Biology of Memristor Minds

Abstract : During the past 3 years, we have exploited the memristor's enabling potentials for designing intelligent machines with learning and adaptive capabilities. We have conducted an in-depth study of the nonlinear dynamics of several ion-channels which underpins the biological basis of life itself, where voltage-gated ion channels, with their complex biochemical synaptic dynamics, are memristors. We have discovered that the Hodgkin-Huxley axon is made of memristors, in addition to conventional circuit elements. In particular, we have proved that the potassium voltage-gated ion channel is a first-order voltage-controlled memristor, and that the sodium voltage-gated ion channel is a second-order voltage-controlled memristor. We have derived the DC V-I curves of the potassium and sodium ion channels, as well as that of the Hodgkin-Huxley Axon. The most significant result of our 3-year research is our derivation of the memristor-based Hodgkin-Huxley Axon circuit model, which along with our principle of local activity and its gem, the edge of chaos, allow us to resolve 3 fundamental unsolved problems from Neurobiology, including the precise nonlinear dynamical mechanism which gives rise to the action potential.