Lecture 2 Resting Potential PDF

Neurons are specialized cells It is important to keep in mind that neurons must perform all of the usual tasks of cells. What is it that makes neurons distinct from other cell types? The ability to generate and propagate electrical signals.  Information transfer and integrati...

Neurons are specialized cells It is important to keep in mind that neurons must perform all of the usual tasks of cells. What is it that makes neurons distinct from other cell types? The ability to generate and propagate electrical signals.  Information transfer and integration in the NS are electrical Electrical signals in the nervous system are a universal currency (highly conserved through the animal kingdom) - Long range signals (action potentials) - Short range signals (graded or electrotonic potentials) -Information transfer between neurons by electrical and chemical synapses -Essential for the electrical signaling is the impermeability of the membrane to ions, and the formation of an electrochemical gradient The membrane permits the passage of small hydrophobic molecules. Small uncharged molecules can pass the membrane at very slow rates. Large uncharged polar molecules cross the membrane very rarely. Water soluble ions cannot cross the membrane at all.  membrane potential The concentrations of ions are different inside and outside the cell Cytoplasm A membrane potential forms when there is a difference in net electrical charge on the two sides of the membrane. Even a small imbalance of ions leads to a membrane potential.  The electrochemical gradient The force on a molecule to move across the membrane is due to both the difference in concentration and the difference in charge. (A) It is energetically favorable for molecules to move to reach a lower concentration. (B) By including the membrane potential (charge) where the positive charge is on the side of the higher concentration the movement of molecule across the membrane is even more energetically favorable. (C) If the membrane potential is opposite of the chemical gradient of the molecules then the forces are acting in opposite directions reducing the overall force. (A) (B) (C) The membrane potential is measured by inserting an electrode in to the cell. An oscilloscope measures the difference in potential between the inside of the cell and the ground (usually the extracellular solution). Ion channels only allow ions to flow down their electrochemical gradient Ion channels are usually regulated, which increases or decreases their probability of being open Ion channels only let specific ions pass Ion channels can be gated in several different ways Voltage-gated channels open in response to a change in voltage across the membrane. Ligand-gated channels open in response to a ligand binding the channel. Mechanically-gated channels open in response to a mechanical stress. When they are not active, neurons usually have a membrane potential between -50 and -80 millivolts. This is the resting potential What is the basis for the resting membrane potential?  K+ “leak” channels spontaneously open and close in the cell membrane Allows for the passage of K+ across the membrane When the force of the concentration gradient = the opposite force due to the charge difference, this is the equilibrium potential  Basis of the resting potential Model of a cell Cannot cross X Cannot cross Calculating the equilibrium potential for K+ The Nernst Equation EK = k (ln [K]o - ln [K]i) EK = RT/zF (ln [K]o - ln [K]i) EK = RT/zF ln ([K]o/[K]i) The Nernst Equation EK = k (ln [K]o - ln [K]i) EK = RT/zF (ln [K]o - ln [K]i) EK = RT/zF ln ([K]o/[K]i) At 20 C, RT/zF = about 25 mV EK = 25 ln ([K]o/[K]i) or 58 log ([K]o/[K]i)  Basis of the resting potential What happens if only K+ can pass? Cannot cross X Cannot cross EK = RT/zF ln ([K]o/[K]i) = 58 log (3/90) = -85 mV  Basis of the resting potential What about Chloride? Cannot cross Cannot cross ECl = RT/zF ln ([Cl]i/[Cl]o) = Notice concentrations are reversed because Cl is negatively charged, so Z = -1  Basis of the resting potential What about Chloride? Cannot cross Cannot cross ECl = RT/zF ln ([Cl]i/[Cl]o) = 58 log (4/120) = -85 mV Squid giant axon Loligo forbesi David Nicholson Marine Biological Association of the UK Use squid giant nerve fiber remove axoplasm replace with solution insert electrode  Measure membrane potential vs K+ concentration Expect EK = 58 log ([K]o/[K]i) Now collect data to determine if our model explains the actual system. If we measure the membrane potential versus the outside potassium concentration, what do we