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• W2079414980 abstract "SummaryHeteroplasmic mtDNA defects are an important cause of human disease with clinical features that primarily involve nondividing (postmitotic) tissues. Within single cells the percentage level of mutated mtDNA must exceed a critical threshold level before the genetic defect is expressed. Although the level of mutated mtDNA may alter over time, the mechanism behind the change is not understood. It currently is not possible to directly measure the level of mutant mtDNA within living cells. We therefore developed a mathematical model of human mtDNA replication, based on a solid foundation of experimentally derived parameters, and studied the dynamics of intracellular heteroplasmy in postmitotic cells. Our simulations show that the level of intracellular heteroplasmy can vary greatly over a short period of time and that a high copy number of mtDNA molecules delays the time to fixation of an allele. We made the assumption that the optimal state for a cell is to contain 100% wild-type molecules. For cells that contain pathogenic mutations, the nonselective proliferation of mutant and wild-type mtDNA molecules further delays the fixation of both alleles, but this leads to a rapid increase in the mean percentage level of mutant mtDNA within a tissue. On its own, this mechanism will lead to the appearance of a critical threshold level of mutant mtDNA that must be exceeded before a cell expresses a biochemical defect. The hypothesis that we present is in accordance with the available data and may explain the late presentation and insidious progression of mtDNA diseases. Heteroplasmic mtDNA defects are an important cause of human disease with clinical features that primarily involve nondividing (postmitotic) tissues. Within single cells the percentage level of mutated mtDNA must exceed a critical threshold level before the genetic defect is expressed. Although the level of mutated mtDNA may alter over time, the mechanism behind the change is not understood. It currently is not possible to directly measure the level of mutant mtDNA within living cells. We therefore developed a mathematical model of human mtDNA replication, based on a solid foundation of experimentally derived parameters, and studied the dynamics of intracellular heteroplasmy in postmitotic cells. Our simulations show that the level of intracellular heteroplasmy can vary greatly over a short period of time and that a high copy number of mtDNA molecules delays the time to fixation of an allele. We made the assumption that the optimal state for a cell is to contain 100% wild-type molecules. For cells that contain pathogenic mutations, the nonselective proliferation of mutant and wild-type mtDNA molecules further delays the fixation of both alleles, but this leads to a rapid increase in the mean percentage level of mutant mtDNA within a tissue. On its own, this mechanism will lead to the appearance of a critical threshold level of mutant mtDNA that must be exceeded before a cell expresses a biochemical defect. The hypothesis that we present is in accordance with the available data and may explain the late presentation and insidious progression of mtDNA diseases. mtDNA defects cause a diverse group of diseases that often result in severe morbidity and premature death (Wallace Wallace, 1992Wallace DC Diseases of the mitochondrial DNA.Annu Rev Biochem. 1992; 61: 1175-1212Crossref PubMed Scopus (1158) Google Scholar; Johns Johns, 1995Johns D Mitochondrial DNA and disease.New Engl J Med. 1995; 333: 638-644Crossref PubMed Scopus (30) Google Scholar; Shoffner Shoffner, 1996Shoffner JM Maternal inheritance and the evaluation of oxidative phosphorylation diseases.Lancet. 1996; 348: 1283-1288Abstract Full Text Full Text PDF PubMed Scopus (66) Google Scholar). Individuals with pathogenic mtDNA defects (deletions and point mutations) usually harbor a mixture of mutant and wild-type mtDNA within each cell (heteroplasmy; Larsson and Clayton Larsson and Clayton, 1995Larsson NG Clayton DA Molecular genetic aspects of human mitochondrial disorders.Annu Rev Genet. 