The biological improvement of triticale, a cereal of increasing importance in agriculture, may be accelerated via the production of doubled haploid lines using in vitro culture. Among the relevant factors affecting the culture efficiency are Cu(II) or Ag(I) acting, e.g., as cofactors of enzymes. The copper ions are known to positively affect green plant regeneration efficiency. However, the biochemical basis, mainly its role in the generation of in vitro-induced genetic and epigenetic variation and green plant regeneration efficiency, is not well understood. Here, we employed structural equation modeling to evaluate the relationship between de novo DNA methylation affecting the asymmetric context of CHH sequences, the methylation-sensitive Amplified Fragment Length Polymorphism related sequence variation, and the concentration of Cu(II) and Ag(I) ions in induction media, as well as their effect on S-adenosyl-L-methionine perturbations, observed using FTIR spectroscopy, and the green plant regeneration efficiency. Our results allowed the construction of a theory-based model reflecting the biological phenomena associated with green plant regeneration efficiency. Furthermore, it is shown that Cu(II) ions in induction media affect plant regeneration, and by manipulating their concentration, the regeneration efficiency can be altered. Additionally, S-adenosyl-L-methionine is involved in the efficiency of green plant regeneration through methylation of the asymmetric CHH sequence related to de novo methylation. This shows that the Yang cycle may impact the production of green regenerants.