Foundations I Fall, 2018 Action Potentials and Associated Voltage-gated Ion Channels
The Bernstein Hypothesis Part II (1912) J. Bernstein ~”Action potential results from a breakdown in selective permeability to potassium”
1946
J. Bernstein 0 for 2 (sort of) but correct on several dozen other key aspects (e.g, discovered the AHP, first to propose use of CRT oscilloscope !!, etc.) 1868 this finding of the AHP actually argues against his hypothesis...
L. Hermann (1838-1914) Local circuit theory late 1870s strömchen
Whitestone Bridge
Wheatstone Bridge R and R are known. What is the value of R ? 3 4 1
adjust until the ammeter reads zero R 2 at that point, V I R = V = I R = I R = d 2 1 b 2 4 1 3 Why?
According to Kirchoff’s Law, the algebraic sum of the potential rises and drops around a closed loop is zero. Since V=IR for all paths in the circuit, if there is no current flowing between d and b, there must be no potential difference between d and b. In other words, Vd=Vb.
I R I = 1 3 1 2 R 4 ? I R I R 1 2 1 3 = R R 1 4 R R 2 3 = V I R = V = I R = I R = R R d 2 1 b 2 4 1 3 1 4 I R = I R 2 1 1 2 R R I R R = 2 4 I = 1 2 1 R 2 R 1 3
V V = I ( R R ) + electrode m totally unbalanced I V V = I R m electrode balanced I V electrode + cell membrane balanced I
654 IMPEDANCE OF SQUID AXON DURING ACTIVITY amplifier was sharply tuned so that a bridge frequency as low as 20 kc. could be used. A balanced modulator was then substituted for the simple mixer and the amplifier tuning broadened as much as possible. A bridge frequency of 2 kc. could then be used and the distortion was greatly decreased. A differential resistance-capacity coupled amplifier with degeneration in the common mode was used for the action potentials. The output of either this amplifier or the 175 kc. bridge amplifier could be switched to the vertical deflecting plates of the cathode ray oscillogrsph through a single stage untuned power K.S. Cole (1900 - 1984) amplifier. The conversion of all bridge output frequencies to 175 kc. before they were impressed on the oscillograph as well as the short time intervals involved precluded I, " OSCILLATOR I BRIDGE 1 , . .. I S T I M U L U S s w E I, V-AMPLIFIER E P I FXG. 2. Schematic diagram of the electrical equipment. The axon is at the Cole and Curtis 1939 left, and the balancing resistance and capacity at the right, of the bridge. The action potential and bridge amplifiers are represented by V-amplifier and Z-ampli- fier respectively and the cathode ray oscillograph by C. R. the use of the Nitell~ motion picture and ellipse technique, but the use of a hori- zontal sweep circuit was convenient since the axon could be stimulated between one and ten times per second as was usually done. The stimulus was a short shock which was taken from the sweep circuit in such a manner that it was applied at the start of the sweep, and a shielded transformer was used in the stimulus circuit to reduce the shock artifact. Procedure Experimental.--After the axon was placed in the measuring cell and had become steady, the resting parallel resistance and capacity were measured at 9 frequencies
40 mS/cm 2 0 Cole and Curtis 1939
large decrease in transmembrane impedance (AC resistance) during action potential less than 2% change in membrane capacitance
Hodgkin and Huxely, 1939 and Cole and Curtis, 1940
at this point all of this research ground to a complete halt
and after a short interlude for killing and maiming, neuroscience resumed
during an action potential the membrane potential changed rapidly the membrane potential change was associated with a very large change in membrane conductance the membrane potential change and the conductance change occurred nearly simultaneously and interdependently how can one tease them apart?