1995; 29: 151-178Crossref PubMed Scopus (390) Google Scholar). In vitro studies have shown that the percentage level of mutant mtDNA must exceed a critical threshold level before a cell expresses a mitochondrial respiratory-chain deficiency (Attardi et al. Attardi et al., 1995Attardi G Yoneda M Chomyn A Complementation and segregation behavior of disease causing mitochondrial DNA mutations in cellular model systems.Biochim Biophys Acta. 1995; 1271: 241-248Crossref PubMed Scopus (103) Google Scholar). The percentage level of heteroplasmy varies between different organs and also between adjacent cells within the same organ. These differences are partly due to the differential partitioning of mitochondrial genomes, between daughter cells, during embryological development (vegetative segregation; Lightowlers et al. Lightowlers et al., 1997Lightowlers RN Chinnery PF Turnbull DM Howell N Mammalian mitochondrial genetics: heredity, heteroplasmy and disease.Trends Genet. 1997; 13: 450-455Abstract Full Text PDF PubMed Scopus (340) Google Scholar). However, there is increasing evidence that the level of mutant mtDNA in nondividing (postmitotic) tissues may change during a human lifetime (Larsson et al. Larsson et al., 1990Larsson NG Holme E Kristiansson B Oldfors A Tulinius M Progressive increase of the mutated mitochondrial DNA fraction in Kearns-Sayre syndrome.Pediatr Res. 1990; 28: 131-136Crossref PubMed Scopus (266) Google Scholar; Poulton and Morten Poulton and Morten, 1993Poulton J Morten K Noninvasive diagnosis of the MELAS syndrome from blood DNA.Ann Neurol. 1993; 34: 116Crossref PubMed Scopus (44) Google Scholar; Weber et al. Weber et al., 1997Weber K Wilson JN Taylor L Brierley E Johnson MA Turnbull DM Bindoff LA A new mtDNA mutation showing accumulation with time and restriction to skeletal muscle.Am J Hum Genet. 1997; 60: 373-380PubMed Google Scholar). The most disabling manifestations of mtDNA disease arise through the clinical involvement of postmitotic tissues such as skeletal muscle and neurons (Chinnery and Turnbull Chinnery and Turnbull, 1997Chinnery PF Turnbull DM The clinical features, investigation and management of patients with mitochondrial DNA defects.J Neurol Neurosurg Psychiatry. 1997; 63: 559-563Crossref PubMed Scopus (92) Google Scholar), and changes in mutation load, with advancing age (longitudinal changes), may explain the late presentation and insidious progression of mtDNA diseases (Wallace Wallace, 1995Wallace DC Mitochondrial DNA variation in human evolution, degenerative disease, and aging.Am J Hum Genet. 1995; 57: 201-223PubMed Google Scholar). Our understanding of mitochondrial disease, therefore, is critically dependent on our knowledge of the mechanisms that determine the level of mutant mtDNA within the cell, but, in the foreseeable future, it is unlikely that we will be able to measure this level directly. We therefore chose a mathematical approach to the investigation of the potential longitudinal changes in mtDNA heteroplasmy in human cells. Each mammalian mitochondrion contains 2–10 copies of mtDNA, resulting in 1,000–100,000 copies in each human cell (Larsson and Clayton Larsson and Clayton, 1995Larsson NG Clayton DA Molecular genetic aspects of human mitochondrial disorders.Annu Rev Genet. 1995; 29: 151-178Crossref PubMed Scopus (390) Google Scholar; Lightowlers et al. Lightowlers et al., 1997Lightowlers RN Chinnery PF Turnbull DM Howell N Mammalian mitochondrial genetics: heredity, heteroplasmy and disease.Trends Genet. 1997; 13: 450-455Abstract Full Text PDF PubMed Scopus (340) Google Scholar). Despite the high copy number, recombination of mtDNA molecules is rare (Howell Howell, 1997Howell N mtDNA recombination: what do in vitro data mean?.Am J Hum Genet. 1997; 61: 19-22Abstract Full Text PDF PubMed Scopus (27) Google Scholar), and each mtDNA molecule replicates independently. Nuclear DNA replicates once during the cell cycle. By contrast, mtDNA turns over continuously. Individual mtDNA molecules replicate at random, making one or more copies at a time while maintaining a relatively constant total number of mtDNA molecules within the cell (relaxed replication; Birky Birky, 1994Birky Jr, CW Relaxed and stringent genomes: why cytoplasmic genes don't obey Mendel's laws.J Hered. 