Lec 4 Handout - Voltage Clamp

Lec 4 Handout - Voltage Clamp - ANALYSES or tors finannsr...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ANALYSES or tors finannsr one The properties of voltage—sensitive sodium and potassium channels underlying the action potential were described in Chapter 4}. This Advanced Topic provides a more quantitative description of these ion channels and their dependence on memr brane voltage. The experimental evidence for the role of voltagerdependent ion channels in the action potential was obtained in voltagerelamp experiments per, formed by Alan L. Hodgkin and Andrew F. Huxley in the period from 1949 to 1952. We begin with the Hodgkin—Huxley model of the nerve action potential and then discuss the behavior of individual voltagesdependent ion channels. VoltagesClamp Analysis in the voltagerclamp technique, membrane voltage is held at a constant value, or “clamped.” The time course of the flow of membrane current at the clamped mem- brane voltage provides an index of the underlying changes in membrane ionic con— ductance. The voltage-clamp procedure is diagrammed in Figure CI. Two long, thin wires are threaded longitudinally down the interior of an isolated segment of a squid giant axon, which can be up to 1 mm in diameter. One wire measures the membrane potential, and the other wire passes current into the axon from the out- put of the voltage-clamp amplifier. The measured membrane potential is connected to one input of the amplifier, and the other input is connected to an external voltage source, the command voltage. The command voltage determines the clamped E DIdOJ. GEDNVAGV membrane potential that will be maintained by the voltagerclamp amplifier. The voltagerclamp amplifier feeds a current into the axon that is proportional to the difference between the command voltage and the measured membrane poten tial, EC —Em. if that difference is zero (that is, if Em 2 Ed, the amplifier puts out no current, and E,,, will remain stable. lem does not equal EC, the amplifier will pass cur rent that drives the membrane pote itial toward the command voltage. For example, if Em is —70 mV and EC is —60 mV, then EC—Em is a positive number, and the amplifier injects positive charge into the axoa and depolarizes the axon. Depolarization con, tinues until the membrane potentia equals the command potential ofiot) mV. A current monitor in the output line of the amplifier allows us to measure the amount of current passed by the amplifier to keep the membrane voltage equal to the command voltage. How does tiis measured current provide information about changes in ionic current and, therefore, changes in ionic conductance of the mem- brane? First, we will examine the memorane current and membrane potential without the voltage clamp, using the principles discussed in Chapter 3. Figure C2 shows the changes in transmembrane ioric current and membrane potential in response to a stepwise increase in 9N3, withg - remaining constant. Under resting conditions, the steady—state membrane potential lies between EN, and EK, at the membrane voltage at which the inward sodium current exactly balances the outward potas— sium current (that is, the total membrane current is zero: lg, + ix : 0). \When 9N6 increases, the steady state is perturbed, and ix, increases, as well. The increase in sodium influx causes Em to become more positive, and the cell depolarizes. Depo- larization enhances potassium current, however, because depolarization increases the electrical driving force for potassium to exit. The membrane potential will reach a new steady state, at which both ix, and iK are larger than their initial values but once again exactly balance one another (see Fig. C2). Consider now what happens if the same change in gm occurs under volt~ age-clamp conditions, as shown in Figure C3. The voltagerclamp apparatus now introduces an addition source of current, i if we set the command voltage, EC, clamp‘ 525 _ Advanced Topic 3 Figure (2.1. A schematic diagram ofa volt- age-clamp apparatus. Two electrodes are inserted into a giant axon, one to measure the membrane potential, Em, and the other to inject current into the axon to alter the membrane potential. The volt- age clamp amplifier injects current that is proportional to the difference between Em and a command voltage, EC, which is under experimental _ controtl Giant axon Measure Em F7 inject current equal to the normal steady-state membrane potential. the current injected by the voltage-clamp apparatus will be zero, because EC; 2 En. \Whenggd increases and the rise in sodium influx begins to depolarize the cell, the voltage—clamp circuit detects the depolarization and injects negative current to counter the increased sodium current isee the trace labeled ing in Fig. C3) The voltage clamp continues to in- ject this holding current to maintain E7. at its usual resting value as long as 9M re— mains elevated. The injected current. i _, is equal in magnitude to the change in C sodium current resulting from the increase in sodium cenductance. Unlike the situ- ation without voltage clamp see Fig. C2 >, it does not change under voltage clamp because neither En. norgK changed. Thus. the current injecred by the voltage clamp Figure (2.2. ionic currents flowing in re— sponse to a stepwise change in gNa. In the absence of volt age clamp, both iNa and 1k in— crease in response to the increase in Ma, and a new steady-state membrane po- tential is reached at a more depolarized level. wry—.wiwes-PW-wgwfig a? ;- l I l I I I I I I I mmmm.m.m._ _..._s .mrm._~_._ «7‘ n t — _ _ — ul 526 161mm -u---_-__-‘ G l" ' i Inward 3N3 i x r I