The idea that microtubule networks form a "cell computer" has been around since the 50s, with increasing data to support it, tough it is still in its very early days. In 2012, Craddock, Tuszynski and Hameroff described 7-tubulin memory bytes^[1], and I have put out the model for 6-tubulin bytes, and it fits with how MTs in neurons are broadly described to be in a B-lattice orientation, and also assumes that the addressing layer is external to tubulin dimers and formed from MAPS, tau proteins being one possible candidate.

New ideas need new symbols, from the cytoskeleton to the spiraeum

The idea that microtubules are a cytoskeleton is a static, older idea from the last century, and like Christopher McCandles said, call things by their right name. The word spiraeum, from Greek for breath (inspire, respiration) and cerebrum, models microtubule networks as a single integrated system, an organelle that provides cognition to the cell, and a potential seat of the soul.

The spindle apparatus as the chromatids of the spiraeum

"Boveri (1901) described the centrosome as "an autonomous permanent organ of the cell-the dynamic center of the cell-the true division center [whose] division creates the center of the daughter cell" (from Mazia 1984). " ^[2]

If cells have a "cell state", encoded in microtubule networks, in single-celled organisms like Paramecium as well as in multi-cellular organisms like humans, it seems possible that it would want to keep its cell state when it replicates into two cells, just like it wants to keep the genome state that is used over larger time-scales.

Does the spindle apparatus orient itself to the chromatids based on shared state?

The "cell state" may want to sort information based on how the genome is organized, if the spiraeum and genome act to some extent as a single integrated system, which could make things like Lamarck's idea of directed mutation possible. If so then that may be reflected in how the spindle, as two copies of the spiraeum, attaches to chromatids during cell division, separate clusters or branches associating with specific chromatids.

Synapses

1. Cytoskeletal Signaling: Is Memory Encoded in Microtubule Lattices by CaMKII Phosphorylation? (2012)

2. Microtubule Organizing Centers (1985)

3. Centrosomes and Mitotic Poles (1984)