  Membrane-mediated particle interactions depend both on the properties of the
particles themselves and the membrane environment in which they are suspended.
Experiments have shown that chiral rod-like inclusions dissolved in a colloidal
membrane of opposite handedness assemble into colloidal rafts, which are
finite-sized reconfigurable droplets consisting of a large but precisely
defined number of rods. Here, we systematically tune the chirality of the
background membrane, and find that in the achiral limit colloidal rafts acquire
fundamentally new structural properties and interactions. In particular, rafts
can switch between two chiral states of opposite handedness, which dramatically
alters the nature of the membrane-mediated raft-raft interactions. Rafts with
the same chirality have long-ranged repulsions, while those with opposite
chirality acquire attractions with a well-defined minimum. Both attractive and
repulsive interactions are explained by a continuum model that accounts for the
coupling between the membrane thickness and the local tilt of the constituent
rods. These switchable interactions enable assembly of colloidal rafts into
intricate higher-order architectures with unusual symmetries, including stable
tetrameric clusters and "ionic crystallites" of counter-twisting domains
organized on a binary square lattice. Furthermore, the properties of individual
rafts, such as their sizes, are controlled by their complexation with other
rafts. The emergence of these complex behaviors can be rationalized purely in
terms of generic couplings between compositional and orientational order of
fluids of rod-like elements. Thus, the uncovered principles might have
relevance for conventional lipid bilayers, in which the assembly of
higher-order structures is also mediated by complex membrane-mediated
interactions.
