Performance Limitations of Relay Neurons

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 transmitted while the modulating input alters the specifics of transmission. For example, the visual thalamus contains relay neurons that receive driving inputs from the retina that encode a visual image, and modulating inputs from reticular activating system and layer 6 of visual cortex that control what aspects of the image will be relayed back to visual cortex for perception. What gets relayed depends on several factors such as attentional demands and a subject's goals. In this paper, we analyze a biophysical based 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. We assume that the modulating input belongs to a class of sinusoidal signals and that the driving input is an irregular train of pulses with inter-pulse intervals obeying an exponential distribution. Our analysis applies to any order model as long as the neuron does not spike without a driving input pulse and exhibits a refractory period. Our bounds on relay reliability contain performance obtained through simulation of a second and third order model, and suggest, for instance, that if the frequency of the modulating input increases or the DC offset decreases, then relay increases. Our analysis also shows, for the first time, 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. In our discussion, we describe how our bounds predict experimentally observed neural activity in the basal ganglia in (i) health, (ii) in Parkinson's disease (PD), and (iii) in PD during therapeutic deep brain stimulation. Our bounds also predict different rhythms that emerge in the lateral geniculate nucleus in the thalamus during different attentional states. Author Summary: In cellular biology, it is important to characterize the electrophysiological dynamics of a cell as a function of the cell type and its inputs. Typically, these dynamics are modeled as a set of parametric nonlinear ordinary differential equations which are not always easy to analyze. Previous studies performed phase-plane analysis and/or simulations to understand how constant inputs impact a cell's output for a given cell type. In this paper, we use systems theoretic tools to compute analytic bounds of how well a single neuron's output relays a driving input signal as a function of the neuron type, modulating input signal, and driving signal parameters. The methods used here are generally applicable to understanding cell behavior under various conditions and enables rigorous analysis of electrophysiological changes that occur in health and in disease.