Cellular Mutation

Overview

We tend to think that humans have one consistent, uniform DNA code throughout all cells in the body. One question I have wondered about is, to what degree do all cells of the body actually share the same DNA?

Rate

There’s some muation rate, after all, when transcring DNA. We know that mutation rates are roughly $2.5\times10^{-8}$ mutations per nucleotide site. The robustness mechanisms for transcribing DNA turn out to be quite good, because this rate is actually shockingly small. For some context..

Human Genome Size

The human genome is roughly 3 billion bp, of which only 1%, or 30M bp are part of the exome. On average, we would expect 75 mutations per whole-genome replication, of which (assuming uniform randomness of mutation) just 0.75 of these mutations (on average) would end up expressed.

Cells in Body

Further, by volume, a typical adult human is on the order of $0.062m^3$ - and if the skin cell is representative of an average cell, the average cell is roughly $(10^{-5}m)^3$, making a human contain an order of 10 trillion cells 1. Given the mutation rate, all cells in the human body would contain just 250,000 mutations. Of these (assuming uniform randomness of mutation), only 2500 mutations would be expressed in any cell’s exome in the entire human body, at a given time; of those mutations, it’s not even guaranteed that the exome would be expressed in that particular cell as part of its transcriptome (since a given cell only runs part of the genetic code).

Biology by the numbers actually verifies the $10^{13}$ number when estimating by volume with similar methodology.2

Pointwise Mutations are Shockingly Low

I think now I finally get the sense for how shockingly low the mutation rate actually is when transcribing DNA. 2500 mutations in the entire body of 10 trillion cells is forgettable.

Caveats

Of course, there are a few simplifications in this argument, that could change the conclusion:


  1. $log_2(10^{13}) \approx 43$ - it only takes about 43 doublings of a cell population to create the same number of cells as a human. If a human cell colony could double daily, it would only take 43 days to build a fully-formed human. Of course, the doublings can’t happen every day, since there are a lot of structural components to consider, nutrients to deliver, etc - so in practice it takes about 18 years to create a fully sized human. This is one of the first exercises in the molecular biology of the cell. ↩︎

  2. However, they note that there can be significantly more cells of different types - for example, red blood cells are quite small, and therefore make up a significant proportion of the total cell count (about 80%). Interestingly, the volumetric calculation still holds up, even taking cell size into account. ↩︎

  3. I call this dynamic: live by the exponential, die by the exponential. The predator-prey chain relies on this dynamic, for instance: plants can grow in memoryless numbers, with growth rate invariant to population size, until their predators (herbivores) come to do the same. Even we computer scientists experience life and death by the exponential: if not for the exponential, then binary could not represent data efficiently. And yet, there are a tremendous number of useful computer science problems that seem out of reach, because of the exponential resources they require to solve. ↩︎