Sunday, 4 February 2018

The Algorithmic Beauty of Plants

(title taken from a wonderful book here)

Last year we ran a second year undergraduate computer practical in Biosciences introducing students to the ways in which computer simulations can be used to model plant growth. There are several neat scientific and practical ideas here. The students find that the diverse and complex range of beautiful plant forms can be mimicked by simulating simple, iterated rules (as in the pic). But the deeper idea is that these forms are not just mimicked by iterated rules  they genuinely emerge from such rules, not represented in a computer but in the biological language of the genome. This is the first time many students have met the idea that computational modelling allows a scientist to "play god"  they can make whatever changes they like to the rules and explore the effect on the simulated plants they grow. They also get to grips with algorithmic thinking  a highly transferrable skill given the expansion of coding and computational approaches across sectors.

Figure 1: L-Studio, simulating plant growth in computers from simple iterated rules. (top) An introductory exercise modelling a highly reduced model plant using a small number of growth rules. (bottom) A more involved simulation, based again around repeated application of simple rules, giving a fairly natural-looking plant structure.

The class is about 50 students, working in pairs or small groups with a computer. They are given some introductory exercises on “L-systems” (have a play e.g. here!), then given increasingly complicated structures to play with – including some famous fractals – and finally meet the translation to plant forms. In this way they learn to think algorithmically in a more abstract sense before the connection to biology is driven home. The exercises start fairly prescriptive, reproducing given structures. They then progress to a more investigative mode – given a particular plant form, how would you change its growth rules to, for example, outcompete tall neighbours, or disperse seeds more broadly? The final, exploratory, mode is the most interesting, where the students are given free rein, and design, adapt, and compare their own plant “designs”.

There are typically two members of staff and a handful of PhD students or postdocs acting in a TA capacity. We help with the initial setup – smoothing the way to this (unnatural for some) way of working with biological model systems in a computer. We then engage in a more scientific way with the groups, posing extension questions, guiding through questioning (careful not to just recite the solution to a given problem). In the final exploratory mode, we reduce the formality and jointly discuss scientific extensions and applications with the students and encourage the social aspect of the comparison and collaboration.

This class is an interesting one from a pedagogical point of view. The mode of learning shifts through the course of the two-hour session, from prescriptive to exploratory. Typically the class is very split in their uptake of this unfamiliar way of thinking. Some students love it, particularly the open-ended parts, and stick around to the end taking pictures of their plants and sending them to friends. Some frequently question the “point” of the class – a common question because logistics often mean they meet this class before lectures that naturally set up the modelling perspective. However, it usually just takes a few minutes of one-on-one discussion – illustrated with examples of our own research using computational modelling – to convince students of the utility both of the science and of the transferrable skill acquisition. One of my most personally rewarding experiences was with a student who started out almost aggressively sceptical about the point of these models – and whether the class would get him a better degree. After a discussion of the science and the transferrable value of computational modelling, he completely switched around and was interested in further pursuit of these topics. Other students are less polarised – they view the class as a box to be ticked. The final section of the class has an interesting influence here, where the enthusiasm of some groups rubs off onto the box-tickers. As such, there’s an interesting dynamic of teaching staff acting to catalyse the spread of enthusiasm – and of information – that emerges from the students’ own exploration.  

Saturday, 10 June 2017

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.

Sunday, 21 May 2017

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

Tuesday, 14 February 2017

Conferences 2017

Some conferences with topics intersecting our research interests coming up in 2017:
Registration | Dates | Title | Location | URL

Apr 20/28 | May 21 | FASEB Mitochondrial Biogenesis and Dynamics in Health, Disease and Aging | West Palm Beach, Florida |

Mar 1 / Sep 1 / Oct 19 | 24-26 Oct | Frontiers in Metabolism: From systems physiology to precision medicine | EPFL Lausanne |

Apr 13 | July 21-25 | ISMBC ECCB (European Conference on Computational Biology) | Prague |

Mar 31 | Aug 23-25 | IEEE International Conference on Computational Intelligence in Bioinformatics and Computational Biology | Manchester |

Mar 9 | June 5-7 | Algorithms for Computational Biology | Aveiro, Portugal | 

yet to open | 11 Sep-19 Sep 2017 | EMBO Practical Course: Current Methods in Cell Biology | EMBL Heidelberg |

Aug 10 | 2-4 Nov | EMBO Quantitative Principles in Biology | EMBL Heidelberg |

Feb 14 | 24-26 Apr | Complexis: Complexity, Future Information Systems and Risk | Porto, Portugal |

Apr 10 | Aug 21-24 | ACM-BCB Bioinformatics, Computational Biology, and Health Informatics | Boston, MA |

Feb 8 | Apr 4-7 | Modelling Biological Evolution 2017: Developing Novel Approaches  | Leicester, UK |

Feb 28 | Jun 25-30 | Mathematical Methods and Models in Biosciences (Biomath 2017) | Kruger Park, South Africa |

Feb 10 | Apr 17-21 | Applied Probability @ The Rock | Ayers Rock |

1 May | Jul 24-28 | 39th Conference on Stochastic Processes and their Applications (SPA) | Moscow |

Feb 27 | Jun 12-16 | Mathematical and computational evolutionary biology | Porquerolles Island, France |

Mar 24 | Apr 24-25 | ICPB 2017 : 19th International Conference on Plant Biology | Boston, MA |

Jul 31 | 9-13 Oct | Mitochondria in life, death and disease | Brindisi, Italy |

Jan 31 | Mar 30 - Apr 1 | “Cell Organelles - Origin, Dynamics, Communication” | Mosbach, Germany |

Mar 15 | Jun 11-17 |  FEBS Advanced Course: Functional imaging of cellular signals | Amsterdam |

May 31 | Sep 24-27 | Molecular Basis of Life | Bochum, Germany |

?? | Nov 27 - Dec 1 | IEEE Symposium on Artificial Life(IEEE ALIFE'17) | Hawaii | 

27 Feb | 10 Apr | Developing efficient methodologies for modelling stochastic dynamical systems in biology | Bath, UK |

Some related lists

Sunday, 8 January 2017

Some EEN science news from 2016!

Our paper on mitochondrial gene loss (paper; free preprint; blog article) was, excitingly, Science magazine's #1 favourite news story of 2016! The other stories in the top 10 are all fascinating too -- highly worth a read!

The Science news coverage of the paper is here
and the story appeared in the print journal too 

We were also involved in some news coverage in Nature of some exciting bits of science and policy from outside the group:
Mitochondrial behaviour may dictate whether or not organisms evolve germlines:
Mitochondrial gene therapy approval in the UK:
Potential issues with mitochondrial gene therapies:

Our work on mtDNA dynamics and human population diversity (paper; free preprint; blog article) was included in the latest policy document on UK implementation of mitochondrial gene therapies

And our other bits of work -- particular our work on vaccine confidence (free paper; blog article) -- appeared in various national and international news outlets too, including Scientific American, New Scientist, Le Monde, Daily Mail, Daily Mirror, Fox News and others; for some appearances see

Monday, 31 October 2016

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

Friday, 28 October 2016

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