Estimation of synapse total number

Measures of the synapse densities in HVC were performed and calibrated to the corresponding densities in the wet brain section state (see Supplementary Method and Data section S.1). The physical volumes of HVC in the wet section state were also measured (see section 3.2.3). As a result, the total numbers of synapses in HVC for each bird could be estimated as the product of HVC synapse density and HVC volume that measured in the same bird.

The volume of HVC has shown to remain constant while its neurons increase in number and decrease in size (Walton et al. 2012), indicating the HVC volume might be regulated differently compared to its local neurostrucutral features. For the estimation of synapse total number, the HVC volume and the HVC synapse density were assumed to be uncorrelated. In the same bird, these two parameters were treated as independent measurements, and in statistical term as two independent random variables. The expected value and variance of the product of two independent random variables were calculated based on Equation (2.9) in (Frishman 1975) and Equation (2) in (Goodman 1960).

When two random variables with expectations 𝑬(𝒙) and 𝑬(𝒚), and variances 𝑽𝒂𝒓(𝒙) and 𝑽𝒂𝒓(𝒚), are independent or uncorrelated, the expected value of their product 𝐸(𝑥𝑦)is simply given by:

Equation 3. 8:

𝐸(𝑥𝑦) = 𝐸(𝑥) ∗ 𝐸(𝑦)

The variance 𝑽𝒂𝒓(𝒙𝒚) and standard deviation 𝑺𝑫(𝒙𝒚) of the product are given by:

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Equation 3. 9:

𝑉𝑎𝑟(𝑥𝑦) = 𝐸²(𝑥) ∗ 𝑉𝑎𝑟(𝑦) + 𝐸²(𝑦) ∗ 𝑉𝑎𝑟(𝑥) + 𝑉𝑎𝑟(𝑥) ∗ 𝑉𝑎𝑟(𝑦) Equation 3. 10:

𝑆𝐷(𝑥𝑦) = √𝑉𝑎𝑟(𝑥𝑦)

The expectations and standard deviations of the total synapse numbers in HVC were calculated for each bird and group, and summarized in Table 3. 15.

Difference in the total synapse numbers among the groups were evaluated by Wilcoxon rank-sum tests. The differences were considered significant with p values less than 0.05.

3.2.8. Linear regression analyses of the neuroanatomical data

Similar to Experiment I, a linear mixed-effects model was fit to the dissector data of each experimental group prior to the pairwise statistical tests to explore the fixed group effects on the neurostructural features of HVC. In contrast to the modeling procedure described in Experiment I, the fixed group effects were further decoupled here into two terms, with one describing the effects of development and the other describing the effects of tutoring. Because the synapse density and symmetric synapse percentage estimations in HVC were both based on the dissector data, the same linear model was applied to both data. The model will be described in detail by taking the synapse density data as an example, to illustrate the meanings of the parameters. Because the densities of the HVC asymmetric synapses, HVC symmetric synapses, and symmetric synapse percentages were modeled in the same way, they will not be repeatedly described.

The synapse density 𝑦_𝑖𝑚 in the dissector 𝑖 of bird 𝑚 was modeled as the linear sum of 1, the fixed group effects 𝛽; 2, the random individual bird effects 𝑏; and 3, the observation errors 𝜖. The fixed group effects 𝛽 in the song-isolated groups (ISO_30, ISO_60, and ISO_90) represent the fixed effect of the different developmental stages on HVC synapse density. Estimated group means of the ISO_30 and ISO_60 groups severed as the baseline values of ISO_60 and ISO_90 groups, respectively. In the song-tutored groups (TUT_60 and TUT_90), the fixed group effects 𝛽 represent the linear sum of the fixed effects of development plus the fixed effect of tutoring on HVC synapse density. The fixed effect of tutoring were modeled by using the values of the age-matched song-isolated groups as the baselines. The model then evaluate whether the fixed effects that characterize the differences among the experimental groups significantly deviated from their baselines. For the ISO_30 group, the synapse density of a given dissector was

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modeled as 𝑦_𝑖𝑚^{𝐼𝑆𝑂_30}, which is the sum of the fixed nonzero mean group estimate value 𝛽^{𝐼𝑆𝑂_30}, the bird individual effect 𝑏𝑚𝐼𝑆𝑂_30

, and the observation error 𝜖_𝑖^{𝐼𝑆𝑂_30}:

Equation 3. 11: 𝑦_𝑖𝑚^{𝐼𝑆𝑂_30}= 𝛽^{𝐼𝑆𝑂_30}+ 𝑏_𝑚^{𝐼𝑆𝑂_30}+ 𝜖_𝑖^{𝐼𝑆𝑂_30}

Similarly the synapse density of a given dissector in the ISO_60 and ISO_90 song-isolated groups were modeled as follows:

