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Start So far you have 5 important equations Name What are they used for? Ohmโs Law V = i*R or V = i*1/g Nernst Equation Goldman equation Describes the current-voltage relationship for ohmic (linear or non-rectifying) channels/ions Used to calculate the equilibrium potential for a particular ion. Note this is also the reversal potential. Also note that in o cells with only one type of channel open at rest, the resting i membrane potential will be equivalent to the equilibrium potential for that ion. [X] RT Ex = ln zF [X] RT PK[K+]o + PNa[Na+]o + PCl[Cl-]i Vm = F ln PK[K+]i + PNa[Na+]i + PCl[Cl-]o Allows you to calculate the resting membrane potential when more than one type of channel is open at rest. Note that permeability (P) reflects the conductance AND the number of open channels per unit membrane. Time Constant Space Constant t= Rm * C This is the time it takes for a passive or electrotonic potential to decay to 63% of its value. Note that increasing either the m membrane resistance or the membrane capacitance will increase the time constant. l = (๐๐/๐๐) This is the distance it takes the potential to decay to 37% of its initial value. Note that the better the insulation of the membrane (increased rm) and the better the conducting properties of the core (decreased ra), the longer is the space constant (potential travels further before decaying). 1) One use of concentration gradients of ions across cell membranes is to drive the flow of ions during action potentials of excitable cells. A concentration gradient of ions across a membrane may be expressed in terms of an electrical potential at equilibrium by use of the Nernst Equation. a) The concentrations of some of the ions inside (i) and outside (o) of a particular muscle cell are as follows: [Na+]o = 140 mM; [Na+]i = 10 mM [K+]o = 4 mM; [K+]i = 140 mM [Ca2+]o = 1 mM; [Ca2+]i = 10-4 mM Calculate the equilibrium potential for each of the ions in the muscle cell, assuming 25oC for temperature. The Nernst equation describes the equilibrium potential for a given ion: At 25oC: Ex = [X]o RT ln zF [X]i [X]o 58 mV Ex = log z [X]i ENa = (58/1 ) log (140/ 10) = 66 mV EK = (58/1 ) log (4/ 140) = -89 mV ECa = (58/2 ) log (1/ 0.0001) = 116 mV Given these ionic concentrations, predict the direction of current flow for each ion at positive and negative membrane potentials. K+ movement (current flow) in a given electrochemical gradient V = I R => I = V/R or I = g V (where g = 1/R) EK = (58/1 ) log (4/ 140) = -89 mV Ohmโs law Nernst i E V EK (Vm โ EK) IK = gK [ -120 โ (-89)] = gK [-120+89] = -31gK Net C If Outward (+ current) + + Inward (- current) Vm = -120 mV K+ driving force K+ K+ movement (current flow) in a given electrochemical gradient V = I R => I = V/R or I = g V (where g = 1/R) EK = (58/1 ) log (4/ 140) = -89 mV Ohmโs law Nernst i slope = gK (conductance) E V EK Net IK = gK [ -120 โ (-89)] = gK [-120+89] = -31gK C Vm = -120 mV K+ If Vm Outward (+ current) = -60 mV C Net + + Inward (- current) E IK = gK [ -60 โ (-89)] = gK [-60+89] = +29gK K+ K+ movement (current flow) in a given electrochemical gradient V = I R => I = V/R or I = g V (where g = 1/R) EK = (58/1 ) log (4/ 140) = -89 mV Ohmโs law Nernst i slope = gK (conductance) E V EK Net IK = gK [ -120 โ (-89)] = gK [-120+89] = -31gK C Vm = -120 mV If Vm E IK = gK [-89 โ (-89)] = gK [-89 +89] = 0 = -89 mV K+ C C Vm = -60 mV Outward (+ current) Net + + Inward (- current) E IK = gK [ -60 โ (-89)] = gK [-60+89] = +29gK K+ K+ movement (current flow) in a given electrochemical gradient V = I R => I = V/R or I = g V (where g = 1/R) EK = (58/1 ) log (4/ 140) = -89 mV Ohmโs law Nernst i slope = gK (conductance) E V EK Net C IK = gK [ -120 โ (-89)] = gK [-120+89] = -31gK Vm = -120 mV E IK = gK [-89 โ (-89)] = gK [-89 +89] = 0 K+ Vm = -89 mV K+ C Vm = 0 mV C C V = -60 mV Net Net m Outward (+ current) + + Inward (- current) E IK = gK [ -60 โ (-89)] = gK [-60+89] = +29gK IK = gK [ 0 โ (-89)] = gK [0+89] = +89gK Na+ movement (current flow) in a given electrochemical gradient V = I R => I = V/R or I = g V (where g = 1/R) ENa = (58/1 ) log (140/ 10) = 66 mV Ohmโs law Nernst i C V INa = gNa [ +120 โ (+66)] = gNa [+120-60] = +54gNa ENa Net Vm = +120 mV C E INa = gNa [+66 โ (+66)] E Na+ Vm = +66 mV Na+ Vm = 0 mV = gNa [-66 +66] = 0 Vm = -60 mV Outward (+ current) + + C Inward (- current) Net C Net INa = gNa [ 0 โ (+60)] = gNa [0-60] = -60gNa E INa = gNa [ -60 โ (+60)] = gNa [-60-60] = -120gNa Ca2+ movement (current flow) in a given