Title: Action potentials in vitro: theory and experiment

Abstract: Action potential generation underlies some of the most consequential dynamical systems on Earth, from brains to hearts. It is therefore interesting to develop synthetic cell-free systems, based on the same molecular mechanisms, which may allow for the exploration of parameter regions and phenomena not attainable, or not apparent, in the live cell. We previously constructed such a synthetic system, based on biological components, which fires action potentials. We call it "Artificial Axon". The system is minimal in that it relies on a single ion channel species for its dynamics. Here we characterize the Artificial Axon as a dynamical system in time, using a simplified Hodgkin-Huxley model adapted to our experimental context. We construct a phase diagram in parameter space identifying regions corresponding to different temporal behavior, such as Action Potential (AP) trains, single shot APs, or damped oscillations. The main new result is the finding that our system with a single ion channel species, with inactivation, is dynamically equivalent to the system of two channel species without inactivation (the Morris-Lecar system), which exists in nature. We discuss the transitions and bifurcations occurring crossing phase boundaries in the phase diagram, and obtain criteria for the channels' properties necessary to obtain the desired dynamical behavior. In the second part of the paper we present new experimental results obtained with a system of two AAs connected by excitatory and/or inhibitory electronic "synapses". We discuss the feasibility of constructing an autonomous oscillator with this system.