The mitochondrial DNA (mtDNA) plays a fundamental role in cell respiration and the maintenance of eukaryotic life. However, respiration also requires proteins encoded in the nuclear DNA (nDNA), leading to an intricate interaction and co-evolution of these two genetic sequences. Maintaining compatibility between proteins from the nucleus and mitochondria is essential for proper cell function. Understanding how this compatibility persists over time, despite the susceptibility of mtDNA to accumulate harmful mutations, is of great importance. Mechanisms like purifying selection in mtDNA and compensatory mutations in nDNA have been proposed and scrutinized. In this talk, I will present an individual-based model that elucidates the timing and mechanisms of these processes. We show that not only the mtDNA mutation rate plays a role in the process but also the strength of mito-nuclear selection and the initial degree of incompatibility.