ARTICLE: Removing mutant mtDNA from cells

2-Deoxy-D-glucose couples mitochondrial DNA replication with mitochondrial fitness and promotes the selection of wild-type over mutant mitochondrial DNA
Boris Pantic, Daniel Ives, Mara Mennuni, Diego Perez-Rodriguez, Uxoa Fernandez-Pelayo, Amaia Lopez de Arbina, Mikel Muñoz-Oreja, Marina Villar-Fernandez, Thanh-mai Julie Dang, Lodovica Vergani, Iain G Johnston, Robert DS Pitceathly, Robert McFarland, Michael G Hanna, Robert W Taylor, Ian J Holt, Antonella Spinazzola
Nature Communications 12 1 (2021)

This is an exciting one! As we've discussed before, mitochondrial DNA (mtDNA) molecules exist in large populations in our cells, encoding vital machinery. Devastating diseases can result when a high proportion of a cell's mtDNA molecules are mutated, but cells can deal with a low proportion of mutant mtDNA. So, it'd be great if we had a way to decrease the proportion of mutant mtDNA in cells -- below the threshold for disease.

Perhaps we do! We recently played a supporting role in a project with Antonella Spinazzola and Ian Holt, looking at what happens when cells containing a mixture of mutant and normal mtDNA are treated with chemicals. They found that a molecule called 2DG (for short) slows down the replication of mutant mtDNA in cells. As mtDNA is constantly replicating, this preferential inhibition of mutant means that normal mtDNA comes to dominate the cellular population over time. We showed this population shifting over time in a variety of human cell lines and growth media, including several chosen to model in vivo behaviour.

The project showed that 2DG compromises mitochondrial respiration much more in mutant than in wildtype mitochondria. This is likely why mutant replication was so challenged -- poorly functioning mitochondria are less likely to replicate. Restricting glutamine and glucose together had the same effect (though is perhaps harder to achieve in a therapeutic context). 2DG is in trials for epilepsy treatment, so may represent a path to new therapies addressing mtDNA disease. There's a press release here with some more commentary.

ARTICLE: Corals to crops -- how life protects the plans for its cellular power stations

Avoiding organelle mutational meltdown across eukaryotes with or without a germline bottleneck
David M Edwards, Ellen C Røyrvik, Joanna M Chustecki, Konstantinos Giannakis, Robert C Glastad, Arunas L Radzvilavicius, Iain G Johnston
PLoS Biology 19 e3001153 (2021)

(this text is from a press release about the article)

An international team of researchers led by the University of Bergen has uncovered how organisms from crops to corals may avoid deadly DNA damage during evolution.

Our cells, and those of animals, plants and fungi, contain compartments that produce chemical fuel. These compartments contain their own DNA, which stores instructions for important cellular machinery. But this so-called oDNA (organelle DNA) can become mutated, corrupting the instructions and preventing cells making enough energy.

In humans and some other animals, a process called the “bottleneck” allows some offspring to inherit less mutated oDNA. This process needs mothers’ egg cells to develop early, like in humans, where a human girl is born with all her egg cells already formed. But other organisms, from plants to fungi, don’t develop these cells early – their flexible body plans mean that eggs are not “set aside” early in development.<\p>

“We wanted to know how these organisms might avoid inheriting mutations without a human-like bottleneck,” said Ellen Røyrvik, a geneticist on the research team, based at UiB.

The scientists used mathematical modelling to show that a process called gene conversion – the controlled overwriting of DNA – could in theory allow some offspring to inherit less mutant oDNA without requiring a bottleneck. Using genome data, they found machinery controlling this process in plants and fungi, but also in soft corals, sponges, and algae – all organisms without fixed body plans. They also found that this machinery was most active in the parts of plants that will end up producing the seeds of the next generation, suggesting that it is indeed used to allow some offspring to inherit fewer mutations.

Organisms without fixed body plans (including octocorals, sea pens, sponges, plants, and fungi) and with fixed body plans (including humans and many animals) may use different strategies to avoid the buildup of damage in their cellular "power stations." CREDIT: Gemma Lofthouse

“Taken together, it looks like organisms without a fixed body plan – plants, fungi, corals, sponges, algae – may have adopted gene conversion to deal with oDNA mutations,” said Iain Johnston, an associate professor in the Mathematics Institute at UiB, who led the research. “Humans and other animals can develop egg cells early and use a bottleneck; other organisms can use gene conversion instead.”

Going forward, the team plans to explore how this overwriting of oDNA causes other issues in the organisms that use it – including crop plants, where it can cause sterility. They are also exploring the broader question of why these compartments contain oDNA at all, given the risk of mutational damage.

ARTICLE: What makes mitochondria selfish, and when do selfish ones win?

MtDNA sequence features associated with ‘selfish genomes’ predict tissue-specific segregation and reversion, Nucleic Acids Research 48 8290 (202)

Mitochondria, the power stations of the cell, are in some senses like people in a company. The company needs several people to contribute if it is to survive. Some people may work hard and contribute lots to the company. Others may selfishly slack off and rely on others doing the work.

The cell needs mitochondria to produce ATP, the chemical that powers many important processes. But there is evidence that some mitochondria are more selfish, and some less so, than others. Unselfish mitochondria produce machinery which helps produce ATP. Selfish mitochondria prefer to replicate, copying their DNA and contributing less to the cell. Interestingly, at the molecular level, there is something like a "switch": a mitochondrion either takes steps to produce useful machinery, or takes steps that will help it replicate.

