Nonlinear analyses of cell proliferation in the central nervous system reveal stochastic and deterministic components

This paper analyzes the dynamics of cell proliferation in the developing central nervous system. Three different algorithms, Fano factor, Allan factor and detrended fluctuations analysis, are used to estimate de scaling exponent of space numerical series obtained by recording the number and position of proliferating cells along the cephalic-caudal axis of the system. It can be concluded that the dynamics of proliferation involves two component: (a) a random noncorrelated stochastic component representing a basal proliferating activity uniformly distributed along the cephalic-caudal axis and (b) a deterministic nonstationary component that imposes a defined global trend to the process. The deterministic nonstationary trend can be interpreted as the effect of a controlling influence operating along the cephalic-caudal axis. This result indicates that the proliferative activity is spatially organized along the cephalic-caudal axis of the system.