Memory is attributed to strengthened synaptic connections among particular brain neurons, yet synaptic membrane components are transient, whereas memories can endure. This suggests synaptic information is encoded and 'hard-wired' elsewhere, e.g. at molecular levels within the post-synaptic neuron. In long-term potentiation (LTP), a cellular and molecular model for memory, post-synaptic calcium ion (Ca²⁺) flux activates the hexagonal Ca²⁺-calmodulin dependent kinase II (CaMKII), a dodacameric holoenzyme containing 2 hexagonal sets of 6 kinase domains. Each kinase domain can either phosphorylate substrate proteins, or not (i.e. encoding one bit). Thus each set of extended CaMKII kinases can potentially encode synaptic Ca²⁺ information via phosphorylation as ordered arrays of binary 'bits'. Candidate sites for CaMKII phosphorylation-encoded molecular memory include microtubules (MTs), cylindrical organelles whose surfaces represent a regular lattice with a pattern of hexagonal polymers of the protein tubulin. Using molecular mechanics modeling and electrostatic profiling, we find that spatial dimensions and geometry of the extended CaMKII kinase domains precisely match those of MT hexagonal lattices. This suggests sets of six CaMKII kinase domains phosphorylate hexagonal MT lattice neighborhoods collectively, e.g. conveying synaptic information as ordered arrays of six "bits", and thus "bytes", with 64 to 5,281 possible bit states per CaMKII-MT byte. Signaling and encoding in MTs and other cytoskeletal structures offer rapid, robust solid-state information processing which may reflect a general code for MT-based memory and information processing within neurons and other eukaryotic cells.