Impact of membrane bistability on dynamical response of neuronal populations

Neurons in many brain areas can develop a pronounced depolarized state of membrane potential (up state) in addition to the normal hyperpolarized state near the resting potential. The influence of the up state on signal encoding, however, is not well investigated. Here we construct a one-dimensional bistable neuron model and calculate the linear dynamical response to noisy oscillatory inputs analytically. We find that with the appearance of an up state, the transmission function is enhanced by the emergence of a local maximum at some optimal frequency and the phase lag relative to the input signal is reduced. We characterize the dependence of the enhancement of frequency response on intrinsic dynamics and on the occupancy of the up state.