Quantitative Analysis of Neurogenesis from NSCs

The mathematical description of neurogenesis was as described previously [29]. Briefly, N_j+1 is defined as the total cell number present at the beginning of the (j + 1)th day; n_j+1 as the total number of neurons (β-III-tubulin⁺ cells) present at that time; β _j as the rate of conversion from progenitors to neurons on that day, and δ _j as the death rate of all cells. Thus, the number of neurons present at the beginning of the (j + 1)th day is obtained by the equation n_j+1 = n_j + β _j (N_j − n_j) − δ _jⁿ n_j; in which δ _jⁿ refers to the death rate of neurons and the quantity δ _jⁿ n_j presents the number of neurons dying during the jth day. This equation reveals that the neuron number at the beginning of the (j + 1)th day is composed of the neurons present at the start of the jth day (n_j), plus those converted from progenitors, β _j (N_j − n_j), minus the number of dead neurons. This death number is unknown, but the inequality δ _j N_j ≥ δ _jⁿ n_j ≥ 0 sets limits on neuronal death. These equations, together with the measured numbers of total cells, neurons, and cell death enable us to obtain the maximum and minimum β on each day.