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 identify how internal or external processes impact galactic structure. However, current observational limits may be obscuring crucial information in the low-mass or low-brightness regime. We use the AMIGA catalog of isolated galaxies to explore the impact of different factors on the structure of these galaxies. In particular, we study the type of disk break based on the degree of isolation and the presence of interactions which are only detectable in the ultra-low surface brightness regime. We present the first results of an extensive observational campaign of ultra-deep optical imaging targeting a sample of 25 low-redshift (z < 0.035) isolated galaxies. The nominal surface brightness limits achieved are comparable to those to be obtained in the 10-year LSST coadds ( mag arcsec−2; 3σ ; 10" × 10"). We find that isolated galaxies have a considerably higher fraction of purely exponential disk profiles and a lower presence of up-bending breaks than field or cluster galaxies. Our extreme imaging depth allows us to detect the presence of previously unreported interactions with minor companions in some of the galaxies in our sample (∼40% of the galaxies show signs of interaction). The results of our work fit with the general framework of galactic structure in which up-bending breaks (Type III) would be produced by mergers and down-bending breaks (Type II) due to a threshold in star formation that would tend to become single exponential disk (Type I) in case of cessation or decrease of star formation.