gives a direct measure of the change in ionic current resulting from a change in membrane conductance to an ion. The measured change in membrane current is related to the underlying change in membrane conductance, using the ionic form of Ohms law II see Chapter 3). For example, for sodium ions, iNa : gNaUEm _ ENa) We can obtain gNa from the measured ix; according to the relation gNa : 'iNa 7 ENa) In this calculation, Em is set by the voltage clamp, and EM can be calculated from the Nernst equation, using the internal and external sodium concentrations for the particular experimental situation. The Gated Ion Channel Model Membrane Potential and Peak ionic Conductance As described in Chapter 4, the voltage—clamp procedure can be used to obtain information about the time course of the voltage-dependent sodium and potassium conductances underlying the action potential {see Figs. 4.16 and +17}. Hodgkin and Huxley used. the voltage clamp to study the voltage dependence of the sodium figure $3.. Ionic currents flowing in re- sponse to a stepwise change in gNa. With voltage clamp= the membrane potential re? mains constant because the voltage-clamp apparatus in, jects current (iclampi that com- pensates for the increased sodium current. Potassium current remains constant be- cause neither gK nor Em Changes. (5 aidol pBDUEAPV Advanced Topic 3 Figure c.4t 528 The voltage dependence of peak sodium conductance (A) and potassium conductance (B) as a function of the ampli- tude of a maintained voltage step. and potassium channels. They found that the peak magnitude of the cenductance change produced by a depolarizing voltage-clamp step depended on the size of the step, as shown in Figure C4. For example, a voltage step to —50 mV barely in- creased gNa, but a step to —30 mV produced a large increase in 9N3. Hodgkin and Huxley suggested a simple model that could account for the volt- age sensitivity of the sodium and potassium conductances. Their model assumes that many individual ion channels, each having a small ionic conductance, deter- mine the behavior of the whole membrane as measured with the voltage-clamp procedure. Each channel has two conducting states: an open state in which ions are free to cross through the pore, and a closed state in which the pore is blocked. Changing the membrane potential alters the probability that a channel enters the open, c0nducting state. Depolarization enhances the probability that a channel opens and hence increases the total membrane conductance to that ion. If the conducting state of the channel depends on transmembrane voltage, an electrical charge assodated with the channel is required to provide sensitivity to the voltage. This electrical charge is called the gating charge of the channel, be- cause it imparts the voltage dependence of channel gating. The S-shaped relation- ship between ionic conductance and membrane potential shOWn in Figure C4 is expected from basic physical principles for the movement of charged particles un- der the influence of an electric field, as is presumed to occur for the gating charge of voltage-sensitive sodium and potassium channels. The distribution of charged particles within the membrane is related to the transmembrane electric field ac- cording to the Boltzmann relation: PCs—e W-zs Em] (C3) where PD is the proportion of positively charged gating particles on the outside of the membrane, 2 is the valence of the gating charge, a is the electronic charge, E,,. is membrane potential, k is Boltzmann’s constant, T is the absolute temperature, and W is a voltage-independent term giving the offset of the relation along the voltage axis. The steepness of the rise in P0 with depolarization depends on the valence, z, of the gating charge,- the larger 2 becomes. the steeper the rise of PO i'and, hence, conductance) is with depolarization. The sodium and potassium conductances are steeply dependent on membrane potential, which implies that the gating charge 5 aidoi PGDUEAPV has a large valence. For example. from Hodgkin and Huxley’s experiments, the eff fective valence of the gating charge for the sodium channel is ~6 lthat is, z x 6 in Equation C3). We now know that the gating charge of the voltage—dependent so- dium channel consists of several positively charged amino acids found in transmembrane segment 4 in each of the four domains that make up the channel (see 1Fig. 4.12). The large number of these charged amino acid residues probably accounts for the high effective valence of the gating charge and the steepness of the voltage dependence of sodium conductance. Kinetics of the Change in Ionic Conductance Following a Step Depolarization Upon depolarization, sodium channel activation. sodium channel inactivation. and the opening of voltage~dependent potassium channels take place on different time scales. These differences in the time course of channel gating are important for generating the actiOn potential [see Chapter 4}. Hodgkin and Huxley assumed that the rate of change of the membrane conductance to both sodium and potas- sium following a step depolarization was governed by the rate of redistribution of gating charges in the channels. For example, consider the kinetics of sodium channel opening following a step depolarization. In the Hodgkinel—luxley theory, channel opening is assumed to be triggered by the movement of gating charges from the inner to the outer surface of the membrane, as shown schematically in Figure C5. At the normal negative rest— l ing membrane potential, the positive charges on the 84 segments of the channel are largely located near the intracellular face of the membrane (see