Figure 5.

Daughter Radii in Pyramidal Neurons Are Optimized for Protein Diffusion Lengths that Overlap with the Experimentally Reported Distribution of Dendritic Proteins

(A) A sketch of a dendritic branch and its corresponding radii, lengths, and density of proteins at the tips of the daughter dendrites.

(B) Predicted protein density at the tips of the daughter dendrites as a function of the daughter radius $\left(r_1\right)$. The second daughter radius is set to the median radius for PPC pyramidal neurons $r_2=0.75$, $L_1=50\mu m$, $L_2=25\mu m$ and diffusion length $\lambda =110\mu m$.

(C) Distribution showing the number of branches optimized for a particular diffusion length for cytoplasmic (red) and surface (blue) proteins. Shown in yellow are diffusion lengths for 26 dendritic proteins with experimentally reported diffusion coefficients and half-lives (STAR Methods). The median values of the distributions are $\lambda =65\mu m$, $\lambda =110\mu m$, and $\lambda =329\mu m$, respectively.

(D) For a given set of λ, $L_1$, and $L_2$, there is only one value of the normalized radius $r_1$ (here, $r_2=0.75$) that minimizes the total amount of proteins needed to ensure at least $N_{\text{target}}$ proteins are localized to the tips of both daughter branches. A normalized radius $r_1$ of less than the optimal $r_1$ leads to a substantial increase in the number of proteins (cost) needed to populate the dendritic arbor, whereas a higher $r_1$ value does not significantly increase the cost.

(E) Proteins with small diffusion lengths (short-diffusivity proteins) incur a larger cost for non-optimal daughter radii than those with large diffusion lengths.

Experimental methods underlying the data can be found in the STAR Methods sections Dendrite Diameter Measurement in Three-Dimensional Electron Microscopy, Hippocampal Neuron Preparation, Neuron Transfection, and Image Acquisition.