1994; 85: 355-365Google Scholar). If there are two or more different types of mtDNA molecules within a cell, then, by chance, any one type of molecule may replicate more frequently than another type, resulting in a change in the level of heteroplasmy within the cell (intracellular drift). We developed a computer simulation of a somatic human cell containing a mixed, nonpartitioned (panmictic) population of two different mtDNA molecules. Because the model was developed to increase our understanding of mtDNA disease, our simulations always began with >1% mutant mtDNA within the cell, and we assumed that rare somatic mutations had no significant effects. We based the model on experimentally derived parameters. Any inaccuracies in these parameters may have influenced the absolute values predicted, but they are unlikely to have altered the overall trends. We first studied the dynamics of intracellular heteroplasmy for two neutral alleles and then studied the effects of a pathogenic allele. We assumed that, in a collection of mtDNA molecules containing two distinct neutral alleles, A and B, each molecule was destroyed with a half-life, T1/2, of 1–10 d (Gross et al. Gross et al., 1969Gross NJ Getz GS Rabinowitz M Apparent turnover of mitochondrial deoxyribonucleic acid and mitochondrial phospholipids in the tissues of the rat.J Biol Chem. 1969; 244: 1552-1562Abstract Full Text PDF PubMed Google Scholar). If new mtDNA molecules are generated at a copy rate C, then the total number N of mtDNA molecules within each simulated cell changes at the following rate: dNdt=C-Nτ ,(1) where τ = T1/2/ln(2). If the bioenergetic demands on the cell remain constant, the cells harboring neutral mitochondrial alleles are likely to maintain a relatively stable number of mtDNA molecules (Clayton Clayton, 1996Clayton DA Mitochondrial DNA gets the drift.Nat Genet. 1996; 14: 123-125Crossref PubMed Scopus (12) Google Scholar). We called this value “NOptimal.” In order to maintain a steady number of mtDNA at NOptimal, the copy rate, determined from equation (1), must be C = NOptimal/τ. Starting with an initial population of mtDNA molecules within a single cell, each mtDNA molecule has a probability Δt/τ of being destroyed during a given time step Δt. Destroyed mtDNA molecules were removed from the population. We then calculated the number of new mtDNA molecules, NNew=CΔt, that were created during the same time step and made a single copy of NNew randomly chosen molecules from the remaining population. This process was repeated for each time increment. Although an mtDNA molecule may be copied more than once when it replicates (Birky Birky, 1994Birky Jr, CW Relaxed and stringent genomes: why cytoplasmic genes don't obey Mendel's laws.J Hered. 1994; 85: 355-365Google Scholar), this is unusual in mammalian cells (Flory and Vinograd Flory and Vinograd, 1973Flory PJ Vinograd J 5-Bromodeoxyuridine labeling of monomeric and catenated circular mitochondrial DNA in HeLa cells.J Mol Biol. 1973; 74: 81-94Crossref PubMed Scopus (39) Google Scholar). For simplicity, we report here the results for single replications. Figure 1a and b shows the results of 10 independent and representative simulation runs for single cells. Each cell contains ∼1,000 mtDNA molecules in which the initial proportions of the two alleles were 75% for allele A and 25% for allele B. Simulated cells that began with the same initial proportions of alleles A and B developed radically different mtDNA populations over a short period of time, and the level of heteroplasmy within any one cell varied greatly throughout the simulation. The average proportions of the two neutral alleles, for as few as 10 simulated cells, remained relatively constant (approximately equal to the starting values). This suggests that single measurements of heteroplasmy in small tissue homogenates or in single cells may be of limited value in elucidating the cellular mechanisms underlying a longitudinal change. However, by use of this model, insight into these processes should be possible, by the study of the distribution of heteroplasmy in a large number of individual cells, at two or more points in time. We then studied the probability of fixation for a particular allele, by performing sufficient simulation runs to ensure that ∼1,000 cells became fixed on that allele. Statistical measurements then were made on the subpopulation of cells that eventually fixed on the chosen allele. We then constructed the probability distribution curves for the fixation time for each allele, over a range of different values for the initial proportions of allele A and allele B, for cells containing 100–2,000 mtDNA molecules and for a T1/2 of 1–10 d. We tested the probability distributions generated by the simulations against a large number of known probability distributions. The inverse Gaussian (Wald) distribution accurately described the distribution drawn from our simulation data (fig. 2a; Johnson et al. Johnson et al., 1995Johnson N Kotz S Balakrishnan N Continuous univariate distributions. John Wiley, New York1995Google Scholar). This may be written as a function of the probability density p(t) of