A simulation model of neuroprogenitor proliferation dynamics predicts age-related loss of hippocampal neurogenesis but not astrogenesis

Adult hippocampal neuroprogenitors give rise to both neurons and astrocytes. As neuroprogenitors are lost with increased age, neurogenesis concomitantly decreases. However, the dynamics of neuron and astrocyte generation throughout adulthood has not been systematically examined. Here, we analyzed the hippocampal niche both longitudinally (from 2 h to 30d of cell life) and transversally (from 1 m to 12 m of age) and generated a Marsaglia polar random simulation model to predict newborn cell dynamics. The sharp decrease in newborn neuron production throughout adulthood was largely predicted by the number of proliferating neuroprogenitors at each age. In contrast, newborn astrocyte decay was slower and associated with their increased yield in mature mice. As a result, the niche shifted from neurogenic to neuro/astrogenic with increased age. Our data provide a simple “end-point” model to understand the hippocampal niche changes across adulthood and suggest yet unexplored functions of newborn astrocytes for the aging hippocampal circuitry.


Marsaglia simulation model. The Marsaglia polar method
was implemented to generate pseudorandom and normally distributed populations of BrdU + cells and their progeny with mean and standard deviation corresponding to those experimentally determined in each age group. Each simulated cell value (v) was generated using the following equation: Where mean and std.dev are the experimentally estimated mean and standard deviation of each age group; and u 1 is a random number between -1 and 1 that satisfies the condition: Where u 2 is a random number between -1 and 1 that is paired to u1 to satisfy the condition s < 1 1 .
We first generated a population of 1,000 simulated BrdU + cells at 2h. For each simulated BrdU + cell, we generated their progeny at 2, 4, 10, and 30d using the Marsaglia polar method with the following biological-related restrictions based on our observations ( Fig. 1, 2): Thus, each simulated BrdU + cell at 2h originated a string of linked simulated neurons and astrocytes up to 30d.
Two possible strategies were compared to satisfy that (NeuN + + GFAP + ) ≤ 30d: randomly determine percentage of GFAP + cells and condition the proportion of NeuN + to this value (GFAP-locked), or viceversa (NeuN-locked). In this supplementary text we summarize the simulated NeuN-locked model (Table S9) and the main findings obtained with it: correlation between NeuN + and GFAP + at 30d with BrdU + at 2h (Table   S10); neuronal and astrocytic yield (Table S11); and neuronal and astrocytic contribution to the increased 30d survival in 6 and 12m mice (Table S12). The same trends and conclusions were reached using the GFAP-locked strategy reported in the main text and the NeuN-locked strategy shown here.
Data modeling. Curve fitting was used to model the longitudinal and transversal decay of BrdU + , NeuN + , GFAP + , and human Dcx + cells. Data modeling was implemented using GraphPad Prism 5 (GraphPad Software, Incl, San Diego, CA) and optimal curve fitting was determined by Akaike's information criteria (AICc) 2 . We compared six alternative fitting curves: straight, semiLog, Log-Log, exponential decay, exponential decay with plateau, and second order polynomial.
Optimal fitting for all data modeled was obtained with exponential curves (with or without plateau). The only exception was human Dcx data, which fit better with semiLog curves. However, we chose to model human Dcx data with exponential curves to compare the decay and half-life with those obtained with our own data.
Each exponential decay curve was defined by the following formula: Where K is the exponential decay constant and the half-life was calculated as: Neuronal:Astrocytic contribution to increased survival at 6 and 12m. To understand the survival of BrdU + cells (neurons + astrocytes) at 30d in 6m and 12m mice, we compared it with the basal survival at 1m. Thus, the number of BrdU + cells at 6m and 12m was modeled as the basal number of cells produced (using the net survival and differentiation rates as in 1m) and a number of extra cells that could be calculated as the sum of extra neurons and extra astrocytes in different proportions.
We explored different scenarios with different neuronal and astrocyte contributions. In addition, we performed an iterative algorithm to search for optimal contributions of neurons and astrocytes. We finally tested which scenario fit best with the experimentally determined and the Marsaglia simulation data comparing the neuron-toastrocyte (N-to-A) ratios.
1. Basal number of neurons and astrocytes at 30d in 6 and 12m mice. Where the extra survival was calculated as a difference with the 1m % survival: The extra differentiation rates were tested in different proportions (100N:0A, 50N:50A, and 0N:100A). The total number of neurons and astrocytes were calculated as the sum of basal + extra cells in each scenario. The N-to-A ratios were calculated and compared to the target ratios (obtained in experimentally estimated and Marsaglia simulation data) (Fig. 4B).

Optimization of neuronal and astrocyte contributions.
We used a simple iterative parameter search algorithm to find the combination of neuronal and astrocytic contribution to the extra survival that resulted in the N-to-A ratio closest to the target ratios. The optimal neuron and astrocyte contributions were determined independently for the experimentally estimated and the Marsaglia simulation data. Initially, the algorithm tested two different combinations of neuronal and astrocyte contributions (C1=100N:0A and C2=0N:100A) and selected the optimal combination that rendered the smallest absolute difference to target N-to-A ratio. In the next step, the selected combination was compared with a newer combination calculated as: Differences with opposite signs indicate that the optimal combination was located between the previous two combinations. In this case, the term was added to C1 or subtracted from C2 depending on which one was selected as optimal, respectively.
Points represent mean ± SEM. N per group as in Fig. S2A.
C, Representative confocal z-stacks of the DG of 1 and 12m mice at 2d after BrdU injection. BrdU + cells (magenta) were co-labeled with the proliferation marker Ki67 (yellow). DAPI staining indicated cell nuclei (in white). Scale bars = 30µm; z = 18µm.