Fig 1.
Schematics for dendritic selections of a Purkinje cell and cerebellar layer reconstruction by granule cells.
Only main neurons are shown, local inhibitory neurons are ignored. (A1) The cerebellar cortex around postnatal day (P) 1, having granule cell precursors (green oval with light green lines as their leading processes or parallel fibers in the external granular cell layer (shaded green). The middle sheet is the molecular layer (shaded in yellow), and the bottom is the Purkinje cell layer (shaded pink) with cell bodies of the Purkinje cell (red) and Bergmann glia (blue). (A2) Structure of the cerebellar cortex after about P15. All granule cells (green ovals) migrated down from the surface to the bottom to form the granule cell layer (shaded in green). The molecular layer (shaded in yellow) is now at the surface with greatly expanded volume and is filled with Purkinje cell dendrites (red), parallel fibers and descending axons (green) left behind by granule cells. (B1) A Purkinje cell before dendritic selection phase at P4 to P10. The red sphere represents its soma, and initial dendritic trees are light or dark red. (B2) Same Purkinje cell after the selection phase at P8 to P10. In this schematic, the dark red dendritic tree was chosen as its primary tree and other candidate trees were retracted.
Fig 2.
Granule cell migration model as an environment for Purkinje cell growth.
(A) A representative simulation cube at the end of the simulation visualized from X side. Red large spheres are Purkinje cell somas. Blue small spheres with processes growing upward are Bergmann glia. Numerous green thin threads are axons of granule cells in the main simulation volume (where Purkinje cell somata and Bergmann glia are present, see panel E), and orange fibers are ingrowing parallel fibers. (B) Schematic representations of how each granule cell migrates using a Bergmann glia process as a guide, see text for explanation. (C) Histogram showing final lengths of the parallel fibers in the representative case, 300 μm is the maximum possible length for the simulation volume. (D) Bar plots showing success rates of soma radial migrations, of parallel fiber branching to form T-junctions, of parallel fiber extensions initiated in the main volume and of parallel fibers growing from the outside into the main volume and fully extending in the main volume. Mean success rates from 10 simulation samplings of the model with error bars showing standard deviations. Coefficient of variation values for each is 0.031, 0.007, 0.007, and 0.004 respectively. (E) Another side view (longitudinal side) of the granule cell model after all green granule cells finish migration. Black to gray stripes represent z-locations of granule cell births during 12 phases. The central part is the main simulation cube (panel A), left and right sides are origin sites of ingrowing parallel fibers. (F) Top view of the model with numbering of Purkinje cell somata. Brown cells were added to provide dendritic repulsion at the borders of the main simulation cube but were not analyzed. Blue structures are Bergmann somata and radial glia.
Fig 3.
Characteristic of 3 control scenarios.
(A1-3) The plots show changes in maximal path length of dendritic trees with a different line color for each tree. Three Purkinje cells were randomly selected from one of 10 RandomRetract simulations. (B1-3) Similar plots as A1-3 from one of 10 NoRetract simulations. (C1-3) Similar plots as A1-3 from one of 7 NoGranCells simulations. Here only C2 shows 2 phases of retraction. In C1 and C3, all dendritic trees at the first screening phase were larger than the retraction threshold and kept growing until the second screening phase. (D) Average number of synapses on each winner dendritic tree in the three scenarios with error bars representing standard deviations. (E) Average maximum length of each winner tree in the three scenarios with standard deviations. (F) Average number of branch points in each winner tree in the three scenarios with standard deviations. P values: **** indicates p < 0.00005, Welch’s t-test. Actual p values, t statistics, and degrees of freedom for comparing each data set are summarized in S1 Table.
Fig 4.
Arbor size of winner trees in 3 control scenarios.
(A1) Side view of Purkinje cells at P12 (cycle 120) for RandomRetract scenario. Only Purkinje cells #21–26 are shown for convenience (see Fig 2F), while other structures in the simulation are hidden. (A2) A top view of A1. (B1) Similar plot for NoRetract scenario. (B2) A top view of B1. (C1) Similar plot for NoGranCells scenario. (C2) A top view of C1. (D) Average maximum y-distance for each scenario, error bars indicating standard deviations. (E) Average maximum x-distance for each scenario with standard deviations. (F) Average number of branch points for each scenario with standard deviations. P values: **** indicates p < 0.00005 and ** is p < 0.005, Welch’s t-test. D-E: 240, 240 and 168 cells. Actual p values, t statistics, and degrees of freedom for comparing each data set are listed in S2 and S3 Tables.
