Mitochondria are the powerhouse of eukaryotes. However, as a byproduct of cellular respiration they also produce mutagenic reactive oxygen species (ROS). Apart from the cell's nucleus, mitochondria are the only organelle which has its own genetic information. Mitochondrial DNA (mtDNA) is very compact with no introns or exons. Human mtDNA is made up of 16,565 base pairs, which encodes 13 polypeptides, 22 tRNAs and two rRNA's that are essential for the functioning of mitochondria [3]. The mitochondrial ROS can damage mtDNAs and this can lead to mtDNA mutations. Accelerated accumulation of mtDNA mutations has been postulated to occur during aging as a result of their proximity to the ROS source. The loss of mitochondrial functions due to these mutations has been associated with many metabolic and degenerative diseases, whose clinical symptoms progress with ageing [3]. The connection between mtDNA mutations and ageing is supported by experimental evidence showing that the amount of somatic mtDNA mutations increases with age [1] and mice with defective mtDNA polymerase show signs of accelerated ageing [2]. In this work, the consequence of inherent biological stochasticity on the maintenance of genomic stability of mitochondrial DNA (mtDNA) is investigated through the development of an in silico model
Mathematical models have been proposed to explain the accumulation of somatic mutations in mtDNAs. Kowald and Kirkwood have done pioneering work in the field of ageing modeling [3]. Their work was based on the hypothesis of ROS ”vicious cycle”. Vicious cycle theory postulates that ROS cause mtDNA mutations and in turn these mutations cause higher production of ROS. Most of the existing models however are deterministic (ODEs). Few exceptions include Langevin-type stochastic models due to Samuels and Chinnery [4], which were based on the assumption of relaxed replication of mtDNA. Here, mitochondrial fusion and fission were assumed to occur frequently enough to justify a single well-mixed mtDNA pool in the cell. This assumption is also used in the present model. One weakness of the existing models in the literature is the requirement of a large number of unknown parameters that need to be set or estimated. Quantitative estimation of most of the parameters needed for such elaborate modeling is challenging. To overcome this limitation, we have proposed a minimal chemical master equation model of mtDNA somatic mutation which can capture features of experimental data on mice [2]. Here, all the model parameters were obtained from published literature values.
2. Model Description:
The model captures two main processes that contribute to the maintenance of mtDNA genomic stability, namely mtDNA degradation and replication
mtDNA → Φ; Propensity a=kd*(W+M)
mtDNA → 2mtDNA; Propensity a=νmax*(1-(Wn/(Wn+Kn))
where kd, νmax, K and n are the model parameters. The a terms are known as the propensity functions, for which a•dt gives the probability that a given process (reaction) takes place in the time range of [t, t+dt). The model further tracks the number of wild type (W) and mutant (M) mtDNA molecules individually. In addition, there exists a probability (km) of wild type mtDNA replication that will produce one mutant molecule M. As the mtDNA replication is known to be regulated by nucleus, perhaps in response to the energetic needs of the cell, the propensity function for mtDNA replication depends on the number of wild-type mtDNAs according to a Hill-type function.
In order to deal with the stochastic nature inherent in cellular processes, the Stochastic Simulation Algorithm (SSA) was used to simulate this model [5]. A modified version of this algorithm has been used for the present work, which is not detailed here for brevity. The parameters were obtained from reported values based on experimental data for mice. The simulations were developed to represent the evolution of mtDNA mutations in the cardiomyocytes of mice, over its natural life span of 36 months. Two stages of the cell developments were considered in the modeling. The first stage involves the developmental stage in which there is a burst of mtDNA replication along with cell divisions. Here, mutations are primarily due to polymerase fidelity error during replication. In the second post-mitotic stage, mtDNA mutations primarily arise due to mtDNA turnover and oxidative damage.
3. Results and Discussion:
To validate the model, experimental results of age dependent accumulation of point mutations in wild type mice were used. In this experiment, point mutations on the TaqI restriction site (TCGA) in the gene encoding region of the 12S rRNA (bp 634-637) subunit of mice mtDNA were tracked using a highly sensitive RMC assay for a period of 36 months (maximum life span of a wild-type mice) [2]. Correspondingly, the simulation tracked the mtDNA population of both types (W and M) for the complete population of heart cells (~0.4 - 6×107 cells). The mutation burden predicted by the model and this experiment are in good agreement. An observation of the data from both simulations and experiments suggested that the mutational burden accumulated exponentially with time. However, the model predicts that the average of the mutation frequency increases in a linear fashion. The apparent exponential increase in the mutational burden was determined to be an artifact of small number of samples taken from a long-tailed distribution. To further validate the model, simulations were done for the mutator mice with a proof-reading deficient activity of DNA polymerase using data from [2, 6]. The model again demonstrated an excellent agreement with the experimental results for both the heterozygous and homozygous mutator mice (data not shown). The mutator model showed that the developmental stage makes a significant contribution to the accumulation of the mtDNA mutation, as seen in experiments [7]. The same observation was also made in the wild-type mice model, but to a much lesser degree. These results suggested that the mtDNA mutations were determined to some extent during its developmental phase.
4. Conclusions:
How cells maintains their mtDNA population in higher organisms is fundamentally important to our understanding of the relationship between mitochondrial genome, ageing, and diseases. In this work, a minimal model, based only on mtDNA turnover and mutations caused by damage and polymerase error, was developed. This model has shown to be in good agreement with experiments. Despite the apparent exponential increase of mtDNA mutation load with time, the model predicted that the average mutation frequency to grow linearly with age. This model provides a starting point for the development of more complex and realistic representations of mtDNA somatic mutation, including the role of mitochondrial fusion and fission
5. References:
1. Khaidakov, M., Heflich, M. H., Manjanatha, M. G., Myers, M. B., and Aidoo, A. 2003. Accumulation of point mutations in mitochondrial DNA of aging mice. Mutat. Res., 526(1-2):1-7.
2. Vermulst, M., Bielas, .J .H., Kujoth, G. C., Ladiges, W. C., Rabinovitch, P. S., Prolla, T. A., Loeb, A. 2007. Mitochondrial point mutations do not limit the natural lifespan of mice. Nat. Genet., 39(4):540-543.
3. Kowald, A. and wood, T. B. 1994. Towards a network theory of ageing: a model combining the free radical theory and the protein error theory. J. theor. Biol., 168(1):75-94.
4. Elson J.L., Samuels, D.C., Turnbull D.M., and Chinnery P.F. 2001. Random intracellular drift explains the clonal expansion of mitochondrial DNA mutations with age. Am. J. Hum. Genet., 68:802-806.
5. Gillespie D. T. 1977. Exact Stochastic simulation of coupled chemical reactions. J. Phys. Chem., 81(25):2340-2361.
6. Trifunovic et al., 2004. Premature ageing in mice expressing defective mitochondrial DNA polymerase. Nature. 429: pp. 417-423.
7. Trifunovic et al., 2005. Somatic mtDNA mutations cause aging phenotypes without affecting reactive oxygen species production. Proc. Natl. Acad. Sci. 102(50): pp. 17993-17998.