  Active matter systems - such as a collection of active colloidal particles -
operate far from equilibrium with complex inter-particle interactions that
govern their collective dynamics. Predicting the collective dynamics of such
systems may aid the design of self-shaping structures comprised of active
colloidal units with a prescribed dynamical function. Here, using simulations
and theory, we study the collective dynamics of a chain consisting of active
Brownian particles with internal interactions via trail-mediated chemicals,
connected by harmonic springs in two dimensions to obtain design principles for
active colloidal molecules. We show that two-dimensional confinement and
chemo-repulsive interactions between the freely-jointed particles lead to an
emergent rigidity of the chain in the steady-state dynamics. In the
chemo-attractive regime, the chain collapses into crystals that abruptly halt
their motion. Further, in a chain consisting of a binary mixture of monomers,
we show that non-reciprocal chemical affinities between distinct species give
rise to novel phenomena, such as chiral molecules with tunable dynamics,
sustained undulatory gaits and reversal of the direction of motion. Our results
suggest a novel interpretation of the role of trail-mediated interactions, in
addition to providing active self-assembly principles arising due to
non-reciprocal interactions.
