Simplified dynamics of human and mammalian neocortical neurons

The behavior of human and mammalian neocortical neurons is governed by the interplay of approximately a dozen ion currents. Due to the complexity of the resulting dynamics, it is sometimes advantageous to resort to simpler systems in order to gain insight into the relationship between underlying dynamical principles and biophysics. This paper presents a new and extremely simple approximation to the dynamics of neocortical neurons based on just four simulated ion currents: I(Na), I(K), I(T), and I(AHP). The formulation incorporates Ohm's law plus explicit representation of Na(+), K(+), and Ca(2+)equilibrium potentials, yet mathematical simplicity is retained by restriction of the dynamics to cubic nonlinearities. The resulting equations produce a good approximation to spike shapes, firing rates, and bursting behavior throughout the physiological range. Analysis of the equations suggests that four unique dynamical regimes form the basis for different categories of neocortical neurons. Synaptic coupling between these model neurons demonstrates their potential utility in simulations by producing network models of bursting and of short-term memory function.