Using linear systems theory to study nonlinear dynamics of relay cells

Relay cells are prevalent throughout sensory systems and receive two types of inputs: driving and modulating. The driving input contains receptive field properties that must be relayed while the modulating input alters the reliability of this relay. In this paper, we analyze a biophysical based nonlinear model of a relay cell and use systems theoretic tools to construct analytic bounds on how well the cell transmits a driving input as a function of the neuron's electrophysiological properties, the modulating input, and the driving signal parameters. Our analysis applies to both 2 ^nd & 3 ^rd order model as long as the neuron does not spike without a driving input pulse and exhibits a refractory period. Our bounds suggest, for instance, that if the frequency of the modulating input increases and the DC offset decreases, then reliability increases. Our analysis also shows how the biophysical properties of the neuron (e.g. ion channel dynamics) define the oscillatory patterns needed in the modulating input for appropriately timed relay of sensory information.