Fig. CSA), and the channel is closed. Upon depolarization, gating charges are less attracted to the cell interior, and the 84 segments begin to relocate within the electric field across the membrane (see fig. CSB). \With sufficient depolarization, the charges eventu— ally redistribute so that they are near the outer face of the membrane (see Fig. C5C). The channel then opens. If m is the proportion of gating charges near the outer surface of the membrane, then i — m is the proportion of charges near the inner surface. The movement of gating charges between these two states can be described by the following first-order kinetic model: mZeTLn—m) (can .iTl The rate constant, u,,,, represents the rate at which gating charges move from the inner to the outer face of the membrane, and B,,, is the rate of reverse movement. A change in membrane voltage instantly alters the rate constants um and pm. For in, stance, a step depolarization would increase Ct,“ and decrease leading to a net increase in m and a corresponding decrease in 1 i m. The equation governing the rate at which the charges redistribute following a change in membrane potential is dim/d1” : an,“ — m) — 13mm (CS) 529 Advanced Topic 3 530 as. Outside i a as a Plasma membrane Em : A70 mV Channel closed Em : e30 mV (Immediately after onset of depolarization) Em = —30 mV (Later after onset of depolarization) Channel open Figure C.S. The change in distribution of the gating charges of a voltage-dependent sodium channel upon depolarization. The positively charged amino acids in transmembrane segment S4 of each domain of the sodium channel are indicated by the plus sign. The four domains are indicated by Roman numerals I through [V Only the S4 domains are shown for simplicity. A. At the normal negative resting potential, the positive charges are located nearer the intracellular face ofthe membrane, and the sodium channel is closed. B. Upon depolariza- tion, the positive charges are less attracted to the cell interior, and the 54 segments begin to alter their positiOn in the membrane. C. With time, all four ofthe 54 segments take on a position nearer the outer surface of the membrane, and the channel opens. The solution of Equation C5 is an exponential function; mit) : ma — (mx — m0)e‘“‘m+fim” (C6) Following a change in membrane potential. in will change exponentially from its initial value (we) to its final value {mm} at a rate governed by the rate constants for movement of the gating charges at the new value of membrane potential. Figure C6 illustrates the exponential rise of m with time after a depolarization. ll the movement of a single 5-} segment were sufficient to cause the channel to open, Figure (2.6. The effect of a step change in membrane potential (top trace) on sodium channel acti- vation. Depolarization alters the rate constants for move? ment of the gating charges across the membrane, am and Bm. The changes in rate con- stants induce a change in the proportion of gating charges on the outer face of the mem- brane (m), where they stimur late channel opening. If movement of a single gating charge could activate the channel, gNa would follow the time course of the change in m (orange trace). The actual change in gNa is proportional to in raised to the third power (yellow trace). the number of open channels—and hence gNagwould be proportional to m, the fraction of gating charges on the outer face of the membrane. ln this case, 9N3 would also rise exponentially after a depolarization. However, Hodgkin and Huxley found that the rise of gNa after a depolarization actually rose along an S-shaped time course (see Fig. C6). The nonexponential time course of 9N3 sug gests that more than one gating charge must move within a single channel to cause the channel to open. The probability that a single 54 segment within a channel will move to the outer position is simply proportional to m. The joint probability that all of the S4 segments will move for a given channel is given by the product of the probabilities that each single 54 segment will alter its position. Thus, the probabil- ity that all S4 segments in the four domains will take on the position required for channel opening is proportional to m4. The actual rise of gNa following a volt, age-clamp step in Hodgkin and Huxley's experiments was proportional to m3, which is close to the relation expected if all of the charged S4 segments within a single sodium channel must respond to depolarization before the channel can en~ ter the open state. A similar analysis was carried out for the change in potassium conductance fola lowing a step depolarization. The gating charges for the potassium channel redis- tributed after a change in membrane potential according to a relation equivalent to Equation CS: a’n/a’t : ornfl — n) — Bfln ((2.7) 53] g 3!d0_[_ paDUBApV Advanced Topic 3 532 _____ emc- By analogy with the sodium channel, it is the proportion of potassium channel gating charges on the outer face ofthe membrane, 1 — ii is the proportion on the inner face of the membrane, and (1,, and [L are the rate constants for particle transition from one face to the other. Equation C7 has a solution equivalent to Equation (2.6: n(t) : Fix 7 (Fix a Hoie‘l“”+f”ll (CS) In this instance, iiD and use are the initial and final values of ii. The rise in potassium conductance following a step depolarization was found to be proportional to 144, which suggests that all four charged 54: segments in the potassium channel redisr tribute across the membrane to trigger Opening of the potassium channel in re— sponse to depolarization. A major difference between the potassium and the sodium channels