Presentation on theme: "Discussion topic for week 6 : Nerve impulses & ion channels"— Presentation transcript:
1Discussion topic for week 6 : Nerve impulses & ion channels Potassium channels conduct the K+ ions but reject the smaller size Na+ ions with a selectivity ratio exceeding 1/1000. How do they achieve this feat?
2Problem of nerve impulses (Nelson, chap. 11, 12) How do we send signals from brain to muscles in milliseconds?The axons, which are the pathways for signals, form leaky cables in a conducting environment (salt solution). Thus compared to a copper wire, sending electric signals across axons is a difficult problem, requiring a novel solution.
3<x2> = 2Dt, with D~10-9 m2/s, and L = 1 m, gives Besides the leaky cable problem, ions in a salt solution move very slowly due to small D, which greatly reduces the signal transmission speed<x2> = 2Dt, with D~10-9 m2/s, and L = 1 m, givest ~ 5 x 108 s ~ 16 years!Also ion concentration and energy are quickly dissipated (cf. pulse solution).Even if there were an applied potential difference between the neurons and muscles (solving the latter problem), it wouldn’t help much with the speed
4Action potential basics: Diffusion limits the distance scale of signal propagation to μm or less.The only obvious place where diffusion of ions could make an observabledifference is across membranes - ion flow could change the potentialdifference across the axon membrane.Experimental facts:Na+ concentration is high outside cells and low inside, and vice versa for K+ ions.There are channels on the membrane that, when open, selectively conduct either Na+ or K+ ions.There are ion pumps (called sodium-potassium pump) on the membrane that help to maintain this concentration difference.In each cycle, Na-K pump uses 1 ATP molecule to pump 3 Na+ ions out of the cell and 2 K+ ions in to the cell.
5Maintenance and propagation of the action potential: Change of membrane voltage opens the sodium channels.Na+ ions flow into the cell, collapsing the membrane potential (−60 mV).This triggers the opening of the potassium channels, while the sodium channels shut down stochastically.K+ ions flow outside the cell, restoring the membrane potential.The potassium channels shut down, returning the system to step 1.5. This process is repeated along the axon, which propagates the action potential.outin
6Lessons from squid giant axon: Squid giant axon played a critical role in understanding nerve signals.It has a diameter 1 mm which is 100 times larger than a typical axon’s.Cells have been known to maintain a potential difference with outside fora long time (Galvani vs Volta, ~1800). What is the source of this ΔV?Two observations:1. Cells are electro-neutralbut have more KCl inside2. K+ is more permeablethan Cl-Thus K+ will leak out of thecell until Nernst equilibriumis reached
7Concentration profiles of K+ and Cl- ionsacross a cell membrane(assuming only K+ ispermeable)Correspondingelectrostatic potential(from PB eqn.)Nernst potential:
8Realistic case:Inside the cells there are negatively charged impermeant macromoleculeswhose charge density is equivalent to c_ = 125 mM of excess electrons.The three major ions, Na+, K+ and Cl- have the concentrations outside (1):c1Na = 140 mM, c1K = 10 mM, c1Cl = 150 mMFrom electro-neutrality, the concentrations inside (2) must satisfyc2Na + c2K - c2Cl – c_ = 0In equilibrium, each permeant species must separately satisfy the Nernstrelation with the same potential difference DV(Gibbs-Donnan relations)
9LetSubstitute in the electro-neutrality equationInside: c2Na = 210 mM, c2K = 15 mM, c1Cl = 100 mMDonnan potential:
10Observed (expected) concentrations in squid giant axon (in mM): c2 (in) c1 (out) Vnernst (mV)K (15) 20 (10) -75 (-10)Na+ 50 (210) 440 (140) “Cl- 52 (100) 560 (150) “All the potentials are different! Hence the cell is not in equilibrium.Na concentration and voltage differs most from the Donnan equilibrium.Ion pumps in membranes actively transport Na+ out and K+ in, and thusmaintain this imbalance in concentrations.In one cycle, the Na-K pump hydrolizes one ATP molecule moving 3 Na+ions out and 2 K+ ions in. Work done for each ion:W(Na+) = e ( ) = 114 meV, W(K+) = e ( ) = 15 meVThus the total work done is W = 3 x x 15 = 372 meV = 15 kTCf. ATP hydrolysis liberates 19 kT, so only 4 kT is lost as heat.
11Experimental demonstration of the active ion pumps in the membrane Flux of Na ions out of an axonstops when toxins are introducedToxins block the pump stoppingthe transport of Na outside.(Hodgkin-Keynes, 1955)The rate of ATP hydrolysis catalyzedby the Na-K pump as a function of theinterior Na and exterior K concentration.Lack of either stops ATP consumption.(Skou, 1957; Nobel 1997)
12Crystal structure of potassium channel (MacKinnon, 1998; Nobel 2003) Crystal structure of potassium channel (MacKinnon, 1998; Nobel 2003). Reveals the mechanisms of selectivity and voltage gatingSelectivity filter has theright size to bind theK+ ions but too largefor the smaller Na+ ions(More details in the video)Voltage gatedion channels:life’s transistors
13Crystal structure of sodium-potassium pump (Poul Nissen et al. Dec
14F0-F1 ATPase: a molecular rotor in mitochondria bda11.4 nm8.2 nm9.2 nm12 nm3.3 nmExploits the proton gradient to synthesize ATP.The work done by transporting 3 protons across the membrane is converted to chemical energy by synthesizing ATP.
15Nerve impulses:Response of axons to a weak stimulus:Injecting positive charges in an axon changes the membrane voltage to a more positive value (depolarization). This stimulus spreads along the axon like a pulse solution—its amplitude is dissipated within a few cm.
16Response of axons to a strong stimulus: Action potential Unless the stimulus is strong enough to change the membrane potential by about 10 mV, it dies down. Above that threshold, it triggers an action potential which propagates along the axon without any loss in amplitude.
17Time course of an action potential Showing how the membrane potential and the corresponding membrane current change in time.An initial stimulus opens Na channels1-3 inward Na currentK channels open;an outward K currentgradually drives the potential back to the resting potential
18Trigger of action potential in giant squid axon:a) A stimulus of 56 mV depolarizing potential is appliedb) Total membrane currentc) Inward Na currentd) Outward K currentNote that the K current starts flowing when the Na current (and the membrane potential)is at a maximum.Both the Na and K channels open in response to changes in the membrane potential (analogous to transistors).
19Modeling action potential: Analogy with electrical circuitsRepresenting each type of current with a different circuit element,we can write for each one:Recall that VNernst > ΔV for Na+ and VNernst < ΔV for K+Capacitive current:
21Cable equation(*)(k=3 W-1m-1 conductiv.of axoplasm)Diff. wrt to x and substitute in (*)
22If we assume Ohm’s law for radial conductance: Linear cable equationAxon’s space and time const.(~1 cm) (~2 ms)
23Solution of the cable equation: Diffusion equation withDecaying pulse solutionThe decaying pulse solution is degraded quickly.Need to give up linearity of g(Na) to sustain the pulse
24Solution of the linear cable equation compared to the pulse solutions D=0.05 m2/s1 cm4cmSolid lines: linear cable equation plotted at x = 1, 2, 3, 4 cmDashed lines: pulse solutions for the same parameters