Morphological homeostasis in cortical dendrites

Abstract

Neurons have significant potential for the homeostatic regulation of a broad range of functional features, from gene expression to synaptic excitability. In this article, we show that dendritic morphology may also be under intrinsic homeostatic control. We present the results from a statistical analysis of a large collection of digitally reconstructed neurons, demonstrating that fluctuations in dendritic size in one given portion of a neuron are systematically counterbalanced by the remaining dendrites in the same cell. As a result, the total dendritic measure (e.g., number of branches, length, and surface area) of each neuron in a given morphological class is, on average, significantly less random than would be expected if trees (and their parts) were regulated independently during development. This observation is general across scales that range from gross basal/apical subdivisions to individual branches and bifurcations, and its statistical significance is robust among various brain regions, cell types, and experimental conditions. Given the pivotal dendritic role in signal integration, synaptic plasticity, and network connectivity, these findings add a dimension to the functional characterization of neuronal homeostasis.

Fig. 1.

Morphological homeostasis between apical and basal dendrites in hippocampal pyramidal cells. (A) Schematic representation of the one apical (Left) and five basal trees of a pyramidal cell. The numbers at the bottom are the count of terminal tips (degree). (Inset) Transversal position of the pyramidal cell in the hippocampus. The thick bar perpendicular to the cytoarchitectonic layers indicates the CA3/CA1 boundary. The position within CA3 and CA1 can be quantified as a percentage. (B) Apical and basal degree of Amaral CA3 pyramidal cells vs. their anatomical position (X > 100 correspond to field CA2). Each point of the full lines corresponds to one of the 23 cells. The dashed lines are quadratic fits. (C) Scatter plot of the difference between measured and fitted data (residual degrees). Fluctuations in basal and apical size are significantly anticorrelated. (D) Residual degree of basal (×) and apical (○) arborizations as a function of the somatic depth in the pyramidal layer (no correlation observed). (E) Scatter plot of residual degrees for Amaral CA1 cells (×) and Turner CA3 cells (⋆) analyzed as in panels A-C. A negative correlation is observed in both cases (see text for R and P values). (F) Scatter plot of residual lengths for Amaral CA3 cells (•), Amaral CA1 cells (×), and Turner CA3 cells (⋆) (values were divided by 10). A negative correlation is observed in all three cases (see text for R and P values).

Fig. 2.

Morphological homeostasis among individual basal trees in hippocampal pyramidal cells. (A) Analysis of basal tree degree as a function of the number of trees in the neuron for Amaral CA3 cells. Each point corresponds to an individual tree (small horizontal scattering has been added to improve visualization); the line represents the averages across a vertical set. The negative correlation is statistically significant (R =-0.25; P = 0.001). (B) Histogram of changes in the standard deviation of total basal degree in Amaral CA3 cells on random shuffling of basal trees among neurons with the same number of trees. The average of 1,000 runs is significantly greater than the original value of standard deviation (gray bar). The corresponding percent increase is labeled ΔSTD% in Table 1.

Fig. 3.

Morphological homeostasis in individual subtrees. (A) Schematization of the partition of the degree p of a bifurcating branch into the two daughters l and r and the four granddaughters a, b, c, and d. (B) Excess partition asymmetry for all data sets (1, Amaral CA3; 2, Amaral CA1; 3, Barrionuevo CA3; 4, Gulyás CA1; 5, Wearne Local Young; 6, Wearne Local Old; 7, Wearne Long Young; 8, Wearne Long Old; 9, Claiborne DG; 10, Turner CA1 Vivo; 11, Turner CA1 Aged; 12, Turner CA1 Vitro; 13, Turner CA3; 14, Turner DG). Averages (gray bars) and standard errors (white tops) were calculated over all bifurcations with two nonterminal daughters in all cells within each class. The numbers of such bifurcations and the P value assessing positivity of the mean are indicated over each bar. (C and D) A representation of the same analysis performed using length asymmetry and area asymmetry instead of partition asymmetry, respectively.