Laws of conservation as related to brain growth, aging, and evolution: symmetry of the minicolumn

Abstract

Development, aging, and evolution offer different time scales regarding possible anatomical transformations of the brain. This article expands on the perspective that the cerebral cortex exhibits a modular architecture with invariant properties in regards to these time scales. These properties arise from morphometric relations of the ontogenetic minicolumn as expressed in Noether's first theorem, i.e., that for each continuous symmetry there is a conserved quantity. Whenever minicolumnar symmetry is disturbed by either developmental or aging processes the principle of least action limits the scope of morphometric alterations. Alternatively, local and global divergences from these laws apply to acquired processes when the system is no longer isolated from its environment. The underlying precepts to these physical laws can be expressed in terms of mathematical equations that are conservative of quantity. Invariant properties of the brain include the rotational symmetry of minicolumns, a scaling proportion or "even expansion" between pyramidal cells and core minicolumnar size, and the translation of neuronal elements from the main axis of the minicolumn. It is our belief that a significant portion of the architectural complexity of the cerebral cortex, its response to injury, and its evolutionary transformation, can all be captured by a small set of basic physical laws dictated by the symmetry of minicolumns. The putative preservations of parameters related to the symmetry of the minicolumn suggest that the development and final organization of the cortex follows a deterministic process.

Keywords: cerebral cortex; minicolumns; neocortex; symmetry.

Figure 1

Box plots of minicolumar width measurements in Brodmann area 17 (human). Width was estimated using a single section of Nissl-stained tissue cut along one of the three principal axes. Materials for this study included 8 brains cut in the transverse plane (4 male, 4 female, age 40–72 years), 15 brains cut in the coronal plane (10 male, 5 female, age 1–94 years), and 11 brains cut in the sagittal plane (5 male, 6 female, age 4–87 years). Minicolumnar width was estimated using computerized image analysis of micrographs of these regions of interest (Casanova and Switala, 2005). There was one possible outlier at 33.3 μm in the sagittal plane. There is no significant dependence of width estimates on the plane of section (F_2,8 = 1.05; p = 0.410).

Figure 2

Little change is seen in minicolumnar structure among 19 persons with a range of ages at death from 4 months to 98 years. The neuropil distribution is derived from the empirical “linear contact distribution,” the distribution of distances from points within the neuropil to the nearest Nissl-stained object, measured along a line with fixed orientation (Casanova et al., 2007). Taking the orientation parallel to the minicolumar axis, the median of the distribution is termed the radial neuropil space s_R, while the same measurement in the orthogonal direction (parallel to the laminar boundaries) provides the tangential neuropol space s_T. Mean s_T/s_R (solid curve) was estimated with a smoothing spline over measurements (points) from up to 6 cortical areas in each of 19 individual brains. The ratio of tangential neuropil space s_T to radial neuropil space s_R remains nearly constant at approximately 0.8 throughout the human lifespan.

Figure 3

We identified the minicolumns in each of 192 micrographs (the same material as was used for Figure 5, excluding individuals on the autistic spectrum) using a line tracing method that groups cells into minicolumns by finding the shortest cell-to-cell paths from one end of the layer to the next (Casanova et al., 2009a). Using the clusters so identified, cell dispersions about the minicolumnar axes were compared to a chi-square distribution with one degree of freedom, which is what one would expect if the neurons were located at random positions in space under a symmetric distribution. The mean displacement of neurons from the minicolumnar axis was very nearly zero, consistent with symmetry; however, the empirical distribution of C² was far from chi-square distributed (Kuiper V = 0.932; p < 0.0001). Examination of a q–q plot confirmed that observed C² were smaller and under-dispersed relative to the expected χ². We suspect this is due to the bias inherent in image processing – as opposed to stereology – and that accurate localization of both neurons and the minicolumnar axis in three-dimensional space is necessary for a proper test of the symmetry hypothesis.

Figure 4

Relationship between average size of minicolums and pyramidal cells. Material included 55 micrographs of Nissl-stained human tissue comprising Brodmann areas 4, 9, 17, 21, 22, and 40; and 19 micrographs of area 17 in the macaque. The average cross-section of pyramidal cell somata is positively correlated with the minicolumnar width estimated from the same set of micrographs. Minicolumnar width was estimated using our established methodology (Casanova and Switala, 2005), while the average neuronal cross-sectional area was estimated using the Boolean model (Casanova et al., 2006). The high degree of linear correlation (r = 0.913; p < 0.0001) is evident.

Figure 5

Relationship between average size of minicolumns and pyramidal cells, revisited. Material included 270 micrographs of Nissl-stained human tissue from up to 16 cortical areas in each of 8 brain donors with autistic spectrum disorder and 10 neurotypical comparison clients. In this instance, mean pyramidal cell cross-section was calculated directly from the segmented neurons used to identify minicolumns. Correcting for the effects of diagnosis, cortical area, and lamina (II–VI), minicolumnar width varies strongly with mean cell cross-section (F_1,1187 = 2417; p < 0.0001).