fixation at time t:p(t)=λ2πt3exp[-λ2μ2t(t-μ)2] ,(2) where μ is the mean time to fixation and λ is a parameter that determines the shape of the distribution. By measuring this probability distribution for many different values of the simulation parameters, we found that the quantities μ and λ were simple functions of the initial allele frequency NOptimal and of T1/2 (fig. 2b and c). By use of figure 2b and c, the mean time to fixation for any initial population of mtDNA molecules can be determined, given the average number of mtDNA molecules in the cell (NOptimal) and the half-life (T1/2). We made four important observations. First, the distribution was highly skewed, with a long positive tail: the final 25% of the cells took much longer to fix than the first 25% of the cells. Second, the mean time to fixation was proportional to the number of mtDNA molecules within the simulated cell and was a function of the initial allele frequency (fig. 2b). Third, shortening of the mtDNA half-life proportionately shortened the mean time to fixation (fig. 2b). Finally, the proportion of cells that became fixed for any particular allele was equal to the initial allele frequency, as would be expected for any simple model of random intracellular drift. In a healthy cell, the number of mtDNA molecules is tightly regulated (Turnbull and Lightowlers Turnbull and Lightowlers, 1998Turnbull DM Lightowlers RN An essential guide to mtDNA maintenance.Nat Genet. 1998; 18: 199-200Crossref PubMed Scopus (15) Google Scholar). By contrast, mtDNA proliferation is one of the hallmarks of heteroplasmic mtDNA mutations involving tRNA genes (rearrangements and point mutations) (Mita et al. Mita et al., 1989Mita S Schmidt B Schon EA DiMauro S Bonilla E Detection of “deleted” mitochondrial genomes in cytochrome-c oxidase-deficient fibers of a patient with Kearns-Sayre syndrome.Proc Natl Acad Sci USA. 1989; 86: 9509-9513Crossref PubMed Scopus (205) Google Scholar; Shoubridge et al. Shoubridge et al., 1990Shoubridge EA Karpati G Hastings KE Deletion mutants are functionally dominant over wild-type mitochondrial genomes in skeletal muscle fiber segments in mitochondrial disease.Cell. 1990; 62: 43-49Abstract Full Text PDF PubMed Scopus (226) Google Scholar; Moraes et al. Moraes et al., 1992Moraes CT Ricci E Petruzzella V Shanske S DiMauro S Schon EA Bonilla E Molecular analysis of the muscle pathology associated with mitochondrial DNA deletions.Nat Genet. 1992; 1: 359-367Crossref PubMed Scopus (142) Google Scholar; Tokunaga et al. Tokunaga et al., 1994Tokunaga M Mita S Murakami T Kumamoto T Uchino M Nonaka I Ando M Single muscle fiber analysis of mitochondrial myopathy, encephalopathy, lactic acidosis, and stroke-like episodes (MELAS).Ann Neurol. 1994; 35: 413-419Crossref PubMed Scopus (40) Google Scholar). In skeletal muscle fibers, these mutations are accompanied by mitochondrial proliferation in the subsarcolemal space (giving rise to a so-called ragged-red appearance). mtDNA proliferation also occurs in other tissues (Kaufmann et al. Kaufmann et al., 1996Kaufmann P Koga Y Shanske S Hirano M DiMauro S King MP Schon EA Mitochondrial DNA and RNA processing in MELAS.Ann Neurol. 1996; 40: 172-180Crossref PubMed Scopus (57) Google Scholar), which suggests that it is an essential compensatory response to the presence of a pathogenic allele (Schon et al. Schon et al., 1997Schon EA Bonilla E DiMauro S Mitochondrial DNA mutations and pathogenesis.J Bioenerg Biomembr. 1997; 29: 131-149Crossref PubMed Scopus (374) Google Scholar). In developing the disease model, we therefore made the assumption that the optimal state for a cell was to contain the same number of wild-type molecules as a cell that did not contain any mutant mtDNA. As in the basic model, we called this number “NOptimal.” If a cell did not contain NOptimal wild-type molecules, then the total intracellular mtDNA pool would proliferate in an attempt to redress the balance. Although it is likely that any one pathogenic mutation would result in only a relative deficiency of mtDNA expression (Schon et al. Schon et al., 1997Schon EA Bonilla E DiMauro S Mitochondrial DNA mutations and pathogenesis.J Bioenerg Biomembr. 