PMC

Spine necks forming regular linear arrays over the shaft surface. Shown are glancing confocal sections from dendritic shafts of the weaver (A) and the wild-type mouse (B). Direction of the shaft axes is vertical. (Scale bar, 1.0 μm.)

Schematic drawing of helically arranged spines projecting into a field of parallel-fiber axons (hexagons). The axial rise per spine is similar to the center-to-center separation of the axons, and spineheads are equally separated around the shaft, penetrating by varying amounts into the axon field. This geometry maximizes the opportunity for each spine to contact a new axon not approached by neighboring spines.

Low-magnification in-plane views of 3,3′-dioctadecyloxacarbocyanine perchlorate-labeled Purkinje cells. Mormyrid fish (A), weaver mouse (B), and wild-type mouse (C) cerebellum. Shown are the typical patterns formed by the spiny dendrites ascending from the cell bodies (bottom) through the molecular layer. The fish dendrites are straighter and less branched than the others, but some weaver dendrites are also straight over lengths of 20-30 μm (arrows). (Scale bar, 50 μm.)

Helical representations of (idealized) spine distributions in densely populated regions along the distal dendrites. The dots tracing helices denote the locations of spines on the dendrite surface, scaled in proportion to the experimental measurements; helical nets next to the helices plot the corresponding surface lattices (a and b are the unit cell vectors). (A) Fish dendrite (5.7 spines per turn, 1.0-μm-diameter shaft). (B) Mouse dendrite (10.7 spines per turn, 2.0-μm-diameter shaft). (C) Two-start helix (9.1 spines per turn, 1.5-μm-diameter shaft). (D) Surface lattice in B plotted at a radius of 3 μm (i.e., 3R) from the axis of the shaft; at this radius (corresponding to the spineheads), each lattice point is approximately equidistant from each of its neighbors.

Dendrites of both the weaver and wild-type mouse exhibit the same regular features as those of the fish. (A-D) Weaver.(E-H) Wild type. (A and E) Images of straight shafts densely populated with spines. (B and F) Corresponding diffraction patterns. (C and G) Filtered images. (D and H) Helical projections simulating the paths traced by the spines. Arrows point to diffraction peaks associated with periodicities in the images; numbers indicate helical pitches; horizontal bars and pair of arrows in A identify, respectively, repeating features close to the shaft surface and a line of spines. [Scale bar (original and filtered images), 1.0 μm.]

The periodicities on the fish dendrites trace helical paths. (A) Two adjacent shafts from the same Purkinje cell (horizontal bars identify the clearest repeat). (B) Diffraction patterns from the “boxed-off”regions i, ii, and iii in A, showing pairs of peaks (arrows) similar to those in . The peaks in i are approximately twice as far apart as those in ii and iii, because they are associated with a different (two-start) helical symmmetry. (C) Corresponding filtered images, together with helical projections (see Materials and Methods), simulating the paths followed by the spines. Both one- (ii and iii) and two-start helices (i) are present. The numbers indicate the helical pitches. (Scale bar, 1.0 μm.)

Regular features along the dendritic shaft of the fish. (A) Spine necks forming regular linear arrays over the shaft surface, revealed in glancing confocal sections (shaft axis is vertical). (B) Periodic arrangement incorporating linear arrays of spines (e.g., circles) in a region of high population density. (C) Diffraction pattern of B, showing two pairs of peaks arranged with approximate mirror symmetry about a vertical axis; the distance of these peaks from the equator indicates that the periodicities repeat every 1.25 μm. (D and E) Filtered images revealing the paths traced by lines of spines on the near (N) and far (F) sides of the shaft, made by including only terms associated with the separate pairs of peaks within the masks (see Materials and Methods). (F) Filtered image made by including terms within all of the masked areas in C; the pair of vertical lines indicate the radius at which the modulations have the greatest contrast. Here and in Figs. , , , and , the contrast has been inverted so that areas of high fluorescence appear dark. (Scale bars, 1.0 μm.)