An example of an aperiodic tiling with 5-fold local symmetry.
Neuron neurotransmitter receptors are in general pentameric. This enables them to form pentagonal components in biological quasicrystals (similar to mathematical aperiodic tilings). As quasicrystals have been proposed to require quantum effects to exist this might introduce such effects as a component of neurotransmission and thus consciousness. Microtubules may play a role in the clustering of the receptors into quasicrystals, thus modulating their function and may even form quasicrystals themselves. Other quaiscrystals in neurons are potentially formed by water, cholera toxin complexes, and the cytoskeletal components actin and ankyrin.
Quasicrystals and Consciousness
The pentagon is a form found commonly in nature, in everything from flowers to hurricanes. It (or rather the pentacle) is also the shape of the path described by Venus in the night sky which has led to its association with witchcraft and devilry. Aperiodic tilings in mathematics have been attracting interest as they reflect the structures found in various metallic alloys called quasicrystals. Yet another example of where mathematical concepts have expression in the physical world. These structures, like aperiodic tilings (Fig. 1), have local 5-fold symmetry but overall a crystal structure. Under the rules of traditional physics they should not exist. Crystalline forms are nature seeking the lowest energy configuration. Roger Penrose has proposed that, since coordination of subunits in quasicrystals requires a global solution, non-localized quantum effects are at play.1