We were interested in why different mitochondria choose different positions of this switch, and what is a good "strategy" for mitochondria under different conditions. We built a simple model of this behaviour to understand it. Unsurprisingly, we found that selfish mitochondria -- favouring replication, and contributing less to the cell -- profilerate over unselfish ones in cells where there's little pressure to co-operate. As they replicate more, selfish mitochondria eventually come to dominate such cells. Where there is cellular pressure, however, unselfish mitochondria may win out. This is because cells full of selfish mitochondria won't perform adequately, and the whole cell and all its mitochondria will die -- leaving those cells with more unselfish mitochondria remaining.

What do we mean by "cellular pressure"? Well, if some type of cells never die, clearly the latter event can't happen, and we'd expect selfish mitochondria to win. If cells die regularly, perhaps there's more capacity to select those filled with unselfish mitochondria. We looked at different tissues where cells die with different rates, in mice where cells had two different types of mitochondrial DNA (mtDNA). We found a consistent pattern where one type of mtDNA proliferated in slow-dying cells and the other proliferated in fast-dying cells. Why different mtDNA types "win" in different tissues is a big question (which we've looked at before!), and it looks like this might help explain some of these differences.

(A) Sequence features may make different mtDNA types more "selfish" (favouring replication) or "unselfish" (favouring the production of useful machinery). (B) Our theory shows how, depending on cellular pressures, one or the other strategy can be favoured, leading to selection for one or the other mtDNA type.

We also asked what it is about a particular mtDNA sequence that might make it more or less selfish. Based on how mtDNA produces useful machinery, and how it replicates, we hypothesised that some features in the so-called "control region" of mtDNA may influence selfishness. Using sequence information, we found that these features tied quite neatly in with the observations in these mouse models, and also in (more limited) observations from human cells. While certainly not resolved, this picture suggests a link between sequence features of mtDNA, cellular selfishness, and proliferation differences across different tissues. You can read more (for free) in Nucleic Acids Research here.

ARTICLE: The inheritance of mtDNA

Regulation of mother-to-offspring transmission of mtDNA heteroplasmy
Ana Latorre-Pellicer, Ana Victoria Lechuga-Vieco, Iain G Johnston, Riikka H Hämäläinen, Juan Pellico, Raquel Justo-Méndez, Jose María Fernández-Toro, Cristina Clavería, Adela Guaras, Rocío Sierra, Jordi Llop, Miguel Torres, Luis Miguel Criado, Anu Suomalainen, Nick S Jones, Jesús Ruíz-Cabello, José Antonio Enríquez
Cell Metabolism 30 1120 (2019)

Mitochondrial DNA (mtDNA) is inherited from mothers to children. If two or more types of mtDNA exist in a cell, the cell is called "heteroplasmic". Mothers may carry a heteroplasmic mixture of different mtDNA types in each of their oocytes (egg cells), so a mixture of different types may be passed on to children. Different oocytes may have different mixtures -- for example, one cel may have 50% type A and 50% type B, and another may have 70% A and 30% B. 

The inheritance of heteroplasmy depends both on a complicated "bottleneck" (see here and here) and whether either type has some advantage over the other -- a question that is hotly debated. The mechanisms that shape the inheritance of mtDNA populations remain poorly understood, so it's hard to predict which offspring will inherit which mixture. It's often the case that a disease is caused by a particular mixture -- for example, over 60% of type B -- so this complex inheritance makes it hard to plan fertility treatments too.

In a new paper in Cell Metabolism, we looked at the inheritance and consequences of heteroplasmy in mice. Strikingly, we found that the presence of any heteroplasmy has generally negative consequences for the cell. This is perhaps surprising, given the above view that we normally need a certain amount of a dangerous mtDNA type to cause disease. But it does match a prediction that we recently made by mathematically considering how a cell must invest energy in controlling mixed mtDNA populations. Correspondingly, we found that regardless of how much type A and type B there is, having a heteroplasmic mixture challenges metabolism in the embryo, and affects how readily induced pluripotent stem cells (iPSCs) can be produced from cells.

Given that heteroplasmy is a challenge, it seems that cells have evolved mechanisms to sense and address the inheritance of heteroplasmy. In addition to the bottleneck, we found (as in our previous work) that cell-to-cell variance of heteroplasmy increased in oocytes with age -- which will have the eventual effect of reducing heteroplasmy. We also found that particular mtDNA types had a selective advantage through inheritance, and identified a set of genes that shape this advantage. Variability in the expression of these genes, and variability in metabolic factors, led to differences in the strength of selection.

Some key findings from this paper, and links to our previous work.

This work was exciting because it provided some insights into the mechanisms that shape mtDNA populations between generations -- but also because it validated several predictions that our theoretical work had proposed in the past:

• Increasing heteroplasmy variance with age (predicted here, observed here)
• MtDNA selection occurs at different developmental stages (as we found here and here)
• Mixed mtDNA populations challenge the cell (predicted here)
• Genes related to mitochondrial dynamics shape mtDNA genetic makeup (predicted here)

We're continuing this exciting collaboration and looking in more depth at the behaviour of mtDNA over time.

ARTICLES: Evolving cellular populations of mtDNA

Evolving mtDNA populations within cells
Iain G Johnston, Joerg P Burgstaller
Biochemical Society Transactions 47 1367 (2019)

and

Varied mechanisms and models for the varying mitochondrial bottleneck
Iain G Johnston
Frontiers in Cell and Developmental Biology 7 294 (2019)

We've recently written two review papers looking at the dynamics of mitochondrial DNA (mtDNA) in cells. As we've written about before, cells contain populations of hundreds or thousands of mtDNA molecules. These molecules replicate and degrade, so that over time, cellular populations of mtDNA change and evolve. The amount of disease-causing mutations, and the number and structure of mtDNA molecules, may all change as organisms develop and age, with different consequences.