electrochemical gradient ECa = (58/2 ) log (1/ 0.0001) = 116 mV V = I R => I = V/R or I = g V (where g = 1/R) Ohmโs law Nernst i C V ICa = gCa [ +150 โ (+116)] = gCa [+150-116] = +34gCa ECa Net Vm = +150 mV E C Ca++ E ICa = gCa [+116 โ (+116)] Vm = +116 mV Ca++ Vm = 0 mV = gCa [+116-116] = 0 Vm = -60 mV Outward (+ current) + + C Inward (- current) Net E ICa = gCa [ -60 โ (+116)] = gCa [-60-116] = -176gCa C Net ICa = gCa [ 0 โ (+116)] = gCa [0-116] = -116gCa Cl- movement (current flow) in a given electrochemical gradient V = I R => I = V/R or I = g V (where g = 1/R) ECl = (58/-1 ) log (140/ 7) = -75 mV Ohmโs law Nernst i Net Chloride is outward, net current is inward. C V ICl = gCl [ -120 โ (-75)] = gCl [-120+75] = -45gCl ECl Net E Vm = -120 mV C ICl = gCl [-75 โ (-75)] Cl- E Vm = -75 mV Cl- Vm = 0 mV = gCl [-75 +75] = 0 Vm = -20 mV Outward (+ current) Cl+ + Cl- Inward C Net (-current) E ICl = gCl [ -20 โ (-75)] = gCl [-20+75] = +55gCl C Net ICl = gCl [ 0 โ (-75)] = gCl [0+75] = +75gCl During the action potential, is there a net influx or efflux of Cl- ions during the action potential? When Vm > ECl expected ~ +25 mV at action potential peak, then chloride ions are trying to drive the membrane to the chloride equilibrium potential at -75 mV. So the answer is a net influx โ you have to move the negative ions into the cell to drive the membrane to a more negative potential. So that is the flow of ions โ but what about the direction of the current?? ALWAYS opposite to anions. So the net current is outward. i V If the experimenter holds the membrane potential of the cell at -90 mV, what happens when GABA is released on the membrane? The GABA receptor is associated with a chloride channel. We have found the chloride reversal potential to be -75 mV. When GABA is released it binds to the receptor, causing the chloride channel to open. Once open they are attempting to drive the membrane to their equilibrium (-75 mV). Since this is more positive than the membrane, a depolarizing (excitatory) current will be produced. Chloride will move out of the cell and the net current will be inward. The actual measured membrane potential for the muscle cell was -90 millivolts. From this information, what conclusion can you draw concerning the relative conductances of sodium and potassium in these cells at rest (i.e. in the absence of action potentials) assuming that sodium and potassium are the only ENa = 66 mV ions that contribute to membrane potentials. EK = -89 mV At rest the sodium current is balanced with that of the potassium current. From Ohmโs law I = gV: gNa(Em-ENa) = - gK(Em โ EK) -gK/gNa = (Em-ENa)/(Em-EK) -gK/gNa = (-90 โ 66) / (-90 - -89) = -156 / 1 gK/gNa = 156 Assume that at rest a particular neuron is permeable to K+ and Na+. If EK = -89 mV and ENa = +60 mV, AND gK = 5*gNa, then calculate the resting membrane potential. At rest, INa = -IK (eq1) and gK = 5* gNa (eq2) Use Ohmโs law to substitute for current values in eq 1: gNa(Em โ ENa) = -gK(Em-EK) Now replace gK = 5*gNa : gNa(Em โ ENa) = -5gNa(Em-EK) gNa is on both sides of equation โ so can remove it: (Em โ ENa) = -5 (Em-EK) multiply the 5 through to separate Em: Em โ ENa = -5Em+5EK Add 5Em to both sides: 6Em โ ENa = 5EK Add ENa to both sides: 6Em = ENa + 5EK Put in actual values: Em = [60 + (5*-89)]/6 = -64.16 mV If a few positive charges were moved from the inside to the outside of a cell, the unbalanced negative charges would a. distribute uniformly in the cytoplasm b. end up at the membrane boundary c. diffuse from the place they were left unbalanced to their final destination d. violate the principle of electroneutrality Answer: d The Nernst potential describes a. The potential at which only K+ channels are open in a neuron b. The resting potential of a cell c. The potential at which the electrical gradient is in balance with chemical gradient (for a specific ion) d The potential at which Na+/K+ ion pump is most active answer: c When you calculate the Nernst potential for K+, what else can this be called? K+ equilibrium potential or K+ reversal potential A particular mammalian cell displays a chloride equilibrium potential of -60 mV. Due to a high resting potassium conductance (K+ equilibrium is at -90 mV) the cellโs resting potential is at -80 mV. Please check the correct answer. What would the direction of the chloride and potassium currents be at rest? Chloride: ___inward ___outward ___no net current Potassium:___inward ___outward ___no net current What would the direction of the chloride and potassium ion movements