Understanding Action Potentials and Ionic Currents: A Deep Dive into Membrane Excitability, Study notes of History of Education

Download Understanding Action Potentials and Ionic Currents: A Deep Dive into Membrane Excitability and more Study notes History of Education in PDF only on Docsity! LECTURE 2, 27 JAN 2005 (1) action potentials are created by brief increases in Na+ permeability (Hille, Fig. 2.1) (A) negative resting Vm is created by selective K+ permeability (EK ~ -90 mV) in pores (ion channels) of the membrane, which is a capacitor that stores the voltage. (B) propagation of action potentials is a wave of depolarization (Hille, Fig. 2.2) (i) active regions depolarize inactive regions, which recruits these regions (ii) the process is regenerative as active depolarization continually invades and (iii) excites membrane regions adjacent to active "sites". (C) action potentials are accompanied by an impedance (resistance) decrease (Hille, Fig. 2.3). (D) action potentials are not "breakdown" of membrane because peak spike amplitude exceeds 0 mV, i.e., overshoot (Hille, Fig. 2.4). (i) selective Na+ permeability creates overshoot, as Vm approaches ENa. (ii) proved using low Na+ experiments. (2) voltage clamp (A) the ionic (Na+) hypothesis was confirmed using voltage-clamp experiments (B) quantitative measure of ionic currents with precise control of Vm: (I) Im = ∑I_ion + Ic = ∑I_ion + Cm*dV/dt (C) step changes in Vm means that dV/dt=0, hence capacity current (Ic) is zero throughout the protocol, except during the instant the step change occurs. (D) all the current (∑Iion) is ion flux through ionophores (i.e., ion channels, pores). (3) sodium and potassium currents (Hodgkin and Huxley, 1950's) (A) membrane currents in response to depolarization are complex (Hille Fig. 2.6) (B) major conceptual advance: currents are separable by ion type (C) ionic current flows inward/outward based on Vm and equilibrium potential, e.g.: (i) Na+ flows IN if Vm<ENa, since Vm-ENa (i.e., driving force) is negative (ii) Na+ flows OUT if Vm>ENa, since Vm-ENa is positive (iii) if Vm=ENa, Na+ current does NOT flow at all. (iv) likewise, IK is OUTWARD if Vm>EK and INWARD if Vm<EK, zero if Vm=EK (D) Early inward currents reverse direction at +55 mV, near ENa (Hille, Fig. 2.7). (E) Late outward currents never reverse at any test voltages from -60 to +90 mV, which would be expected for K+ current with EK<-60 mV. (F) isolation of currents via ion substitution and subtraction (Hille, Fig. 2.8). (G) I-V curves for INa and IK (Hille, Fig. 2.9). (i) INa plots "peak" inward current, INa = gNa(V)*(Vm - ENa) (ii) IK plots steady-state late current, IK = gK(V)*(Vm - EK) (iii) write out chord-conductance equations, understand current components (a) activation, gNa(V) and gK(V) (b) effect of driving force, (Vm - ENa) and (Vm - EK) (4) sodium and potassium conductances (Hodgkin and Huxley, 1952) (A) HH confirmed that open Na/K conductances are "Ohmic", i.e., the I-V curve is linear through the open pore, determined using instantaneous I-V protocols, Fain gives a good description in Chapter 5. (B) isolate conductance from current (Hille, Fig. 2.10): (i) gNa(V,t) = INa/(Vm - ENa) (ii) gK(V,t) = IK/(Vm - EK) (C) time course of gNa(t) and gK(t) at step depolarization (Hille, Fig. 2.11) (i) gNa(t): activation, followed by inactivation while Vm remains depolarized (a) distinguish inactivation from deactivation (dotted lines in 2.11) (b) deactivation is channel closure if Vm repolarizes (ii) gK(t): slow activation (D) family of activation/inactivation and slow activation plots shows voltage- dependent properties of gNa(V,t) and gK(V,t) (Hille, Fig. 2.12). (E) peak gNa(V) and steady-state gK(V) saturate at high Vm (Hille, Fig. 2.13). (i) this is maximal activation, all available channels are OPEN. (5) voltage dependence and kinetics of