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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 "35 Types of neurons "36 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) "37 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 "38 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 "39 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 "40 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 "41 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 "42 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 "43 Hodgkin-Huxley Model • Studied the squid giant axon (1mm diameter) Channel opening "voltage! Key technique: Fix one and study the other "44 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 "45 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+ "46 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 "47 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 "48 Refractory period • Na channels remain inactivated for a few ms after a depolarizing event! • Absolute refractory period "49 Hodgkin-Huxley Model • Ion selective channels • 3 currents: Sodium INa, potassium IK, and leak current IL "50 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 "51 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 "52 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 "53 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 "54 Action potential dynamics • From static conditions they simulated dynamical evolution of voltageconductance "55 Animation http://www.blackwellpublishing.com/matthews/channel2.swf "56 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 "57 Electrode Voltage across axon wall (mV) • = Time (s) Why action potentials? "58 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 "59 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 "60 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 "61 Animation http://www.blackwellpublishing.com/matthews/actionp.swf "62 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. "63 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 "64 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