Download Types of neurons

3G3 Introduction to Neuroscience: Excitability
Voltage across axon wall (mV)
Electrode
=
Time (s)
•
Action potentials: Primary means by which neurons signal!
– Sequence: Resting ! Excited ! Refractory ! Recovery
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Types of neurons
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Membrane Channels
1) Resting cell Different ionic concentration on either side of membrane=
Battery !
!
2) Cell membrane !
! Lipid bilayer= Capacitor!
!
3) Membrane channels=proteins spanning the bilayer
Two classes (can be selective for particular ions)!
– Resting (leak) channels= Resistors !
• Not influenced by extrinsic factors !
!
– Gated channels=Transistors!
• Usually closed at rest !
• Probability of opening determined by!
– Membrane potential (voltage gated)!
– Ligand (chemical) binding!
– Membrane stretch
φe
Gated!
channel
bilayer
φi
Ion channel pore similar size as Pentium 4 transistor (2nm)
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Membrane potential
Consider membrane with one resting channel only (semi-permeable)!
• Permeable to K+ but not oppositely charged protein molecule A-!
– inside has a high concentration of K+ and A-!
•
Assume the charges are balanced on each side
K+
A-
Equal +/-
Equal +/-
{
{
+
+
-
+
+
+
+
- +
+
+ + -
Extracellular
-
Intracellular
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Sequence of events
2. Increases +ve charge outside cell and -ve
charge inside!
5. PD opposes further flow of K+ - thereby
self-limiting!
!
3. The +ve and -ve charge attract each other and
collect locally on either side of the membrane!
!
4. Generates a potential difference (PD) across
the membrane
+ +
++
-
-
- +
+ +
Intracellular
-
Potential gradient
Potential gradient
+
- +
+
+ + -
Intracellular
Chemical driving force (concentration)!
=Electrical driving force (PD)
Extracellular
+ Diffusion gradient
+
+
+
+
+
+ + -
Extracellular
+ - ++
++
Diffusion gradient
Extracellular
+ - +
+
!
6. Equilibrium reached when !
!
Diffusion gradient
1. K+ diffuses down gradient
- +
+
Intracellular
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Ionic reversal potentials
• Ions are subject to two forces driving them across membrane!
– Chemical gradients!
– Electrical gradient
Chemical gradient!
Electrical gradient
-20mV
0mV
-75mV
Equilibrium potential where the two gradient balance= -75mV for K+ (given by Nernst equation )!
This is the reversal potential for K+!
!
-perturbation of the membrane potential from this reverses the net direction of ion flux !
!
But Sodium (Na) is high outside cell (as is Chloride) and also has channels!
Consider a Na only system
Na+
0mV
Cl-
Na+
Na+
+20mV
Cl-
Na+
Na+
reversal potential for Na+ =+55mV
+55mV
Cl-
These reversal potentials depend mainly on relative concentration between inside and outside
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How do different ionic gradients contribute to resting membrane
potential?
Neuron channels!
!
– Permeable to three ions: Na+ , Cl- and K+ ions!
– Impermeable to A- (proteins and amino-acids) !
1) If the neuron was only permeable to K+ then Vr= -75mV (+55mV if only permeable to Na+)!
!
!
2) Consider what happens if there are a few Na channels!
!
– Two forces drive Na+ influx: Concentration & electrical gradient !
– As Na+ flows in the K+ is driven out by the reduced potential!
3) Equilibrium is reached when Na+ influx matches K+ outflow !
– electrical + chemical driving force!
– depends on membrane permeability: Na+ permeability << K+ permeability (1:25)!
– around -60mV
K+
K+
-75mV
1
Na+
K+
K+
Na+
-65mV
2
Na+
K+
K+
Na+
Na+
-60mV
3
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Pumps maintain gradient in the long term
•
•
Na-K pump moves Na and K against their net electrochemical gradients!
At rest – net flow of passive Na+ and K+ matched by Na-K pump!
– Driven by ATP!
– One ATP pumps 3 Na+ out and 2 K+ in!
– Restores battery - but battery discharges only slowly
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Gated channels
•
•
Changing the concentration of the external ions changed the action potential!
It was found that the !
– conductance depended on the voltage!
– voltage depend on conductance!
•
Relationship between channels opening and voltage difficult to ascertain
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Hodgkin-Huxley Model
• Studied the squid giant axon (1mm diameter)
Channel opening "voltage!
Key technique: Fix one and study the other
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Voltage clamp technique (1940s)
•
Voltage Clamp!
– Negative feedback circuitry to inject current to fix the voltage Vm!
– Once membrane potential is constant there are no capacitive currents!
– allows to examine membrane currents
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Currents after voltage step
Outward current
Inward current
Consists of different currents!!
Can be separated by !
– manipulating ion concentration!
– blocking channels !
• TTX blocks Na+!
• TEA blocks K+
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Voltage-dependent conductances
• Turn current into conductances gNa & gK
(divide by difference to reversal
potential)
• potassium !
– voltage gated!
– open slowly !
– do not inactivate!
!
!
• sodium !
– voltage gated!
– open faster than K+!
