engleski

Neurogenesis : from Experimental Data to System Dynamics Model

Neurogenesis (NG), as generation of neurons of the cortical plate (CP), includes processes of proliferation, migration and programmed cell death, which have been thoroughly studied on murine model through the series of experiments by Takahashi, Nowakowski, Caviness et al. Simple 11 cell cycle mathematical model of NG within pseudostratified ventricular epithelia (PVE) has been proposed and magnitude of the programmed cell death in CP during early postnatal life has been estimated. We developed system dynamics model of the NG in mouse neocortex that integrates available experimental data. Simulation experiments were run in order to establish its stability, validity and dependence on initial parameters. Following experimental data were used for PVE and CP at future area 1 of the murine neocortex: 1) cell cycle duration ; 2) q factor (proportion of the ongoing mitosis giving birth to young postmitotic neurons (PN)) during neurogenetic interval (NI) ; 3) growth fraction ; 4) duration of migration ; 5) distribution of young postmitotic neurons within CP as function of their time of birth ; and 6) proportion of cells that undergoes programmed cell death within CP in early postnatal life. Model was developed and tested with system dynamics software Stella 8.0 for Windows XP operating system. Duration of the cell cycle, cortical distribution of young postmitotic neurons and proportion of dying cells were implemented as table-vice-linear function with linear interpolation. Growth fraction and duration of migration were constant. Q factor was estimated by polynomial fit that was obtained by Microsoft Excel 2003 software. Simulation experiments were conducted with starting population of 1*103 cells, equally distributed throughout cell cycle, for the time frame from 11th embryonal (E11) to 22nd postnatal (P22) day. Euler’ s integration method was used ; with integration time (DT) equaled 1/10 hours. NI lasted for 150 hours (E11+4, 9h – E17+10, 9h). Each cell of the starting population of the PVE at the beginning of NI gave rise to ~145 postmitotic neurons. Population of the PVE was largest at E14+13, 5h. Distribution by layers (in %) was as follows: VI-23, 1 ; V-9, 0 ; IV-26, 4 ; III/II-41 ; I-0, 6. During NI, cells of the PVE executed 11 cell cycles if they just entered G1 phase at the onset of neurogenetic interval, but only 10 cycles if they were anywhere in the cell cycle at least 1.6 hours away from the start of G1 phase. Overall reduction PN number within CP in the early postnatal life (P0-P14) was 28, 0%. Reduction by layers (in %) was as follows: VI – 16, 6 ; V-11, 5 ; IV-24, 5 ; III/II-40, 3 ; I-20, 7. Final number of PN linearly depends on the size of the founder population within PVE, but polynomial (2nd order) on the length of the cell cycle. Alteration of q-factor considerably influenced final neuron number. Model was shown to be stable for given parameters providing repeatable results in each performed experiment. Results of simulation experiments were in accordance to experimentally observed facts for onset of NI, its duration, time of maximal size of PVE, and persistent migration of PN during early postnatal life. Cortical distribution of PN and postnatal cell death within CP showed differences when compared with previously published data that might be attributed to the numerical estimation methods used and populations of neurons that were not included in the model (SPP, GE, ML, SP). System dynamics was found suitable for simulation modeling of quantitative developmental cellular processes enabling integration of available experimental data into single model.

system dynamics; modeling; computer simulation; neurogenesis; cerebral cortex development

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