Kavli Affiliate: Ariel Amir
| First 5 Authors: Deng Pan, Jie Lin, Ariel Amir, ,
| Summary:
The Luria-Delbr"uck model is a classic model of population dynamics with
random mutations, that has been used historically to prove that random
mutations drive evolution. In typical scenarios, the relevant mutation rate is
exceedingly small, and mutants are counted only at the final time point. Here,
inspired by recent experiments on DNA repair, we study a mathematical model
that is formally equivalent to the Luria-Delbr"uck setup, with the repair rate
$p$ playing the role of mutation rate, albeit taking on large values, of order
unity per cell division. We find that although at large times the fraction of
repaired cells approaches one, the variance of the number of repaired cells
undergoes a phase transition: when $p>1/2$ the variance decreases with time,
but, intriguingly, for $p<1/2$ even though the fraction of repaired cells
approaches 1, the variance in number of repaired cells increases with time.
Analyzing DNA-repair experiments, we find that in order to explain the data the
model should also take into account the probability of a successful repair
process once it is initiated. Taken together, our work shows how the study of
variability can lead to surprising phase-transitions as well as provide
biological insights into the process of DNA-repair.
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