Plant tissue culture techniques are handy tools for obtaining unique plant materials that are difficult to propagate or important for agriculture. Homozygous materials derived through in vitro cultures are invaluable and significantly accelerate the evaluation of new varieties, e.g., cereals. The induction of somatic embryogenesis/androgenesis and the regeneration and its efficiency can be influenced by the external conditions of tissue culture, such as the ingredients present in the induction or regeneration media. We have developed an approach based on biological system, molecular markers, Fourier Transform Infrared spectroscopy, and structural equation modeling technique to establish links between changes in sequence and DNA methylation at specific symmetric (CG, CHG) and asymmetric (CHH) sequences, glutathione, and green plant regeneration efficiency in the presence of variable supplementation of induction medium with copper ions. The methylation-sensitive Amplified Fragment Length Polymorphism was used to assess tissue culture-induced variation, Fourier Transform Infrared spectroscopy to describe the glutathione spectrum, and a structural equation model to develop the relationship between sequence variation, de novo DNA methylation within asymmetric sequence contexts, and copper ions in the induction medium, as well as, glutathione, and green plant efficiency. An essential aspect of the study is demonstrating the contribution of glutathione to green plant regeneration efficiency and indicating the critical role of copper ions in influencing tissue culture-induced variation, glutathione, and obtaining green regenerants. The model presented here also has practical implications, showing that manipulating the concentration of copper ions in the induction medium may influence cell function and increases green plant regeneration efficiency.