LECTURE 2 BASIC PRINCIPLES OF ELECTRICITY REQUIRED READING

LECTURE 2: BASIC PRINCIPLES OF ELECTRICITY REQUIRED READING: Kandel text, Appendix Chapter I Neurons transmit electrical currents Behavior of synaptically linked neurons has similarities to behavior of solid-state electrical circuits Therefore, a fundamental appreciation of the nervous system requires understanding its electrical properties THIS LECTURE INTRODUCES BASIC CONCEPTS, TERMINOLOGY, AND EQUATIONS OF ELECTRICITY ESSENTIAL TO OUR TACKLING THE ELECTROPHYSIOLOGY OF NEURONS AND NEURAL CIRCUITS

CHARGED PARTICLES AND ELECTROSTATIC FORCE Some particles have electrical CHARGE; charge can be POSITIVE or NEGATIVE Charged particles exert FORCE on each other: LIKE charges REPEL OPPOSITE charges ATTRACT {examples of charged particles: electrons (-), ions (- OR +)} + - - + NEUTRAL + + -+ + FORCE + REPULSIVE NO FORCE + ATTRACTIVE Force experienced by charged particle determined by the sum and distances of surrounding charges + + -+ - -+ POSITIVE NEGATIVE POSITIVE + - -+ NEGATIVE

ELECTRICAL CONDUCTANCE AND RESISTANCE + + + WHEN CHARGED PARTICLES ARE SUBJECT TO ELECTRICAL FORCE, THEIR ABILITY TO MOVE A - POSITIVE FROM POINT A TO B IS INFLUENCED BY CONDUCTIVE PROPERTY OF MATERIAL + CONDUCTANCE (g) {units=siemens, S} measure of material’s ease in allowing movement of charged particles B RESISTANCE (R) {units=Ohms, W} measure of material’s difficulty in allowing electrical conduction Resistance is the INVERSE of Conductance. I. e. : R= 1 g OR g= 1 R - -+ NEGATIVE

VOLTAGE AND CURRENT When there is a charge differential between two points, energy is stored. This stored energy is called ELECTRICAL POTENTIAL or VOLTAGE DIFFERENTIAL (DV) {units = volts, V} VA + + + A - POSITIVE DV = VA - VB When there is a voltage differential between two points in a conductive material, charged particles will be forced to move. Movement of charge is an ELECTRICAL CURRENT (I) {units = amperes, A} is the RATE of charge flow. I = dq / dt DV B + - -+ I NEGATIVE VB Where q = amount of charge {units = coulombs, Q} and t = time {units = seconds, s} NOTE: I > 0 means net flow of positive charge; I < 0 means net flow of negative charge

OHM’S LAW The amount of current flow is directly proportional to both the voltage differential and the conductance I = DV x g Since g = 1 / R I = DV / R SCHEMATIC DIAGRAM I VA VB R DV = VA - VB = IR I = DV / R OR DV = I x R WATER PRESSURE ANALOGY VALVE PA FLOW RATE PB Water Pressure is analogous to Voltage Differential Valve Resistance is analogous to Electrical Resistance Flow Rate is analogous to Electrical Current Flow Rate = Water Pressure / RVALVE

THE “I-V PLOT” & OHM’S LAW I VA I = DV x g VB R CONDUCTANCE ( g ) is SLOPE of line in I - V PLOT In a simple resistive circuit, the relationship between current and voltage is LINEAR - 20 I I 20 20 10 10 - 10 10 20 - 20 HIGH CONDUCTANCE DV - 20 - 10 10 20 DV - 20 WEAKER CONDUCTANCE

MULTIPLE RESISTANCES IN SERIES RESISTANCES SUM TO GIVE OVERALL RESISTANCE POSITIVE a R 1 b R 2 I 1 I 2 DV 1 DV 2 c NEGATIVE Two resistances are summed to give the overall resistance between points a and c RTOTAL (a, c) = R 1 (a, b) + R 2 (b, c) Currents are equal along the series ITOTAL (a, c) = I 1 (a, b) = I 2 (b, c) By Ohm’s Law, the total voltage differential equals the sum of the component voltages DVTOTAL (a, c) = DV 1 (a, b) + DV 2 (b, c)

