  Neurons in many brain areas can develop pronounced depolarized state of
membrane potential (up state) in addition to the normal hyperpolarized down
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 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.