Fig 5.
Dependence of number of synapses and arbor size of winner trees on parameter sets.
The scatter maps show number of synapses by darkness for each combination of control parameters. The sizes of circles on the plot represent average maximum path length of winner trees. The parameter set with the most numbers of synapses is marked with a red asterisk, corresponding parameter values are listed in Table 1. (A) FixedRetract scenario: the control parameters are cycles at which each retraction phase occurs. X-axis shows the first retraction cycle and y-axis shows number of additional cycles to trigger second retraction. Each point represents 10 or 20 samples. (B) SizeRetract scenario: has 3 control parameters. X-axis shows number of fronts required to trigger first retraction and y-axis to trigger second retraction. In addition, during first retraction, a parameter (named ‘1st_f_th’ in Table 1) sets minimum number of fronts required to survive, 20 for this figure (range 20–160 evaluated). Each point represents 20 samples, surviving trees without synapses excluded. (C) SynapseRetract scenario: has 3 control parameters. X-axis shows total number of synapses required to trigger second retraction, and y-axis is minimum number of synapses required to survive first retraction. Total number of synapses required to trigger first retraction (named ‘1st_s_th’ in Table 1) is set at 90 (range 60–110 evaluated). Each point represents 20 samples. (D) InputRetract scenario: X-axis shows integrated synaptic signal required to trigger first retraction and y-axis does the same to trigger second retraction. Each point represents 10 to 20 samples. (E) Plotting average maximum x-distance of winner trees from all simulations of SynapseRetract with different parameter values as a representative example for all scenarios. Vertical lines indicate standard deviations. (F) The same plot as E, but for average maximum y-distance.
Table 1.
Summary of the data from the seven different scenarios.
Number of synapses were counted per a cell if not indicated. Numbers of fronts, path length, number of branch points, number of terminals, max x-distance, max-y distance were counted per a winner tree.
Fig 6.
Change in path lengths with during simulation in retraction scenarios.
The plots show changes in max path length of candidate trees at every simulation cycle with a different line color for each tree. Three Purkinje cells were randomly selected from one of 20 simulations. Max path lengths of a tree drops to 0 when they are retracted. Some trees stop growing before the retraction phase, resulting in more shallow lines, for example blue line in A2. (A1-3) FixedRetract scenario. Since this scenario induces retractions at two fixed cycles, all retractions occur at either cycle 90 or 97. (B1-3) SizeRetract scenario. Similar plots as A1-3. Some cells skipped the first retraction because all the dendritic trees had a larger number of fronts than the threshold (20 fronts) when a cell reached the first retraction threshold (300 fronts), resulting in a single retraction event. (C1-3) SynapseRetract scenario. (D1-3) InputRetract scenario. Plots were generated by data using parameters as in Table 1, except D1 and D2 are from a parameter set with Whole_signal_1st = 10,000 and Whole_signal_2nd = 13,000.
Fig 7.
Size of winner trees in the retraction scenarios depends on local parallel fibers.
(A) Average number of branch points on winner trees for the retraction scenarios with error bars indicating standard deviations. P values: * indicates p < 0.05 and ** is p < 0.005, Welch’s t-test. Actual p values, t statistics, and degrees of freedom for comparing each data set are listed in S3 Table. (B) FixedRetract: correlation between volume of all fronts of a winner tree and volume of all parallel fibers in the same neighborhood. (C) SizeRetract: similar correlation as in B. (D) SynapseRetract: similar correlation as in B. (E) InputRetract: similar correlation as in B.
Fig 8.
Changes in synapse numbers and morphology of individual winner trees from single samples in the retraction scenarios.
(A1, B1, C1, and D1) Plots to show change in number of synapses at every simulation cycle in one of the simulations (seed 11). Colors refer to Purkinje cell numbers (see Fig 2F). (A2, B2, C2, and D2) Top view of selectively visualized Purkinje cells at P10 (cycle 100). Purkinje cells with highest (H), lowest (L), and medium (M) number of synapses from A1-D1 plots were selected for each. See Fig 2F for location of the cells. (A3, B3, C3, and D3) Plots to show morphology of winner trees in A2-D2 viewed from different directions.
Fig 9.
Variability of synapse numbers in all winner trees for the retraction scenarios.
Histograms for numbers of synapses on winner trees from all 20 simulations in each retraction scenario, and 10 simulations in each control scenario. Average and standard deviation of each data set is shown in each plot. P values, t statistics, and degrees of freedom for comparing each data set are listed in S4 Table.