#import "../preamble.typ": *
 
#show: conf.with(num: 1)

= Membrane Potential

Outside the cells in the brain there is salt.
Inside there is potassium.

== Prerequisites for a Neuron to fire

_Watch the embedded movie._

There are different potentials build up in the membrane.

+ The charge is in equillibrium. But there is a gradient of Pr and Cl
+ Cloride will diffuse $==>$ on that side there are too many negative charges
+ The negative charge pushes the potassium to this side
+ Finally a potassium gradient stabilizes

Why is the resulting potential negative?

== Nernst and general Nernst eqation 
$
	V_(x) = (R T) / (z F) ln ([X]_(o) ) / ([X]_(i) ) \
	V_(x) = (R T) / (z F) ln (P_("K") [K]_(o) + P_("Cl") ["Cl"]_(o) + ...  ) / (P_("K") [K]_(i) + P_("Cl") ["Cl"]_(i) + ... ) \

$

When the permeability for the potassium is low then the other ones play a bigger role.
Potential is only there when permeability is existing.

Q: What is similar to a low pass filter.

In reality there are multiple conducters connected in parralel. Also the conductivity of the Na and K channles are changable.

Q: What does a conductivity of $oo$ mean?

= Hodgkin and Huxley

Q: What have they done?
A: They used squids to measure the axons, because they are $1"mm"$ thick

Types of Neuronal Recording Methods
- EEG (on top of the head)
- ECoG (small hole in the head)
- Extracellular (needles in the brain)
- Intra cellular (needles in the cell of the brain)

== Action Potential

+ The cell gets excited
+ Chainreaction of channel opening and gradient stabilisation
	- Sodium channels open
	- K chanels open
	- Na channels become refactory
	- ...
+ Refactory period
+ ...

#highlight[TODO: continue the steps]

Currents can add up to trigger an AP. THe refactory period is the time after an AP when Na channles are inactive. The firing rate is increaed with a highter input strenght.

The lenght of the potiential depends on the type of cell. Then the refactory period is also longer. \
The maximum firing rate is limited by the absolute refactory period.

== The actual model

$
	I_("inj") = I_(C) + sum I_(k) (t) , space C = Q/u , space I_(C) = C (dif u) / (dif t) = C (dif V) / (dif t) \
	I_(x) = I_(x) \
	C (dif V_m ) / (dif t) = - sum I_(k) +  I_("inj") (t) \
	sum I_k = g_("Na") (V_m - V_("Na") )+ g_(K)  (V_m - V_(K) )+ g_(L) (V_(m) - V_(L)  )\
	C (dif V_m ) / (dif t) = - g_("Na") (V_m - V_("Na") )- g_(K)  (V_m - V_(K) )- g_(L) (V_(m) - V_(L)  ) + I_("inj") (t) \
$

Now the Equation becomes time dependent

$
	C (dif V_m ) / (dif t) = - macron(g)_("Na") m^(3) h  (V_m - V_("Na") )- macron(g)_(K) n  (V_m - V_(K) )- macron(g)_(L) (V_(m) - V_(L)  ) + I_("inj") (t). \
	dot(x)= - (1) / (tau_(x)  u_(b))  A .
$

Capacitance is a biological constant.

== Voltabe clamp method

With this method it is possible to stimulate a cell and measure the floating current at the same time.

There are substances to kill certain types of channels in the cell. If done so the graph of the potential changes.

Also there is a method to measuer individual channels and their current they leave through.The AP is a positive feedback loop.

The sodium channels cannot immeadiately open again. It takes about 1ms for them to open again. When measuring one always measurers multiple fibres (Suberposition).

In the heart there are calcium channels.

_Max firing frequency is about $1"kHz"$_

== Propagation of AP

There are multiple Methods of propagation the AP. One is to recreate the AP along the way (this takes time but is faster with higher diameter of the axon).

The other method is the saltatory "jumpy" conduction. This is much faster and the AP jumps between the isolations.


