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. 2022 Nov 16;11:e76120. doi: 10.7554/eLife.76120

Figure 4. Latent state correlations between spines at dual connections.

(a) Scatter plot of spine volumes (black, lexicographic ordering) for dual connections. Data points are mirrored across the diagonal (gray). The joint distribution is fit by a mixture model (orange) like that of Figure 3f, but with latent states correlated as in (e). (b) Projecting the points onto the vertical axis yields a histogram of spine volumes for dual connections (Figure 3d). Model is derived from the joint distribution. (c) Projecting onto the x=y diagonal yields a histogram of the geometric mean of spine volumes (Figure 3e). Model is derived from the joint distribution. (d) Projecting onto the x=−y diagonal yields a histogram of the ratio of spine volumes. (e) The latent states of synapses in a dual connection (H1 and H2) are more likely to be the same (SS or LL) than different (SL/LS), as shown by the joint probability distribution. (f) When conditioned on the latent states, the spine volumes (V1 and V2) are statistically independent, as shown in this dependency diagram of the model. (g), (h) Sampling synapse pairs to SS and LL states according to their state probabilities. The top shows a kernel density estimation of multiple iterations of sampling. The bottom shows the distribution of Pearson’s r correlations across many sampling rounds (N=10,000). Error bars are ±n of the model fit.

Figure 4.

Figure 4—figure supplement 1. Fits versus raw distributions.

Figure 4—figure supplement 1.

Plots are analogous to Figure 4 and Figure 4—figure supplement 4. (a) Synapse pairs from all dual connections. (b) Dual connections of synapse pairs less than the median distance apart. (c) Dual connections of synapse pairs more than the median distance apart.
Figure 4—figure supplement 2. Latent state correlations between clefts at dual connections.

Figure 4—figure supplement 2.

(a) The latent states of synapses in a dual connection are positively correlated with each other. The latent states are more likely to be the same (SS or LL) rather than different (SL or LS), as shown by the joint probability distribution. (b) Scatter plot of cleft sizes (black, lexicographic ordering) for dual connections between layer 2/3 (L2/3) pyramidal cells. Scatter plot points are mirrored across the diagonal (gray). The joint distribution is fit by a mixture model (orange) like that of Figure 3f, but with latent states that are correlated as described below. (c) Projecting the points onto the vertical axis yields a histogram of cleft sizes for dual connections, the same as in Figure 3d. Model is derived from the joint distribution. (d) Projecting the points onto the x=y diagonal yields a histogram of the geometric mean of cleft sizes for dual connections, the same as in Figure 3e. Model is derived from the joint distribution. (e) Projecting the points onto the x=−y diagonal yields a histogram of the ratio of cleft sizes for dual connections. Error bars are ±n of the model fit.
Figure 4—figure supplement 3. Residuals spine head volume after subtracting binary components.

Figure 4—figure supplement 3.

We assigned the synapse pairs from the 160 dual synaptic connections to their most likely state (SS, SL, LS, LL) and subtracted the mean of the binary components. (a) shows the residual components. (b) shows the residual components when restricting assignments to SS and LL states.
Figure 4—figure supplement 4. Synapses in a dual connection: near versus far pairs.

Figure 4—figure supplement 4.

Spine volumes (left) and cleft sizes (right). (a) Dual connections of synapse pairs less than 46.5 μm apart (phi = 0.534). (b) Dual connections of synapse pairs more than 46.5 μm apart (phi = 0.745). (c) Mixture component means of model fits as a function of the minimum distance separating synapse pairs. (d) Mixture component means of model fits as a function of the maximum distance separating synapse pairs. Error bars are ±n of the model fit.
Figure 4—figure supplement 5. Dual connection correlations are not a result of axon or dendrite biases.

Figure 4—figure supplement 5.

Synapses are shuffled between dual connections to measure the correlations between synapses that have the same axon (red) or the same dendrite (blue) against a fully random baseline (black). Shuffled synapses are not allowed to be paired with other synapses within their original connection. Each shuffling procedure was performed on a subset of data where at least one valid shuffling exists for each synapse (e.g. where each dendrite receives at least two dual connections). (a–c) Joint distributions of spine head volumes in the dual connections used for shuffling. Slope of linear fit shows Pearson’s r value. (a) Subset of data used for random shuffling (all 160 synapse pairs). r=0.42. (b) Subset of data used for axon-preserved shuffling (141 pairs). r=0.45. (c) Subset of data used for dendrite-preserved shuffling (89 pairs). r=0.51. (d) Example shuffle of data in (a). r=0.00. (e) Example shuffle of data in (b). r=–0.08. (f) Example shuffle of data in (c). r=–0.11. (g) Diagram of a possible shuffle of two dual synaptic connections onto the same dendrite. (h) Distribution of Pearson’s r correlation for paired spine head volumes after shuffling (100,000 shuffles each). Dashed lines indicate correlation value for the unshuffled subset. (i) Distribution of Pearson’s phi correlation for paired spine head volumes after shuffling.
Figure 4—figure supplement 6. Removing constraints on the synaptic population eliminates bimodality and reduces correlations.

Figure 4—figure supplement 6.

Spine volumes (top) and cleft sizes (bottom). (a) Distribution of synapse sizes in dual connections received by layer 2/3 (L2/3) pyramidal cells, including those from orphan axons (566 synapses). (b) Distribution of geometric means of synapse sizes in same dual connections as in (a) (283 pairs). (c) Joint distribution of synapse sizes in dual connections received by L2/3 pyramidal cells, including those from orphan axons (283 pairs). (d) Distribution of synapse sizes for excitatory synapses received by L2/3 pyramidal cells, including those from orphan axons (700 synapses).