1997; 29: 131-149Crossref PubMed Scopus (374) Google Scholar), we assumed, for simplicity, that the pathogenic allele rendered the mitochondrial gene completely functionless. Pathological mtDNA proliferation was incorporated into the model by identification of our two types of mtDNA as “wild-type” and “mutant.” We then made the mtDNA population copy rate C a linear function of the number of wild-type mtDNA, NWild, according to the following equation: C = C0 α+ 1-α (NWild/NOptimal), where C0=NOptimal/τ and where the growth coefficient α is a constant >1. Thus, when the cell contains the optimal number of wild-type mtDNA (i.e., when NWild=NOptimal), the copy rate is C=C0, which is identical to that for neutral alleles (see eq. [1]). As the number of wild-type mtDNA molecules falls below NOptimal, the copy rate increases linearly until it reaches a maximum value of αC0 when NWild=0. Increasing the copy rate by a factor of α causes the stable number of mtDNA to increase by the same factor α. We derived α from experimentally determined values for maximal mtDNA proliferation (5–17-fold [Mita et al. Mita et al., 1989Mita S Schmidt B Schon EA DiMauro S Bonilla E Detection of “deleted” mitochondrial genomes in cytochrome-c oxidase-deficient fibers of a patient with Kearns-Sayre syndrome.Proc Natl Acad Sci USA. 1989; 86: 9509-9513Crossref PubMed Scopus (205) Google Scholar; Shoubridge et al. Shoubridge et al., 1990Shoubridge EA Karpati G Hastings KE Deletion mutants are functionally dominant over wild-type mitochondrial genomes in skeletal muscle fiber segments in mitochondrial disease.Cell. 1990; 62: 43-49Abstract Full Text PDF PubMed Scopus (226) Google Scholar; Moraes et al. Moraes et al., 1992Moraes CT Ricci E Petruzzella V Shanske S DiMauro S Schon EA Bonilla E Molecular analysis of the muscle pathology associated with mitochondrial DNA deletions.Nat Genet. 1992; 1: 359-367Crossref PubMed Scopus (142) Google Scholar; Tokunaga et al. Tokunaga et al., 1994Tokunaga M Mita S Murakami T Kumamoto T Uchino M Nonaka I Ando M Single muscle fiber analysis of mitochondrial myopathy, encephalopathy, lactic acidosis, and stroke-like episodes (MELAS).Ann Neurol. 1994; 35: 413-419Crossref PubMed Scopus (40) Google Scholar]). Thus, in this model, the mutant mtDNA molecule does not have a replicative advantage over a wild-type molecule. The other parameters of the basic simulation were left unchanged. Figure 3a and b shows a typical time evolution for the wild-type and mutant alleles in 10 individual simulations. The development of the two populations was strikingly different. Within an individual cell, the number of wild-type alleles tended to remain close to the optimal value, whereas the number of mutant alleles fluctuated greatly. As with the simple model, the total number of cells that became fixed on each allele was equal to the initial starting frequency for that allele. However, the mean time to fixation in these simulations was delayed for both the wild-type and mutant alleles (fig. 4). This delay was greater for cells that ultimately became fixed on the mutant allele, and, as a consequence, the time that each cell maintained a near-optimal number of wild-type mtDNA molecules was greatly lengthened.Figure 4Relationship between mean time to fixation and initial allele frequency, for the disease model. Simulated cells initially contained 1,000 mtDNA molecules, and we set α=5 (see text). The unblackened circles indicate neutral alleles (as in fig. 1b). Proliferation delays the mean time to fixation, for both mutant and wild-type alleles. For cells that ultimately become fixed on mutant mtDNA, the delay is greater than for those that become fixed on wild-type mtDNA.View Large Image Figure ViewerDownload Hi-res image Download (PPT) We also observed an inverse correlation between the levels of the mutant and wild-type alleles. Over a large number of independent simulations, the level of mutant mtDNA was found to be related to the level of wild-type mtDNA, according to the following equation: NWild+1αNMutant≈NOptimal .(3) If RMutant=NMutant/NTotal (the percentage mutation load, a value that usually is determined for patients with mtDNA disease) and NTotal=NWild+NMutant, then equation (3) can be written in terms of NWild/NOptimal: NWildNOptimal=α(1-RMutant)α+(1-α)RMutant .