be at rest? Chloride: ___inward ___outward ___no net movement Potassium:___inward ___outward ___no net movement Answers: What would the direction of the chloride and potassium currents be at rest? Chloride: __X_inward ___outward ___no net current Potassium:___inward __X_outward ___no net current What would the direction of the chloride and potassium ion movements be at rest? Chloride: ___inward __X_outward ___no net movement Potassium:___inward __X_outward ___no net movement Remember that the direction of current is in the direction of positive charge movement. So if Cl- ions are moving out of the cell, then the direction of current is into the cell. Assume that a particular cell is equally permeable to chloride and potassium ions and that gK = gCl. If the equilibrium potential for chloride is -60 mV, while for potassium is -90 mV, what would you predict the resting membrane potential to be? Show all work. At rest IK = -ICl (inward and outward currents are equal and opposite in direction so there is no net current). Thus gK (Vr - EK) = -gCl (Vr - ECl) gK (Vr - (-90 mV)) = -gCl (Vr - (-60 mV)) gK (Vr +90 mV) = -gCl (Vr +60 mV) (Vr +90 mV) = -(Vr +60 mV) 2Vr = -150 mV Vr = -75 mV Two microelectrodes are inserted into a cell: one is connected to a voltmeter to measure the transmembrane potential; the second is hooked up to a tunable current source (battery of variable output), which allows us to inject current into the cell. These electrodes are then connected to a feedback circuit that compares the measured voltage across the membrane with the voltage desired by the experimenter. If these two values differ, then current is injected into the cell to compensate for this difference. Thus the amount of current we provide equals the amount of current passing through the cell membrane. What is this mode of recording called? Answer: Voltage Clamp Can voltage clamp mode of recording be applied to whole cell recordings? Can it be applied to inside-out patches of membrane? Can it be applied to outside-out patches of membrane? Answer: yes to all Neuronal Membranes, Ion Channels and Pumps What is a neuronal membrane made of? Phospholipid bilayer with glycoproteins What is one purpose of the membrane? Maintain separation of charge Artificial gramicidin โinduced channels in membranes behave according to what function? Ohmโs Law V = iR For a linear or Ohmic channel, when recording a single membrane potential, does the amplitude of the current vary? No. The opening of the channel is all or none. For a linear or Ohmic channel, how would you measure the conductance of the channel? Using a patch clamp recording, hold the cell at different membrane potentials and measure the amplitude of the current through the channel at each membrane potential. Plot this and then measure the slope to obtain the conductance. V = iR, y = mx + b, in this case you are measuring the current, i, so you need to solve for i. Also we want conductance. Remember that conductance g = 1/R. V= i/g, now solve for i. i = gV. So the โmโ or slope is g. Why might a channel not be Ohmic, and how could you tell? Measure the current at different membrane potentials. If there is a change in slope at some part of the graph, it is not Ohmic. Can be due to blocking particles. When a channel passes more current at certain potentials than at others, what is this called? Rectification What is happening to the ion channel protein when the channel opens? A conformational (structural) change How does gating of the channel work? Conformation change in one part, along the whole channel length, or with a blocking particle swinging in. What are the ways to open a channel? Ligand, voltage, phosphorylation, stretch/pressure What is desensitization, and what causes it and relieves it? A reduced second channel response after first opening. Typically caused by ligands after exposure. In some cases a particular voltage must be reached to alleviate it. Why might a channel respond differently early as opposed to late in development? Channels are made of subunits that can have varying expression patterns over development. AND changing the subunit composition of a receptor/channel can change its function โ including conductance, channel open time, desensitization, etc. What are the 3 type of gene superfamilies? Ligand-gated, gap junction, and Voltage-gated How do ion pumps differ from ion channels? Ion pumps move some ions against their electrochemical gradient; Ion pumps require energy (ATP) Ion pumps are very slow Ion pumps have 2 gates not one.