Figure 6.

Influence of Dendritic Morphology and Radius Optimization on the Distribution of Proteins

(A) Synthetic dendritic morphologies with zero, two, and eight consecutive branches.

(B) Protein number ratio between surface and cytoplasmic proteins versus distance calculated for proteins with the same diffusion coefficient and half-life. Red, blue, and green correspond to synthetic morphologies in (A). The solid black line corresponds to an average of 65 reconstructed pyramidal morphologies obtained from the NeuroMorpho database (Ascoli et al., 2007).

(C) Predicted number of proteins per micrometer in a pyramidal neuron (morphology taken from Dalrymple-Alford et al., 2015). The color code represents the predicted number of proteins per micrometer. The number of proteins in the distal parts is larger for surface proteins than for cytoplasmic proteins. Here we considered symmetrical daughter branches where the radius of a daughter dendrite is $R_1=R_2=0.75R_0$.

(D) Predicted number of proteins per micrometer for optimized radii.

(E) Dendritic trees with optimized radii need smaller protein counts to supply dendritic compartments with at least one protein per compartment.

(F) Percent cost $\left(\left(N-N_{opt}\right)/N_{opt}100\text{\%}\right)$ versus fraction of compartments supplied. The diffusion coefficient and half-life are kept constant throughout: $D=0.36\mu m^2/s$ and $T_{1/2}=5.0$ days, respectively, leading to a diffusion length of $472\mu m$ corresponding to GABA-A subunit $\alpha 2$ (Table S1).