The first article, in Biochemical Society Transactions, takes a broad look at how cellular mtDNA populations change over time, considering a range of organisms from humans and other animals to plants and fungi. We look at the different processes that change mtDNA populations, which include replication and degradation but may also include recombination (particularly in plants) and cell-to-cell exchange of mitochondria. The review particularly highlights the importance of understanding cell-to-cell variability in mtDNA populations -- as it only takes a few cells with lots of mutant mtDNA to cause disease, it's important to understand the statistics of mtDNA populations across cells. We review experiments and theory aiming to do so, including our recent work showing that cell-to-cell variability of mtDNA mutant load increases over time in a wide variety of circumstances.

The second article, in Frontiers in Cell and Developmental Biology, focuses on the so-called "mtDNA bottleneck", a process that shapes mtDNA populations in early mammalian development, and helps prevent the inheritance of mutant mtDNA. Specifically, mtDNA undergoes a "genetic bottleneck" between generations, meaning that mothers' egg cells, and offspring, often have dramatically different mtDNA populations. The review emphasises that this "genetic bottleneck" is an effective quantity, not a directly measurable observation, that arises from several physical processes, including but not limited to a "physical bottleneck" or mtDNA depletion during development. Different ways of modelling, analysing, and explaining the "genetic bottleneck" are reviewed, from human populations to mouse egg cells and Adélie penguins. We invest some time in trying to explain the different assumptions, symbols, and methods that researchers have used to quantify the bottleneck over the years. Again, the importance of understanding cell-to-cell variance in mtDNA populations is a core theme.

A. Different processes shaping mixed mtDNA populations inside cells. B. The "genetic bottleneck", increasing mtDNA variance between egg cells and offspring.  

Like all reviews, these articles don't have new results, but attempt to summarise existing knowledge and thinking on these topics. We hope that both papers provide some interesting insights, references, and (in the case of the bottleneck paper) visualisations that may help understand these often confusing topics.

ARTICLE: The cell's power station policies

Energetic costs of cellular and therapeutic control of stochastic mitochondrial DNA populations

Hanne Hoitzing, Payam A Gammage, Lindsey van Haute, Michal Minczuk, Iain G Johnston, Nick S Jones

PLoS Computational Biology 15 e1007023 (2019)

(Hanne's also written a post about this paper, you can read it here)

Our cells are filled with populations of mitochondrial DNA (mtDNA) molecules, which encode vital cellular machinery that supports our energy requirements. The cell invests energy in maintaining its mtDNA population, like us using electricity-powered tools to help maintain our power stations. Our cellular power stations can vary in quality (for example, mutations can damage mtDNA), and are subject to random influences. How should the cell best invest energy in controlling and maintaining its power stations? And can we use this answer to design better therapies to address damaged mtDNA?

In a new paper here in PLoS Computational Biology, we attempt to answer this question using mathematical modelling, linking with genetic experiments done by our excellent collaborators at Cambridge (Payam Gammage, Lindsey Van Haute and Michal Minczuk). We first expand a mathematical model for how diverse mtDNA populations within cells change over time – building new power stations and decommissioning old ones, under the “governance” of the cell. We then produce an “energy budget” for the cellular “society” – describing the costs of building, decommissioning, and maintaining different power stations, and the corresponding profits of energy generation.

We find some surprising results. First, it can get harder to maintain a good energy budget in a tissue (a collection of individual cellular “societies”) over time, even if demands stay the same and average mtDNA quality doesn’t change. This is because the cell-to-cell variability in mtDNA quality does increase, carrying with it an added energetic challenge. This increased challenge could be a contributing factor to the collection of problems involved in ageing.

An overview of our approach. A mathematical model for the processes and "budget" involved in controlling mtDNA populations makes a general set of biological predictions and explains gene-therapy observations

Next, we found that cells with only low-quality mtDNA can perform worse than cells with a mix of low- and high-quality mtDNA. This is because low-quality mtDNA may consume less cellular resource, although global efficiency is decreased. Linked to this, removal of low-quality mtDNA (decommissioning bad power stations) alone is not always the best strategy to improve performance. Instead, jointly elevating low- and high-quality mtDNA levels, avoiding this detrimental mixed regime, is the best strategy for some situations. These insights may help explain some of the negative effects recently observed in cells with mixed mtDNA populations.

Our theory suggests that mixed mtDNA populations may do worse than pure ones, even if the pure population is a low-functionality mutant. Image from Hanne's post here 

We identified how best to control cellular mtDNA populations across the full range of possible populations, and used this insight to link with exciting gene therapies where low-quality mtDNA is preferentially removed through an experimental intervention (using so-called “endonucleases” to cut particular mtDNA molecules). We found that strong, single treatments will be outperformed by weaker, longer-term treatments, and identified how the mtDNA variability we know is present can practically effect the outcome of these therapies. We hope that the principles found in this work both add to our basic understanding of ageing and mixed (“heteroplasmic”) mitochondrial populations, and may inform more efficient therapeutic approaches in the future. Iain, Hanne, Nick

ARTICLE: Coupling mitochondrial physics and genetics

Mitochondrial Network State Scales mtDNA Genetic Dynamics
Juvid Aryaman, Charlotte Bowles, Nick S. Jones and Iain G. Johnston
Genetics Early online July 10, 2019; https://doi.org/10.1534/genetics.119.302423

Mitochondrial DNA (mtDNA) populations within our cells encode vital energetic machinery. MtDNA is housed within mitochondria, cellular compartments lined by two membranes, that lead a very dynamic life. Individual mitochondria can fuse when they meet, and fused mitochondria can fragment to become individual smaller mitochondria, all the while moving throughout the cell. The reasons for this dynamic activity remain unclear (we’ve compared hypotheses about them before here and here, with blog articles here). But what influence do these physical mitochondrial dynamics have on the genetic composition of mtDNA populations?

