I read the paper from Tomasetti and Vogelstein in 2015. As the title suggests, the paper attempts to answer an extremely interesting question of why are some cancer types more common than others. I really liked this question as unlike most groups racing to find more mutations in different cancer cohorts the authors of this paper took a step back and tried to explain the findings of the field(perhaps a bit like the Omnigenic model.) The main result of the paper was that the variation in different cancer incidences can be explained by the number of stem cell divisions in that tissue. This would mean that most of the mutations are replicative in origin and only a small fraction could be attributed to mutagens or environmental exposures. This is the “cancer is mostly bad luck” model.

The paper and the suggested finding caused a lot of furor in the cancer field. For a good read about some problems associated with this paper please see this really well written and accessible editorial by George Davey Smith et al.in the International Journal of Epidemiology here Some of the arguments against the paper were that we know from epidemiological incidences of the same cancer-type vary by region/cancer. Cancer rates also vary over time, for example drops in lung cancer and stomach cancer after relevant interventions. Does this invoke a bad-luck varies with time model. I think Vogelstein would argue from his paper that some cancers are more susceptible to environment than others. So how do we explain the correlation shown in the paper and align it with increases in mutation risk when exposed to mutagens?

I read a fascinating paper by Gao et al. from the Przeworski lab that proposed an explanation. The title of the paper is “Interpreting the Dependence of Mutation Rates on Age and Time”. I liked this paper for several reasons. Again, this paper attempted to use a simple(?) model to explain the findings to date. The model is pretty elegant and captures the core essence of the major players involved without worrying too much about the actual molecular mechanism. I find this extremely soothing to read. So how does the model work?

There are two different models. The first model is for replication dependent mutations. The model is an additive model with different mutation rates(replication error rates in this case) at different life stages. The authors split the life stages into four parts from fertilization to the production of gametes in each individual. For females the last two parts don’t count since eggs don’t replicate unlike sperm which are continously made during a male’s lifetime from spermatagonial stem cells. The total number of mutations de-novo in the offspring is then the sum of the mutations in the maternal and paternal gametes. The findings of the paper are not immediately clear. Increases in generation time will lead to stronger maternal biased mutations. One assumption is all mutations are neutral, we know this isn’t the case for example FGFR mutations in the male gametes lead to an advantage to those stem-cells. Increases in generation time lead to a stronger male mutation bias as expected. If the intercept of the extrapolated line at age zero is positive, mR,y decreases with G, consistent with the observed “generation time effect” in primates. Therefore, we argue that there is almost certainly an effect of generation time on yearly mutation rate in humans, although the magnitude of the effect could be small. we should not expect neutral substitution rates to be constant across mammalian species

The second model considers non-replicative mutations. Non-replicative mutations happen due to lesions on the DNA. Some forms of lesions on DNA on one strand cause it to not pair with the strand and this can affect DNA replication. These cells may die if the lesion is not repaired. Other lesions can pair with the wrong base pair and then replication proceeds. This would lead to one daughter cell having the right nucleotide at the position with the lesion and the daughter other cell having a mutation at that position. The model considers two processes, one a mutation process that happens at a mutation rate u and a repair process that occurs at a rate r. The number of mutations is then just a balance between these two processes. The authors consider two scenarios: 1. When the rate of repair is much slower compared to the cell division time. In this case the mutation repair is inefficient and mutations accumulate at a rate proportional to absolute time. 2. When the rate of repair is highly efficient compared to the rate of cell division. In this case, the mutation rate and the repair rate achieve an equilibrium. The cell division rate does not matter in this case. This is fascinating and suggests that no matter how fast or how quickly the cells divide the mutation rate remains constant due to the efficiency of repair. The only new mutations are the ones that are produced right before cell division and hence these haven’t had a lot of time to be repaired. These could in theory look like the replication errors, that Tomasetti and Vogelstein propose, but could actually be non-replication errors.

This simple yet elegant model produces such a fascinating result. This suggests that the correlation that Vogelstein and Tomasetti see doesn’t necessarily have to be the result of a replication error. We would see a similar pattern with mutations induced by exogenous/internal agents or if the rate of repair is highly inefficient compared to the cell division rate. So the jury is still out on this one, we cannot accept the “cancer in bad luck” model yet.

Like I mentioned earlier, I love this paper. The insights of this model will be tested soon when we begin to study mutations in more detail in different tissues, at different stages of life, different allelic backgrounds etc. What happens when the mutations confer a selective advantage or disadvantage? We are only beginning to scratch the surface at this time. I’d love to write models like these to explain and understand phenomena we see around us.