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

Abstract

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.

Fig. 1. Successful and unsuccessful response.

Examples of successful and unsuccesful response for a relay neuron. The neuron must produce one or more action potentials (i.e., a burst) within W ms of a pulse in driving input in order to successfully relay information.

Fig. 2. Region of interest.

A) Evolution of the membrane potential of the thalamic neuron right after a burst of action potentials. B) Zoom in of the region of interest. Right after generating an action potential, the membrane potential hyperpolarizes and enters the refractory zone (i.e., it cannot generate an action potential). After time T_R the voltage recovers and the neuron is ready to fire again. In this study $T_R\simeq 100\hspace{0.17em}\text{ms}$.

Fig. 3. Cortico-BG-thalamo-cortical loop.

Red, black, and green arrows are glutamatergic, GABAergic, and dopaminergic projections, respectively. The anatomical structures explicitly modeled are depicted with black boxes (number of neurons reported inside each box), while the remaining nuclei are depicted with gray boxes. GPe (GPi)=external (internal) globus pallidus; SNpc=substantia nigra pars compacta; STN=subthalamic nucleus.

Fig. 4. Modulating and driving inputs.

Modulating (A,B) and driving (C,D) inputs in healthy (A,C) and PD (B,D) conditions. The same modulating input drives all the thalamic neurons, while each neuron receives different cortical inputs, as in raster plot.

Fig. 5. Statistical properties of the modulating input.

Histogram of the values of the modulating input in healthy (A) and PD (B) conditions.

Fig. 6. Modulating input and the neuron’s transfer function.

A) Power spectrum P_h(ω) of the modulating input in healthy and PD conditions. B) Power spectrum P_G(ω) of the transfer function of the thalamic neuron.

Fig. 7. Relay reliability in healthy and PD.

Theoretical and numerical bounds on the relay reliability in healthy (A) and PD (B) conditions. The theoretical bounds are calculated assuming a colored Gaussian modulating input. Solid black lines denote numerically computed relay reliability across 10 thalamic neurons with 95% error bars, dashed lines are theoretical lower and upper bound on the reliability across 10 thalamic neurons.