week 8, neuronal dynamics

Question 1

what is a differential equation in terms of the solution

Answer 1

Differential equations are equations where the solution is not a single number, but instead the solution is a function of time f(t).

So it would be a bunch of numbers about how something changes in time

Question 2

How to solve equations

Answer 2

1. Analytical using a pen and paper
2. Numerical using a computer. Thats what we do.

Usually when things are complex you only have the numerical, approximate solution. Comp neuro is almost always finding approximate solutions

Question 3

what is the leaky integrate and fire model

Answer 3

you model the membrane potential and the summation of firing

Question 4

Modelling membrane potential

Answer 4

Membrane potential:

Potential V is due to a difference in concentration of charged ions inside and outside the cell.

It can be increased by input currents from other neurons

Ohms law:
Voltage = Current (I) x Resistance (R)

Question 5

Neuronal firing as summation:

Answer 5

Postsynaptic neuron receiving two presynaptic inputs (j)

Neuron firing is a summation

Question 6

What is the integrate and fire model?

Answer 6

Two ingredients:
1. A differential equation describing evolution of the membrane potential
2. A mechanism to generate spikesW

Question 7

what is added to the leaky integrate and fire model

Answer 7

3. Charge slowly leaks through the membrane. This is known as leak resistance R.

Question 8

how to compare neural models to empirical data

Answer 8

You could compare to firing rate

Or you could compare to inter-spike interval (1/firing-rate)

You can consider different spiking patterns as vectors in high dimensional space and compute the notion of distance between them. There are papers describing distance specifically between different spiking trains.