The mathematics of neocortical neuronogenesis.

Neocortical neuronogenesis occurs in the pseudostratified ventricular epithelium (PVE) which forms the margin of the ventricular system of the embryonic cerebral wall. We have determined that in mouse the neuronogenetic interval continues 6 days and is divisible into 11 integer cycles. The fraction of daughter cells which leaves the cycle (Q) following a curvilinear path from 0 to 1.0 over the neuronogenetic interval. Q reaches 0.5 in the course of cell cycle 8 at which point the number of daughter cells which leaves the PVE is equal to the number that remains to renew the proliferative process. Over the course of the neuronogenetic interval in mouse, the founder population is amplified 140 fold. If, theoretically, the operation of the process were altered so that the total number of integer cycles were kept constant but that Q varied so that it reached 0.5 in the course of cell cycles 7, 9 and 10, the total neuronal production from the same founder population would be 60%, 160% and 550%, respectively, that observed in mouse. If, on the other hand, the number of integer cycles was varied but the relative rate of progression of Q with respect to the neuronogenetic interval was kept the same as in mouse, the total neuronal production would be 50% with 9 cycles, 2 fold with 13 cycles and 60 fold with 22 cycles with respect to the 140 fold amplification of the founder population seen in mouse. These large scale amplifications in neuronal output from the PVE illustrate the predominant effect of the number of integer cycles, but also the substantial effect of variations in Q as potential control parameters in the regulation of neuronogenesis.