Modeling mitochondria, where are the numbers?

Models and simulations are particularly useful for exploring ideas and concepts in the biological sciences that are experimentally impracticable.

In silico methods are also gaining acceptance with regulatory authorities as an alternative to animal testing. For example, the Environmental Protection Agency aims to eliminate animal testing by 2035, and both the Food and Drug Administration and European Medicine Agency no longer require animal testing for biosimilars or generic products if the in vitro and in silico data is acceptable.

The parameters for models that are predominantly dependent on the biophysical properties of a particular compound are relatively easy to determine. Conversely, the parameters for models that are dependent on biological parameters can be difficult to obtain and the values in the literature tend to be more variable.

To illustrate this, our research on mitochondrial DNA (mtDNA) behavior, utilizing stochastic simulations, revealed a challenge of working with biological parameters is that they are often qualitative rather than quantitative. Published values for many parameters related to mitochondria, such as mitochondrial numbers per cell, mtDNA copy number, mutation rate, and half-life cover a considerable range in the literature. Other aspects of mitochondrial biology have become accepted knowledge without substantive justification.

For example, contrary to the depiction often found in publications and textbooks, the portrayal of cells containing 1000–2000 or more rice grain-shaped mitochondria is a misleading oversimplification. In reality, mitochondria exhibit an amorphous and dynamic morphology that has been recognized for over a century. They can manifest as thread-like structures (mitos) or granular forms (chondros). Cellular stress levels, nutrient availability, exposure to xenobiotics, and other unidentified factors influence the fragmentation or fusion of mitochondria, and consequently, the number of individual mitochondria. A realistic value of the number of mitochondria per cell is between one and many (Figure 1).

Figure 1.

A realistic value of the number of mitochondria per cell is between one and many.

How many mitochondria? The mitochondria in an unstressed fibroblast (right) form a fused network with few individual mitochondria. When stressed (left) the mitochondria fragments to form many mitochondria (Images: Personal collection; unpublished data).

To simulate the behavior of a population of mtDNA within a mitochondrion, a useful question is how many copies of the mtDNA are there per cell, not how many per mitochondrion.

A common assumption is that cells with a low energy demand have a low mtDNA copy number. As such the high mtDNA copy number in neurons is commonly attributed to the high-energy demand of neurons (Wang et al., 2021), but compared to other organs the energy expenditure of the brain, on a gram-for-gram basis, is not exceptional (Wang et al., 2010). The brain uses 240 kcal/kg/day and the similarly sized liver uses 200 kcal/kg/day, but the heart and kidneys use 440 kcal/kg/day. Furthermore, the hypothesis that the energy expenditure of a cell is directly proportional to the copy number of the mtDNA is probably incorrect. Experimental evidence suggests that an increase in mtDNA copy number only impacts the respiration rate up to a certain threshold of a few hundred copies beyond which there is no further effect (Baron, 2010). Therefore, the high mtDNA copy number in neurons must serve purposes other than energy demand. While it is not possible to change the mtDNA copy number in a neuron, in vitro or in vivo, and monitor the behavior for a lifetime, it is possible to run many simulations with different-sized populations. Our simulations (submitted) indicate that the size of the mtDNA population in neurons is a functional adaptation to prevent neuron loss at a young, pre-reproductive, age loss rather than to facilitate energy demand.

A consequence of a high copy number is that there is a population of replicons in a closed environment where we may expect to see Darwinian behavior (Gitschlag and Patel, 2019).

In the abstract, the mtDNA can be regarded like any population replicons that replicate, mutate, expire, and potentially compete. A ramification of mutation is that the population mtDNA will contain more than one variant or species, that is to say, it will be heteroplasmic. The term heteroplasmy is poorly defined as it is used for a mitochondrion with a single mutant mtDNA that clonally expands, or a mitochondrion with many species of mutant mtDNA each present at a low level. While it is true that both situations are examples of heteroplasmy, the population dynamics, and mutation rates that lead to these outcomes are distinct.

Each individual mtDNA in a cell has a relatively short half-life, and as such the population has a rapid turnover. As such the aggregate mutation rate for mtDNA over many generations can be quantified, but the rate of damage within the lifespan of a somatic cell is almost impossible to determine.

To accurately simulate the behavior of a population of mtDNA over time it is essential to know the half-life of mtDNA and the rate of damage. As far as we are aware the mtDNA half-life has only been measured twice, both studies being conducted with rodents (Gross et al., 1967; Korr et al., 1998). The widely adopted half-life of 10–30 days, based on these rodent studies, is commonly used in various models and simulations, including our own. However, it is possible that the half-life of mtDNA in human neurons could differ significantly, at present it is not known.