gNa(V,t) (A) activation is FAST and STEEPLY voltage dependent (B) inactivation is SLOW and also voltage dependent (Hille, Fig. 2.14). (C) steady-state voltage dependence of inactivation: two-pulse protocols (i) multiple prepulses of long duration that achieve steady-state inactivation of gNa at each prepulse voltage (ii) test pulse to fixed level to determine the fraction of gNa that were NOT inactivated via the prepulse. (D) recovery from inactivation, i.e., de-inactivation (Hille, Fig. 2.15). (i) another type of two-pulse protocol (ii) identical depolarizing pulses separated by variable time interval (∆t) (iii) first pulse activates, and fully inactivates gNa(V,t) (iv) second pulse tests how much recovery of gNa(V,t) has taken place in ∆t (v) amount of recovery vs. ∆t can be fitted by time constant tau-h. (vi) tau-h can be determined at any voltage level using two-pulse protocols and ∆t intervals. (6) the Hodgkin-Huxley model of membrane excitability (A) gNa and gK are functions of maximum conductances and gating variables: (B) consider gK(V,t) first (Hille, Fig. 2.16 and 2.17): (i) gK(t) takes sigmoidal time course during Vm depolarization (ii) gK(V,t) = gK_max*n*n*n*n (4 gating particles) (iii) gating particles move independently with voltage: (1 - n)<-->n, according to voltage-dependent forward/backward rates alpha_n/beta_n (iv) steady-state voltage dep.: n_infinity = alpha_n/(alpha_n + beta_n) (v) kinetics: tau_n = 1/(alpha_n + beta_n) (vi) differential equations for gating particle movements: (a) dn/dt = alpha_n*(1 - n) - beta_n*n, or (b) dn/dt = (n_infinity - n)/tau_n (vii) therefore, IK = gK_max*n^4*(Vm - EK) (C) gNa(V,t) follows similar description (Hille, Fig. 2.16 and 2.17): (i) gNa(t) activates with sigmoidal time course: 3 activation gating variables (ii) inactivation utilizes 1 gating variable: gNa(V,t) = gNa_max*m*m*m*h (iii) in response to depolarization: m --> 1 and h --> 0. (a) conductance is the product of all four gating variables. (b) conductance high at onset, low/zero after time when h≈0. (iv) gating particles move independently with voltage according to voltage- dependent rate constants: (a) kinetic expression: (1 - m) <--> m, rates: alpha_m/beta_m (b) kinetic expression: (1 - h) <--> h, rates: alpha_h/beta_h (v) steady-state voltage dependence: (a) m_infinity = alpha_m/(alpha_m + beta_m) (b) h_infinity = alpha_h/(alpha_h + beta_h) (vi) kinetics: (a) tau_m = 1/(alpha_m + beta_m) (a) tau_h = 1/(alpha_h + beta_h) (vii) differential equations for gating particle movements: (a) dm/dt = alpha_m*(1 - m) - beta_m*m, or (b) dm/dt = (m_infinity - m)/tau_m (c) dh/dt = alpha_h*(1 - h) - beta_h*h, or (d) dh/dt = (h_infinity - h)/tau_h (viii) therefore, INa = gNa_max*m^3*h*(Vm - ENa) (A) HERMANN LOCAL CIRCUITS, (C) COLE-CURTIS MEMBRANE. (B) HERMANN CABLE Axon “core” 2.2 Early Descriptions of Excitation Biophysicists sought to repre- sent excitation and propagation of action potentials in terms of simple electrical circuits. (A) Hermann (1872) suggested that the potential differ- ence between excited and unexcited regions of an axon would cause small currents (later named local circuit currents by Hodgkin) to flow between them in the correct direction to stimulate the previously unexcited region. [Drawing after Hermann 1905a.] (B) Hermann (1905b) described the pas- sive spread of potentials in axons and muscle by the theory for a “leaky” telegraph cable. Here the protoplasmic core and extracellular region are represented as chains of resistors and the region between them (now called the membrane), as parallel capacitors and resistors. (C) Cole and Curtis (1938) used this equivalent circuit to interpret their measurements of mem- brane impedance during the propagated action potential. They concluded that during excitation the membrane conductance increases and the emf decreases