Nerve Excitation

Topic II-2

Biophysics

Neurons

• Nerve signals due to modulations of membrane potential• Motor Neurons have dendrites

Motor neuron

Sensory neuron

History

• Hodgkin and Huxley observe membrane potential reverses during pulse and goes to +100 mV

• They also see that conductance of membrane increases 40X and propose have transient changes in Na and K conductance → Nobel Prize

Calamari Andrew Fielding Huxley

Alan Lloyd Hodgkin

Action potential is electrical pulse that travels much slower than electrical current

K+ and especially Na+

play big role

Hodgkin and Katz: as [Na+] decreases velocity of action potential decreases

Voltage Clamp

• Measure current to keep voltage constant

• INa = gNa(Vm – VNa), IK = gK(Vm -VK), IL = gL(Vm – Vk)

• Voltage Clamp makes IC = Cm dV/dt = 0

• Itot = INa + IK + IL (with clamp)

• Vm = Vh = 1/gtot (gKVK + gNaVNa + gLVL + I), clamp and look at I

Positive current: + ions out of axon

VK = -72 mV,

VNa = + 55 mV

V = Vin - Vout

Voltage Clamp experiments

•Set concentrations of ions so can get Nernst potentials equal membrane potential and reduce variables

•gNa, gK ~ 0 at resting potential and they are only activated when the axon is depolarized (becomes less negative). H&H get gL when hyperpolarize

•I = IL = gL (Vm – VL), VL < Vresting (-60 mV)

Action Potential

1. Resting Na m gate closed h gate open; n-gate closed

2. Sufficient initial depolarization →

open m-gate, Vm → VNa;

3. h gate closes (inactivation) and K n-gate opens, Vm → Vk

4. n-gate closes and h-gate opens (de-inactivation), Vm → Vrest

h

Do Axon 1 Dynamics

H&H Voltage Clamp experiments• When depolarize, get early negative current and later positive current

•As V increases

•Amplitude of Ineg decreases; V = 117 have Ineg = 0; V > 117 have early positive current

•Rate of current development increases (both + and -)

•Switch from negative current to positive gets earlier

•Note: VK = -72 mV, VNa = +55 mV, Vresting = -60mV; INa = gNa(Vm – VNa), IK = gK(Vm – VK)

•So IK always positive; INa negative for small V but becomes positive for V>115 mV

•I reversal could be due to cessation of early I- or stronger/earlier I+

•H&H isolate currents by setting Vm = VNa so get voltage dependence of IK

•Deduce voltage dependence of INa since Itot = INa + IK

Do Axon 2&3 Voltage Clamp Currents

Na activation and inactivation and deinactivationV activation , time inactivation deinactivation deinactivation is also voltage dependent

H&H use conditioning steps:

Brief conditioning depolarization reduced INa during 2nd step

As t for conditioning step increases INa 2nd step decreases (more sodium channels inactivated during conditioning step) H&H find time and voltage dependence of inactivation

ex – conditioning step + 29 mV inactivation = 2 ms (nearly complete) step + 8 mV inactivation > 8 ms (less inactivation)

They found that even at resting potential, many sodium channel are inactive.

H&H used long conditioning steps to study de-inactivation This turned off (closed) Na channels then set 2nd voltage to recovery voltage – vary time to 3rd voltage to look at current.

Do Axon 4 Voltage Clamp Na Inact

Empirical Equations

1 timesticcharacteri state, initialg

state, steadygth wi,egggg

0

t

0

Generally dg/dt = (1-g) – g; = opening (fwd rate), = closing

Potassium, have gk = gkmaxn4; gkmax = max conductance (all open)

Sodium, have gNa = gNamaxm3h, m is like n for K, h describes inactivation

Each has time dependence like n

m3 = fraction activated, h is fraction de-inactivated

open channels offraction nth wi,ennnn 4t

0

t

0

LmLKm4

KNam3

Nam

ennn n likeequation haveh n,m, ofeach for

I)VV(gVVmgVVhmgdtdVC

maxmax

If know parameters (max g, taus, nernst potentials etc) can get action potential and explain all observed phenomenon.

Do Axon 5 Voltage Clamp Na K conductance

Action Potential

Do Axon 6 Impulse conductance

Threshold and Refractory Period

There is a minimum initial depolarization you need to get action potential – this is the threshold. “All or none” aspect of action potential

After action potential, threshold is infinity (Na h gates closed), this leads to a refractory period.

http://www.biocrawler.com/encyclopedia/Action_potential

http://cwx.prenhall.com/bookbind/pubbooks/morris5/medialib/images/F02_03.gif

Do Axon 7&8 Impulse Threshold and Refractory

Spread of Action Potentialhttp://www.arts.uwaterloo.ca/~bfleming/psych261/image25.gif

Na comes in and causes depolarization at neighboring sites. Refractory period insures unidirectional event.

Want current to go along axon, not out of axon

Invertebrates: large radius → small R

Vertebrates: large R along axon (myelin sheath and nodes of Ranier)

•Have ligand gated channel (eg Ach receptor that needs two Ach to open).

•When open both Na and K can get through → get depolzarization