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: 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: Transport planning in biology

Efficient vasculature investment in tissues can be determined without global information
S Duran-Nebreda, IG Johnston, GW Bassel
Journal of the Royal Society Interface 17 20200137 (2020)

We need roads. Roads link up different parts of our society, allowing us to send messages and supplies from one region to another. But they come at a cost. If we lay down a road across the country, we can't use that land to farm or build houses, and maintaining roads costs a lot of tax money.

Multicellular organisms have the same issue. They also need to send supplies (e.g. nutrients) and messages (e.g. chemical signals) from one place to another. So they build roads. Our blood vessels are one example, transporting oxygen and hormonal messages throughout our bodies. So-called vasculature -- our blood vessels are one example, as are xylem and phloem in plants -- is used to allow transport around an organism. But again, if some parts of the organism are being used for transport, they can't be used for doing other useful things.

Given this cost of producing "roads", organisms would presumably like to be efficient as possible when laying out their transport systems. This may involve, for example, making journey lengths as short as possible while using as little land as possible for roads. But while city planners and engineers can look at maps and run simulations to work out how best to place roads, organisms lack a top-down "planner" with a large-scale map. How then do organisms efficiently resolve this tradeoff? Specifically, how is it decided where best to place vasculature to minimise the effective distance between cells?

We took a look at this using a theoretical model where an organism's tissue is modelled as a collection of cells in a 2D layer, a 3D block, or an intermediate case involving a set of layers, or a more realistic structure taken from experimental characterisation of plant tissues. We considered different ways that an organism might produce vasculature by fusing together cells in this model tissue to make "roads". This method for making vasculature models the case in immobilised cells, like we find in plants. We considered different ways that cells might be chosen to fuse, based on the physical structure of the tissue, and allowing some randomness in this decision.

 How has this plant made efficient "roads" (vasculature, like the veins seen here) without having a map of the whole leaf? We found that it can do a pretty good job without a global map, just using local sensing.

We found that using a "top-down" planner (with a map of all cells – which organisms don't have!) to choose which cells to fuse is usually the best way of producing an efficient transport network. But, we found that "bottom-up" approaches, where cells fuse based on purely local information (as opposed to a global map of the whole tissue) can actually do almost as well as the top-down planner. Strikingly, we found that these bottom-up approaches can provide "scale-free" improvements in transport. This means that the amount by which having more roads decreases journey lengths doesn't depend on the overall size of the system. The transport improvements from vasculature were more pronounced in 3D than in 2D, and the best approach for vasculature production varied in the different plant tissues we looked at. This suggests that there may be some evolutionary back-and-forth between the rules that plants use to create vasculature and the form of their tissues, which we plan to explore further in future!

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.

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: Getting to the root of the problem

Model selection and parameter estimation for root architecture models using likelihood-free inference
Clare Ziegler, Rosemary J. Dyson, Iain G. Johnston
J Roy Soc Interface (online, doi.org/10.1098/rsif.2019.0293 , 2019)

Roots bridge plants and soil, making vital contributions to crops, the environment, and fundamental biology. Because of this importance, understanding how roots grow under different conditions is a key scientific target. Experimental approaches to study roots can be challenging: being underground, it’s hard to observe root systems without perturbing them. Computer models can help here: we can simulate root growth and the “architecture” of root systems under lots of different conditions, without having to dig up and destroy real plants.

 
Observing roots growing underground is hard, but not impossible: here's a shot from our "minirhizotron" experiments using underground cameras to watch roots grow in an experimental woodland facility (see article here, and 3D version here!)

As computers have become more powerful, more and more sophisticated models for root growth and architecture have emerged. These simulation approaches typically take as input a set of parameters, and produce as output a model root system. These parameters are numbers describing, for example, the rates of root elongation, distances between lateral root branches, and so on – there may be dozens, or hundreds, of parameters in a sophisticated root model.

The output of a model depends strongly on these parameter values. So how can we choose the “right” ones? We may know some from experiments – for example, the widths of roots can be readily measured. But others may be less easy to observe. It is quite common to make educated guesses at these parameters, and see if the resulting root system “looks right”. This approach has a few issues – it can be subjective, and doesn’t give us information on how flexible our guesses are. For example, is a growth rate of 0.1cm per day just as likely as 0.5cm per day, or 0.02cm per day? And how can we tell if one version of a model does “better” than another, and is more supported by real observations?

