A Computational Approach To Understanding the Neuronal Control of Leech Swimming

LEECH SWIM INITIATION PATHWAY

Cell TR1 SWIM VARIABILITY

SOURCE OF VARIABILITY

PURPOSE

- Quantify pattern of neuronal activity in the leech CNS that predicts swimming by Tr1 stimulation.
- Determine whether the nervous system have to be in a specific 'state' for swimming to be triggered.
- Determine whether the activity pattern in the leech CNS that predicts swimming is the same when swimming follows Tr1 stimulation or occurs spontaneously.

EXPERIMENT

- Preparation
- Physiological Results

NONLINEAR TIME SERIES ANALYSIS

Background

Lorenz

dx/dt = a (y – z)

dy/dt = x (R – z) – y

dz/dt = xy – bz

where a = 16, R=45.92, and b=4.

Time series plot

State space

Embedding

Suppose we have a time series,

x(t) = {x_{1}, x_{2}, …, x_{N}}

let m = 3, and L = 5,

We get vectors of the form;

X_{1} = (x_{1}, x_{6}, x_{11})

X_{2} = (x_{2}, x_{7}, x_{12})

X_{3} = (x_{3}, x_{8}, x_{13})

ß

X_{n} = (x_{N-11}, x_{N-5}, x_{N})