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Recording membrane voltage in current-clamp mode from Carbone, Cicirata, Aicardi, EdiSES, 1° ed. (2009) Recording resting potentials, neuronal firings (trains of APs), pacemaker activities, graduate potentials requires glass microelectrodes of high resistance (10-100 M ) The cell can also be hyperpolarized or depolarized to regulate the resting and to evoke APs by passing a constant or stepwise membrane current. The current electrode is usually low-ohmic (k -M ) and does not necessarily penetrate the cell. Measuring voltages and passing currents can be done with the same microelectrode How?

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It can be used to make sums, subtractions, integrals, derivatives or any other mathematical operation of the input signals Recording membrane potentials with operational amplifiers What is an operational amplifier? Is a solid-state amplifier with the following characteristics: With open circuit: high gain (A) = ∞ (≈ 2x10 5 ) high R in = ∞ (≈ 1x10 14 ) low R out = 0 (≈ 10 )

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1 st example - The voltage inverter Due to the high gain of the op. amplif., the blue point acts as a “virtual ground”. There is no current flowing behind: = 0 and i a =0 (V i - ) ( -V o ) R1R1 = + i a R2R2 At the blue junction: i 1 = i 2 + i a ViVi VoVo R1R1 = - R2R2 VoVo R2R2 ViVi R1R1 (inverting) The gain is A = - R2R2 R1R1 R in = R 1 R out = 0

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2 nd example - The non-inverter but i = ViVi R2R2 (V o - V i ) = R 1 i Assuming i a = 0 and = 0: (non-inverting) The gain is A = 1 + R1R1 R2R2 R in = ∞ R out = 0 V o = V i + R 1 ViVi R2R2 thus V o = 1 + V i R1R1 R2R2

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3 rd example - The unity-gain, buffer amplifier (the “voltage-follower”) It has the same configuration of the previous case except that: R 2 = ∞ and R 1 = 0 V o = 1 + V i R1R1 R2R2 The previous equation: becomes: VoVo ViVi = 1 It is the ideal “buffer amplifier” for coupling high-resistance microelectrodes (>100 M ) with instruments which measure the voltage (oscilloscopes, computer interfaces, ….) The gain is A = +1 (unity) R in = ∞ R out = 0

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A single-electrode current-clamp amplifier

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Current-clamp and voltage-clamp recordings for complete electrophysiological analysis Under these conditions, the Ohm law: V m = R m I m can be simplified to: K = R m I m I m = I m g m K RmRm Action potential recordings in current-clamp (I m = 0) is optimal for recording neuronal activity without perturbing the cell Data interpretation in terms of voltage-gated ion channels, however, is difficult since membrane voltage changes continuously with time A good compromise is “clamping” the voltage to a fixed value and measure the current (V m = K)

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from Carbone, Cicirata, Aicardi, EdiSES (2009) The voltage-clamp circuit (Cole & Curtis, 1948)

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The patch-clamp technique Neher & Sakmann (1981)

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Na + and K + currents at fixed voltages (Hodgkin & Huxley, 1952)

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Physiological and pharmacological separation of Na + and K + currents

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The voltage dependence of Na + and K + conductances To calculate the Na + and K + conductances we use the following equations: I Na = g Na (V m – E Na ) I K = g K (V m – E K ) with E Na = +63 mV with E K = -102 mV

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The voltage dependence of Na + and K + conductances

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Tetrodotoxin (TTX): the classical Na + channel blocker A pufferfish containing TTX

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The -conotoxin GVIA: the N-type Ca 2+ channel blocker The conus geographus from Philippines

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Noxiustoxin (NTX): a blocker of voltage-gated K + channels Centruroides noxius (female from St. Rosa, México)

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The voltage-gated Na +, K + and Ca 2+ channels

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Suggested readings: General: Chapters 1-3 in Purves et al. Neuroscience, Sinauer, 4° ed. Chapters 1-3 in Carbone et al. Fisiologia: dalle molecole ai sistemi integrati, EdiSES, 1 st ed. Technical: The axon guide: A Guide to Electrophysiology & Biophysics Laboratory Techniques Down-load from: http://www.moleculardevices.com/pages/instruments/axon_guide.html

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MATHEMATICAL MODEL FOR ACTION POTENTIAL

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