MtDNA populations can, naturally or as a result of gene therapies, consist of a mixture of different mtDNA types. Typically, different cells will have different proportions of, say, type A and type B. For example, one cell may be 20% type A, another cell may be 40% type A, and a third may be 70% type A. This variability matters because when a certain threshold (often around 60%) is crossed for some mtDNA types, we get devastating diseases.

We previously showed mathematically (blog) and experimentally (blog) that this cell-to-cell variability in mtDNA proportions (often called “heteroplasmy variance” and sometimes referred to via the “mtDNA bottleneck”) is expected to increase linearly over time. However, this analysis pictured mtDNAs as individual molecules, outside of their mitochondrial compartments. When mitochondria fuse to form larger compartments, their mtDNA is more protected: smaller mitochondria (and their internal mtDNA) are subject to greater degradation. More degradation means more replication, and more opportunities for the fraction of a particular type of mtDNA to change per unit time. In a new paper here in Genetics, we show (using a mathematical tour de force by Juvid) that this protection can dramatically influence cell-to-cell mtDNA variability. Specifically, the rate of heteroplasmy variance increase is scaled by the proportion of mitochondria that exist in a fragmented state. (It turns out that it's the proportion of itochondria that are fragmented that's important -- not whether the rate of fission-fusion is fast or slow).

This has knock-on effects for how the cell can best get rid of low-quality mutant mtDNA. In particular, if mitochondria are allowed to fuse based on their quality (“selective fusion”), we show that intermediate rates of fusion are best for removing mutants. Too much fusion, and all mtDNA is protected; too little, and good mtDNA cannot be sorted from bad mtDNA using the mitochondrial network. This mechanism could help explain why we see different levels of mitochondrial fusion in different conditions. More broadly, this link between mitochondrial physics and genetics (which we’ve also speculated about here (blog) and here) suggests one way that selective pressures and tradeoffs could influence mitochondrial dynamics, giving rise to the wide variety of behaviours that remain unexplained. Juvid, Nick, and Iain

ARTICLE: How mitochondria can vary, and consequences for human health

(cross-posted from Imperial Mitochondriacs)

Mitochondria are components of the cell which are involved in generating “energy currency” molecules called ATP across much of complex life. Since many mitochondria exist within single cells (often hundreds or thousands), it is possible for the characteristics of individual mitochondria to vary within cells, and within tissues. This variation of mitochondrial characteristics can affect biological function and human health.

Since mitochondria possess their own, small, circular, DNA molecules (mtDNA), we can split mitochondrial characteristics into two categories: genetic and non-genetic. In our review, we discuss a number of aspects in which mitochondria vary, from both genetic and non-genetic perspectives. 

In terms of mitochondrial genetics, the amount of mtDNA per cell is variable. When a cell divides, its daughters receive a share of its parents mtDNA, but the split isn’t precisely 50/50, so cell division can cause variability in the number of mtDNAs per cell. As mtDNAs are replicated and degraded over time, errors in the copying process may give rise to mtDNA mutations, which may spread throughout a cell. Factors such as: the total amount, the rate of degradation/replication, the mean fraction of mutants, and the extent of fragmentation in the mitochondrial network, can all influence how variable the fraction of mutated mtDNAs becomes through time (see here for a preview of some upcoming work on this topic). The total amount, and mutated fraction of mtDNAs, are implicated in diseases such as neurodegeneration, as well as the ageing process.

Apart from genetic variations, there are many non-genetic features of mitochondria which also vary within and between cells. Changes in mtDNA sequence can change the amino-acid sequence of the proteins encoded by mtDNA, causing structural changes in the molecular machines which generate ATP. The shape of the membranes of mitochondria are also highly variable, and respond to mitochondrial activity through quantities such as pH, where mitochondrial activity itself may depend on mtDNA sequence. The previous two examples (mitochondrial protein and membrane structure) demonstrate how the genetic state of mitochondria may influence their non-genetic characteristics. Mitochondrial non-genetic characteristics may also influence the genetic state: for instance, mitochondrial membrane potential can influence the probability of a mitochondria being degraded, along with its mtDNA.

The inter-dependence of genetic and non-genetic characteristics demonstrate the complex feedback loops linking these two aspects of mitochondrial physiology. We suggest here that, since changes in mitochondrial genetics occur more slowly than most physical aspects of mitochondrial physiology, understanding mitochondrial genetics may be especially important in explaining phenomena such as ageing, which appears to be closely related to mitochondrial heterogeneity. You can freely access our work, which has recently been published in Frontiers in Genetics, as “Mitochondrial Heterogeneity” https://www.frontiersin.org/articles/10.3389/fgene.2018.00718/full Juvid, Iain and Nick.

 

ARTICLE: Time marches on -- mitochondria, ageing, and disease

Burgstaller, J.P., Kolbe, T., Havlicek, V., Hembach, S., Poulton, J., Piálek, J., Steinborn, R., Rülicke, T., Brem, G., Jones, N.S. and Johnston, I.G. Large-scale genetic analysis reveals mammalian mtDNA heteroplasmy dynamics and variance increase through lifetimes and generations. Nature communications, 9 2488 (2018)

DNA in mitochondria, the powerhouses of the cell, is passed down from mother to child. But there are many mitochondria in each cell, and these mitochondria may have different genetic features. If a mother carries a mixture of mitochondrial DNA (mtDNA) types, this can make it hard to say which features their children will inherit. For mothers carrying a disease-causing mtDNA mutation, this makes family planning and clinical therapies challenging.

