Microtubules and actin fibres are dynamic fibres constituting the cell skeleton. They show seemingly computational behaviours. Indeed, depending on conditions of reaction, they self-organise into temporal and/or spatial morphologies in vitro and act as micro-machine processors and actuators in living cells. I discuss here about their possible reuse to construct microtubule-based computational systems. I analyze particularly the possible existence of computational events based on 'chemical collision' between microtubules. A molecular model of microtubule disassembly has been developed to verify that heterogeneities of composition and/or concentration of the chemical medium can form from shrinking microtubules and persist. They could serve as an efficient communication channel between microtubules. numerical simulations show that diffusing tubulin molecules can explore large distances (0.5 μm) during the disassembly of only one molecule. This leads to the formation of only very weak heterogeneities of composition. However, the model predicts that they could be more important due to microtubule arrays.