MULTIPLE RESISTANCES IN PARALLEL R 1 I 1 POSITIVE ITOTAL I 2 Total current is the sum of individual parallel currents Total conductance is the sum of parallel conductances The voltage differential between two points is the same no matter what the path By Ohm’s Law, larger current travels thru the “path of least resistance” NEGATIVE R 2 ITOTAL = I 1 + I 2 g. TOTAL = g 1 + g 2 DVTOTAL = DV 1 = DV 2 I 1 x R 1 = I 2 x R 2

CIRCUIT DIAGRAM POSITIVE ITOTAL I 1 R 1 I 2 R 2 EQUIVALENT REPRESENTATIONS I 1 R 1 I 2 ITOTAL + R 2 ITOTAL NEGATIVE + - SYMBOL DESIGNATES A VOLTAGE GENERATOR (POWER SOURCE) WHICH MAINTAINS A CHARGE DIFFERENTIAL FROM ONE SIDE TO THE OTHER (e. g. A BATTERY)

BEHAVIOR OF A SIMPLE RESISTIVE CIRCUIT SWITCH OPEN AT t = 0 sec SWITCH CLOSED AT t = 5 sec I I + R DV (10 W ) - 10 V + R DV (10 W ) - I (Amps) DV (volts) CIRCUIT PROPERTIES 10 0 1 0 0 5 t (sec) 10 V

CAPACITANCE SOME MATERIALS CANNOT CONDUCT ELECTRICITY, BUT CAN ABSORB CHARGE WHEN SUBJECTED TO A CURRENT OR VOLTAGE CAPACITANCE (C) {units = farads , F} is the measure of the AMOUNT OF CHARGE DIFFERENTIAL which builds up ACROSS a material when subjected to a voltage differential. q = DV x C or DV = q / C I. e. Larger capacitance ----> Larger charge stored A material that has capacitance is called a capacitor. The schematic symbol for a capacitor is: C

BEHAVIOR OF A SIMPLE CAPACITIVE CIRCUIT SWITCH OPEN AT t = 0 sec SWITCH CLOSED AT t = 5 sec I I + DV C - (10 F ) + 10 V C DV - (10 F ) Q (coulombs) I (Amps) DV (volts) CIRCUIT PROPERTIES 10 0 100 0 0 5 t (sec) 10 V

RELATIONSHIP OF CAPACITANCE AND CURRENT AS DESCRIBED BEFORE: q = C x DV SINCE dq/dt I = dq /dt = I = C x d. DV/dt I. e. As current flows into a capacitor, the voltage across it increases

CIRCUIT WITH CAPACITANCE & RESISTANCE IN SERIES SWITCH OPEN BEFORE t = 0 SWITCH CLOSED AT t = 0 sec I I R + DVA (5 W ) - R 10 V DVA (5 W ) DVB C - DVB C (1 F ) + (1 F ) ( REMEMBER: After switch closed, DVA + DVB = DVTOTAL = 10 V ) 10 0 -5 0 5 t (sec) 10 10 I (amps) DVB (volts) DVA (volts) CIRCUIT PROPERTIES 0 -5 0 5 t (sec) 10 2 0 -5 0 5 t (sec) 10 10 V

LOGARHYTHMIC DECAY OF CURRENT THROUGH A CIRCUIT WITH CAPACITANCE & RESISTANCE IN SERIES SWITCH OPEN SWITCH CLOSED AT BEFORE t = 0 sec I R DVA C DVB (5 W ) + - I R 10 V (5 W ) C DVB + - 10 V (1 F ) Equ. A DVA d VC I=C dt Equ. B VR VTOT - VC I= = R R Combine equations A & B and integrate VC (t) = VTOT ( VR (t) = VTOT 1 - e t / RC ) t / RC e ( ) As capacitor charges, VR and I decay logarhythmically