In particular, the role of a mother's age has long been a mystery. Is the probability of a child inheriting a particular mtDNA feature higher when mothers are younger or older? An answer to this question could help plan clinical strategies to improve fertility and prevent the inheritance of deadly mitochondrial disease.

To address this, we worked with our excellent collaborators with a combination of maths, statistics, and experiment. Our collaborators used cutting-edge technology to reveal the mixtures of mtDNA in the egg cells of mother mice at a wide range of ages, and in the litters of offspring the mothers produced. This experimental work was the largest-scale study of mammalian mtDNA that we're aware of, involving thousands of observations throughout lifetimes and between generations. In concert, we developed a mathematical model describing the changes to, and inheritance of, mtDNA from mother to offspring. We combined the model and data to learn how different biological processes affect mtDNA through and between generations.

Cells contain populations of mitochondria, and these populations change over time. In European mice, we observed how variability in these populations evolves as mammals age and reproduce. We found that older mother have more varied mitochondria and pass this variance on to their offspring -- of central importance in the inheritance of genetic disease. 

We found that the variability of mtDNA dramatically increased as mothers aged. This means that the probability of inheriting more extreme -- both lower and higher -- levels of a genetic feature increases for older mothers. We also found that different mtDNA mixtures were inherited in different ways - with some mtDNA types favoured for inheritance and some disfavoured. We used our findings to create a way to predict how the risk that offspring would inherit disease-causing mtDNA features changes over time. Moving forward, we're aiming to harness these powerful ways of using large datasets to describe and predict the dynamics of mtDNA inheritance in humans, and to learn what it is about these mtDNA types that predicts their evolution across generations. You can read the article for free in Nature Communications here.

ARTICLE: How cells adapt to progressive increase in mitochondrial mutation

Aryaman, J., Johnston, I.G. and Jones, N.S. Mitochondrial DNA density homeostasis accounts for a threshold effect in a cybrid model of a human mitochondrial disease. Biochemical Journal, 474 4019 (2017).

Mitochondria produce the cell's major energy currency: ATP. If mitochondria become dysfunctional, this can be associated with a variety of devastating diseases, from Parkinson's disease to cancer. Technological advances have allowed us to generate huge volumes of data about these diseases. However, it can be a challenge to turn these large, complicated, datasets into basic understanding of how these diseases work, so that we can come up with rational treatments.

We were interested in a dataset (see here) which measured what happened to cells as their mitochondria became progressively more dysfunctional. A typical cell has roughly 1000 copies of mitochondrial DNA (mtDNA), which contains information on how to build some of the most important parts of the machinery responsible for making ATP in your cells. When mitochondrial DNA becomes mutated, these instructions accumulate errors, preventing the cell's energy machinery from working properly. Since your cells each contain about 1000 copies of mitochondrial DNA, it is interesting to think about what happens to a cell as the fraction of mutated mitochondrial DNA (called 'heteroplasmy') gradually increases.  We used maths to try and explain how a cell attempts to cope with increasing levels of heteroplasmy, resulting in a wealth of hypotheses which we hope to explore experimentally in the future.

The central idea arising from our analysis of this large dataset is that cells seem to attempt to maintain the number of normal mtDNAs per cell volume as heteroplasmy initially increases from 0% mutant. We suggest they do this by shrinking their size. By getting smaller, cells are able to reduce their energy demands as the fraction of mutant mtDNA increases, allowing them to balance their energy budget and maintain energy supply = demand. However, cells can only get so small and eventually the cell must change its strategy. At a critical fraction of mutated mtDNA (h* in the cartoon above), we suggest that cells switch on an alternative energy production mode called glycolysis. This causes energy supply to increase, and as a result, cells grow larger in size again. These ideas, as well as experimental proposals to test them, are freely available in the Biochemical Journal "Mitochondrial DNA Density Homeostasis Accounts for a Threshold Effect in a Cybrid Model of a Human Mitochondrial Disease". Juvid, Iain and Nick

ARTICLE: The maths of mitochondrial DNA

Evolution of Cell-to-Cell Variability in Stochastic, Controlled, Heteroplasmic mtDNA Populations

IG Johnston, NS Jones

The American Journal of Human Genetics 99 (5), 1150-1162 (2016)

• Vital populations of mtDNA are constantly evolving in our cells in response to random influences and control from the nucleus: we build a general mathematical theory describing this poorly-understood process and show that it predicts a wide range of existing experimental outcomes and gives us lots of new insights into biology and disease

Mitochondrial DNA (mtDNA) contains instructions for building important cellular machines. We have populations of mtDNA inside each of our cells -- almost like a population of animals in an ecosystem. Indeed, mitochondria were originally independent organisms, that billions of years ago were engulfed by our ancestor's cells and survived -- so the picture of mtDNA as a population of critters living inside our cells has evolutionary precedent! MtDNA molecules replicate and degrade in our cells in response to signals passed back and forth between mitochondria and the nucleus (the cell's "control tower"). Describing the behaviour of these population given the random, noisy environment of the cell, the fact that cells divide, and the complicated nuclear signals governing mtDNA populations, is challenging. At the same time, experiments looking in detail at mtDNA inside cells are difficult -- so predictive theoretical descriptions of these populations are highly valuable.

Why should we care about these cellular populations? MtDNA can become mutated, wrecking the instructions for building machines. If a high enough proportion of mtDNAs in a cell are mutated, our cells struggle and we get diseases. It only takes a few cells exceeding this "threshold" to cause problems -- so understanding the cell-to-cell distribution of mtDNA is medically important (as well as biologically fascinating). Simple mathematical approaches typically describe only average behaviours -- we need to describe the variability in mtDNA populations too. And for that, we need to account for the random effects that influence them.  

