Thursday, 24 November 2016

Evolution, Energetics & Noise

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. Crossed from here.

The largest survey of opinions on vaccine confidence

Monitoring trust in immunisation programmes is essential if we are to identify areas and socioeconomic groups that are prone to vaccine-scepticism, and also if we are to forecast these levels of mistrust. Identification of vaccine-sceptic groups is especially important as clustering of non-vaccinators in social networks can serve to disproportionately lower the required vaccination levels for collective (or herd) immunity. To investigate these regions and socioeconomic groups, we performed a large-scale, data-driven study on attitudes towards vaccination. The survey — which we believe to be the largest on attitudes to vaccinations to date with responses from 67,000 people from 67 countries — was conducted by WIN Gallup International Association and probed respondents’ vaccine views by asking them to rate their agreement with the following statements: “vaccines are important for children to have”; “overall I think vaccines are safe”; “overall I think vaccines are effective”; and “vaccines are compatible with my religious beliefs”.

Our results show that attitudes vary by country, socioeconomic group, and between survey questions (where respondents are more likely to agree that vaccines are important than safe). Vaccine-safety related sentiment is particularly low in the European region, which has seven of the ten least confident countries, including France, where 41% of respondents disagree that vaccines are safe. Interestingly, the oldest age group — who may have been more exposed to the havoc that vaccine-preventable diseases can cause — hold more positive views on vaccines than the young, highlighting the association between perceived danger and pro-vaccine views. Education also plays a role. Individuals with higher levels of education are more likely to view vaccines as important and effective, but higher levels of education appear not to influence views on vaccine safety.



Vaccine World map of percentage negative ("tend to disagree" or "strongly agree") survey responses to the statement "overall I think vaccines are safe"

Our study, "The State of Vaccine Confidence 2016: Global Insights Through a 67-Country Survey" can be read for free in the journal EBioMedicine here with a commentary here. You can find other treatments in Science magazine, New Scientist, Financial Times, Le Monde and Scientific American. Alex, Iain, and Nick.