– inactivates spontaneously
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Sequence of events
1. Depolarization causes Na channels to open fast!
2. Na rushes in causing further depolarization!
Potential driven towards ENa = +55mV !
positive !
feedback
3. Limited by!
Gradual inactivation of Na channels!
Gradual activation of K channels!
4. Outward K current repolarises membrane
•
All or none nature depends on whether positive
feedback 1 & 2 becomes unstable !
–
•
Crosses threshold
Relative refractory period !
–
Increase opening of K channels
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Refractory period
• Na channels remain inactivated for a few ms after a depolarizing event!
• Absolute refractory period
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Hodgkin-Huxley Model
• Ion selective channels
• 3 currents: Sodium INa, potassium IK, and leak current IL
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Ionic conductances
Each ionic currents is typically of the form!
!
!
Where!
• g(V,t) is the conductance
~ the total number of open channels!
!
Hodgkin and Huxley estimated these using voltageclamp experiments
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Gating variables
Mathematical model for
with gating variables
Resting!
potential
2 [0, 1]
Resting!
potential
At resting potential !m & n low and h high ! INa and IK low!
At 70mv ! m & n high and h low eventually ! low INa and high IK!
•But time constant for m an order of magnitude faster than for h or n!
•So INa initially high then low, IK initially low then high!
•This is the basis for excitability
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Four states of Na channel
h normally open and m normally closed!
! Channel closed at resting potential!
!
Increase voltage !
1. m opens rapidly!
• Na rushes in and increases the potential!
• Positive feedback!
2. h closes slowly and stops INa !
3. m closes fast !
4. h opens slowly !
• so channel not open on way back !
• absolute refractory period
m
h
m closes!
before h opens
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States of K channel
•
•
•
•
voltage gated K channel normally closed!
opens slowly in responses to depolarization!
K rushes out to repolarize cell!
Close slowly !
–
lead to relative refractory period
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Action potential dynamics
•
From static conditions they simulated
dynamical evolution of voltageconductance
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Animation
http://www.blackwellpublishing.com/matthews/channel2.swf
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Passive electrical properties of the neuron
Important passive properties!
–
–
–
–
•
Resting membrane resistance!
Membrane capacitance!
Intracellular axial resistance!
[Extracellular resistance ~0]!
!
Affect!
– Time course and amplitude of potentials!
– Determine when threshold will trigger AP!
– Determine the speed of AP conduction
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Electrode
Voltage across axon wall (mV)
•
=
Time (s)
Why action potentials?
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Why the need for active propagation
As neurons works with salty water (not copper)!
1. Steady-state membrane potential amplitude decreases with
distance!
2. Time to steady-state potential slows with distance!
!
Combined, these degrade the fidelity of impulses along passive
dendrites, axon
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Voltage decay
•
•
Consider constant amplitude current after steady state reached (Ic=0)!
Each pathway out of the membrane is made of two components
- axial current
- membrane current
•
Cable equation
•
•
λ (length constant) is the distance over which steady-state voltage falls to
37% of its initial value !
Bigger λ means more efficient electrotonic (passive) spread
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Length constant
•
•
•
For!
– Squid giant axon (1 mm diameter), λ = 13 mm!
– Frog muscle fiber (50 µm diameter), λ = 1.4 mm!
– Mammalian nerve fiber (1 µm diameter), λ = 0.3 mm!
Length constant increase!
– with axon diameter!
– with membrane resistance!
Increase λ!
– more efficient longitudinal spread of current!
• faster propagation.!
• spread causes adjacent areas to reach threshold!
– increased spatial summation
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Animation
http://www.blackwellpublishing.com/matthews/actionp.swf
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Conduction speed
•
How quickly does the voltage settle to a new level!
–
–
–
•
Depend on both Ra and Cm!
Low Ra allows quick spread!
Low Cm require less charge to be deposited!
Conduction can be increase by!
–
–
increasing axon diameter (area) !
Myelination !
•
•
Increases membrane thickness x100!
AP jump between nodes of Ranvier!
!
Myelination
• Grey matter is composed of unmyelinated neurons. !
–
•
forms the surface of the cerebral cortex and the deep parts of
the spinal cord.!
White matter is composed of myelinated axons,!
–
forms the bulk of the deep parts of the brain and the
superficial parts of the spinal cord.
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Drugs & Disease
Sodium channels!
• Local anaesthetics (Lignocaine) !
–
–
•
blocking the sodium (Na+) channels in the cell membrane.!
membrane will not depolarise and so not transmit an action potential, leading to
its anaesthetic effects. !
Puffer fish!
–
Tetrodotoxin block Na+ channels!
•
Paralyses diaphragm!
!
Potassium channels!
• Disorders of channel can broaden action potential and lead to epilepsy !
!
Na-K pump!
• Block eventually leads to no action potentials depending of axon diameters!
!
–
–
Squid axons can fire 1000s action potentials after block!
Human neurons ~10 action potentials!
Myelin damage!
• Damage in multiple sclerosis
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Overview
• Resting membrane potential !
– Depends on balance between !
• Chemical gradient!
• Electrical gradient!
• Action potential arises !
– Positive feedback system (Na)!
– Negative feedback system (K)!
• Can be explained based on channel dynamics!
• Propagation of action potential depends on passive cable properties!
– Sped up by large axonal diameter!
– Myelination
"65