A Biophysical Model of Adaptive Noise Filtering in the Shark Brain

Abstract

Sharks detect their prey using an extremely sensitive electrosensory system that is capable of distinguishing weak external stimuli from a relatively strong background noise generated by the animal itself. Experiments indicate that part of the shark’s hindbrain, the dorsal octavolateralis nucleus (DON), is responsible for extracting the external stimulus using an adaptive filter mechanism to suppress signals correlated with the shark’s breathing motion. The DON’s principal neuron integrates input from afferents as well as many thousands of parallel fibres transmitting, inter alia, breathing-correlated motor command signals. There are a number of models in the literature, studying how this adaptive filtering mechanisms occurs, but most of them are based on a spike-train model approach.

This paper presents a biophysically based computational simulation which demonstrates a mechanism for adaptive noise filtering in the DON. A spatial model of the neuron uses the Hodgkin–Huxley equations to simulate the propagation of action potentials along the dendrites. Synaptic inputs are modelled by applied currents at various positions along the dendrites, whose input conductances are varied according to a simple learning rule.

Simulation results show that the model is able to demonstrate adaptive filtering in agreement with previous experimental and modelling studies. Furthermore, the spatial nature of the model does not greatly affect its learning properties, and in its present form is effectively equivalent to an isopotential model which does not incorporate a spatial element.

Appendix:  Hodkgin–Huxley Equations

$$\begin{aligned} C_\mathrm{m}\frac{dV}{dt}&=-\bar{g}_\mathrm{K}n^4(V-V_\mathrm{K})- \bar{g}_\mathrm{Na}m^3h(V-V_\mathrm{Na})- \bar{g}_\mathrm{L}(V-V_\mathrm{L}) + I_\mathrm{app}(t), \end{aligned}$$

(22)

$$\begin{aligned} \frac{dm}{dt}&=\alpha_m(1-m)-\beta_mm, \end{aligned}$$

(23)

$$\begin{aligned} \frac{dn}{dt}&=\alpha_n(1-n)-\beta_nn, \end{aligned}$$

(24)

$$\begin{aligned} \frac{dh}{dt}&=\alpha_h(1-h)-\beta_hh, \end{aligned}$$

(25)

$$\begin{aligned} \alpha_m&=0.1\frac{V+40}{1-\exp{ (\frac{-(V+40)}{10} )}}, \end{aligned}$$

(26)

$$\begin{aligned} \beta_m&=4\exp{ \biggl(\frac{-(V+65)}{18} \biggr)}, \end{aligned}$$

(27)

$$\begin{aligned} \alpha_h&=0.07\exp{ \biggl(\frac{-(V+65)}{20} \biggr)}, \end{aligned}$$

(28)

$$\begin{aligned} \beta_h&=\frac{1}{1+\exp{ (\frac{-(V+35)}{10} )}}, \end{aligned}$$

(29)

$$\begin{aligned} \alpha_n&=0.01\frac{V+55}{1-\exp{ (\frac{-(V+55)}{10} )}}, \end{aligned}$$

(30)

$$\begin{aligned} \beta_n&=0.125\exp{ \biggl(\frac{-(V+65)}{80} \biggr)}. \end{aligned}$$

(31)

Table 2 Parameters for the Hodgkin–Huxley equations (Paulin 2005)