Lifespan Differences in Hematopoietic Stem Cells are Due to Imperfect Repair and Unstable Mean-Reversion
Figure 8
Breakdown of Mean-Reverting Behavior in the Failure Rate Kinetics of Long-term Repopulating HSCs.
A: An experimental failure rate kinetic (blue scatter-line plot; values vertical axis) compared to the kinetics of 100 realizations (thin red lines) of an Ornstein-Uhlenbeck process over the lifespan period (horizontal axis) of a clone with lifespan
months. The realizations of the process were obtained using the iteration schema in eq 4. The same values of
,
and
as in the experimental data were used. For simplicity, the initial condition was set at
for
(equivalent to assuming a load-free transplant). The important observation is that without additional conditions on the Ornstein-Uhlenbeck process, the expected behavior of the kinetic generated from data (blue curve) will not occur. B: The moving average (vertical axis; window size = 6) of the same failure rate kinetic as in Part A (blue line-scatter curve) reveals that the parameter
increases slowly during the mean-reverting regime (raw moving average data (denoted “Moving Avg
”) are in black). The slow increase changes to rapidly increasing failure rates at around 82% of the lifespan. Both behaviors combine into the model of equation 9 with parameters
,
and
(p-values =
,
,
, respectively;
).