(4) Figure 5 shows a plot of equation 4. When α=1 (as in the basic model), the relationship NWild/NOptimal against NMutant/NTotal was linear. However, with increasing values of α, a “shoulder” appeared in the graph. For cells containing low to moderate levels of mutant mtDNA, the ratio NWild/NOptimal remained approximately constant and near unity. In other words, the cell maintained a level of wild-type mtDNA that was similar to the level in cells that contained no mutant mtDNA (homoplasmic wild-type mtDNA). However, once a critical level of mutant mtDNA was exceeded, then the ratio NWild/NOptimal fell abruptly. Because an individual cell maintained a near-optimal level of wild-type mtDNA at the expense of an increasing level of mutant mtDNA, the mean percentage level of mutant mtDNA, averaged over a number of cells, increased with time (fig. 3c). The mean value shown in figure 3c was obtained from an average over only 10 cells, and, even with this small number of cells, the large fluctuations seen in the individual cells were not apparent. Precisely how a cell fixes or removes a pathogenic mtDNA mutation is fundamentally important to our understanding of the relationship between the mitochondrial genome and disease. It seems intuitive that a high mtDNA copy number will protect against the accumulation of deleterious mutations, but how this protective effect might occur has not been clear. Our model has shown that, within the constraints of human physiology, relaxed replication alone will tend to prevent new mutations from reaching significant levels. If correct, it is highly unlikely that such a fundamentally important mechanism would have arisen by chance. Human mtDNA accumulates mutations at 10–16× the rate of the nuclear genome (Larsson and Clayton Larsson and Clayton, 1995Larsson NG Clayton DA Molecular genetic aspects of human mitochondrial disorders.Annu Rev Genet. 1995; 29: 151-178Crossref PubMed Scopus (390) Google Scholar), but, despite the importance of each mitochondrial gene, mitochondria are relatively deficient in DNA-repair mechanisms (Lightowlers et al. Lightowlers et al., 1997Lightowlers RN Chinnery PF Turnbull DM Howell N Mammalian mitochondrial genetics: heredity, heteroplasmy and disease.Trends Genet. 1997; 13: 450-455Abstract Full Text PDF PubMed Scopus (340) Google Scholar). The results that we present here are consistent with the hypothesis that, at least in part, human cells contain a high copy number of mtDNA molecules in order to protect them against the accumulation of mutant alleles during their lifetime. This may be part of the reason why short-lived human cells (such as leukocytes and sperm [Zhang et al. Zhang et al., 1994Zhang H Cooney DA Sreenath A Zhan Q Agbaria R Stowe EE Fornace AJ et al.Quantitation of mitochondrial DNA in human lymphoblasts by a competitive polymerase chain reaction method: application to the study of inhibitors of mitochondrial DNA content.Mol Pharmacol. 1994; 46: 1063-1069PubMed Google Scholar; Ankel-Simons and Cummins Ankel-Simons and Cummins, 1996Ankel-Simons F Cummins JM Misconceptions about mitochondria and mammalian fertilization: implications for theories on human evolution.Proc Natl Acad Sci USA. 1996; 93: 13859-13863Crossref PubMed Scopus (191) Google Scholar]) have a low mtDNA copy number (≤1,000), despite a heavy dependence on mitochondrial oxidative metabolism, whereas long-lived cells (such as skeletal muscle cells, central neurons, and oocytes [Lightowlers et al. Lightowlers et al., 1997Lightowlers RN Chinnery PF Turnbull DM Howell N Mammalian mitochondrial genetics: heredity, heteroplasmy and disease.Trends Genet. 1997; 13: 450-455Abstract Full Text PDF PubMed Scopus (340) Google Scholar]) contain many mtDNA molecules (>100,000). This model also sheds light on the mechanisms that potentially are responsible for the late presentation and progression of mtDNA diseases. In designing the model, we assumed that each cell attempts to maintain an optimal level of native mtDNA and that each cell must “sense” that it does not contain an optimal number of wild-type molecules. This mechanism presumably is a function of the nucleus and does not necessarily need to occur through a biochemical respiratory-chain deficiency (Schon et al. Schon et al., 1997Schon EA Bonilla E DiMauro S Mitochondrial DNA mutations and pathogenesis.J Bioenerg Biomembr. 1997; 29: 131-149Crossref PubMed Scopus (374) Google Scholar). The proliferation of mtDNA will delay the time necessary to fix an allele but only up to a critical point (fig. 5). After this point, relaxed replication will lead to an abrupt reduction in the number of wild-type molecules, which has two important consequences. First, the mean tissue level of mutant mtDNA will increase over time (fig. 3c). This increase occurs through the proliferation of mtDNA in heteroplasmic cells that contain suboptimal levels of wild-type mtDNA. Thus, this model illustrates a potential mechanism for the accumulation of mutant molecules in postmitotic tissues; it is supported by observations from the study of patients with progressive mtDNA disease (Larsson et al. Larsson et al., 1990Larsson NG Holme E Kristiansson B Oldfors A Tulinius M Progressive increase of the mutated mitochondrial DNA fraction in Kearns-Sayre syndrome.Pediatr Res. 1990; 28: 131-136Crossref PubMed Scopus (266) Google Scholar; Weber et al. Weber et al., 1997Weber K Wilson JN Taylor L Brierley E Johnson MA Turnbull DM Bindoff LA A new mtDNA mutation showing accumulation with time and restriction to skeletal muscle.Am J Hum Genet. 