DSB clustering

To simulate the fusion of DSBs, we assume that they undergo restricted Brownian motion. In the absence of other influences, they are subject to binding forces arising from their own structure, which can be simplified using a restoring force F ⃗=-kr ⃗. With the Langevin equation and based on Euler’s scheme, the displacement at time t+∆t is modeled as:
r ⃗(t+∆t)=r ⃗(t)+(F ⃗∆t)/γ+σ√2D∆t
where σ is a standard normal variable, γ=6πr_0 η is the damping coefficient, and 〖D=k〗_B T/γ is the diffusion coefficient. r_0 is the radius of 53BP1 foci; η is the viscosity coefficient of water; k_B is the Boltzmann constant, and T is temperature.
Using this equation, the mean displacement at each time point can be simulated through the Monte Carlo method. This simulated displacement is then fitted against experimentally measured mean squared displacement (MSD) to determine the value of k. It is noted that, since the experimentally measured MSD is a two-dimensional quantity, the above equation must also be simulated in two dimensions. Due to the independence of motion in each dimension and assuming that k is equal in all three directions, simulating the motion in each dimension separately and then summing them does not affect the outcome. By computation, an appropriate value for k/γ was selected as 10 /s.