Some comments on the formation of murine hemopoietic colonies grown in vivo and in vitro: quantitative analysis.

Experimental distributions of in vitro colonies are analyzed and compared to numerically calculated distributions. The experimental data are those of Nakahata et al. [J. Cell. Physiol., 113, 455-458, 1982], who studied the development of primary and secondary murine hemopoietic colonies in vitro. The cumulative probability distributions of the secondary colonies are simulated by a simple proliferation tree model. The model consists of four subsequent generations of distinct cells undergoing self-renewal and differentiation governed by an unspecified control process. It is assumed only that the control mechanism is so complex that the resulting commitment can be well described by probabilistic formalism. The calculated and experimental distributions are found to be in reasonable agreement. Furthermore, 25 additional experimental distributions have been examined, corresponding to various sets of in vitro and spleen-grown colonies reported in the literature. It is shown that most of the cumulative distributions analyzed are well approximated by the exponential function f(n) = exp(alpha n), where f(n) is the relative number of originating elements (e.g., cells or clones) producing groups having at least n members. A formula is suggested relating the exponent alpha and the probability of self-renewal for a simple single-generation case.