I went (a long time ago it has to be admitted) to what people call an ‘old-fashioned’ grammar school. It wasn’t really old-fashioned – we didn’t wear wigs and frock coats – it just put great emphasis in getting its kids into good universities. To this end we were, at an early stage, split into scientists and the rest (aka arts students). It was a bit more severe even than that because the ‘scientists’ were sub-divided: those considered bright did Maths, Chemistry and Physics whilst the rest did Biology instead of Maths (or anything instead of Maths). All of which was consistent with the view that biologists – and that includes medics – could get by without being able to add up. That was a long time ago, of course, but to some extent the myth lives on. In tutorials with first year medical students I found an ace way of inducing nervous breakdowns was to ask them to do a sum in their heads (“Put that calculator away Biggs minor”).
But times do change and when I asked a doctor the other day which branches of medical science required maths, he paused for moment and then said “All of them.” By that he meant that pretty well every area of current research relies on the application of mathematics. We hear much about DNA sequencing, genomics and its various offshoots but all of these need ‘bioinformaticists’ (whizzos at sums) to extract the useful grains form the vast mass of data generated. Much the same may be said of research in what are called imaging techniques – developing methods of detecting tumours – and there is now a vast subject in itself of ‘systems biology’ in which mathematical modeling is applied to complex biological events (e.g., signalling within cells) with the aim of being able to reconstruct what goes on – what folk like to call a holistic approach. A variation on this theme is studying how large populations of cells behave – for example, tumour cells when exposed to an anti-cancer drug. And that’s an important matter: if your drug kills off every cancer cell bar one but that one happens to be very good at reproducing itself, before long you’ll be back to square one. The way to avoid going round in circles is to detect and interrogate individual survivor cells to find out why they are such good escape artists.
Girls will be girls
All of which brings us to Franziska Michor. Born in Vienna of a mathematician father who, she has recounted, told her and her sister that they had either to study maths or marry a mathematician. Sounds a frightening version of tradition to me – and it had perhaps the intended effect on the girls: frantic sprints to the nearest Department of Mathematics. That’s a bit unfair. As they say, some of my best friends are mathematicians – so they’re not at all the stereotypical distrait, inarticulate, socially inept weirdos. Although most of them are.
But Fräulein Michor was clearly one of the exceptions. She’s now a professor at the Dana-Farber Cancer Institute and Harvard School of Public Health in Boston and, with colleagues, she’s had a go at an important question: when cancer cells become resistant to a drug, is it because they acquire new mutations in their DNA or is it that some cells are already resistant and they are the ones that survive and grow. Their results suggest the simple answer is ‘the latter’ – resistant clones are present before treatment and they’re the survivors. So the upshot is clear but the route to it was very clever – not least because the maths involved in teasing out the answer is positively frightening. Fortunately (medics breathe a sigh of relief!) we can ignore the horrors of ‘Stochastic mathematical modeling using a nonhomogeneous continuous-time multitype birth–death process’ – yes, really – and just look at the biology, which was ingenious enough. To get at the answer they developed a tagging system that tracked the individual fates of over one million barcoded cancer cells under drug treatment.
Barcoding cells. Strings of DNA 30 base pairs in length and of random sequence are artificially synthesized (coloured bars). These fragments are inserted in the genomes of viruses. The viruses infect cancer cells in culture and, after drug treatment, cells that survive (drug resistant) are harvested, their DNA is extracted and barcode DNA is detected (redrawn from Bhang et al. 2015).
Check this out!
Barcodes were pioneered by two young Americans, Bernard Silver and Norman Woodland, for automatically reading product information at checkouts and nowadays they’re used to mark everything from bananas to railway wagons and plane tickets. Their most familiar form is essentially a one-dimensional array that Woodland said he came up with by drawing Morse code in sand and just extending the dots and dashes to make narrow and wide lines.
Cellular barcoding uses the same idea but the ‘label’ is an artificial DNA sequence. Such is the power of the genetic code that a random string made up of 30 of its four distinct units (A, C, G & T) can essentially make an infinite number of different tags. Just like those on supermarket labels, two different codes look the same at first glance:
The tags are made in an oligonucleotide synthesizer (a machine that sticks the units together) and then incorporated into virus backbones, just as we described for immunotherapy. The viruses (+ barcodes) then infect cells in culture, these are treated with a drug and the survivors present after a few weeks have their barcode DNAs sequenced. The deal here is that the number of different barcodes detected reflects the proportion of the original cell population that survived – and it indeed turned out that it’s very rare, pre-existing clones that are drug resistant. For one of the cell lines (derived from a human lung cancer) about one in 2,000 of the starting cell population showed resistance to the drug erlotinib.
The obvious question then is ‘What’s special about those few cells that they can thumb their noses at drugs that kill off most of their pals?’ To begin to get answers Bhang, Michor and colleagues noted that, for the lung cancer line, resistance to erlotinib occurs in cells that have multiple copies of a gene called MET – which makes a signalling protein. Exposing the cells to erlotinib and a MET inhibitor (crizotinib) greatly reduced the size of the resistant population (to one in 200,000).
This still leaves the question of the genetic alterations in that 0.0005% – and of course, finding drugs to target them. A further point is that this was a study of cells grown in the lab and it’s not possible to use this system in patients – but it could be used in mice to follow the development of implanted human tumours. If the causes of resistance can be tracked down it would open the way to using combinations of drugs that target both the bulk of tumour cells and the small sub-populations in which resistance lurks. That upshot would bring us to clinicians at the bedside (non-mathematicians!) – but not before running up a big debt to the maths geeks and in this case to a Viennese Dad who really did know best (offspring of the world please note!).
Bhang, H.C. et al. (2015). Studying clonal dynamics in response to cancer therapy using high-complexity barcoding. Nature Medicine 21, 440-448.