Same Birthdays and Double Double Strand Breaks

There's this conceit among technically trained elitists that only they can understand basic science. My view is that, if I can't explain something to an intelligent, open minded lay man, then I don't understand it. Here's a test.

You do have to know that radiation dose is measured in grays (Gy), which is the amount of energy (joules) the radiation deposits in a kilogram of tissue.

Figure 1. Green and Red are repair RIF's working on translucent DNA with a double DSB. The DSB's are labeled DNA A and DNA B.\cite{brahme-2023}[Figure 9] The Ku's quickly identify and clamp on to the broken ends, and then call in the DNA-Pkcs' to reconnect them.

In past posts including The Case for 2 mSv per day and Why are we so good at repairing radiation damage?, I have pinned radiation harm on double strand breaks(DSB) of our DNA. Single strand breaks (SSB), which leave one side of the helix intact, are a non-problem. The intact side is used as a template to make a quick and essentially error-less repair. DSB's, damage to both sides of the DNA helix, are much harder to repair correctly than SSB damage, since during most of the cell cycle a template is no longer available.

But that story is seriously incomplete. It turns out we are also quite good at repairing isolated DSB's. Molecules called Ku's are always drifting around in the cell waiting for a DSB to happen. When one occurs, they quickly --- in a matter of seconds --- clamp on to the broken ends. The Ku's then call in a large complex of proteins to do the rejoining, which normally takes about 30 minutes.

By tagging the right proteins with fluorescent molecules, these repair clusters, dubbed RIF's (Radiation Induced Foci,) can be viewed, Figure 2. This process, known as an NHEJ repair, does not use a template; but for isolated DSB's, NHEJ almost always works. Even if NHEJ does not get it quite right, some NHEJ misrepairs can be corrected later in the cell cycle when the cell is preparing for replication. At this point, a template is available and a proof reading process takes place. This template dependent correction is called an HR repair. But this only works for relatively small residual errors.

Figure 2. UCB pictures of cell repair. The bright spots in the three screenshots are clusters of damage sensing and repair proteins, dubbed Radiation Induced Foci (RIF). Berkeley found that the number of RIF's increases less than linearly with dose. At 0.1 Gy, they observed 73 RIF's/Gy. At 1.0 Gy, they saw 28 RIF's/Gy. If a RIF is faced with a single DSB, the repair is almost always correct. If a RIF is faced with more than one DSB, the error rate skyrockets. We expect 25 to 40 DSB's per gray. Do the math. 40 DSB's and 73 RIF's, no problem. 40 DSB's and 28 RIF's, trouble.

The real problem is closely spaced DSB's, which Brahme calls double double strand breaks (DDSB), a rare case of the acronym being better than the name. The RIF's are larger in size than the portions of the DNA they are attempting to repair, Figure 1.\cite{brahme-2023} If the DSB's are too close together, multiple RIF's simply do not have room to form. This would explain why UCB found that the number of RIF's did not rise proportionally with the number of DSB's, Figure 2.\cite{bissell-2011}

When a single RIF is faced with multiple DSB's, all sorts of bad things can happen, probably the worst of which is rejoining the wrong ends creating an uncorrectable misrepair. A few of these mutations will be viable, a few of the viable mutations will escape our immune system, and a few of those could become cancerous.

Multiple studies support this basic picture. Here’s how Rothkamm et al put it.

After 80 Gy of X-irradiation at a high dose rate (23 Gy/min), wild-type [normal] cells repaired 50% of the induced DSBs within 24 h by incorrect rejoining. Low-dose-rate experiments, in which the cells were exposed to 80 Gy over a period of 14 days under repair conditions, led to no detectable misrejoining in wild-type cells

However, if multiple DSBs coincide, even wild-type cells form genomic rearrangements [misrepairs] frequently. We propose that it [NHEJ] serves as an efficient pathway for rejoining correct break ends in situations of separated breaks but generates genomic rearrangements if DSBs are close in time and space.\cite{rothkamm-2001}

If double DSB's are the real problem, harmful damage is highly non-linear in the number of unrepaired hits. In fact, this kind of damage is S-shaped in the number of currently unrepaired DSB's. Stay with me. If it takes two closely spaced DSB's to cause harm, we are dealing with a version of the same birthdays problem.

This is an old bar hustle, in which the hustler bets even money that among the 30 patrons in the bar, there is at least one duplicate birthday. People thinking linearly do the numbers in their head. There's one chance in 365 that somebody's birthday is on any given day of the year. Therefore, the hustler's chance of winning the bet is 30 times 1/365 or less than 10%. They take the bet. 70% of the time they lose. If the number of patrons is 35, they lose 81% of the time.

What does this have to do with double DSB's? Define a hit as something that causes a DSB. Divide the DNA into 365 target zones. (You can substitute any other number for 365. The shape of the curve will be the same.) Two hits in the same target zone cause a DDSB. A single hit has no chance of causing a double DSB. The second hit only has one chance in 365 of hitting the same target zone and causing a double DSB. But if it doesn't, the third hit has two chances in 365 of creating a DDSB. If it doesn't, the fourth hit has three chances. And so on. This builds up pretty quickly. In the hustler's case, if there has been no duplicate by the time he gets to patron 30, there is an 8% chance that number 30 has the same birthday as one of the other 29.

Of course, with more and more hits, the chance that we've already had a double DSB becomes so large, that an additional hit hardly changes the chance that we have had a double DSB.

Figure 3. Probability of a Same Birthday(DDSB) versus number of patrons(hits per repair period)

Figure 3 puts this all together.¹ Not only do we have a sigmoid harm model, but the lower left hook of the S is smaller than the upper right hook. This general shape is built into the need for multiple hits in nearly the same place.

Given our ability to repair DSB’s, it is important to bring the time dimension into the problem. At any point in time, it is the number of unrepaired DSB's, which sets the number of target zones in which a hit will produce a double DSB. The number of unrepaired DSB's is closely related to the rate of damage relative to the time to repair, the number of hits per repair period, which is proportional to the dose rate in each repair period. The dose rate profile is all important.

What we have here is yet another argument that LNT, the hypothesis that the dose response curve is a straight line, is nonsense. More importantly, we have good reason to expect that, within a repair period, the dose response curve should be sigmoid in the dose in that repair period.

1. It easier to work with the probability of no matches. The probability of no matches in N+1 tries equals the probability of no matches in N tries times the probability of no match in the (N+1)st try. The probability of 1 or more matches is simply 1.0 minus the probability of no matches.