Using maths to model the “bet hedging” of biology

 21 September 2015   Institute News

Susan Watts

Vahid Shahrezaei is the new mathematician–in-residence at the MRC’s Clinical Sciences Centre, based at the Imperial College Hammersmith campus. As he settled in, he spoke to Susan Watts about his love of maths, physics and biology, and what each can learn from the other.

Mathematician in residence at the CSC

Sam Marguerat and Vahid Shahrezaei: modelling cellular uncertainty may eventually mean better treatments

There’s a certain breed of scientist that seems well suited to a role that brings new dimensions to the work of others. It’s got a lot to do with humility, and it’s hard not to admire

“Generally you can think of what I do and people like me as providing an additional tool. It allows you to explore certain aspects of the hypothesis you have that’s not accessible because it’s very difficult to do experimentally, or very expensive.”

Iranian-born Vahid Shahrezaei is a physicist by training, but he’s been working with experimental biologists from the early days of his career, in Canada, and says he’s enjoyed it. He did his PhD with a synaptic physiologist in the physics department of Simon Fraser University in British Columbia, and his postdoc in a theoretical group in the physiology department of McGill University, Montreal.

“Mathematicians can occasionally be naive about what can actually be done experimentally.”

He’s been running a biomathematics group in the maths department of Imperial College since 2008, and is now taking up a visiting position that teams him up with biologists at the MRC’s Clinical Sciences Centre (CSC), based at the Imperial College Hammersmith campus. He plans to spend a day or two every week at the CSC, and I asked him if it makes a difference to be physically located with the people he works with.

“It’s educational to actually see experimentalists going through the process of thinking about the problems they encounter. Mathematicians can occasionally be naive about what can actually be done experimentally,” he says, ”making all sorts of impossible demands.”

He’s looking forward to bumping into biologists day-to-day, and though hasn’t yet sat in a lab with the CSC’s scientists, he’d like to try that out too. Regular interaction with biologists, Vahid says, is an important part of the atmosphere of the CSC, and key to creative collaborations.

“The CSC has a vision that you need to really understand the fundamental biological processes behind human health. My impression is that a lot of its researchers are doing research that is very quantitative – either they use maths in their actual work, or produce very quantitative data for integration into mathematical models.”

Matthias Merkenschlager is head of the CSC’s three-year old Integrative Biology section, where much of the emphasis is on research at the interface between biology and maths

“Integrative Biology brings together experimental biology with computational and statistical mathematical methods. This is a new area of science. At the CSC we see it as building a resource, both for the UK and internationally. There will be an increasing need for this sort of approach,” Merkenschlager said.

So what specific projects will Vahid be tackling? His primary interest is in thinking about the effect and role of noise and stochasticity, or randomness, in cellular systems. Experimentally it’s very challenging to probe every aspect of what’s going on in such systems, because they’re so complex.

“In biology, a lot of behaviour is a product of multiple components – so for pretty much every problem, biologists are studying a few players but they know that this is part of a big, complex pathway. Experimentally you can perturb different components and see what happens, and you might have a cartoon representation of what’s going on. The role of the mathematician is to put all of those observations together and test if the system does indeed work as suggested by the biologists cartoon and hypothesis, through mathematical modelling and computer simulation,” Vahid said.

He explained that although every function in a cell is down to some form of biochemical interaction, the timing of those events is random. In traditional chemistry people don’t worry so much about this because in a reaction in a test tube there are so many molecules that on average things look very deterministic – you see a reaction is happening and within a few minutes the reaction has taken place.

But in a single cell, these molecules – the genes themselves – are only present in a few copies. In a traditional biological sense, in each signalling pathway certain genes are thought to behave in certain ways, but in reality every pair of these interactions is quite random.

“What you actually see is that the cell as a whole has very robust and reliable behaviour. You don’t see bacteria failing to do their thing, but at the same time the components they use are not perfect. So cells seem to have evolved ways of designing their networks so that they can filter out this unwanted variability.”

What he means is that cells seem to have a “certain” end point but a lot of uncertainty along the way. “It’s a bit like having a car that works perfectly, but at the same time you know that some of the components don’t work perfectly,” Vahid explained. “From uncertain behaviour you can get a reliable outcome. The way that works is to be clever about how you use these poor components. So for example a computer doesn’t fail that often. You can trust it to do its thing even though it relies on movement of electrons, which is basically quite random. The way it works in computers is they use a digital approach, so small fluctuations don’t make a difference.”

“Cells basically do the same thing, but it is somewhat unclear how they achieve this.”

Traditionally people have used mathematical models that pretty much ignore the variability – so-called deterministic models built on differential equations. “That kind of model can be insightful, but more and more these kind of models are failing to capture the biology because the dominant dynamics of the biological system is basically stochastic, or random”.

Initially, Vahid will be working with Sam Marguerat. “We have a common interest,” Sam said, “to understand what happens when a cell grows and the impact that has on gene expression. When you have a change in size, the number of molecules in the cell will change. The large cell has more molecules than the small cell, and the faster the cell grows the faster the number of molecules in a cell change. That brings us back to stochasticity. This noise in the reactions depends very tightly on those numbers, and together we want to try to understand how.”

“We believe in something different. It’s about designing the experiment together.”

The pair also aims to find out more about the different pathways in a cell, and how these behave when a cell grows under different growth conditions. Sam said the big idea behind it all is to investigate evidence that the way cells grow effects diversity in the eventual behaviour of those cells. “That brings us to disease, cancer for example. When a tumour grows it becomes heterogeneous and that’s what kills people. One of the things we want to understand is how the growth itself impacts on this diversification of phenotypes.”

To do this they use the fission yeast Schyzosaccharomyces pombe as a model organism. “It’s one of the fields where working with a unicellular organism is extremely useful, because to study the effect of growth you need to separate out the cycling of the cell as it grows and divides – from growth itself. That’s extremely difficult to do in a mammalian cell because the two are ‘mixed up’, and impossible to do in a tissue because it’s so heterogeneous and complex. We use a simple system, and hope the principles will apply to more complex systems relevant to disease.”

Understanding more about random behaviour in cells may one day lead to better treatments. If the pair can learn how it is that cells filter out noise and at the same time have evolved to take advantage of this variability they may be able to shed light on one of the conundrums of cancer drug responses.

When doctors treat a tumour, some cells in that tumour respond differently to others. It seems that even if they all have same genetic background, some cells can have different levels of particular proteins, because of variability in their internal chemical reactions, and escape the drugs.

“Somehow the population of cells appears to be doing a kind of bet hedging,” Vahid said. “A certain fraction of the population is stochastically in a phenotype that may not be perfect for growth, but is good for surviving.”

Sam explained that in the past, this sort of collaboration has been seen as a service, with the biologist going to a data-hungry mathematician. “We believe in something different. It’s about designing the experiment together, and it’s also about thinking about the concept together – deciding the sort of scientific question we want to ask.”

Vahid smiled as he summed up: “A biologist has maybe a microscope, a sequencing machine, perhaps they study behaviour in the laboratory. Mathematical modelling is just another one of those tools.”

“That’s very humble,” I said.


For further information, get in touch:

Susan Watts
Head of Public Engagement and Communications
07590 250 652
0208 383 8247