1997; 60: 373-380PubMed Google Scholar); and it may explain the late presentation and subsequent clinical progression in patients with mtDNA disease (Wallace et al. Wallace et al., 1995Wallace DC Shoffner JM Trounce I Brown MD Ballinger SW Corral-Debrinski M Horton T et al.Mitochondrial DNA mutations in human degenerative diseases and aging.Biochim Biophys Acta. 1995; 1271: 141-151Crossref PubMed Scopus (204) Google Scholar). Second, on the basis of this model, measurements of single cells likely will fall into one of two groups. Those cells with percentage levels of mutant mtDNA below the abrupt shoulder will contain a near-normal number of wild-type mtDNA molecules. By contrast, cells with percentage levels of mutant mtDNA above the abrupt shoulder will contain substantially less wild-type mtDNA molecules. Thus, for cells around this transition zone, subtle changes in the percentage of mutant mtDNA will be accompanied by dramatic changes in the amount of wild-type mtDNA. This effect, on its own, will lead to the appearance of a critical threshold level of mutant mtDNA that must be exceeded before the genetic defect is expressed. This model suggests that the threshold effect (Wallace Wallace, 1995Wallace DC Mitochondrial DNA variation in human evolution, degenerative disease, and aging.Am J Hum Genet. 1995; 57: 201-223PubMed Google Scholar) is a direct consequence of the maintenance of wild-type copy numbers by relaxed replication of mtDNA. In patients with mtDNA disease, different genetic defects have subtly different effects on mtDNA expression (Moraes et al. Moraes et al., 1992Moraes CT Ricci E Petruzzella V Shanske S DiMauro S Schon EA Bonilla E Molecular analysis of the muscle pathology associated with mitochondrial DNA deletions.Nat Genet. 1992; 1: 359-367Crossref PubMed Scopus (142) Google Scholar; Schon et al. Schon et al., 1997Schon EA Bonilla E DiMauro S Mitochondrial DNA mutations and pathogenesis.J Bioenerg Biomembr. 1997; 29: 131-149Crossref PubMed Scopus (374) Google Scholar). In our disease model, α is related to the maximal rate of proliferation of mtDNA measured in vivo and, thus, reflects the nature of the genetic defect. A higher level of α not only will delay the time to fixation of an allele but also will determine the abruptness and the absolute level of the apparent critical threshold. Since mtDNA proliferation is a response to the presence of suboptimal mtDNA molecules, higher rates of mtDNA proliferation will occur in cells harboring molecules that have a major effect on mtDNA function. According to our model, this will lead to a high apparent threshold (80%–90% for α=17), which is consistent with observations from the study of patients with the A3243G MELAS (mitochondrial myopathy, encephalopathy, lactic acidosis, and strokelike episodes) mutation (Tokunaga et al. Tokunaga et al., 1994Tokunaga M Mita S Murakami T Kumamoto T Uchino M Nonaka I Ando M Single muscle fiber analysis of mitochondrial myopathy, encephalopathy, lactic acidosis, and stroke-like episodes (MELAS).Ann Neurol. 1994; 35: 413-419Crossref PubMed Scopus (40) Google Scholar) and the A8344G MERRF (myoclonic epilepsy with ragged red fibers) mutation (Boulet et al. Boulet et al., 1992Boulet L Karpati G Shoubridge EA Distribution and threshold expression of the tRNA(Lys) mutation in skeletal muscle of patients with myoclonic epilepsy and ragged-red fibers (MERRF).Am J Hum Genet. 1992; 51: 1187-1200PubMed Google Scholar). By contrast, mutations that have a less detrimental effect will be accompanied by less proliferation, and the apparent threshold will be less abrupt and at a lower value (50%–70% for α=7). This is consistent with observations from the study of patients harboring mtDNA deletions (Hayashi et al. Hayashi et al., 1991Hayashi J Ohta S Kikuchi A Takemitsu M Goto Y Nonaka I Introduction of disease-related mitochondrial DNA deletions into HeLa cells lacking mitochondrial DNA results in mitochondrial dysfunction.Proc Natl Acad Sci USA. 1991; 88: 10614-10618Crossref PubMed Scopus (496) Google Scholar; Shoubridge Shoubridge, 1994Shoubridge EA Mitochondrial DNA diseases: histological and cellular studies.J Bioenerg Biomembr. 