The Effect of Mitochondrial DNA Half-Life on Deletion Mutation Proliferation in Long Lived Cells

Abstract

The proliferation of mitochondrial DNA (mtDNA) with deletion mutations has been linked to aging and age related neurodegenerative conditions. In this study we model the effect of mtDNA half-life on mtDNA competition and selection. It has been proposed that mutation deletions ($\text {mtDNA}_{del}$) have a replicative advantage over wild-type ($\text {mtDNA}_{wild}$) and that this is detrimental to the host cell, especially in post-mitotic cells. An individual cell can be viewed as forming a closed ecosystem containing a large population of independently replicating mtDNA. Within this enclosed environment a selfishly replicating $\text {mtDNA}_{del}$ would compete with the $\text {mtDNA}_{wild}$ for space and resources to the detriment of the host cell. In this paper, we use a computer simulation to model cell survival in an environment where $\text {mtDNA}_{wild}$ compete with $\text {mtDNA}_{del}$ such that the cell expires upon $\text {mtDNA}_{wild}$ extinction. We focus on the survival time for long lived post-mitotic cells, such as neurons. We confirm previous observations that $\text {mtDNA}_{del}$ do have a replicative advantage over $\text {mtDNA}_{wild}$. As expected, cell survival times diminished with increased mutation probabilities, however, the relationship between survival time and mutation rate was non-linear, that is, a ten-fold increase in mutation probability only halved the survival time. The results of our model also showed that a modest increase in half-life had a profound affect on extending cell survival time, thereby, mitigating the replicative advantage of $\text {mtDNA}_{del}$. Given the relevance of mitochondrial dysfunction to various neurodegenerative conditions, we propose that therapies to increase mtDNA half-life could significantly delay their onset.

Appendices

Appendix A

1.1 Markov Model for Half-Life

In this appendix, we present a Markov model to derive a value of $P_{damage}$ that yields a given half-life. The model comprises a series of states where each state represents the $m_{ttl} = n$ value of the mtDNA. The Markov model transitions from state n to state $n-1$ with a probability of $p=P_{damage}$. Consequently, the mtDNA remains in the same state (that is, $m_{ttl}$ is unaffected) with probability $1 - p$, The transition probability matrix $\mathbf {P}$ for $maxTTL = 10$ is given by:

(5)

The initial state $\pi ^0$ is:

(6)

We demonstrate the Markov model by computing the mutation probability for a half life of 10 days. Given that the iteration interval is 15 min, then 10 days is 960 intervals ($24 \times 4 \times 10$). We ran the Markov model for various values of p until we achieved result close to:

(7)

When $\pi [0]^{960} \approx 0.5$, approximately half of the mtDNAs have expired as they have a TTL value $m_{ttl}=0$. Similarly, approximately half of the population is still alive, that is, $m_{ttl} > 0$: We found $p=0.0101$ yielded a half life of 10 days.

Appendix B

2.1 Simulation Pseudocode

This appendix contains the pseudocode for the simulator. Table 4 describes the data structures and functions used in the pseudocode.

Table 4 Simulation data structures and Functions