Complex-phase stochastic modeling of mitochondrial heteroplasmy

Mitochondrial heteroplasmy the coexistence of both wild-type and mutant copies of mitochondrial DNA ( mtDNA ) within a cell is a key factor in the pathogenesis of mitochondrial diseases. Classical approaches, which rely solely on the scalar fraction of mutant DNA, fail to fully account for threshold effects, the stochastic nature of heteroplasmy dynamics , and tissue specificity. The aim of the work is to construct a complex stochastic model of heteroplasmy dynamics , which for the first time combines the effects of selection, genetic drift, migration of mitochondrial genomes between tissues and threshold mechanisms of pathology development, for a quantitative assessment of the risk of mitochondrial diseases. In this paper, we propose a complex-phase formalism in which the state of a cell's mitochondrial genome is described by a complex number Z = a + ib , where a and b are the absolute numbers of normal and mutant mtDNA copies , respectively. This approach naturally combines information on copy number and heteroplasmy level , and the argument {phi} = arctan ( b / a ) is interpreted as a phase characterizing the mutant load. Based on this formalism, we developed a stochastic model of tissue dynamics that includes the processes of selection, genetic drift, and intertissue migration of mitochondrial genomes. Using Monte Carlo methods (1000 simulations), we demonstrated that neuronal tissues are characterized by high heteroplasmy variability and a significant probability of reaching a pathological threshold even with a relatively low systemic mutant load. Kaplan-Meier survival analysis demonstrates that the development of pathology is probabilistic and can be described as a time -to-event process . The proposed approach enables quantitative assessment of the individual risk of developing mitochondrial diseases and opens the door to personalized prognosis.