In a new paper here in Journal of the Royal Society Interface, we propose a platform to provide answers to these questions, using so-called “approximate Bayesian computation” or ABC. This is a way of learning which parameter values and models are most compatible with observed data, by running many simulations with many different choices, and comparing the output of each choice to our observations using specific criteria. This replaces the subjective “looks right” and explores a wide set of parameterisations, allowing us to learn what ranges of values are most likely given our data. We can also use ABC to compare different mechanisms for root growth, finding which is most supported by observation. This helps us gain scientific insight and ensures that the outputs of our models can be more reliably intepreted.

Overview of our approach. Using ABC allows us to identify governing parameters and mechanisms for root growth that are most supported by real observations.

We tested our ABC approach with synthetic observations from models of thale cress and narrowleaf lupin, confirming that we can recover the parameter values we put in. We then used real thale cress plants (wild and mutant) to show that our platform distinguishes genetically different plants and identifies most-likely parameters and model structures for real root growth. We used the platform to select models for growth and branching, showing how it can be used to compare existing models from the literature. We hope that this approach can be used to further help improve the interpretability and rigour of plant modelling and simulation! Iain and Clare

ARTICLE: Plant stem cells strive towards equality

Jackson, Matthew DB, et al. "Global Topological Order Emerges through Local Mechanical Control of Cell Divisions in the Arabidopsis Shoot Apical Meristem." Cell Systems 8 53 (2019).

 
We recently wrote this paper (available in Cell Systems here -- and featured on the journal's front cover below!) about how cells are globally organised through local behaviour in an important plant organ. There's a blog article about the paper on "The Node", a developmental biology blog, here:

http://thenode.biologists.com/plant-stem-cells-strive-towards-equality/research/

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 do plants roll dice?

Johnston, I.G. and Bassel, G.W. Identification of a bet-hedging network motif generating noise in hormone concentrations and germination propensity in Arabidopsis. Journal of the Royal Society Interface, 15 141 (2018)

Seeds feed the world, and uniform, reliable harvests of seeds and grains is essential for food security. However, there's a fundamental tension between the evolutionary priorities of plants and the agricultural priorities of humans. Evolutionarily, it is good for plants to "hedge their bets" by having seeds germinate at different times. A plant whose seeds all germinate in March will be susceptible to a frost in April, potentially leading to the loss of a generation of offspring. By contrast, a plant whose seeds germinate throughout March and April will have a subset of its offspring survive that frost, and its genes will be passed on to the next generation.

This bet-hedging poses a challenge for agriculture. In agricultural settings, we have more control over plant environments, and so plants have less need to withstand unpredictable environmental fluctuations. At the same time, non-uniform germination decreases crop yields, makes harvesting harder, and makes crops more susceptible to pest invasion. If we can learn how plants generate this evolved germination variability, we can design engineering and/or breeding strategies to reduce this and improve crop yields.

Plants have evolved to "hedge their bets" by having seeds germinate at different times -- this makes generations of plants more robust to environmental fluctuations. Our work reveals a mechanism that "rolls dice" within plant cells, acting like a random number generator to produce variability in germination propensity. 

In a previous paper (blog post here), we looked at how germination is controlled by an interaction between two hormones known as ABA and GA. During that project, we noticed a surprising feature of the cellular pathways affecting ABA. Oddly, it seemed that ABA both activated a pathway that increased its own production, and at the same time (and in the same place) activated a pathways that increased its own degradation. These two pathways seemed to be competitive -- one increases levels of ABA, the other decreases them. Why would cells spend energy in this "futile" way?

We hypothesised that these competitive pathways might have the effect of generating variability in ABA levels. The pathways are fundamentally "noisy", involving random interactions in the chaotic environment of the cell. Consider increasing the activity of both pathways simultaneously. One pathway would act to increase levels of ABA, the other would act to decrease it. The increased "push and pull" of these noisy pathways would increase the spread of levels of ABA in different cells, even if average levels stayed the same.

Because it's hard to measure the levels of hormones in individual cells over time, we initially took a theoretical approach. We showed, with maths, that the competing pathways did indeed have this variability-inducing effect. By varying the activity through these pathways, the cell can increase variability in ABA levels, and hence increase variability in germination propensity. We showed that the theory we developed was compatible with some experiments where the ABA circuitry was artificially manipulated. The theory went on to reveal various aspects of cellular machinery that we could conceivably target through synthetic approaches, in order to reduce germination variability. Put together, our quantitative theory, supported by experiment, explained the mysterious competitive pathways and revealed several new interventions with the potential to improve food security. You can read about it for free in the Journal of the Royal Society Interface here. Iain  

ARTICLE: Which genes are essential for bacterial survival?

