  In the standard cosmological model of galaxy evolution, mergers and
interactions play a fundamental role in shaping galaxies. Galaxies that are
currently isolated are thus interesting, allowing us to distinguish between
internal and external processes affecting the galactic structure. However,
current observational limits may obscure crucial information in the low-mass or
low-brightness regime. We use optical imaging of a subsample of the AMIGA
catalogue of isolated galaxies to explore the impact of different factors on
the structure of these galaxies. We study the type of disc break as a function
of the degree of isolation and the presence of interaction indicators like
tidal streams or plumes only detectable in the low surface brightness regime.
We present deep optical imaging of a sample of 25 isolated galaxies. Through
careful data processing and analysis techniques, the surface brightness limits
achieved are comparable to those to be obtained on the 10-year LSST coadds. The
extreme depth of our imaging allows us to study the interaction signatures of
20 galaxies, given that the presence of Galactic cirrus is a strong limiting
factor in the characterisation of interactions for the remaining 5 of them. We
detect previously unreported interaction features in 8 (40%) galaxies in our
sample. We identify 9 galaxies (36%) showing an exponential disc (Type I), 14
galaxies (56%) with down-bending (Type II) profile and only 2 galaxies (8%)
with up-bending (Type III) profiles. Isolated galaxies have considerably more
purely exponential discs and fewer up-bending surface brightness profiles than
field or cluster galaxies. We suggest that major mergers produce up-bending
profiles while a threshold in star formation probably forms down-bending
profiles. Unperturbed galaxies, evolving slowly with a low star formation rate
could cause the high rate of Type I discs in isolated galaxies observed.