pari passu, but the membrane capacitance stays constant. The diagonal arrows signify circuit components that change with time. ?) Conductance (mS/em’ 0 al Day ae Gin poy alo Time (ms) 2.3 Conductance Increase in Excitation This classical illustration shows the first direct demonstration of an ion permeability increase during the propagated action potential. The time course of membrane conductance increase in a squid giant axon is measured by the width of the white band photographed from the face of an oscilloscope during the action potential (dotted line). The band is drawn by the imbalance signal of a high-frequency Wheatstone bridge applied across the axon to measure membrane impedance. [From Cole and Curtis 1939.] Stimulus: Squid axon 2.4 Na*-Dependence of the Ex (mV) j Action Potential This is the 20 first experiment to demonstrate... .eeeeeae Dee Weettreemieerta macau that external Na* ions are need- ed for propagated action poten- tials. Intracellular potential is recorded with an axial micro- electrode inside a squid giant axon. The action potential is smaller and rises more slowly in solutions containing less than the normal amount of Na”. External bathing solutions: Records 1 and 3 in normal sea- water, record 2 in low-sodium solution containing 1:2 or 1:1 mixtures of seawater with iso- tonic glucose. An assumed 15- mY junction potential has been subtracted from the voltage scale. [From Hodgkin and Katz 1949,] Time after shock (ms)  (B) 10% Nat BO 11 ola eM cena tt heey oe (malem2 ° (A) 100% Nat (C) Difference current TNa pbbouel Gay vile ferrpataniviiors Py 0 1 2 3 4 5 Time after start of test pulse (ms) 2.8 Separation of Na* and K* Currents _ An illustration of the classical ion sub- stitution method for analyzing the ionic basis of voltage-clamp currents. Ionic currents are measured in a squid axon membrane stepped from a holding potential of 65 mV to-9 mV. The component carried by Na’ ions is dissected out by substituting imper- meant choline ions for most of the external sodium. (A) Axon in seawater, showing inward and outward ionic currents. (B) Axon in low-sodium solution with 90% of the NaCl substituted by choline chloride, showing only outward ionic current. (C) Alge- braic difference between experimental records (A) and (B), showing the transient inward component of current due to the inward movement of external Nat ions. T=8.5°C. [From Hodgkin 1958; adapted from Hodgkin and Huxley 1952a.]  2.9 Current-Voltage Relations of a Squid Axon = The axon mem- brane potential is stepped under voltage clamp from the negative holding potential (E,,) to various test potentials, as in Figure 2.7. Peak tran- sient Na* current (triangles) and steady-state K* current (circles) from each trace are plotted against the test potential. The nonlinearity of the two LE relations between -50 to -20 mV reflects the voltage-dependent open- ing of Na and K channels by depolar- izations, as explained in Figure 1.6. [From Cole and Moore 1960. | 2.10 Equivalent Circuit of an Axon Membrane Hodgkin and Huxley de- scribed the axon membrane as an electrical circuit with four parallel branches. The capaci- tative branch represents the dielectric properties of the thin membrane. The three conduc- tive branches represent sodi- um, potassium, and leak con- ductances with their different electromotive forces. The resis tors with arrows through them denote time- and volt- age-varying conductances arising from the opening and closing of ion channels. [From Hodgkin and Huxley 1952d.