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Simultaneous estimation of T(G2+M), T(S), and T(pot) using single sample dynamic tumor data from bivariate
R A White1, M L Meistrich, A Pollack
1Department of Biomathematics, The University of Texas M.D. Anderson Cancer Center, Houston 77030, USA. allen@odin.mdacc.tmc.edu
Background:
Estimating the duration of S phase (T(S) ) and the potential doubling time (T(pot) ) from a single time measurement of the movement of cells using bivariate cytometry is common. However, these estimates require an assumption of the duration of G2 + M (T(G2+M) ). Inspection of the measured dynamic quantities, relative movement [RM(t)], fractions of labeled divided and undivided cells (f(lu)(t) and f(ld)(t)) suggests that T(G2+M), T(S), and T(pot) can be determined simultaneously.
Methods:
An equation connecting the growth of the cell population, time, and the dynamic quantities was determined. The equation cannot be solved analytically, but accurate approximations can be used to find T(pot). From this result, the value of T(G2+M) can be determined from f(ld)(t), and T(S) can be determined from RM(t).
Results:
Kinetic parameters obtained from single time estimates using the new method compared to those obtained from the analysis of multiple time-point measurements of MCa-K and MCa-4 murine tumors are shown to be in close agreement. Moreover, estimates of T(G2+M) in MCa-4 tumors, treated with paclitaxel, provide extra information on the changes in T(G2+M). When applied to the rat R3327-G prostate tumor model following androgen ablation, a correlation analysis of the T(pot) values obtained by the new and previous single time-point methods demonstrates that the rank order from shortest to longest T(pot) values are largely preserved.
Conclusions:
The new procedure makes direct estimation of T(G2+M) possible from single time-dynamic measurements. The results from previous studies on T(S) and T(pot) are largely unchanged, but extra information is now available.