is that the rate constants, 11,, and B“, are smaller for potassium channels. That is, the sodium channel gating charges are more mobile than their potassium channel counterparts and are able to move more rapidly in response to depolarization. As a result, the so— dium channel opens more rapidly after depolarization—a crucial part of the action potential mechanism, Sodium Channel Inactivation The change in Jag-E during sustained depolarization is transient. That is, the so dium channel first activates, then inactivates in response to depolarization. To study the voltage dependence of inactivation, Hodgkin and Huxley performed ex, periments like that shown in Figure CIA. A test depolarization was preceded by a prepulse whose amplitude was varied. Depolarizing prepulses reduced the ampli- tude of the response to the teSt depolarization by closing inactivation gates, whereas hyperpolarizing prepulses increased the size of the test response by open— ing inactivation gates that were closed. This effect of prepulses allowed Hodgkin and Huxley to establish the voltage dependence of the inactivation gate on mem~ brane potential, which is shown in Figure CTB. The time course of sodium channel inactivation was studied by varying the du- ration of the prepulse, as shown in Figure CS. The relation between the size of the test respOnse and the duration of the prepulse {see Fig. C88) revealed that inactis vation proceeds exponentially during a depolarizing prepulse. By analogy with the sodium channel activation parameter, in. Hodgkin and Huxley described the time course of inactivation with the following exponential equation: hit) : h, a (h a ripe—“tide” (C9) The gating parameter, It. governs the opening of the inactivation gate of the so, dium channel, jUSt as the parameter in governs the opening of the activation gate. in this case, however. i’z decreases with depolarization. instead of increasing with depolarization, to reflect the fact that the inactivation gate closes upon depolariza- tion. Thus. upon depolarization, it declines exponentially from its original value Ute} to its final value it.” . at a rate governed by the rate constants, 01;, and B,,, for movement of the inactivation gating charge through the membrane. As expected from the discussion in Chapter 4. the closing of the inactivation gate is slower than the opening of the activation gate. implying that the inactivation gating charge is less mobile ithat is. the rate constants are smaller‘; figure (2.7. Tcstdepolmizafion The procedure for measuring l the voltage dependence of so- ' ' ' l dium channel inactivation. A. A test depolarization is pre* ceded by a prepulse whose amplitude is varied. The sub, sequent response to the test depolarization provides an in- Prepulse amplitude can be van'ed lNa In response to test _______________ in: _________ _~ . , dication of how much sodium depolarization . . . 3 channel inactivation was pro, Time ,_ ' E duced by the prepulse. B. The '——""+ relation between amplitude of an inactivating prepulse and the peak sodium conductance in response to a subsequent test depolarization. This rela— tion illustrates the voltage de- pendence of sodium channel inactivation. Peels: gNa 113 response to test depolarization Resting Em Membrane potential during prepuise mewwmwwwmuwuwwefg—e7a"Vesfimmfihfi/is‘rwmmwm—feJ Figure (2.8. ‘ A The procedure for measuring Time Test depolarization the time course of sodium :_ channel inactivation. A. A test Duration of depolarization is preceded by prepulse canbe van‘ed a depolarizing prepulse of l 5 varying duration. B. The relaa ' tion between the duration of the prepulse and the peak sodium conductance in re— Sodium currentin sponse to the test depolari— response to , _ zation provides an estimate of ' testdepoiarization the time course of sodium channel inactivation during the prepulse. The decline of the response to the test depo- larization follows an exponen- tial time course. s33. I E jidoi peaumpv Advanced Topic 3 Figure C3. 534 The time courses of sodium conductance and potassium conductance following a step depolarization. A. Sodium conductance reflects the time course of both inactivation (h) and activation (m). in the case ofactivation, channel opening is proportional to the third power of m. The rise and fall of sodium conductance is pro- portional to m3h. B. The rise of potassium conductance is proportional to the fourth power of the activation pa— rameter, n. The Temporal Behavior of Sodium and Potassium Conductance The behavior of the gating parameters m, n, and It provides a quantitative de- scription of the change in sodium and potassium conductance following a depolar- izing voltage step under voltage clamp. The sodium conductance is given by gNa : .éNarm‘3h (C10) The potassium conductance is given by gK = in“ ((3.11) where EM and EK are the maximal sodium and potassium conductances, and m, n, and h are given by Equations C6, CS, and C9, respectively. Thus, following a de- polarization, the sodium conductance rises in proportion to the third power of the activation parameter, in, and falls in direct proportion to the decline in the inactiva— tion parameter, it. Figure C.9A summarizes the responses of each gating parameter separately and the product m3h, which governs the time course of the sodium con- ductance in response to depolarization. The potassium conductance rises as the fourth power of its activation parameter, 11, and does not inactivate, as shown in Figure C.9}3_ ...
View Full Document

Page1 / 10

Lec 4 Handout - Voltage Clamp - ANALYSES or tors finannsr...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online