​In our cells, signals from the "control tower" nucleus lead to the replication (orange) and degradation (purple) of mtDNA. These processes affect mtDNA populations that may contain normal (blue) and mutant (red) molecules. Our mathematical approach -- extending work addressing a similar but simpler system -- describes how the total number of machines, and the proportion of mutants, is likely to behave and change with time and as cells divide.

In the past, we have used a branch of maths called stochastic processes to answer questions about the random behaviour of mtDNA populations. But these previous approaches cannot account for the "control tower" -- the nucleus' control of mtDNA. To address this, we've developed a mathematical tradeoff -- we make a particular assumption (which we show not to be unreasonable) and in exchange are able to derive a wealth of results about mtDNA behaviour under all sorts of different nuclear control signals. Technically, we use a rather magical-sounding tool called "Van Kampen's system size expansion" to approximate mtDNA behaviour, then explore how the resulting equations behave as time progresses and cells divide.

Our approach shows that the cell-to-cell variability in heteroplasmy (the potentially damaging proportion of mutants in a cell) generally increases with time, and surprisingly does so in the same way regardless of how the control tower signals the population. We're able to update a decades-old and commonly-used expression (often called the Wright formula) for describing heteroplasmy variance, so that the formula, instead of being rather abstract and hard to interpret, is directly linked to real biological quantities. We also show that control tower attempts to decrease mutant mtDNA can induce more variability in the remaining "normal" mtDNA population. We link these and other results to biological applications, and show that our approach unifies and generalises many previous models and treatments of mtDNA -- providing a consistent and powerful theoretical platform with which to understand cellular mtDNA populations. The article is in the American Journal of Human Genetics here and a preprint version can be viewed here. Iain

ARTICLE: Controlling the control of our cellular power stations

Modulating mitochondrial quality in disease transmission: towards enabling mitochondrial DNA disease carriers to have healthy children

Alan Diot, Eszter Dombi, Tiffany Lodge, Chunyan Liao, Karl Morten, Janet Carver, Dagan Wells, Tim Child, Iain G Johnston, Suzannah Williams, Joanna Poulton

Biochem Soc Trans (in press) (2016)

• Dysfunctional mitochondria are recycled by the cell in a process that helps avoid disease; we summarise extending and provide new information about this process, and show -- agreeing with our mathematical theory -- that it can be modulated with drug treatments, providing potentially new therapeutic avenues.

Mitochondria -- a focus of our research -- are "power stations" in our cells that produce the energy we need to live. Like the power stations we build, mitochondria contain machines that work to produce this energy. They also contain the genetic "instructions" on how to build these machines, in the form of mitochondrial DNA (mtDNA). MtDNA can become mutated, spoiling these instructions, giving rise to dysfunctional machines and causing problems in our cells. Thankfully, our cells have systems that helps remove these mutant mtDNAs and recycle the bad machines that they've produced. One example is "mitophagy" (from mito-(chondria) and -phagy (eating)), as we've written about before.

Mitophagy uses "autophagosomes" to remove mtDNA from the cell, but it's hard to observe and measure: our understanding of the process, and how we may influence it to address diseases, is limited. In a recent paper, we summarise current understanding of mitophagy, particularly during early development (of importance for the inheritance of mtDNA diseases). As experiments and models explore the process in more detail, different types of mitophagy (progressing through different pathways) have been identified, as have fascinating "surges" of mitophagy at different developmental stages. In a new paper in Biochemical Society Transactions we discuss how these individual results are helping to build an overall picture of how mtDNA populations are controlled by cells.

Figure: single-cell microscopy determines how many autophagosomes (green), potentially recycling dysfunctional mitochondria, exist in cells during development. Drug treatments (lower row) can influence this number, potentially allowing us to control cellular mtDNA populations.

We also present some interesting preliminary results that may help us better understand, and control, mitophagy. Very soon after fertilisation, as an egg cell starts to divide, it seems that the amount of mtDNA in the growing embryo may decrease, rather more than previously reported. The experimental team, centred on Alan Diot, explored how many autophagosomes existed within cells during this process, and also showed that post-fertilisation treatment with drugs can affect the number of autophagosomes and hence the mtDNA populations in dividing cells (see figure). We've previously shown using mathematical modelling that decreasing mtDNA content may help avoid the inheritance of mtDNA diseases -- these new results highlight the feasibility of these potential new therapeutic strategies to address mtDNA disease inheritance. Iain

ARTICLE: Go green -- recycle mitochondria

A novel quantitative assay of mitophagy: Combining high content fluorescence microscopy and mitochondrial DNA load to quantify mitophagy and identify novel pharmacological tools against pathogenic heteroplasmic mtDNA

• Mitophagy degrades mitochondria, and likely plays important roles in the cell's responses to mitochondrial disease, but is hard to measure and thus poorly understood: we propose new ways of measuring mitophagy and use them to explore drugs that may help change damaged mitochondrial populations

Mitochondria, as we've written about before, are important entities in our cells that produce energy and take part in many other vital processes. Mitochondrial DNA (mtDNA), inherited from our mothers, contains instructions on how to build important mitochondrial machinery. MtDNA is sometimes mutated, leading to problems with our mitochondria. How do our cells cope?

