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BME 502 / 1997 / handout #3 BME 502: Handout on Active Membrane Properties regenerative characteristics of the action potential first noted in experiments using a variety of preparations, but clearest demonstration of regenerative property from use of preparations such as the giant squid axon, because two recording electrodes can be placed at different spatial locations along its length in such experiments, clear that there was a delay between the appearence of an axon potential at one recording site vs the other, yet amplitude-time course remained unchanged also clear that there was a specific threshold of depolarization that must be reached for the regenerative event to be initiated 1 BME 502 / 1997 / handout #3 using voltage-clamp, observe the following in response to voltage steps from resting membrane potential to - 9 mV three major currents observed capacitive current transient inward current delayed, sustained outward current ion substitution and channel blockade experiments (see figure below) allow separation and 2 BME 502 / 1997 / handout #3 identification of each current capacitive Na+ TTX, eliminates inward current command voltage past +60 mV, ENa ion substitution: e.g., replace Na+ with choline K+ TEA, eliminates most of outward current command voltage past -85 mV, EK residual leakage current (K+ and Cl-) so if in the presence of TTX and TEA apply depolarizing command voltage, see capacitive current and sustained outward current 3 BME 502 / 1997 / handout #3 resolves into a transient inward current, a delayed outward current, and a sustained leakage current 4 BME 502 / 1997 / handout #3 transient inward current and delayed outward current reflect two different channel species: 5 BME 502 / 1997 / handout #3 voltage-clamp analyses performed by stepping membrane potential from rest to various test potentials, and plotting peak transient Na+ current and steady-state K+ current reveals voltagedependence of currents in curvature of I-V relation 6 BME 502 / 1997 / handout #3 on the basis of these and other data, an equivalent circuit model of the conductances underlying the resting membrane potential and action potential: previously have seen that an equivalent circuit can be specified for a channel (population) g, conductance for the ion passing through the membrane E, equilibrium potential for that ion using a modified form of Ohm's Law, ionic conductance for a given ion, e.g., K+ I K+ = g K+ ( V m - E K+ ) g K+ = I K+ ( V m - E K+ ) concept of equivalent circuit for a channel can be extended to entire membrane equivalent circuit for a patch of membrane considering individual conductances for each ion species conductances for total current flow through all channels of same species variable conductances for voltage-sensitive conductances 7 BME 502 / 1997 / handout #3 ** for the equivalent circuit model to be justified, it is necessary to demonstrate that the relation between ionic current and membrane potential is linear for a condition of constant permeability, i.e., satisfies Ohm's law -- requires a determination of "instantaneous currentvoltage relation" -- stepping the voltage to a first holding potential (V1 in figures below) long enough to increase permeability and then stepping to a second holding potential (V2 in figures below) and measuring the current with 10-30 μsec before additional changes in permeability can occur ** for Na+ current: for K+ current: 8 BME 502 / 1997 / handout #3 given a linear relation between current and voltage (see above), changes in conductances gNa and gK during a voltage-clamp can now readily calculated by applying the equations below to the separated currents g K+ = I K+ ( V m - E K+ ) g Na+ = I Na+ ( V m - E Na+ ) characteristics of inward Na+ current rapidly activating (compared rates of rise below for Na+ and K+) rate of activation depends on magnitude of membrane depolarization (left panel) 9 BME 502 / 1997 / handout #3 Na+ conductance rapidly inactivates inactivation process is both both voltage-dependent (p.43, fig. 14, Hille) and time-dependent (p.45, fig. 15, Hille) once inactivated, membrane must be hyperpolarized to remove inactivation experimental analysis of inactivation process: voltage-dependence small depolarizing step; followed by large depolarizing step initial small step activates voltage-dependent Na, but channels inactivate quickly so when large step etc can determine the percentage of channels that are inactivated at different Vm thus, if include hyperpolarizing pre-step, find that current