Equation 3. 12: 𝑦_𝑖𝑚^{𝐼𝑆𝑂_60}= 𝛽^{𝐼𝑆𝑂_30}+ 𝛽^{𝐼𝑆𝑂_60}+ 𝑏𝑚𝐼𝑆𝑂_60+ 𝜖_𝑖^{𝐼𝑆𝑂_60}

Equation 3. 13: 𝑦_𝑖𝑚^{𝐼𝑆𝑂_90}= (𝛽^{𝐼𝑆𝑂_30}+ 𝛽^{𝐼𝑆𝑂_60}) + 𝛽^{𝐼𝑆𝑂_90}+ 𝑏𝑚𝐼𝑆𝑂_90+ 𝜖_𝑖^{𝐼𝑆𝑂_90}

The terms 𝛽^{𝐼𝑆𝑂_60} and 𝛽^{𝐼𝑆𝑂_90} represent the fixed effect of development on the synapse densities. For the modeling of the group ISO_60, 𝛽^{𝐼𝑆𝑂_30} served as the baseline value to represent the synapse density of the birds at 30 dph. For the modeling of the group ISO_90, the sum (𝛽^{𝐼𝑆𝑂_30}+ 𝛽^{𝐼𝑆𝑂_60}) served as the baseline value to represent the synapse density of the birds at 60 dph. The sum of the fixed effect of ISO_60 and ISO_90 groups then served as the baselines for their age-matched song-tutored groups.

The synapse density of a given dissector in the TUT_60 and TUT_90 song-tutored groups were therefore modeled as follows:

Equation 3. 14: 𝑦_𝑖𝑚^{𝑇𝑈𝑇_60}= (𝛽^{𝐼𝑆𝑂_30}+ 𝛽^{𝐼𝑆𝑂_60}) + 𝛽^{𝑇𝑈𝑇_60}+ 𝑏𝑚𝑇𝑈𝑇_60+ 𝜖_𝑖^{𝑇𝑈𝑇_60} Equation 3. 15: 𝑦_𝑖𝑚^{𝑇𝑈𝑇_90}= (𝛽^{𝐼𝑆𝑂_30}+ 𝛽^{𝐼𝑆𝑂_60}+ 𝛽^{𝐼𝑆𝑂_90}) + 𝛽^{𝑇𝑈𝑇_90}+ 𝑏𝑚𝑇𝑈𝑇_90+ 𝜖_𝑖^{𝑇𝑈𝑇_90}

The terms 𝛽^{𝑇𝑈𝑇_60} and 𝛽^{𝑇𝑈𝑇_90} are the fixed effect of tutoring on synapse densities. The fixed effects (𝛽^{𝐼𝑆𝑂_30}+ 𝛽^{𝐼𝑆𝑂_60}) and (𝛽^{𝐼𝑆𝑂_30}+ 𝛽^{𝐼𝑆𝑂_60}+ 𝛽^{𝐼𝑆𝑂_90}) were obtained from the song-isolated groups, and they served as the baseline density values, which were when the birds were at 60 dph and 90 dph, respectively.

The model described here only makes four comparisons as defined by the four model fitting equations Equation 3. 12, Equation 3. 13, Equation 3. 14, and Equation 3. 15. The four comparisons are: ISO_60 compared to ISO_30, ISO_90 compared to ISO_60, TUT_60 compared to ISO_60, and TUT_90 compared to ISO_90. The differences between other pairs of groups in the results will be determined by the pairwise statistical tests that using individual birds as sampling unit.

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3.3. Results

3.3.1. Song learning performances in the tutored groups

The song learning performance were measured as described in Experiment I (see Methods section 2.2.1 and Results section 2.3.1). It need note here that the tutoring paradigms differed between Experiment I and Experiment II. Sample song spectrograms and the sampling distributions of the selected juvenile songs and tutor songs are shown in Figure 3. 2 to Figure 3. 9. The song similarity scores of each bird and the group means are summarized in Table 3. 1.

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Similarity to tutor song of bird g15o4 (2404 TUT_90) Similarity score, median ± MAD: 53.00 ± 8.46

Figure 3. 2: Similarity of 20 juvenile songs of bird g15o4 (2404 TUT_90) compared with 20 tutor songs. See Figure 2. 11 legend for more information.

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Similarity to tutor song of bird g15k15 (2603 TUT_60) Similarity score, median ± MAD: 22.00 ± 3.08

Figure 3. 3: Similarity of 20 juvenile songs of bird g15k15 (2603 TUT_60) compared with 20 tutor songs. See Figure 2. 11 legend for more information.

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Similarity to tutor song of bird g15k7 (2908 TUT_90) Similarity score, median ± MAD: 61.00 ± 6.33

Figure 3. 4: Similarity of 20 juvenile songs of bird g15k7 (2908 TUT_90) compared with 20 tutor songs. See Figure 2. 11 legend for more information.