1994; 26: 301-310Crossref PubMed Scopus (60) Google Scholar). The extreme variability both between and within our simulated cells highlights the need for many measurements when single cells are studied (figs. 1 and 3). This variability also may explain apparently conflicting data from different laboratories (Mita et al. Mita et al., 1989Mita S Schmidt B Schon EA DiMauro S Bonilla E Detection of “deleted” mitochondrial genomes in cytochrome-c oxidase-deficient fibers of a patient with Kearns-Sayre syndrome.Proc Natl Acad Sci USA. 1989; 86: 9509-9513Crossref PubMed Scopus (205) Google Scholar; Shoubridge et al. Shoubridge et al., 1990Shoubridge EA Karpati G Hastings KE Deletion mutants are functionally dominant over wild-type mitochondrial genomes in skeletal muscle fiber segments in mitochondrial disease.Cell. 1990; 62: 43-49Abstract Full Text PDF PubMed Scopus (226) Google Scholar; Moraes et al. Moraes et al., 1992Moraes CT Ricci E Petruzzella V Shanske S DiMauro S Schon EA Bonilla E Molecular analysis of the muscle pathology associated with mitochondrial DNA deletions.Nat Genet. 1992; 1: 359-367Crossref PubMed Scopus (142) Google Scholar; Tokunaga et al. Tokunaga et al., 1994Tokunaga M Mita S Murakami T Kumamoto T Uchino M Nonaka I Ando M Single muscle fiber analysis of mitochondrial myopathy, encephalopathy, lactic acidosis, and stroke-like episodes (MELAS).Ann Neurol. 1994; 35: 413-419Crossref PubMed Scopus (40) Google Scholar). We present this model as a hypothesis that is supported by experimental observation. The expression of mtDNA is complex, and we recognize that nuclear and mitochondrial genetic factors may influence the transcription and translation of mitochondrial genes (Larsson et al. Larsson et al., 1998Larsson NG Wang J Wilhelmsson H Oldfors A Rustin P Lewandoski M Barsh GS et al.Mitochondrial transcription factor A is necessary for mtDNA maintenance and embryogenesis in mice.Nat Genet. 1998; 18: 231-236Crossref PubMed Scopus (1100) Google Scholar; Turnbull and Lightowlers Turnbull and Lightowlers, 1998Turnbull DM Lightowlers RN An essential guide to mtDNA maintenance.Nat Genet. 1998; 18: 199-200Crossref PubMed Scopus (15) Google Scholar). This model is not intended to provide a comprehensive explanation of human mtDNA maintenance and expression. For example, we have not considered the possibility of more than two alleles within a cell, because significant levels of triplasmy are probably very rare (Lightowlers et al. Lightowlers et al., 1997Lightowlers RN Chinnery PF Turnbull DM Howell N Mammalian mitochondrial genetics: heredity, heteroplasmy and disease.Trends Genet. 1997; 13: 450-455Abstract Full Text PDF PubMed Scopus (340) Google Scholar). Furthermore, the intracellular drift of mtDNA heteroplasmy likely will be influenced by the packaging of mtDNA into discrete units (such as mitochondria or nucleoids), which we will include in later models. We believe, however, that the simulations we have described clearly demonstrate the potential for temporal dynamics of intracellular heteroplasmy in human cells. Relaxed replication also may be involved in the clonal expansion of somatic mtDNA mutations during aging (Brierley et al. Brierley et al., 1998Brierley EJ Johnson MA Lightowlers RN James OFW Turnbull DM Role of mitochondrial DNA mutations in human aging: implications for the central nervous system and muscle.Ann Neurol. 1998; 43: 217-223Crossref PubMed Scopus (247) Google Scholar) and may contribute to the diverse genotypes and phenotypes seen in families harboring pathogenic mtDNA mutations (Lightowlers et al. Lightowlers et al., 1997Lightowlers RN Chinnery PF Turnbull DM Howell N Mammalian mitochondrial genetics: heredity, heteroplasmy and disease.Trends Genet. 1997; 13: 450-455Abstract Full Text PDF PubMed Scopus (340) Google Scholar), further highlighting the importance of this mechanism in our understanding of mtDNA and its relationship to aging and disease. We are indebted to Prof. Neil Howell for his comments during the preparation of this manuscript and to Prof. Douglass Turnbull and Dr. Bob Lightowlers for their support. P.F.C. is a Wellcome Trust Research Fellow." @default.
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• W2079414980 title "Relaxed Replication of mtDNA: A Model with Implications for the Expression of Disease" @default.
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