generated by command voltage step is greater than if pre-step is resting membrane 10 BME 502 / 1997 / handout #3 potential some channels are inactivated even at rest time course of inactivation process paired pulse experiment compare magnitudes of currents in response to identical command steps as a function of inter-pulse interval equivalent to examination of a feedback system, or a feedforward system in the case of the pre-step or inactivation at rest characteristics of outward K+ current slowly activating rate of activation depends on magnitude of membrane depolarization no inactivation 11 BME 502 / 1997 / handout #3 explanation for transmembrane changes accompanying action potential change in permeability initially due to ligand-gated channel opening PNa+ increases large driving force, Na+ enters causes change in Vm change in Vm leads to opening of voltage-dependent Na+ channels also leads to opening of voltage-dependent K+ channels driving force greater for Na+ so depolarization predominates as Vm ENa, driving force for Na+ and driving force for K+ Na+ channels inactivate membrane current carried increasingly by K+ because of EK, K+ current leads to repolarization and hyperpolarization (undershoot) 12 BME 502 / 1997 / handout #3 Functional Consequences of Na+ and K+ Channel Kinetics given the characteristics of the Na+ and K+ currents underlying the action potential, there are multiple functional consequences for the functional, dynamic properties of neurons: consequences w/re to threshold when INa exceeds IK thus, no constraint on part of soma that initiates action potential except density of Na+ channels relative to other channels consequences w/re to shape of action potential sharp rise-fall "over-shoot" consequences w/re to input required for triggering action potential slow depolarization not sufficient release of hyperpolarizing current can lead to action potential w/o epsp consequences w/re to propagation of action potential directionality of action potential propagation when initiated at soma (initial segment) bi-directionality of propagation when initiated at center of axon Interactions Between Active and Passive Membrane Properties other functional consequences emerge when the properties of these active conductances are considered in terms of their interaction with passive membrane properties: consequences w/re to rate of propagation axon (cell) diameter: larger cell diameter and rm , ri , and λ (already discussed) large axon diameter also increases velocity of axon potential propagation: 13 BME 502 / 1997 / handout #3 ri 1 d 2 so with larger diameter axons, lateral spread is greater, i.e., passive membrane properties determine speed of conduction of action potential 14 BME 502 / 1997 / handout #3 myelination: myelination consists of wrapping of glial cell processes around axon leads to saltatory conduction: action potential propagation at Nodes of Ranvier only myelination leads to an apparent increase in thickness of the membrane by increasing rm increasing rm increases the ratio of rm to ri , just as would occur if diameter increased, so current flows farther in the axial direction (shown in figure below) conduction velocity increases with higher specific membrane resistance and/or myelination of the axon 15 BME 502 / 1997 / handout #3 degree of axonal branching: branch point failure from small diameter to larger diameters from myelinated portion of axon to non-myelinated portion en passage axons and terminal fields 16 BME 502 / 1997 / handout #3 Active Conductances In Addition to Na+ and K+ Currents Underlying Action Potential Generation conductances introduced to date: IK(l) leakage K+ conductance; linear, voltage-independent current resting Vm largely determined by this conductance blocked by cesium, injected intracellularly blocked by TEA extracellularly INa(f) fast, voltage-dependent Na+ conductance characteristics:strongly voltage-dependent rapidly activating rapidly inactivating pharmacology: TTX or QX-314 distributon: greatest density within axon and particularly axon hillock this species of Na+ conductance is the basis for the action potential, so clearly present in axons; but also found in soma and dendrites 17 BME 502 / 1997 / handout #3 IK(DR) voltage-dependent K+ conductance also called the "delayed rectifier" because conductance increases only with depolarizing steps slow kinetics; slow activation (5 msec) and no inactivation partially responsible for repolarization and initial hyperpolarization of membrane blocked by TEA thus, three major conductances: (i) leak