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Similarity to tutor song of bird g15k19 (3308 TUT_90) Similarity score, median ± MAD: 62.00 ± 7.30

Figure 3. 5: Similarity of 20 juvenile songs of bird g15k19 (3308 TUT_90) compared with 20 tutor songs. See Figure 2. 11 legend for more information.

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Similarity to tutor song of bird b1g16 (3402 TUT_90) Similarity score, median ± MAD: 70.00 ± 2.22

Figure 3. 6: Similarity of 20 juvenile songs of bird b1g16 (3402 TUT_90) compared with 20 tutor songs. See Figure 2. 11 legend for more information.

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Similarity to tutor song of bird g16o7 (3603 TUT_60) Similarity score, median ± MAD: 57.00 ± 6.51

Figure 3. 7: Similarity of 20 juvenile songs of bird g16o7 (3603 TUT_60) compared with 20 tutor songs. See Figure 2. 11 legend for more information.

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Similarity to tutor song of bird g16o13 (4103 TUT_60) Similarity score, median ± MAD: 55.50 ± 7.36

Figure 3. 8: Similarity of 20 juvenile songs of bird g16o13 (4103 TUT_60) compared with 20 tutor songs. See Figure 2. 11 legend for more information.

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Similarity to tutor song of bird g16p18 (4211 TUT_60) Similarity score, median ± MAD: 53.00 ± 9.69

Figure 3. 9: Similarity of 20 juvenile songs of bird g16p18 (4211 TUT_60) compared with 20 tutor songs. See Figure 2. 11 legend for more information.

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All juvenile songs had developed distinguishable syllable and motif structures, which are outlined by the red rectangles in the juvenile song spectrograms. Only one bird, g15k15, failed to copy the tutor song, as shown by its low similarity score of 22.00 ± 3.08. All of the rest of the juvenile birds scored higher than 50.

No noticeable outliers were observed in any of the song selections of the birds (as shown by the histograms and heatmaps in Figure 3. 2 to Figure 3. 9). Systematically higher similarity scores were obtained compared with the tutored juveniles in Experiment I (see section 2.3.1). This can be seen clearly for the age-matched groups that were subjected to the same length of tutoring (Experiment I: LONG group and Experiment II: TUT_60). This systematic difference most probably resulted from the different tutoring paradigms applied in these two experiments because the ages of the juvenile (though with 1 day difference as 59 dph and 60 dph), initial tutor song exposure times, and total days of tutoring were the same in these two groups. It need to note, Experiment I and Experiment II were conducted a year apart by me. This difference, however, was ignored here. The birds were kept in a controlled laboratory environment without seasonal condition changes, the time of year was also considered to not affect the results. The different tutoring paradigms and their impact on the final song learning performances in the two experiments are discussed in section 3.4.1.

Table 3. 1: Song similarity score values for the tutored birds in the TUT_60 and TUT_90 groups. The bird and group identities were coded (2^nd column) to ensure unbiased (group-blind) analyses. The song similarity scores were determined by averaging the 400 comparisons, and the median ± MAD values are shown in the 4^th column. The group average scores were determined by averaging across all of the birds within the groups, and the group means ± SE are shown in the last column.

The mean song similarity scores for each bird ranged from 22 to 57 in the TUT_60 group and from 53 to 70 in the TUT_90 group. In the TUT_60 group, bird g15k15 had a score that was much lower than the scores of the rest of the birds in the group.

Instead, it was similar to the age-matched birds in the Experiment I LONG group (see Table 2. 1). The low similarity scores of some birds at 60 dph were thought to

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have been a result of the bird not learning very well or learning slowly, while still in the middle of the song learning period. The scores of bird g15k15 were still included in the analysis of the group mean. Birds in the TUT_90 group all had higher scores than the birds in the TUT_60 group, except one bird g15o4, scoring lower than two birds, g16o7 and g16o13, in the TUT_60 group.

Figure 3. 10: The song similarity scores (for data, see Table 3. 1). The boxes represent the similarity scores of individual birds, and the error bars indicate the MAD. The colored bars represent the group means, with group means ± SE are written in them. The colors in the boxes and bars indicate their group (dark blue: TUT_60; light blue:

TUT_90).

Table 3. 2: The results of the Wilcoxon rank-sum test of the song similarity score differences between the TUT_60 and TUT_90 experimental groups. No significant difference was found between the two tutored groups.

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The group means ± SE of the song similarity scores were 46.88 ± 8.33 in the TUT_60 group and 61.50 ± 3.48 in the TUT_90 group. No significant difference was found between the tutored groups (Table 3. 2).

Im Dokument Developmental and Experiencedependent. of a Song-control Brain Region in the Zebra Finch (Seite 105-119)