A biological junction with quantum-like characteristics

A model of chemical synapse as an electric junction is proposed. Estimations and analysis of the model show that the junction has unique physical characteristics reminding the Josephson junction. The basic assumption is made that the electric coupling across the synaptic gap is indirectly provided by means of approximately quantized portions of a chemical mediator, each the portion is content of a synaptic bubble. We suppose that effective quantum of charge is q, |q| ≫ |e|. The synapse characteristics are dominated by electrostatic energy, Q/2C, Q = qN , N = 0, 1, 2...; where C is electric capacity of membrane. Estimations show that the integer-valued character of N must be explicitly taken into account. The consistent theory of the junction is constructed on the basis of operator realization of number-phase canonical pair in the Hardy space. The charge passing from one side of the junction to other is described by the Toeplitz operators. The synapse state space is constructed explicitly. The unique physics of the model is investigated in detail. We do not exclude the possibility that the model is prototype of a molecular electronics device.