The model (29122012_EN)
1. The flow Fp is functionally critical since the compartment of P cells (progenitors) is not selfsustaining („is leaky“ and without the inflow of cells from the compartment HSC would
empty by 1 to 3 months)
2. The flow Fp depends on: (1) number of HSCs, (2) division rate of HSCs, (3) Ps value
3. The initial number of HSCs remaining after irradiation by 6 Gy can be estimated from the
total number of HSCs in the mouse (2000 – 10000) and their survival after irradiation (0.4 –
0.1%). The initial number of HSCs is thus between 2 to 40.
4. The division rate of HSCs is not known. The cells are mostly dormant (not dividing) in normal
mice. If all HSCs were dormant after irradiation, the flow Fp would be zero, independently on
the number of HSCs, and the system (hematopoiesis) would collapsed from exhaustion of P
cells by 1 to 3 months.
Hence, HSCs surviving irradiation have to divide. The frequency of cell divisions can
be estimated to be twice a day (each 12 hours) to once in two days (each 48 hours).
There might be a delay of 1 to 2 days before HSCs begin to divide. I suggest to ignore
it during the first approximation of the model data to the experimental data.
5. The Ps value (the probability that after a division of a HSC one of the two daughter cells will
be the HSC) can be, theoretically, between 0.0 to 1.0.
If Ps were between 0.0 – 0.5, the system would collapse because of HSCs exhaustion.
Hence, the Ps value must be equal or higher than 0.5. If it were 0.5, the HSCs pool
would not regenerate and the number of HSCs would remain 2 to 40 in the mouse.
This is not the case. Hence, the Ps value is higher than 0.5.
If the Ps value were 1.0, the functionally important (“critical”) flow Fp would be zero
and the system would collapse due to exhaustion of P cells. Hence, the Ps value must
be higher than 0.5 and lower than 1.0 (0.5<Ps<1.0).
Goals of the model:
1. The first goal of the model is to estimate the Ps value in the period 1 – 30 days
after irradiation of mice by 6 Gy
(we have quantitative experimental data showing how the number of HSCs
increases from 2-40 up to 1000-4000 during this period).
2. The second goal of the model is to show how the flow Fp is influenced by the
value of Ps in the course of the regeneration of the HSC pool
from 2-40 up to 1000-4000.