Separation of deterministic and stochastic neurotransmission

We analyze relations between neurobiology-based jump-diffusion model neurons and diffusion model neurons. We introduce a scaling which leads the jump-diffusion models to diffusion models, and apply an algebraic input analysis to this scaling. We show that jump-diffusion neurons, under a uniform scaling applied to all inputs, lead asymptotically to either diffusion neurons whose mean membrane potential is equal to zero, or to deterministic neurons. We modify the scaling assumptions by separate scaling of various classes of inputs. It is shown that in this case the classes of inputs can be divided into stochastic classes and deterministic classes. The deterministic classes influence only the drift of the diffusion model, and the stochastic classes influence only the diffusion function. These novel hypotheses call for experimental verification in real biological systems.