neurophysics adrian negrean - part 1 - adrian.negrean@cncr.vu.nl

Neurophysics

Adrian Negrean

- part 1 -

adrian.negrean@cncr.vu.nl

Contents

1. Aim of this class

2. A first order approximation of neuronal biophysics

1. Introduction

2. Electro-chemical properties of neurons

3. Ion channels and the Action Potential

4. The Hodgkin-Huxley model

Introduction

(5)

(4)

(3)

(1)

(2)

1) Cell body

2) Axon

3) Apical dendrite

4) Basal dendrite

5) Synapses

histological staining of a single neuron in a rat brain (photo credits: Cristiaan de Kock, CNCR, VU, Amsterdam)

Let’s watch a brief video clip for a quick check of what you (might) know about neurons:

http://www.youtube.com/watch?v=DF04XPBj5uc&feature=related

• Neurons connect to each other via synapses

• Fast communication (a few milliseconds) occurs through Action Potentials

• Action Potentials release neurotransmitters at the synapse

• Neurotransmitters bind to “special gates” on the other side of the synapse and let

in a “flood of charged particles” which start up a new electrical signal in the receiving

neuron

• A bunch of neurons forming intricate connections allows us to think imaginatively

Q: How is this possible ? physically speaking ?!

• There is a great diversity of neurons, and

people are still struggling to classify them

Electro-chemical properties of neurons

• Membrane capacitance

d

AC 0

“ parallel plate capacitor “

• Ion-channels:

1) Leak-channels

2) Voltage-gated ion-channels

3) Ligand-gated ion-channels

4) Metabotropic ion-channels Structure of a voltage-gated potassium selective ion-channel from the Kv1.2 gene

• Electrical circuit of a simple cell having:

1) Capacitance C

2) Leak ion-channels R

3) Membrane potential Vm

…keeping in mind that there are ions instead of electrons

Na+

Na+

Na+

Cl-

Cl-

Cl-

A

Cl- permeablemembrane

water

E=0B

Na+

Na+

Na+

Cl-

Cl-

Cl-

E=ECl

• Ions and electrochemical potentials:

A) A Cl- semi-permeable membrane separates a salty solution from water

B) As time passes, Cl- diffuse, creating a potential difference

in

oution ion

ion

zF

RTE

][

][ln

where z is the valence of the ion, R is the gas constant (8.315 J K-1mol-1), T is the temperature (K), F is Faraday’s constant (96.485 C mol-1) and [ion]o and [ion]i are the

concentrations of the ion inside and outside of the cell respectively

• Nernst’s equation for equilibrium potentials:

The membrane potential of a simple cell can be calculated using this

formula if the membrane is permeable only to one ion type.

• Goldman-Hodgkin-Katz equation for equilibrium potentials:

(generalization of Nernst’s equation for membranes permeable to multiple ions simultaneously)

oCliNaiK

iCloNaoKm ClpNapKp

ClpNapKp

F

RTV ln

for example, the membrane relative permeability coefficients for the Squid Giant Axon are pK : pNa : pCl = 1.00 : 0.04 : 0.45 when the axon is at rest.

…so if you know the ion concentrations inside and outside the cell at rest

…and the relative permeability ratios

…then using the GHK equation you can calculate the resting membrane potential of the cell

but the simplest thing to do in practice is to just measure it

Intracellular and extracellular concentrations of different ions (millimoles) given in parentheses for a typical mammalian neuron and their Nernst

equilibrium potentials (mV).

• Ion-channels:

- membrane-bound proteins

- conduct ions across the membrane

- are selective for certain ions

- they open/close in response to a wide range of stimuli:

a) electrical

b) mechanical

c) chemical

d) thermal

e) optical

f) intracellular

• Ion-channel gating is a stochastic process

C: Gramicidin A peptide has been added to a

phospholipid bilayer membrane to form trans-

membrane channels that allow passage of ions.

A: The formation of functional Gramicidin A

channels can be seen as random step-increases

in current when a potential difference is applied

to the membrane. B: The size of the current

steps is related to the applied potential through

Ohm’s law.

example: an Ohmic leak channel

• when describing Ohmic single channel leak currents, the reversal potential has to be also taken into account:

revLL EEgI

single channel conductance

single channel current

membrane potential

reversal potential for the ions involved

• for the great majority of ion-channels, the single channel conductance is not constant but depends on the membrane potential

voltage-gated ion-channels

Q: So what are voltage-gated ion-channels good for ?

A: Action Potentials, among other many interesting examples

The nerve impulsewatch video:

An Action Potential propagates down the axon, and causes the release of a neurotransmitter at the synaptic cleft

watch video: Synaptic transmission

Finally the released neurotransmitter binds to ion-channels in the post-synaptic neuron, and depolarizes the cell.

Action Potential propagationwatch video:

Let’s have a closer look at what the ion-channels do during an Action Potential:

Ion-Channels involved in the Action Potentialwatch video:

main points:

1) Voltage-gated ion-channels have gates

2) These gates open/close with different

speeds

3) The opening / closing of ion-channels is

actually a change in the coformational state of

the protein

• Single-channel kinetics involved in AP production

K+ channels

- the opening of the channel requires 4 independent subunits to change conformation

kK nP

probability of a subunit to change conformation

k=4

probability for channel to be open

- the subunit open probability n is related to the membrane potential through a first order kinetic scheme

closed / open subunit conformation

voltage-dependenttransition rates

- in practice the voltage-dependent transition rates are fitted to measured data, still in this case, thermodynamic arguments give a good result

here’s the thermodynamic argument:

1) the subunit contains a charged domain q that couples to the

transmembrane electric field E=V/d

2) a movement of the subunit means that a fraction Bα from the charge

q moved within the electric field E doing a work of q BαV

3) Boltzmann statistics says that the probability to make a transition to

a state of higher energy, qBαV is proportional to:

)/exp( TkVqB B temperature

Boltzmann’s constant

energy separating the two states

thus )/exp()( TkVqBAV Bn

(in Chemistry this kind of equation is known as

Arrhenius’s law describing reaction rates)

- a similar equation can be written also for the reverse transition rate

Na+ channels

hmP kNa

k=3

- in addition to three activation subunits m they also have an inactivation

subunit h that closes the channel after a while, even if the activation subunits

are open

- same thermodynamic arguments as for the K+ channels

The Hodgkin-Huxley model of AP’s

- describes the phenomenon of Action Potential generation in neurons

- the model was applied to the Squid Giant Axon and later generalized to

other neurons

(1)

(2)

(3)

(4)

(5)time

LNaK I

LL

I

NaNa

I

KKinj EVgEVhmgEVngIVC )()()( 34

using Kirchhoff’s laws:

(the dot is a time derivative)

capacitor current

- now we have to add the single-channel gating kinetics for both Na+ and K+ as described before:

nVnVn nn )()1)((

mVmVm mm )()1)((

hVhVh hh )()1)((

110

10exp

1001.0)(

VV

Vn

80

exp125.0)(V

Vn

110

25exp

251.0)(

VV

Vm

18exp4)(

VVm

20

exp07.0)(V

Vh

110

30exp

1)(

V

Vh

- and specify also the channel conductances and reversal potentials

and the result is: