Check Sum Computing in Doubly Frustrated Microtubule Clusters

Abstract

The hitherto unexplained presence of 12 or 13 tubulin dimmers forming parallel protofilament subunits in microtubules (MTs) is supposed to ensure sum checking in the system of two MTs, each one being a potential computing ‘core’. The recently proposed, frustration – originated, double well potential is mapped, exclusively for modelling reasons, onto the Ising – type Hamiltonian acting in the rings with an intra-site nearest neighbours interaction. We infer that the final state of energetically favourable 12 qubit ‘calculation’ at physiological temperature is randomly ‘corrected’ by the conjugated nearest 13 qubit ‘core’ (via inter-site, as yet indeterminate, long-rage interaction) in the double MT cluster. Helmholtz free energy is calculated to show that such computing cluster lowers the system demands for ATP energy while retaining the possibility of higher accuracy calculations. By performing calculation for two model systems, we find the frustration – originated energy enhancement at physiological temperatures of the human brain for the semi-classical system against the corresponding quantum one. Also, existing studies have not clearly dissociated the neural processes supporting short- and long-duration memories – we propose a possible localization of durable/flash memory in MTs, through introducing a double frustration concept. By extension to double frustration description it may be meaningful to make the next intuitive leap to the question of quantum computing and its possible function in a theory of consciousness.