Goodall, E.C., Robinson, A., Johnston, I.G., Jabbari, S., Turner, K.A., Cunningham, A.F., Lund, P.A., Cole, J.A. and Henderson, I.R., 2018. The essential genome of Escherichia coli K-12. mBio, 9 e02096 (2018)

Bacteria cause diseases, and are developing resistance to the drugs we use to kill them. Anti-microbial resistance (AMR) is one of the most pressing global health challenges facing society. In the immense scientific endeavour of creating new, effective treatments for bacterial infections, fundamental biological knowledge about how bacteria live and proliferate is of vital importance.

One way we can obtain this knowledge is by discovering what cellular machinery that bacteria need to survive and proliferate. A common (and famous) bacterium called Escherichia coli (E. coli) has over 4000 protein-coding genes, but we're not really sure which of these genes is essential for the bacterium, and how many provide some non-essential "added value". If we can learn which genes are essential for bacteria, we have a more specific set of targets to shoot for in designing new drugs and therapies.

So -- how can we find out which genes are essential for E. coli? One neat way involves a new experimental approach called transposon-directed insertion site sequencing (TraDIS). Transposons are elements of DNA that can be inserted into a bacterial genome -- when they are inserted into part of the genome that codes for a gene, they prevent that gene being properly expressed, effectively removing it from the bacterium. TraDIS, in essence, takes a large population of bacteria and inserts one transposon into a random position in each bacterium. The population is then left to evolve for some time. After that time, we look at the genomes of bacteria within the surviving population, and see exactly where transposon insertions have been retained in some living bacteria.

A stylised representation of the E. coli genome and the positions within it where we found transposons to have been retained (corresponding to non-essential genes). 

The idea is that any bacteria in the population that have a transposon inserted into an essential gene will die. As such a gene is essential, it's required for survival, and a transposon preventing its expression will kill the bacterium. Therefore, if some bacteria in a population retain an insertion in gene X and survive, it follows that gene X is not essential. Conversely, if we see a large region of the genome within which no insertions are retained in the final population, it is likely that that region corresponds to an essential gene. 

There's some mathematical subtlety in the "it is likely". Depending on how many transposon insertions originally occur, and the length of the genome, some regions without insertions may occur just by chance. We did a bit of maths to work out how unlikely it is to see an insertion-free region of a given length arise by chance; and, by extension, how likely it is that a gene identified by this analysis is indeed essential for the bacterium. However, the maths was only one part of this project -- it was first and foremost an experimental tour de force by our excellent collaborators. We jointly provided a new atlas of essential genes in E. coli, provide a new way of reasoning about the powerful TraDIS technique, and provide several new insights into bacterial physiology and biochemistry. The work is freely available in the journal mBio here. Iain 

ARTICLE: How plants decide when to germinate

Topham, A.T., Taylor, R.E., Yan, D., Nambara, E., Johnston, I.G. and Bassel, G.W. Temperature variability is integrated by a spatially embedded decision-making center to break dormancy in Arabidopsis seeds. PNAS 114 6629 (2017)

A plant's choice to germinate is one of the most important decisions in the world. If it is made too soon, the plant may be damaged by harsh winter conditions; if too late, the plant may be outcompeted, and crop yields may be lower. If crops in a field make the decision at different times, there is more room for weeds to grow and pests to take over. 

In a recent study, we combined mathematical modelling with several neat experiments to identify sets of cells that make this germination choice in a much-studied plant called thale cress (Arabidopsis thaliana), and have learned how it makes decisions based on the plant's environment.

Two views of the plant embryo from laser microscopy, highlighting cells where different components of the germination control machinery are expressed. The background shows the "attractor basins" in a mathematical description of the germination decision: horizontal and vertical axes give the levels of two hormones ABA and GA, the blue region corresponds to dormant seeds and the red region to germination. 

This germination circuitry functions through a circuit of chemical stimuli and responses. Using laser microscopy, we found that different parts of this circuit exist in different parts of the plant embryo -- and that the separation of these parts is central to how the brain functions. We used mathematical modelling to show that communication between separated elements of the germination circuitry controls the plant's sensitivity to its environment. Following this theory, we used a mutant plant where cells were more chemically linked -- essentially enhancing communication between circuit elements -- to show that germination depends on these intra-cellular signals.

The separation of circuit elements allows a wider palette of responses to stimuli. It's like the difference between reading one critic's review of a film four times over, or amalgamating four different critics' views before deciding to go to the cinema. Our mathematical theory predicted that more plants would germinate when exposed to varying environments -- like three short pulses of cold -- than constant environments -- like one long cold period. We tested this theory in the lab and found exactly this behaviour.