CIRCUIT WITH CAPACITANCE & RESISTANCE IN SERIES CONTROL OF CURRENT FLOW BY SIZE OF R AND C SWITCH OPEN SWITCH CLOSED I R C I DVA DVB + R C DVA + - DVB THE LARGER THE RESISTANCE (R) ----> THE SMALLER THE INITIAL CURRENT SIZE THE LONGER IT TAKES FOR CAPACITOR TO CHARGE THE SLOWER THE DECLINE IN CURRENT FLOW THE LARGER THE CAPACITANCE (C) ----> THE LONGER IT TAKES FOR CAPACITOR TO CHARGE THE SLOWER THE DECLINE IN CURRENT FLOW NO EFFECT ON INITIAL CURRENT SIZE t 1/2 -max (sec) = 0. 69 x R (W) x C (F)

CIRCUIT WITH CAPACITANCE & RESISTANCE IN SERIES CHARGE AND DISCHARGE OF A CAPACITOR CHARGE SWITCH CLOSED AT t = 0 sec CHARGE SWITCH OPENED AT t = 10 sec DISCHARGE SWITCH CLOSED AT t = 10 sec I R + DVA (5 W ) 10 V - DVB C (1 F ) CIRCUIT PROPERTIES 0 -10 10 DVB (volts) 2 RESISTOR VOLTAGE I (amps) DVA (volts) 10 0 5 10 t (sec) 15 20 CAPACITOR VOLTAGE -10 -2 0 0 0 5 10 t (sec) 15 20

CIRCUIT WITH CAPACITANCE & RESISTANCE IN PARALLEL DVA (volts) SWITCH OPEN BEFORE t = 0 sec SWITCH CLOSED AT t = 0 sec ITOT (5 W ) IB RB (5 W ) - -5 C (1 F ) 0 10 V IC DVB 5 + DVA I TOT (amps) RA 10 ITOT 0 -5 0 5 t (sec) 10 I B (amps) DVB (volts) I C (amps) 1 10 5 0 -5 0 5 t (sec) 10 2 1 0 -5 0 5 t (sec) 5 10 0 5 10 2 1 0 -5 2 0 t (sec) CURRENT FLOW THROUGH PARALLEL RESISTOR IS DELAYED BY THE CAPACITOR { 10

CIRCUITS WITH TWO BATTERIES IN PARALLEL + IB RB - + VB VA I B (amps) SWITCH CLOSED AT t = 0 sec 0 -5 - VA = VB + IBRB In this circuit, what is VC at steady state? (eq. 1) also 0 or RB VB + - RA VA IA + CONCLUSION: - IC VC 10 / IB = (VA - VB) RB VC = VA + IARA = VB + IBRB IA + I B + I C = 0 therefore, (eq. 2) IB 5 t (sec) and IC = 0 IA = - I B Combining eq. 1 & 2, and converting R to g VC = VA gg. A ++Vg. B A B VC is the weighted average of the two batteries, weighted by the conductance through each battery path

RESISTANCES & CAPACITANCES ALONG AN AXON ION CHANNEL (g) MEMBRANE (C) CYTOSOL (g) Lipid bilayer of plasma membrane is NONCONDUCTIVE, but has CAPACITANCE Ion channels in membrane provide sites through which selective ions flow, thereby giving some TRANSMEMBRANE CONDUCTANCE Flow of ions in cytosol only limited by diameter of axon; the WIDER the axon, the greater the AXIAL CONDUCTANCE

MODELLING THE AXON AS RESISTANCES & CAPACITANCES RM CM RM RAXON CM RM CM RAXON The axon can be thought of as a set of segments, each having an internal axon resistance in series with a transmembrane resistance and capacitance in parallel When a point along the axon experiences a voltage drop across the membrane, the SPEED and AMOUNT of current flow down the axon is limited by RAXON, RM, and CM. IM 1 IA 1 IC 1 IA 2 Axon current nearest the voltage source (IA 1) does not all proceed down the axon (IA 2). Some current is diverted through membrane conductance (IM 1), and current propogation down axon is delayed by diversion into the membrane capacitance (IC 1). +

Next lecture: ION CHANNELS & THE RESTING MEMBRANE POTENTIAL REQUIRED READING: Kandel text, Chapters 7, pgs 105 -139