6 ms·
>" The natural conclusion is that in individuals with a competent immune system and diverse enough pools of healthy stem cells, it's not that big of an issue."
by nonbel 10y ago
>" The natural conclusion is that in individuals with a competent immune system and diverse enough pools of healthy stem cells, it's not that big of an issue."
Thanks, I have been thinking along those lines for a few years now after looking at the age-specific incidence of a bunch of different cancers from SEER. You see that many cancers peak consistently year after year at a given age, while the height of the curve may change drastically. The same was true when I looked at some data from other countries, although I never followed up very much on that aspect.
Then if you read the paper which spawned the multi-stage model of cancer that has been widely adopted[1], you see they make some assumptions for computational reasons that are unnecessary in these days of cheap computing power:
pt ~ 1-(1-p)^t, if p<<1,
where,
p = probability a required mutation occurs during a given time interval
t = number of elapsed time intervals (ie age)
Then by the product rule of probability they derive that, if cancer is due to accumulation of errors (usually considered to be mutations), the incidence at a given age would be:
I(t) = k*p1*p2*...*pn*t^n = k*(p'*t)^n
where
I(t) = incidence at age t
n = number of required mutations
p' = geometric mean of the probabilities for mutations 1:n
k = a constant determined by the number of cells in each tissue,
the proportion of times that a detectable tumor forms from
the carcinogenic cell, and possibly the sequence in which the
mutations occur
If you use the non simplified version of their theory you would instead get:
I(t) = k*(1 -q^t)^n
where
q = 1-p'
In contrast to the model that was simplified for computational reasons, this has a turnover. By setting the second derivative to zero you can get the age at which the peak incidence should occur as a function of number of required mutations (n) and geometric mean of the probabilities each mutation occurs (q = 1-p'):
t_peak = log(1/n, base = q)
From this you will see either the multi-stage model is totally wrong, the error rate must be much higher than commonly thought, and/or the cell division rate of the error-accumulating cells must be much higher than commonly thought (the age is usually taken as a stand in for number of divisions). The last two possibilities suggest that we are constantly generating these cancerous cells and they are being cleared somehow.
[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2007940/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2007940/
- apathy 10y agoArmitage-Doll was a nice advance over previous models, but it's also incomplete (and probably flat wrong in some cases, although working on pediatric malignancies has convinced me that a second cooperating event usually is mandatory). In normal stem cells, it appears that attrition and immune clearance gets rid of damaged cells when they cycle and senescent cells all the time (subject to some variation, not entirely age related, at least in our volunteers). We may expect higher rates in filter organs, but liver cancer isn't too common, and the paper I referenced earlier shows that this can't be just an issue of fewer divisions (I despise the oversimplified Tomasetti & Vogelstein paper because the facts simply don't support it). Colorectal is probably more common because the crypts are "facing out" ala melanocytes, thus prone to accumulating lots of environmental damage. Anyways, the latter of your possibilities (proliferative mutants divide faster and error more often than normal counterparts) makes the most sense -- the eventual "winner" in a tumor is the cell that produces the most progeny and resists apoptosis due to stress the best. It's probably not a coincidence that these are traits which adapt a mutated cell to survive chemotherapy as well. However, spawning nonself mutations willy-nilly is a great way to attract immune attention -- particularly if you haven't blown the immune system away by nuking it with chemotherapy. :-/
- nonbel 10y ago>"pediatric malignancies" maybe, or you can use the full Armitage and Doll model I described above and replace t with something like a discrete exponential decay where N(t) = number of divisions since zygote as a function of time. Ie N(t) = N0(1 - k)^t + 1 where N0 = N_birth - N_adult That is, take the difference between division rate at birth and division rate as adult and fit a constant k between zero and one. It is just a first approximation at best because data on division rate by age in various tissues doesn't seem available... https://s18.postimg.org/9cn5vi8t5/div_Rate.jpg https://s18.postimg.org/9cn5vi8t5/div_Rate.jpg
- apathy 10y agoThe majority of pediatric malignancies are either germline related, in utero (de novo mutation/SV, potentially caused or facilitated by maternal environmental exposures), or a reverse lottery winner. There simply isn't enough time for somatic mutation to cause the sort of devastating fallout that you see in DIPG or infant leukemias. (Furthermore, even the point mutations seen in pediatric cases are characteristic and rare or absent in adults; some structural variants are also observed in adults, but they are much rarer and accompanied by fewer cooperating events)