Generalizing performance limitations of relay neurons: application to Parkinson's disease

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. Relay reliability of a relay cell is defined as the fraction of pulses in the driving input that generate action potentials at the neuron's output, and is in general a complicated function of the driving input, the modulating input and the cell's properties. In a recent study, we computed analytic bounds on the reliability of relay neurons for a class of Poisson driving inputs and sinusoidal modulating inputs. Here, we generalize our analysis and compute bounds on the relay reliability for any modulating input. Furthermore, we show that if the modulating input is generated by a colored Gaussian process, closed form expressions for bounds on relay reliability can be derived. We applied our analysis to investigate relay reliability of thalamic cells in health and in Parkinson's disease (PD). It is hypothesized that in health, neurons in the motor thalamus relay information only when needed and this capability is compromised in PD due to exaggerated beta-band oscillations in the modulating input from the basal ganglia (BG). To test this hypothesis, we used modulating and driving inputs simulated from a detailed computational model of the cortico-BG-thalamo-cortical motor loop and computed our theoretical bounds in both PD and healthy conditions. Our bounds match well with our empirically computed reliability and show that the relay reliability is larger in the healthy condition across the population of thalamic neurons. Furthermore, we show that the increase in power in the beta-band of the modulating input (output of BG) is causally related with the decrease in relay reliability in the PD condition.