conductance, carried primarily by K+, which contributes substantially to resting membrane potential (ii) voltage-dependent Na+ conductance that is highly voltage-dependent, and is primarily responsible for reaching threshold and the rising phase of the action potential (iii) voltage-dependent K+ conductance that is primarily responsible for the repolarization of the membrane following the action potential can account for the resting membrane potential, and the rising and falling phases of the action potential what is right with this picture? exactly the set of mechanisms that is optimal for low-failure transmission over cables, i.e., for communication between neurons -- and is what is found in axons what is wrong with this picture? will result in a system that is not very information rich, particularly if a frequency code is the basis for information transmission in the nervous system will be difficult for a relatively small depolarization to lead to an action potential (because of leakage current -- the driving force for which will increase as the membrane depolarizes), because of the rapid inactivation of Na+ conductances, and because of the voltage-dependent K+ conductances for any input that is sufficiently strong to initiate an action potential, will be very difficult to modulate the interspike interval given the removal of Na+ channel inactivation that results from repolarization by the K+ channels and the steep voltage-dependence of the Na+ channels 18 BME 502 / 1997 / handout #3 must introduce more mechanisms that allow greater variation of interspike interval as a function of variation in the subthreshold membrane potential INa(s) slow, voltage-dependent Na+ conductance activated near rest, and non-inactivating near rest blocked by TTX but not by QX-314 can be separated from fast Na+ conductance by using ramp depolarizations: ramp 19 BME 502 / 1997 / handout #3 stimulation effective because slow depolarizations result in rapid inactivation of fast Na+ conductances 20 BME 502 / 1997 / handout #3 the less rapid the rate of depolarization, the more linear is the I-V curve because of the greater inactivation of fast Na+ conductances relative to their inactivation, and thus, the more predominant is the slow, voltagedependent Na+ conductance the more rapid the rate of depolarization, the greater activation of fast Na+ conductances relative to their inactivation, and thus, the greater the magnitude of the negative slope conductance reflecting the fast Na+ functional significance of slow Na+ current is an amplification of small synaptic potentials: responses with and without INa(s) functional upper panel: responses at rest; EPSP leads to action potential discharge with INa(s) functional lower panel: responses during hyperpolarization relative to rest; EPSP is enhanced with INa(s) functional 21 BME 502 / 1997 / handout #3 IK(C) K+ conductance; also called IC or fast AHP activated by an increase in intracellular free Ca2+ (and because of voltage-dependence of Ca2+ channels, also exhibits a voltage-dependence indirectly) rapid kinetics; activated with 1-2 msec; total duration of 20-50 msec responsible for repolarization and hyperpolarization of membrane highly sensitive to TEA determines inter-spike interval and # spikes in a burst shortened action potential duration means that inactivation of Na+ channels removed sooner that if repolarization determined only by delayed rectifier, so increases the dynamic range of neuron by increasing upper limit of firing frequency IK(AHP) calcium-activated K+ conductance; also called slow AHP very slow kinetics; duration can extend to beyond 1000 msec insensitive to TEA; relative voltage insensitive contribution easily seen in phenomenon called "accomodation" if apply a depolarizing, long duration pulse initial response of several action potentials inter-spike interval gradually lengthens; cell eventually stops firing determines inter-burst interval and to a certain extent, # spikes in a burst 22 BME 502 / 1997 / handout #3 triggered by increase in intracellular Ca2+; but current also regulated by a second messenger events, because manipulations that increase intracellular cAMP also decrease AHP so can block current with blockade of Ca2+, or with activation of cAMP; e.g., membrane permeable cAMP analog, 8-bromo cAMP, decreases AHP but with no change in Ca2+ currents sensitive to NE, ACh ICa Ca2+ conductances; voltage-dependent typically examined in the presence of TTX and TEA, with cesium in electrode typical waveform: long-duration depolarization; plateau potential first Ca2+ conductance discovered was a high threshold, non-inactivating channel; now termed the L-type 23 BME 502 / 1997 / handout #3 ICa(L) L-type channels activation requires relatively large depolarizations because of high threshold holding potential: -50 to -20; command voltage: half-maximal at -15 mV comparison of inactivation properties of high-threshold (right) and low-threshold (left) calcium currents sustained inward current; does not exhibit strong inactivation, so longer duration currents however, shows inactivation that depends on [Ca+]i but not voltage (see right) much larger conductance than other Ca2+ channels blocked by many divalent cations, but especially by Cd2+ pharmacology: agonist, dihydropyridines such as Bay K8644 antagonist, nimodipine or nifedipine can substitute Ba2+ for Ca2+ for L-type channel 24 BME 502 / 1997 / handout #3 later became clear that there was a low threshold Ca2+ conductance vs. high threshold 25 BME 502 / 1997 / handout #3 in above figure, Ca2+ currents are emphasized by using a high Ba2+ concentration extracellularly and including Cs+ in the recording electrode two holding (EH) potentials are used, -30 mV and -80 mV several command voltages used, but results to two are shown, -20 mV and +10 mV because of high threshold of L-type channel and fast inactivation of T-type channel, stepping from -30 mV will reveal L-type Ca2+ current only stepping from -80 mV will reveal both L-type and T-type currents (shown in left panels) subtracting results for -30 mV from results for -80 mV (shown in right panels) gives data for T-type 26 BME 502 / 1997 / handout #3 ICa(T) T-type channels "low-threshold" calcium current activated and inactivated over a range similar to that for Na+ channels holding potential: -65 to -85 command voltage: half maximal at -40 mV transient inward current; 100-200 ms duration conductance not that large insensitive to dihydropiridines; but blocked by Ni2+ T-type vs L-type Ca2+ channel kinetics: 27 BME 502 / 1997 / handout #3 ICa(N) N-type channels high threshold, so requires depolarization, and inactivates slowly large holding potential: -65 to -85; command voltage: -25 mV (half-maximal) transient inward current; 500 ms duration blocked by ώ-conotoxin T-type vs N-type vs L-type Ca2+ channel I-V curves 28 BME 502 / 1997 / handout #3 IK(A) voltage-dependent K+, called the A-current (can only detect in presence of TTX and Mn2+ to block Ca2+) conductance=0 at rest but quickly activated when depolarized: within 5-10 msec; relatively rapid inactivation: within 20-30 msec blocked by 4-aminopiridine; relatively insensitive to TEA; can be separated from IK(DR) by substraction (see below) IK(D) voltage-dependent K+ much like the IK(A) current except that activation and inactivation occurs within a voltage range that is 15-20 mV more depolarized than for the A-current so introduces a hyperpolarizing effect to slow larger magnitude depolarizations inactivates very slowly: over the course of seconds 29 BME 502 / 1997 / handout #3 function: has a stabilizing effect on membrane potential; activated during initial phases of a depolarization and acts to shunt what otherwise would be a rapid initiation of action potentials IK(IR) voltage-gated inward K+ current, or inward rectifier activated by hyperpolarization, with no inactivation; characteristics are the basis of hyperpolarization leading to a decrease in input resistance, and thus, a rectification of the I-V relationship passes K+ ions inward more efficiently than in the outward direction voltage range for activation shifts as a function of [K+]o; voltage-dependency of activation due to channel block by Mg2+ (from intracellular fluid; thus, differs from NMDA), which is removed by hyperpolarization function of IK(IR) is to contribute to stabilization of membrane potential by preventing severe hyperpolarization of neuron to membrane potentials at which the membrane would become unstable figure: dashed lines show instantaneous I-V relation; solid lines show steady-state 30 BME 502 / 1997 / handout #3 IQ q-current, or, "queer" current inward rectifying, non-selective cation channel top panel: when recording membrane potential (not voltage clamp, injecting hyperpolarizing current activates IQ, decreasing membrane resistance, which leads to the "sag" in the membrane potential record bottom panel: under voltage clamp conditions, a hyperpolarizing command step activates IQ ; slowly increasing current illustrates slow activation kinetics 31 BME 502 / 1997 / handout #3 32 BME 502 / 1997 / handout #3 33 BME 502 / 1997 / handout #3 34