in inter-filament geometry has a
profound affect on the nature of cohesive interactions. In this paper, we study
two theoretical models of inter-filament cohesion in the opposite limit, in
which filaments are sufficiently flexible to maintain cohesive contact along
their contours, and address, in particular, the role played by
helical-interfilament geometry in defining interactions. Specifically, we study
models of featureless, tubular filaments interacting via 1) pair-wise
Lennard-Jones (LJ) interactions between surface elements and 2)
depletion-induced filament binding stabilized by electrostatic surface
repulsion. Analysis of these models reveals a universal preference for cohesive
filament interactions for non-zero helical skew, and further, that in the
asymptotic limit of vanishing interaction range relative to filament diameter,
the skew-dependence of cohesion approaches a geometrically defined limit
described purely by the close-packing geometry of twisted tubular filaments. We
further analyze non-universal features of the skew-dependence of cohesion at
small-twist for both potentials, and argue that in the LJ model the pair-wise
surface attraction generically destabilizes parallel filaments, while in the
second model, pair-wise electrostatic repulsion in combination with
non-pairwise additivity of depletion leads to a meta-stable parallel state.