The Voltage Clamp Marmount, Cole, Hodgkin, Huxely and Katz (1947-49)
Hodgkin and Huxley introduced the concept of ionic conductances to study the instantaneous current-voltage relations as follows: Recall that conductance, g=1/R and that R=V/I. Thus, g=I/V g =I /(E -E ) Na Na m Na and driving force g =I /(E -E ) K K K m Note that V here is not the resting membrane potential but the difference between the resting membrane potential and the equilibrium potential for the ion. This called the driving force.
g and g were plotted after stepping to different Na K command voltages Text g The kinetics of and are both voltage and time dependent g K Na
H&H assumed that some physical event, like a molecular change, underlay the voltage and time dependent change in G. The K current, the onset was sigmoidal in time and the decay exponential Such behavior could be accounted for if the voltage sensor consisted of one or more membrane bound dipoles that could be either in a permissive (conductance on) or non-permissive (conductance off) state If the probability that such a dipole particle is in the permissive state is n, then the probability that x particles are in state in is n x
For the K conductance, based on the sigmoidal shape of the rise in current, the best fit was obtained by g ( 4 I n V V ) = − K m k k where the voltage and time-dependent changes of n are given by α n 1-n n β n
The change in n over time is given by dn dt = α n (1 − n ) − β n n as an alternative to using rate constants, H-H defined a voltage dependent time constant, and a steady state value τ n for n, n ∞ 1 n ∞ = α n τ n = α n + β n α n + β n Then the change of n with time, which is formally equivalent to the changes in the K+ conductance is calculated by solving the ODE dn dt = n ∞ − n τ n
Similarly, the Na conductance was formalized as = m 3 h I V V ) ( g − Na m k Na Na The extra term h is required for the inactivation
The values for the sodium conductance are obtained by solving these h − h dh dm m − m ∞ = ∞ = τ τ dt dt h m where α 1 1 α h = h τ = τ = m = m β β m h ∞ β β ∞ α + α + α + α + m m h h m m h h
h is actually 1- probability of inactivation or probability that the gate is not inactivated
Predictions of the H-H Model 1. refractory period
The absolute refractory period is due to Na+ channel inactivation The relative refractory period is due to partial Na channel inactivation and the delayed rectifier K+ conductance
Predictions of the H-H Model 1. refractory period 2. threshold
20 mV 2 nA 40 ms
Threshold Individual channels have no fixed threshold For a particular K channel, if its 4 n particles are in the permissive state, it will open - this is a probabilistic thing As the membrane depolarizes, m increases, but so do n and h, according to their voltage dependence and their voltage dependent time constants Threshold is that voltage at which the inward currents just overbalance the outward currents. At the point the inward current becomes regenerative and the action potential takes off.
Dai et al., NYAS, 1998
Predictions of the H-H Model 1. refractory period 2. threshold 3. accomodation and adaptation
ISI1 ISI10 S1 S10 spike frequency adaptation ISI1 ISI10 10 mV accommodation 50 ms
Predictions of the H-H Model 1. refractory period 2. threshold 3. accomodation 4. gating currents
step to positive step to positive +TTX Armstrong and Bezanilla, 1974
Action Potential Conduction Mechanism of propogation
Action Potential Conduction Conduction Velocity ...in unmyelinated axon, depends on electrotonic properties of axon conduction velocity is inversely proportional to τ = r c m i note that this tau is based on , the axial r i resistance, not , the membrane resistance r m r R Recall from last lecture) ⋅ a m m = r R 2 i i Larger axons have smaller axial resistance, a faster time constant and faster conduction velocity
Action Potential Conduction Conduction Velocity II Conduction velocity also depends on the length constant, λ R r m ⋅ d m From last lecture, λ = r i = R 4 i Thus λ dictates how far the local depolarizations that underly action potential conduction spread - and the farther they spread, the fewer times they need to re- initiate at a different membrane location The larger the diameter, the larger λ is and the faster the action potential spreads
Action Potential Conduction Conduction Velocity III - Saltatory Conduction Myelination increases conduction velocity by increasing λ to the internodal distance, and by decreasing τ C= ee o A/d
Normal Saltatory Conduction The graphics represent membrane current at various sites along nerve fibers derived from recordings of external longitudinal current in undissected fibers from rat spinal roots – in some cases demyelinated with diphtheria toxin. Outward membrane current is represented as upward, inward membrane current as downward. Hugh Bostock at Institute of Neurology, University of London
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