expect to see? EK = 58 log ([K]o/[K]i) Membrane potential = 58 log ([K]o/[K]i) y = mx + b A line with the slope of 58 and y intercept = 0 Measure membrane potential vs K+ concentration Expect EK = 58 log ([K]o/[K]i) Line predicted from the Nernst equation Data points Measure membrane potential vs K+ concentration Expect EK = 58 log ([K]o/[K]i) Deviation? Measure membrane potential vs K+ concentration Due to sodium permeability Approx 1% to 10% of K+  Basis of the resting potential Can cross Cannot cross ENa = 58 log ([Na]o/[Na]i) = 58 log (117/30) = 34 mV  Basis of the resting potential To find the resting potential must consider all ions (not just K+) Inward current, i, for each ion is dependent on the force on each ion Driving force = (Vm - Eion) Vm is membrane potential, Eion is equilibrium potential for that ion Also proportional to the conductance for each ion, gion Because K+ has higher conductance than Na+, it will have a larger effect on the resting potential  Basis of the resting potential To find the resting potential must consider all ions (not just K+) Inward current, i iNa = gNa(Vm - ENa) gNa is sodium conductance, Vm is membrane potential, ENa is sodium equilibrium potential iK = gK(Vm - E K) iCl = gCl(Vm - ECl) If cell is in equilibrium gK(Vm - E K) = - gNa(Vm - ENa) What is the relationship between conductance (g) and E for the ions?  Basis of the resting potential gK(Vm - E K) = - gNa(Vm - ENa) Solve for Vm Vm = (gK E K + gNa Ena)/ (gK+ gNa) Include Cl Vm = (gK E K + gNa Ena + gCl ECl )/ (gK+ gNa+ gCl ) A similar relationship exists between concentration and permeability Vm= 58 log(PK[K]o+ PNa[Na]o+ PCl[Cl]i)/(PK[K]i+ PNa[Na]i+ PCl[Cl]o) Goldman Hodgkin Katz (GHK) equation aka constant field equation Membrane potential depends on relative conductances, concentrations of permeable ions, and equilibrium potentials. In most cells, resting permeability to K+ and Cl- is high compared to Na+  Basis of the resting potential Unlike our simple model cell Intracellular sodium and potassium are kept constant by a sodium-potassium pump Energy is used to maintain a steady state Three Na+ are pumped out for every two K+ pumped in  Moving molecules against their electrochemical gradient requires energy => This is active transport 1. COUPLED PUMPS transport a molecule AGAINST the gradient (uphill) by allowing the passage of a molecule along the gradient (downhill). 2. ATP-driven PUMPS couple an uphill transport with the hydrolysis of ATP, thereby using energy to carry a molecule against the gradient. 3. LIGHT-DRIVEN PUMPS utilize energy from light to carry molecules against the chemical gradient. These occur mostly in bacteria. Sodium-Potassium ATPase pump Very high Na affinity Very low K affinity Very high K affinity Very low Na affinity  Basis of the resting potential Therefore, iNa = iK Instead iNa : iK = 3:2 (from pump) iNa / iK = gNa(Vm - ENa)/ gK(Vm - E K) = -1.5 or Vm = (1.5 gK E K + gNa Ena)/ (1.5 gK+ gNa) Again can express this in terms of permeabilities and equilibrium potentials Vm= 58 log(rPK[K]o+ PNa[Na]o)/(rPK[K]i+ PNa[Na]i) where r = absolute value of transport ratio (3:2) here  Basis of the resting potential Can measure concentrations and permeability For squid Ratio of PK to PNa = 1.0:0.04 Vm= 58 log(rPK[K]o+ PNa[Na]o)/(rPK[K]i+ PNa[Na]i) Vm = 58 log {(1.5)(10) + (0.04)(460)}/{(1.5)(400) + (0.04) (50)} Vm = -73 mV If there was no pump (r=1) Vm = 58 log {(1.0)(10) + (0.04)(460)}/{(1.0)(400) + (0.04) (50)} = -67 mV So the pump changes the resting potential by about 6 mV  Basis of the resting potential The electrochemical gradient is due to differences in both concentration and charge The membrane potential is due to a difference in charge across the membrane The equilibrium potential for an ion is the membrane potential at which the force driving the ion across the membrane is zero. Calculated with the Nerst equation. The contribution of ions towards the resting potential is dependent on the difference in concentration across the membrane and proportional to the relative conductance of that ion. Calculated with the GHK equation. Because the membrane potential of a neuron is not equal to the equilibrium potential of any ion, all ions are subject to a driving force and will move across the membrane if they can.  Basis of the resting potential What is the equilibrium potential for an ion? How do you calculate the equilibrium potential for a specific ion? How do you determine the membrane potential? What determines if an ion will move across a membrane? What must be present for an ion to move across a membrane?