Mitophagy (from mito-(chondria) and -phagy (eating)) is a process by which cells degrade and recycle mitochondria, allowing dysfunctional mitochondria to be removed and replaced. Mitophagy is one of a number of cellular mechanisms that maintain a healthy population of mitochondria, and appears to play a central role in determining the inheritance and evolution of mtDNA over our lifetimes. However, our understanding of mitophagy is limited because it is hard to observe.

In a recent and epically-titled paper in Pharmacological Research here, we explore two different approaches for measuring mitophagy in cells. The first is physical. We used chemicals to make mitochondria glow red, and autophagosomes (the cellular machines responsible for the degradation of mitochondria) glow green. We then used a microscope to examine large numbers of cells and recorded how often red (mitochondria) and green (autophagosomes) were seen together, which we took to imply that mitophagy may be occurring. We confirmed that various drugs and chemicals known to affect mitophagy had the expected effects on this estimate of mitophagy, and that perturbing ATG7 (an essential part of the autophagic machinery) sustantially reduced our observed mitophagy levels.

We also subjected cells to stress by growing them with a less plentiful supply of energy. We found that this energy stress increased the amount of mitophagy (perhaps as cells struggle to make the very best of their mitochondrial populations). We also found that mitophagy broadly decreased in cells from older people, and was increased in cells from people carrying an mtDNA disease (negatively affecting mitochondrial functionality).

The second approach is genetic. In cells from patients with mtDNA disease, some mtDNA is normal and some is mutated -- we used genetic tools to measure the proportion of mutant mtDNA in cells. We observed that when we stressed patients' cells, levels of mutant mtDNA decreased while our physically observed measure of mitophagy increased, supporting a picture in which mitophagy removes dysfunctional mitochondria when energy output is of central importance. We also found evidence for undirected mitophagy, where mtDNA copy number is depleted with no preference for mutant or wildtype.

Observing the colocalisation of autophagosomes (green) and mitochondria (red), as well as the proportion of mutant mtDNA (white stars), allows a bilateral characterisation of mitophagy. The patterns of changes in these observations tell us about how drug treatments and different environments change mitochondrial populations.

The physical and genetic approaches give us two largely independent means to estimate mitophagy, placing our understanding of this vital process on a solid analytical foundation. We used these tools to assess the effects of various drugs on mitophagy, allowing us to characterise the effects of drugs like metformin (inhibiting mitophagy) and phenanthroline (inducing undirected mitophagy) in unprecedented detail and facilitating more precise statements about their utility in clinical contexts. Iain

ARTICLE: Generations of generating functions in dividing cells

Closed-form stochastic solutions for non-equilibrium dynamics and inheritance of cellular components over many cell divisions

• Populations of important machines in our cells behave quite randomly: we build a mathematical framework to better understand these populations (which has already helped us understand the inheritance of mtDNA disease)

Cell biology is a unpredictable world, as we've written about before. The important machines in our cells replicate and degrade in processes that can be described as random; and when cells divide, the partitioning of these machines between the resulting cells also looks random. The number of machines we have in our cells is important, but how can we work with numbers in this unpredictable environment?

In our cells, machines are produced (red), replicate (orange), and degrade (purple) randomly with time, as well as being randomly partitioned when cells split and divide (blue). Our mathematical approach describes how the total number of machines is likely to behave and change with time and as cells divide.

Tools called "generating functions" are useful in this situation. A generating function is a mathematical function (like G(z) = z², but generally more complicated) that encodes all the information about a random system. To find the generating function for a particular system, one needs to consider all the random things that can happen to change the state of that system, write them down in an equation (the "master equation") describing them all together, then use a mathematical trick to push that equation into a different mathematical space, where it is easier to solve. If that "transformed" equation can be solved, the result is the generating function, from which we can then get all the information we could want about a random system: the behaviour of its mean and variance, the probability of making any observation at any time, and so on.

We've gone through this mathematical process for a set of systems where individual cellular machines can be produced, replicated, and degraded randomly, and split at cell divisions in a variety of different ways. The generating functions we obtain allow us to follow this random cellular behaviour in new detail. We can make probabilistic statements about any aspect of the system at any time and after any number of cell divisions, instead of relying on assumptions that the system has somehow reached an equilibrium, or restricting ourselves to a single or small number of divisions. We've applied this tool to questions about the random dynamics of mitochondrial DNA (which we're very interested in! And this work connects explicitly with our recent eLife paper) in cells that divide (like our cells) or "bud" (like yeast cells), but the approach is very general and we hope it will allow progress in many more biological situations. You can read about this, free, here in the Proceedings of the Royal Society A. Iain and Nick [blog article also here]

ARTICLE: How evolution deals with mitochondrial mutants (and how we can take advantage)

Stochastic modelling, Bayesian inference, and new in vivo measurements elucidate the debated mtDNA bottleneck mechanism

• Disease-causing mutant mtDNA is inherited through a complicated process: we use maths and statistics to shed light on this process and suggest possible therapeutic strategies to address disease inheritance and onset

Our mitochondrial DNA (mtDNA) provides instructions for building vital machinery in our cells. MtDNA is inherited from our mothers, but the process of inheritance -- which is important in predicting and dealing with genetic disease -- is poorly understood. This is because mitochondrial behaviour during development (the process through which a fertilised egg becomes an independent organism) is rather complex. If a mother's egg cell begins with a mixed population of mtDNA -- say with some type A and some type B -- we usually observe hard-to-predict mtDNA differences between cells in the daughter. So if the mother's egg cell starts off with 20% type A, egg cells in the daughter could range (for example) from 10%-30% of type A, with each different cell having a different proportion of A. This increase in variability, referred to as the mtDNA bottleneck, is important for the inheritance of disease. It allows cells with higher proportions of mutant mtDNA to be removed; but also means that some cells in the next generation may contain a dangerous amount of mutant mtDNA. Crucially, how this increase in variability comes about during development is debated. Does variability increase because of random partitioning of mtDNAs at cell divisions? Is it due to the decreased number of mtDNAs per cell, increasing the magnitude of genetic drift? Or does something occur during later development to induce the variability? Without knowing this in detail, it is hard to propose therapies or make predictions addressing the inheritance of disease.

