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

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.