An analytical study of relay neuron's reliability: dependence on input and model parameters

Abstract

Relay neurons are widely found in our nervous system, including the Thalamus, spinal cord and lateral geniculate body. They receive a modulating input (background activity) and a reference input. The modulating input modulates relay of the reference input. This modulation is critical for correct functioning of relay neurons, but is poorly understood. In this paper, we use a biophysical-based model and systems theoretic tools to calculate how well a single relay neuron relays a reference input signal as a function of the neuron's electro physiological properties (i.e. model parameters), the modulating signal, and the reference signal parameters. Our analysis is more rigorous than previous related works and is generalizable to all relay cells in the body. Our analytical expression matches relay performance obtained in simulation and suggest that increasing the frequency of a sinusoidal modulating input or decreasing its DC offset increases the relay cell reliability.

Fig. 1. Block diagram of a Relay Neuron

It receives two inputs 1. reference input r(t) and 2. modulating input u(t), and generates one output V (t).

Fig. 2. A. Phase-Plane diagram B. Steady State Orbit and The Orbit Tube of a Relay Neuron

A. The v-nullcline denotes the collection of points where Ẋ₁ = 0 and the h-nullcline is where Ẋ₂ = 0. These two lines divide the phase-plane into four different regions marked by balck arrows. In each region, the black arrows indicate the direction in which the state vector evolves. B. Shows the steady state orbit and the orbit tube of a relay neuron

Fig. 3. Successful Spike, Unsuccessful Spike and Time to Resting State

A. The time profile of a successful spike (1) and unsuccessful spikes (2,3). T_r is the time between spike onset and point where system state enter orbit tube at point X_r. B. Successful spike and unsuccessful spike in the phaseplane. C. 𝕏_s and 𝕏_us. Note that unsuccessful spike(2) occurs as a result of the reference pulse occurring when X ∉ 𝕏_r.

Fig. 4. R vs ω/2π

Solid line is from the (18). Dotted line is plotted by running simulations on (1), for different ω.