Fig 1.
Flow diagram of the DNA-repair process.
A: The average time of MRE11, NBS1 or RAD50 getting recruited to the DNA-damage site is denoted t* and consists of the characteristic time of all three of MRE11, RAD50 and NBS1. The different activation rate constants are labelled k1−5. These processes include phosphorylation which starts protein kinase cascades. B: The broken DNA strand recruits proteins MRE11, NBS1, and RAD50 after a characteristic time, tN, tM and tR respectively. The combined recruitment time is denoted t*.
Fig 2.
Sketch of the studied cell model.
The outer shell has a radius R = 25 μm, and the outer membrane is modelled through reflective boundary conditions. MRE11 and NBS1 is modelled as a Brownian particle and is initially made by the ribosome which is placed at a radial distance within Δr0 which is within the range 11-20 μm away from the center of the nucleus. The nucleus has a radius of ra = 5 μm, and is modelled as an absorbing sphere due to the nuclear pore complexes on its surface.
Table 1.
Summary of biological parameters of MRE11 and NBS1 transportation.
The cell is modelled after the human bone marrow cell (osteoblast) [32], and the diffusion coefficients, DNBS1, for NBS1 of 85 kDa and DMRE11 for MRE11 of 80 kDa are found in the literature. [34, 35].
Fig 3.
Distribution for the first passage times of NBS1 protein.
A: The blue histogram shows the first passage times of NBS1 obtained by simulations. The red line shows the approximation for fast diffusion, and the green line shows the theoretical approximation for slow diffusion theory. None of the distributions fits the entire spectrum of the first hitting times for NBS1. B: The blue histogram shows the simulated first passage time of fast NBS1 recruitment by the nucleus and the red line shows the theoretical probability distribution for the first hitting time, which follows from Eq (18). The faded area marks the time interval outside the validity of the theoretical approximation. C: The blue histogram shows the slow first passage time of NBS1 being recruited to the nucleus and the green line shows the theoretical probability distribution for the slow first hitting time, predicted using Eq (14). The faded area marks the time interval outside the validity of the theoretical approximation.
Fig 4.
Accumulated fraction of NBS1 in the nucleus.
A: The lines represent the faction of accumulated NBS1 proteins in the nucleus, N(tN) defined by Eq (21). The squares represent the corresponding numerical results for the different starting points. In the short time limit, the two methods agree, which is further highlighted in the insert B. C: The lines represent the faction of accumulated NBS1 proteins in the nucleus for the slow diffusion, N(tN) defined by Eq (19). The squares represent the corresponding numerical results for the different starting points. In the long time limit, the two methods agree, as evidenced in the insert D.
Fig 5.
Recruitment of MRE11 and NBS1.
The red crosses show the experimental data for recruitment fraction of the MRE11 protein. The orange crosses show the experimental data for NBS1. Both experiments are performed by Haince et al. [16]. Numerically, the NBS1 protein has been placed at 14-20 μm from the shell of the nucleus, where the blue line shows the average value of the recruitment time of NBS1. The MRE11 protein has been placed at 11-17 μm away from the nucleus and the green line shows the average value of the recruitment time of MRE11.