| Outside ‘Ic fia Vk th acta. i a —— ™ Na 8k 8L Ei | Pe ] Bye Inside (A) Na CONDUCTANCE Relative maximum conductance 1.0 © e 3 0.001 (B) KCONDUCTANCE ive maximum conductance O1 0.001 50 0 Test pulse potential (mV) 0 Test pulse potential (mV) of a %@ gor Rrebo 50 ° 2.13 Voltage Dependence of Ionic Conductances Peak gy, (A) and steady-state 8x (B) are measured during depolarizing voltage steps under voltage clamp. Symbols are measurements from sever- al squid giant axons, normal- ized to 1.0 at large depolariza- tions, and plotted ona logarithmic scale against the potential of the test pulse. Dashed lines show limiting equivalent voltage sensitivities of 3.9 mV per e-fold increase of na and 4.8 mV per e-fold increase of gy for small depolorizations. [Adapted from Hodgkin and Huxley 1952a.] (A) Na CURRENT (B) ANALYSIS ; h 4, (ms) LOr 5 Node of Ranvier 22°C: S 4 & ab 3 05 2 Exa 1 0 7 Seal) 100, -50 0 +50 E=-15mV en E (my) Ee 0.5 ms. 2.14 Inactivation of Sodium Current A voltage-clamp experiment to measure the steady-state voltage dependence of inactivation. A node of Ranvier of frog myelinated nerve fiber is bathed in frog Ringer’s solution and voltage clamped by the Vaseline gap method shown in Figure 2.5. (A) Sodium currents elicited by test pulses to -15 mV after 50-ms prepulses to three differ- ent levels (E,..). Kia is decreased by depolarizing prepulses. (B) Symbols plot the relative peak size of hy, versus the potential of the prepulse, forming the “steady-state inactivation curve” or the “h,, curve” of the HH model. The bell- shaped 1, curve shows the voltage dependence of the exponential time con- stant of development or recovery from inactivation, measured as in Figure 2.15. T = 22°C. [From Dodge 1961, © American Association for the Advancement of Science.] (A) TWO-PULSE EXPERIMENT Pulse 1 Pulse 2 I (nA) (B) RECOVERY CURVE 1.0 S ala B12 4 Elz 08 aie ‘ Zhe 0 5 10 15 Recovery interval (ms) 2.15 Recovery from Sodium Inactivation A two-pulse experiment measuring the time course of recovery from sodium inactivation in a frog node of Ranvier. (A) The first pulse to -15 mV activates and inactivates Na channels. During the interpulse inter- val, some channels recover from inactivation. The second pulse determines what fraction have recovered in that time. Dotted lines show the estimated contribution of potassium and leak currents to the total current. (B) Relative peak J\,, recovers with an approxi- mately exponential time course (1), = 4.6 ms) during the interpulse interval at -75 mV. T = 19°C. [From Dodge 1963.]  Theory Eyg (mV) L 0 1 x 3 Time (ms) 2.18 Calculated Propagating Action Potential Computer- calculated responses of a simulated axon of 476-um diameter and 35.4 Q.- cm axoplasmic resistivity assumed to have a membrane described by the HH model adjusted to 18.5°C. In this simulation, a stimulus cur- rent is applied at x = 0 for 200 kis. It depolarizes the membrane locally but not as far away as x = 1 cm. However, the stimulus is above thresh- old for excitation of an action potential, which appears successively at x=0, 1,2, and 3 em, propagating at a calculated steady velocity of 18.7 m/s. [From Cooley and Dodge 1966.]  @) SUF EN, Squid axon r action potential Na channels \ ton Membrane potential (mV) L ea auerquiau yo unl aad sjamueyp vedo (B) ° 2 3 4 Time (ms) 1 1 ! L 0 25 50 75 Distance (mm) 2.19 Channel Openings and Local Circuits Events during the propagated action potential. These diagrams describe the time course of events at one point in an axon, but since the action potential is a wave moving at uniform velocity, the diagrams may equally well be thought of as an instantaneous “snapshot” of the spatial extent of an action potential. Hence both time and distance axes are given below. (A) Action potential and underlying opening of Na and K channels calculated from the HH model at 18.5°C, (B) Diagram of the local cir- cuit current flows associated with propagation; inward current at the excited region spreads forward inside the axon to bring unexcited regions above firing threshold. The diameter of the axon is greatly exaggerated in the drawing and should be only 0.5 mm. [Adapted from Hodgkin and Huxley 1952d.]