Next, the hope is to learn about the germination brain in other plants and crops, and to show how our new knowledge of the germination machinery can be used to enhance and synchronise germination in crops. You can read the paper for free in the journal PNAS here. Iain

ARTICLE: Supply, demand, energy, and death

Mitochondrial heterogeneity, metabolic scaling and cell death
J Aryaman, H Hoitzing, JP Burgstaller, IG Johnston, NS Jones
BioEssays e201700001; doi:10.1002/bies.201700001 (2017)

•  The links between mitochondrial functionality and various aspects of cell physiology remain unclear; we combine recent experimental insights with mathematical modelling to produce quantitative hypotheses linking metabolism, cell proliferation, and mitochondria.

Cells need energy to produce functional machinery, deal with challenges, and continue to grow and divide -- these activities and others are collectively referred to as "cell physiology". Mitochondria are the dominant energy sources in most of our cells, so we'd expect a strong link between how well mitochondria perform and cell physiology. Indeed, when mitochondrial energy production is compromised, deadly diseases can result -- as we've written about before.

The details of this link -- how cells with different mitochondrial populations may differ physiologically -- is not well understood. A recent article shed new light on this link by looking at a measure of mitochondrial functionality in cells of different sizes. They found what we'll call the "mitopeak" -- mitochondrial functionality peaks at intermediate cell sizes, with larger and smaller cells having less functional mitochondria. The subsequent interpretation was that there is an “optimal”, intermediate, size for cells. Above this size, it was suggested that a proposed universal relationship between the energy demands of organisms (from microorganisms to elephants) and their size predicts the reduction in the function of mitochondria. Smaller cells, which result from a large cell having divided, were suggested to have inherited their parent's low mitochondrial functionality. Cells were predicted to “reset” their mitochondrial activity as they initially grow and reach an “optimal” size.

We were interested in the mitopeak, and wondered if scientifically simpler hypotheses could account for it. Using mathematical modelling, our idea was to use the observation that as a cell becomes larger in volume, the size of its mitochondrial population (and hence power supply) increases in concert. We considered that a cell has power demands which also track its volume, as well as demands which are proportional to surface area and power demands which do not depend on cell size at all (such as the energetic cost of replicating the genome at cell division, since the size of a cell's genome does not depend on how big the cell is). Assuming that power supply = demand in a cell, then bigger cells may more easily satisfy e.g. the constant power demands. This is because the number of mitochondria increases with cell volume yet the constant demands remain the same regardless of cell size. In other words, if a cell has more mitochondria as it gets larger, then each mitochondrion has to work less hard to satisfy power demand.

To explain why the smallest cells also have mitochondria which do not appear to work hard, we suggested that some smaller cells could be in the process of dying. If smaller cells are more likely to die, and if dying cells have low mitochondrial functionality (both of these ideas are biologically supported), then, by combining this with the power supply/demand picture above, the observed mitopeak naturally emerges from our mathematical model.

As an alternative model, we also suggested that the mitopeak could come entirely from a nonlinear relationship between cell size and cell death, with mitochondrial functionality as a passive indicator of how healthy a cell is. This indicates the existence of multiple hypotheses which could explain this new dataset.

A recent study has provided new data for the relationship between cell physiology and mitochondrial functionality. We have used mathematical modelling to suggest that a mixture of cellular power demand scaling, as well as cell death, could intuitively account for these new data. However, a nonlinear relationship between cell death and cell size could also account for these data, as well as a nonlinear relationship between mitochondrial functionality and cell size, as proposed by the original authors of the dataset. By integrating such a relationship between cell size and mitochondrial functionality into one of our existing models, we found that this “mitopeak” helps explain a wider set of cell physiological data. Using our model to highlight these competing hypotheses, we suggest future experiments to gather further support for these potential explanations.

Interestingly, we also found that the mitopeak could be an alternative to one aspect of a model we used some time ago to explain a different dataset, looking at the physiological influence of mitochondrial variability. Then, we modelled the activity of mitochondria as a quantity that is inherited identically by each daughter cell from its parent, plus some noise -- noting that this was a guess at the true behaviour because we didn't have the data to make a firm statement. We needed this relationship because observed functionality varied comparatively little between sister cells but substantially across a population. The mitopeak induces this variability without needing random inheritance of functionality, and may thus be the refined picture we've been looking for. These ideas, and suggestions for future strategies to explore the link between mitochondria and cell physiology in more detail, are in our new BioEssays article here. Juvid, Nick, and Iain.

ARTICLE: A healthy dose of mathematics

Toward Precision Healthcare: Context and Mathematical Challenges

C Colijn, N Jones, IG Johnston, S Yaliraki, M Barahona

Frontiers in Physiology 8 136 (2017)

• The continuing explosion of available biomedical data will help us tailor and optimise therapies for individual patients; we are designing new maths and statistics to help this process and to include social and other data into an overarching "precision healthcare" approach.