Employing stochastic simulations can be invaluable in exploring different scenarios and determining what are physiologically plausible values for the mtDNA half-life in human neurons. In our simulations, we assigned different values to the half-life, then assessed the outcomes to make more informed predictions regarding the behavior of mtDNA populations over several virtual decades. Our simulations indicate that a short half-life of weeks is likely and is an adaptation optimized for functionality up to post-reproductive age. The detrimental effects of neuron loss due to clonal expansion of deletion mutants are in part due to the extended lifespan that we currently enjoy.

Like any replicon mtDNAs are subject to damage, which can lead to mutation. Free radicals, which can leak from the electron transport chain during the reduction of molecular oxygen, are well established as being able to damage DNA (Harman, 1956). Though, surprisingly, the rate of formation of reactive oxygen species, in vivo, in mitochondria is not known.

A common assertion is that the leak of free radicals from the electron transport chain amounts to 2% or more of the oxygen consumed in respiration. Not only is this value implausibly high, it implies that exercise which increases oxygen consumption, would be detrimental to health. The origin of the 2% value can be traced back to the work of Boveris, Chance, and Oshino in the 1970s (Boveris, 1972). However, their findings indicated that the leakage from the electron transport chain could reach up to 2% when measured in vitro in isolated mitochondria under ADP-limited (state 4) respiration conditions. They clearly demonstrated that when ADP is added, state 3 respiration is initiated, and the generation of free radicals becomes negligible. It is safe to assume that state 4 respiration does not occur in vivo. Therefore, under normal physiological conditions, the rate of free radical generation in vivo must be much closer to negligible than it is to 2%. Nevertheless, in spite of making little sense, and being refuted by several authors, this value has become common knowledge and continues to be commonly cited.

It is possible to culture neurons in vitro, but the gene expression and the observable phenotype are dependent on the culture conditions, and the cells are only viable for a matter of weeks to months. As we are interested in the population dynamics of the mtDNA that take place over decades, it would be a major assumption that values obtained from short-term in vitro studies are reflective of the in vivo situation over many decades. We have a particular interest in simulating how changes in the population of mtDNA in a neuron can impact the incidence and progression of dementia. In this case, many of the various parameters that are necessary are not readily available, but simulations can enable reasonable estimates to be made.

In our simulations, in contrast to other models, we do not try to maintain a specific number of mtDNA, but allow the mtDNA copy number to adjust depending on the energetic requirements of the cell via the ATP feedback mechanism (Holt and Davies, 2020), assuming that any particular mtDNA is responsible for a fraction of the total ATP generated. In effect, our model seeks to maintain a steady population of the wild-type functional mtDNA, regardless of the total population of wild-type and non-functional mutant mtDNA populations. We do, however, assume that there is a maximum possible population of total mtDNA, and that replication is permitted in response to demand for ATP only until a maximum capacity is reached. This capacity could be a lack of space or other limiting resource. When the capacity is reached the wild-type mtDNA will then be in competition with the mutant species(s) for the limiting resources. In our model when defective mitochondria reach a specific threshold of greater than 70% heteroplasmy the cell dies. This value was chosen based on the observation that phenotypic expression of a mitochondrial disease requires greater than 70% heteroplasmy (Russell et al., 2020). In our virtual neuronal mitochondria, there is an mtDNA copy number of approximately 2000 copies and a maximum capacity of 10,000. There is observational evidence that the mtDNA copy number is controlled, but not necessarily fixed, as seen with the compensatory increase in the mtDNA copy number in Leber's hereditary optic neuropathy (Bianco et al., 2017).

We have applied these stochastic simulations to a population of mtDNA in a neuron that would, over time, cause neuron loss and cognitive decline. In our simulations, we can change the parameter defining the mtDNA copy number, the mtDNA half-life, or the mutation rate. By specifying many variations and running many simulations we are able to make a prediction of the final state, and thus the likely physiological values of mtDNA copy number, the mtDNA half-life, or the mutation rate.

It is not possible to specify a mutation rate in vivo, but in silico, many mutation rates can be defined and the long-term effects explored.

For example, a mutation rate that could lead to a single mutant mtDNA that clonally expands would be so low as to make neuron loss and consequent cognitive decline improbable. A mutation rate high enough to cause significant cell loss will inevitably lead to multiple mtDNA species; there may be one or more species that dominate, but there will always be a background of other species present at a low level. More recent publications confirm that this is indeed the case.

Although not without its challenges, simulating various scenarios can provide valuable insights. Notably experimental investigation is not possible, such as studying the behavior of mtDNA populations in vivo over a human lifespan. Sampling human brain tissue at regular intervals over several decades is neither feasible nor ethically justifiable. However, conducting in silico simulations and virtual sampling allows for the investigation of the effects of simulated interventions. In these situations, models and simulations contribute significantly not just by making empirically testable predictions, but by forcing explicit acknowledgment of underlying assumptions, and admission that many in vivo parameters are unknown, unknowable, or based on little empirical evidence.