Mitochondrial dysfunction is involved in a wide array of devastating diseases but the heterogeneity and complexity of these diseases' symptoms challenges theoretical understanding of their causation. With the explosion of -omics data, we have the unprecedented ability to gain deep understanding of the biochemical mechanisms of mitochondrial dysfunction. However, there is also a need to make such datasets interpretable, and quantitative modelling allows us to translate such datasets into intuition and suggest rational biomedical treatments. Working towards this interdisciplinary goal, we use a recently published large-scale dataset, and develop a mathematical model of progressive increase in mutant load of the MELAS 3243A>G mtDNA mutation to develop a descriptive and predictive biophysical model. The experimentally observed behaviour is surprisingly rich, but we find that a simple, biophysically-motivated model intuitively accounts for this heterogeneity and yields a wealth of biological predictions. Our findings suggest that cells attempt to maintain wild-type mtDNA density through cell volume reduction, and thus energy demand reduction, until a minimum cell volume is reached. Thereafter, cells toggle from demand reduction to supply increase, upregulating energy production pathways. Our analysis provides further evidence for the physiological significance of mtDNA density, and emphasizes the need for performing single-cell volume measurements jointly with mtDNA quantification. We propose novel experiments to verify the hypotheses made here, to further develop our understanding of the threshold effect, and connect with rational choices for mtDNA disease therapies.