We set out to answer this question with maths! Several studies have provided data on this process by measuring the statistics of mixed mtDNA populations during development in mice. The different studies provided different interpretations of these results, proposing several different mechanisms for the bottleneck. We built a mathematical framework that was capable of modelling all the different mechanisms that had been proposed. We then used a statistical approach called approximate Bayesian computation to see which mechanism was most supported by the existing data. We identified a model where a combination of copy number reduction and random mtDNA duplications and deletions is responsible for the bottleneck. Exactly how much variability is due to each of these effects is flexible -- going some way towards explaining the existing debate in the literature.  We were also able to solve the equations describing the most likely model analytically. These solutions allow us to explore the behaviour of the bottleneck in detail, and we use this ability to propose several therapeutic approaches to increase the "power" of the bottleneck, and to increase the accuracy of sampling in IVF approaches.

A "bottleneck" acts to increase mtDNA variability between generations. But how is this bottleneck manifest? Our approach suggests that a combination of copy number reduction (pictured as a "true" copy number bottleneck), and later random turnover of mtDNA (pictured as replication and degradation), is responsible.

Our excellent experimental collaborators, lead by Joerg Burgstaller, then tested our theory by taking mtDNA measurements from a model mouse that differed from those used previously and which, could in principle have shown different behaviour. The behaviour they observed agreed very well with the predictions of our theory, providing encouraging validation that we have identified a likely mechanism for the bottleneck. New measurements also showed, interestingly, that the behaviour of the bottleneck looks similar in genetically diverse systems, providing evidence for its generality. You can read about this in the free (open-access) journal eLife here. Iain and Nick [blog article also here]

ARTICLE: Great technological power, great statistical responsibility

Multiple hypothesis correction is vital and undermines reported mtDNA links to diseases including AIDS, cancer, and Huntingdon’s

• Several papers perform incorrect and misleading statistical analyses in seeking links between mtDNA and cancer: these statistical issues must be corrected before scientific and policy progress can be made from these investigations

Biologists often report a result as a "significant" sign of exciting new science if there is less than a 1-in-20 chance that the result they observe could have emerged by chance from boring old science. This is silly (although we do it too!) -- by contrast, for example, physicists require less than a 1-in-3,500,000 chance. But this post won't discuss too many problems with this state of affairs -- that is done admirably elsewhere.

The problem can be compounded when scientists take lots of measurements. Say we take 50 measurements of a boring old system, and every time we see something that has less than a 1-in-20 chance of appearing in a boring old system, we call it "significant". We're playing the odds 50 times, so we expect to see 1-in-20 results appear around 2 or 3 times; just as if we roll a dice 50 times, we'd expect to roll a good few sixes. If we call every 1-in-20 result "significant" without accounting for the fact that we've looked at lots of measurements (and are thus more likely to see 1-in-20s by chance), we are in danger of reporting exciting new science when in fact the boring old science has been true all along.

There are lots of ways of doing this accounting, but a series of papers that have been recently published linking mtDNA to diseases have made no attempt to do it. Generally, these papers look at the mtDNA of people without the disease and the mtDNA of people with the disease. If any mtDNA features appear more in the people with the disease, the paper calculates the chance of that difference occurring in the boring old picture (in which there is no link between the mtDNA feature and the disease). If they drop below the 1-in-20 mark, they report an exciting new link between that feature and the disease. But they test dozens of features and never account for this multiple testing -- so, as above, we'd expect them to see "significant" results emerging just by chance. In a paper in Mitochondrial DNA here (free here) I show, by creating artificial data, that this problem is rife, that most of these reported links are spurious, and that scientists really need to be more responsible, before their flawed analysis starts to misguide health policy and medicine.

The top graph shows how the probability of seeing a 1-in-20 occurrence (p < 0.05 in the jargon), when in fact there is nothing new and exciting to report, increases as a scientist investigates more things. If an experiment consists of one test, then a 1-in-20 occurrence indeed has a 1-in-20 probability (0.05). But as soon as we do more tests, the chance of seeing at least one 1-in-20 occurrence starts to increase, as we are "playing the game" more times. If we do 6 tests there is a 0.27 probability -- between a 1-in-4 and 1-in-3 chance -- that we will see at least one 1-in-20 event. This is illustrated below, where we have six dice and think some of them may be unfair. We roll each one five times and count the number of 6s. One of them comes up 6 three times -- the chance of this happening for one fair die is less than 1-in-20. But because we've looked at six dice, we should be less surprised to see this rare event, because we've looked at more events in total. We need more evidence to claim that this die is unfair.

This quick note only represents the tip of the iceberg. MtDNA studies are often statistically unsound; statistical misdemeanours in biomedical studies are so common that most published research is wrong; scientists increasingly focus on the 1-in-20 chance as opposed to the size and importance of the effect they're measuring; the majority of hallmark papers in vital fields like cancer science are unreproducible (though this last point may have other causes than statistical problems). The 1-in-20 idea was only ever meant to be a step in identifying interesting scientific avenues, not the final measure of scientific truth. This is a big, and growing, problem! Iain

(For accessibility I have used "exciting", "boring", and "1-in-20" instead of their usual, more technical labels; they of course are usually called the "alternative hypothesis", "null hypothesis", and "p < 0.05" respectively).