Our research combines tools from maths and statistics with biological data to learn more about the biological world. An exciting, growing, and much-discussed branch of science -- precision medicine -- is a specific instance of this idea. The vision of precision medicine is to use the expanding volume of data that's emerging from medicine and biology to tailor and optimise medical therapies for individual patients, making the therapies as effective as possible. This idea isn't new -- we are well aware, for example, that an individual's blood type dictates which blood transfusions they can successfully receive. But precision medicine is a much bigger picture, potentially taking into account large amounts of genetic, environmental, dietary, and other features to identify the optimal treatment for a disease -- for example, tailoring chemotherapy treatments to match the genetic specifics of a particular cancer case.

Dealing with these large and diverse datasets will need new mathematical and statistical approaches, built with an ongoing link to clinical practice. At the same time, we're interested in expanding the idea of precision medicine to include the "big data" that's increasingly available about individuals' social and logistic contexts. Social networks can dictate how diseases spread -- and how knowledge and views about therapies, vaccines, and other medically pertinent ideas are transmitted and shaped from person to person. A person's home region determines the genetic structure of local people who may act as donors. We're looking at the idea of "precision healthcare" -- using new maths and statistics to optimise healthcare strategy, not just individual therapies, in the light of large-scale datasets.

One aspect of precision healthcare we'll be exploring is exploring how progressive diseases -- those that involve the accumulation of symptoms over time -- develop in patients, using transition networks like those above to model "disease spaces" and find pathways in those spaces.

We're excited to be part of a new initiative -- the Centre for the Mathematics of Precision Healthcare -- involving six parallel and related research projects that align with this goal. Some of our previous work -- for example, estimating social structures of big UK cities to explore the challenges that genetic diversity poses to gene therapies for mtDNA disease -- already has a precision healthcare feel. In a new review paper (available for free) we discuss this and other examples of past and future work that we hope will contribute to the precision healthcare goal, along with some key ideas and context for the initiative. Iain

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: Random number seed

Variability in seeds: biological, ecological, and agricultural implications 

J Mitchell, IG Johnston, GW Bassel

Journal of Experimental Botany, erw397 (2016) 

• Natural variability across scales, from the molecular to the environmental, means that individual seeds behave differently; we explore the challenges this variability poses for agriculture and food security, and how modern science can help address these challenges.

Seeds feed the world. Whether eaten themselves, or allowed to develop into crop plants which are then consumed by humans or livestock, seeds are the fundamental starting point for agriculture. But each seed has a different story. Throughout millions of years of evolution, plants have evolved to -- forgive the pun -- "hedge" their bets from one generation to the next. A parent plant cannot completely predict the environmental conditions that its offspring will face, so it induces variability in the seeds it produces. If some seeds are better at surviving in environment A and some are better in environment B, the plant has a way of ensuring its genes will survive regardless of whether the environment is A-like or B-like in future.

This bet-hedging is a sensible evolutionary strategy when environments are unpredictable. But modern agriculture makes environments much more predictable than the wild situations plants have been exposed to throughout evolutionary history. Now bet-hedging becomes a bad thing -- if we know the environment will always be C, energy spent ensuring that seeds survive in environments A and B is wasted, reducing potential yields.

Understanding and controlling the variability within populations of seeds thus has huge implications for agriculture. Variability inherent within populations of seeds, in addition to differences in the environments that seeds experience, means that, for example, seed lots germinate asynchronously (some quickly, some slowly or not at all). This leads to non-uniform and sub-optimal crop production, allows pests to enter fields, and challenges our ability to plan agricultural strategies. If we could control seed variability, these problems would be diminished, with a host of positive consequences for food security.

A given set of seeds will vary in their behaviour due to influences on many scales, from random molecular processes within cells to large-scale environmental stimuli. As a result, important features like germination propensity vary across seed lots (perhaps taking a broad distribution like that illustrated here), posing a challenge to agriculture and food security, which scientific understanding can mitigate.

In a new review, we survey our current understanding of the sources of variability in seeds, and its biological and agricultural implications. Processes across many scales induce variability in seed behaviour, from random cell biological interactions (like we've written about before!), through seed position in a parent plant, to large-scale environmental differences. We particularly focus on germination, an aspect of seed behaviour of crucial biological and agronomic importance, which takes place when a "developmental switch" in a seed is flipped. We discuss the genetic and molecular players that modern science has discovered to influence this decision to germinate in seeds, and describe the challenges in furthering our understanding of this vital question -- and how cool new tech, and maths, can help us make new progress! The review is in the Journal of Experimental Botany 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