Hacker News Reader

Comment by nonbel | Hacker News Reader

Thanks, I later found this paper that claims something different. Can you explain where this logic has gone wrong, they seem to start out with a similar error rate (~10^-9 per site per division):

"For example, the intestinal epithelium contains approximately 10^6 independent stem cells, each of which generates transient daughter cells every week or two. Thus, the intestinal epithelium of a 60-y-old is expected to harbor >10^9 independent mutations. This implies that, not far beyond the age of 60 y, nearly every genomic site is likely to have acquired a mutation in at least one cell in this single organ." http://www.pnas.org/content/107/3/961.full

Edit:

>"A reasonable error rate of DNA replication (not under stress) is about 1 write error in 1 billion reads"

I think it is that you are using the 10^-9 value to be per genome while that reference uses it as per basepair

View on HN

Write error == (fixed) base pair mutation. A classic example is a methylated cytosine spontaneously deaminating to yield thymine. Our DNA repair enzymes can't tell the difference (in terms of which is the "right" base) between the thymine and the guanine left behind, but since they don't match, one of them has got to go. Thus there is a 50-50 chance that the mutation will be fixed. That's the easiest example because it's not an "error" per se (rather a thermodynamics problem) but genuine proofreading errors also occur. The net rate is about one in a billion bases.

These estimates ignore indels and SVs but empirical evidence suggests that the "everyone over 50 has a 50/50 chance of at least one adult stem cell harboring a mutation in at least one interesting gene". My personal favorite is

http://www.nature.com/nature/journal/v518/n7540/abs/nature13...

but Druley's follow up was equally awesome:

http://www.nature.com/articles/ncomms12484

and the recent survey of adult stem cell mutations is nice:

http://www.nature.com/nature/journal/vaop/ncurrent/full/natu...

One take-away from all this is that, while 95% of a sensitively surveyed population of 50-60 year olds had at least one stem cell with at least one known preleukemic mutation, it is equally clear that most people aren't walking around with anything resembling an acute leukemia. 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. Only when bad luck and/or stresses to which the mutants are adapted (e.g. TP53 mutations in therapy-related leukemia) afflict people, or the natural diversity of their stem cell populations collapses (as with really old people and individuals whose immune system actively attacks their stem cells, as in severe aplastic anemia) do you see the sort of massive, life-endangering takeover that we recognize clinically as disease.

Furthermore, nearly all of us are born with 5-10 predicted-to-be-lethal variants in our genomes. Clearly, we're also not dead, so our conception of "lethal" can't be quite right. There is an enormous amount of complexity in how real live multicellular organisms deal with variation and mutation, something we're really only just starting to grasp, and of course all of that then interacts with the person's environment to manifest (or not) their genetic tendencies. We build models of reality because the actual thing is too complicated to be tractable; it's important never to confuse the two :-)

>" 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/

Armitage-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. :-/

>"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

The 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)

>"There simply isn't enough time for somatic mutation to cause the sort of devastating fallout that you see in DIPG or infant leukemias."

This depends on the error + division rates (along with number of cells) in that tissue at that age though. From my research there not really such data available on any of those terms. Also, the errors need not be somatic mutation. For example, chromosomal missegregation may be much more common and potent since it can mess up the expression of many genes at once:

"Nevertheless, the rate of chromosome missegregation in untreated RPE-1 and HCT116 cells is 0.025% per chromosome" https://www.ncbi.nlm.nih.gov/pubmed/18283116

I'm just saying there are a number of other assumptions being made here, and if we get rid of the standard ones the Armitage-Doll model is capable of fitting the data surprisingly well.

p.s. I edited the earlier response too many times already...

But my point is that I think a key epidemiological variable should be the age of peak incidence. This has been largely missed due to various common practices like:

  1) Binning into 5/10 year age groups
  2) Looking at age adjusted data
  3) Truncating the age-specific incidence data at 70-85 
     years old because the later data is deemed unreliable

Reply on news.ycombinator.com