3 Neurophisiology

ions are always enveloped by a hydrate layer due to the dipole characteristics of water molecules, and thus cannot pass across the lipid bilayer membrane.

C = ε0 • ε •A •d-1

• unit Farad (F) = Coulomb • Volt^-1

• ε0 = dielectricity constant of vacuum,

• ε = dielectricity constant of the membrane,

• A = membrane area,

• d = membrane thickness

the thinner the membrane, the larger the membrane area, and the higher the dielectricity constant, the more charges can be stored.

Ion channels are transmembrane proteins that form a hydrophilic pore across the membrane. This is achieved by charged amino acids in the center of a large three-dimensional protein that form a charged (and therefore hydrophilic) tunnel which allows the ions to pass.

If selective, the entrance of the channel carries charges that repel the „wrong“ charges, and the center of the pore has a diameter (and possibly additional charges) that restrict the passage further.

Ligand-gated: open/close when ligand binds

Voltage-gated: open/close when electric field changes

• E= potential,

• R = gas constant,

• T = temperature in °Kelvin,

• n = number of charges per ion,

• F = Faradayconstant

The Nernst-equation computes the resulting voltage for given chemical gradients, provided enough time is given

In this equilibrium, both chemical and electrical gradient are in balance.

The voltage-gated sodium channel is special: it possesses two gates. One (the „m“- gate) is controlled by the voltage across the membrane; if this gate is opened, it triggers the closing of a second gate (h-gate) which shuts ca. 1 ms afterwards. Refreshing the channel (=reopening of the h-gate) takes time: a refractory period.

a = resting potential

b = Depolarization

c = upstroke

d = plateau

e = Repolarization and afterhyperpolarization

GNa= sodium permeability

GK= potassium permeability

h: = value describing the possibility to open Sodium-channels by voltage. Note that long after the action potential, h is still decreased, resulting in the refractory period where the cell is first not excitable and then only excitable by strong depolarization

Summary of the action potential

1. A neuron is at resting potential.

2. Sodium channels open (e.g., by binding a ligand such as a neurotransmitter)

3. A sodium influx results that depolarizes the neuron.

4. As soon as the threshold of the first voltage-gated (vg) sodium channel is reached, it opens and additional sodium flows in that depolarizes the cell further.

5. A positive feedback couples opening of vg sodium channels, sodium influx and further depolarization and leads to a fast increase in sodium permeability.This leads to the upstroke of the action potential.

6. The voltage-gated sodium channels close after ca 2 msec (GNa goes back to 0).

7. Now potassium permeability is increased through opening of delayed vg potassium channels that were activated in parallel to the vg sodium-channels.

8. Inactivation of vg sodium channels and delayed opening of vg potassium channels lead to a repolarization.

9. After the action potential, the membrane potential temporarily falls beneath the regular resting potential, since both leak channels and vg channels for potassium are open; this is called an afterhyperpolarization.

10.Only after the vg potassium channels have closed after a delay (closing caused by the voltage returning to resting potential, the former resting potential is reached.

Hyperpolarization is caused by efflux of K+ through K+ channels

they do not open simultaneously during an action potential because they have different activation and inactivation kinetics — in other words, they open and close at different speeds.

This temporal separation ensures the proper sequence of events in an action potential:

1. Rapid depolarization (Na⁺ in),

2. Repolarization (K⁺ out),

3. Return to resting state.

• A passive (or electrotonic) conductance that is not regenerative and decreases with time and distance. The conduction velocity is fast.

• An actively regenerated potential (action potential) that is actively generated by the voltage-gated channels of the neuron. The propagation of action potentials is comparatively slow, since the signal needs to be regenerated at each membrane area.

• Both types of potentials are propagated differentially in neurons.

The „range“ of the depolarization can be increased by either

1. Increase of the membrane resistance (Rm) by isolation (myelinisation)

2. Decrease of the inner resistance (Ri) relative to Rm : giant fibers (Membrane surface (=Rm) increases with radius, membrane area (Ri) however with radius² )

no isolation reduces membrane resistance and increases the capacitance of the membrane

• giant fibers (where Ri is small due to the large diameter), mostly in invertebrates

• isolation of the fiber increases Rm and decreases the capacitance of the membrane (=Myelinisation; mostly in vertebrates).

saltatory conduction.

The measure for the range of a depolarization is the length constant λ.

λ = Rm/Ri or the distance (in cm), where the depolarization is reduced to 37% of its original value.

membrane resistance (Rm)

inner resistance (Ri)

- isolation of the fiber increases Rm and decreases the capacitance of the membrane

Thick fibers have relatively smaller restistance along the fiber than resistance across the membrane compared to thin fibers

• transmitter

• receptor

• ion gradients at the postsynaptic membrane

• Ca flows through the activated channels in the head

• since diffusion along the neck is restricted

• the resulting concentration change in the head is huge enough to trigger molecular cascades