lecture 2: basic principles of electricity required reading: kandel text, appendix chapter i neurons...

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 +)}

Force experienced by charged particle determined by the sum and distancesof surrounding charges

+ +

+ + -

-

+

- + - -

+ + +

-

NO

FO

RC

E

RE

PU

LS

IVE

FO

RC

E

AT

TR

AC

TIV

E

FO

RC

E

NEUTRAL POSITIVE NEGATIVE

+

+ - - -

+ + +

-

NEGATIVE

POSITIVE

ELECTRICAL CONDUCTANCE AND RESISTANCE

+

+ - - -

+ + +

-

NEGATIVE

POSITIVEA

B

WHEN CHARGED PARTICLES ARE SUBJECT TOELECTRICAL FORCE, THEIR ABILITY TO MOVE

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

RESISTANCE (R) {units=Ohmsmeasure of material’s difficulty in allowing

electrical conduction

Resistance is the INVERSE of Conductance. I.e.:

R = 1g OR g = 1

R

VOLTAGE AND CURRENT

+

+ - - -

+ + +

-

NEGATIVE

POSITIVEA

B

VA

VB

V I

When there is a charge differential between two points, energy is stored. This stored energy is called ELECTRICAL POTENTIAL or

VOLTAGE DIFFERENTIAL (V) {units = volts, V}

V = 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

CURRENT (I) {units = amperes, A} is the RATE of charge flow.

I = dq / dt

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 boththe voltage differential and the conductance

I= V x g

Since g = 1 / R I = V / R V = I x R

SCHEMATIC DIAGRAM

R

VA VB

I

V = VA - VB = IR

I = V / R

WATER PRESSURE ANALOGY

PA

PB

FLOW RATE

VALVE

Water Pressure is analogous to Voltage DifferentialValve Resistance is analogous to Electrical ResistanceFlow Rate is analogous to Electrical Current

Flow Rate = Water Pressure / RVALVE

OR

THE “I-V PLOT” & OHM’S LAW

I= V x gR

VA VB

I

In a simple resistive circuit, the relationship between current and voltage is LINEAR

10

20

- 20 - 10 10 20- 10

- 20

V

I

10

20

- 20 - 10 10 20- 10

- 20

V

I

HIGH CONDUCTANCE WEAKER CONDUCTANCE

CONDUCTANCE ( g )is SLOPEof line inI - V PLOT

MULTIPLE RESISTANCES IN SERIES

V1 V2

R2R1

I2I1

a cb

IN SERIES RESISTANCES SUM TO GIVE OVERALL RESISTANCE

RTOTAL (a,c) = R1 (a,b) + R2 (b,c)

ITOTAL (a,c) = I1 (a,b) = I2 (b,c)

VTOTAL (a,c) = V1 (a,b) + V2 (b,c)

Two resistances are summed to give the overall resistance between points a and c

Currents are equal along the series

By Ohm’s Law, the total voltage differential equals the sum of the component voltages

POSITIVE NEGATIVE

MULTIPLE RESISTANCES IN PARALLELR1

POSITIVE NEGATIVE

R2I2

I1

ITOTAL = I1 + I2

gTOTAL = g1 + g2

VTOTAL = V1 = V2

I1 x R1 = I2 x R2

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”

ITOTAL

POSITIVE

NEGATIVE

R1 R2

I2I1

ITOTAL

EQUIVALENTREPRESENTATIONS

+

-SYMBOL DESIGNATES A VOLTAGE GENERATOR (POWER SOURCE)WHICH MAINTAINS A CHARGE DIFFERENTIAL FROM ONE SIDETO THE OTHER (e.g. A BATTERY)

R1 R2

I2I1

+

-

ITOTAL

ITOTAL

CIRCUIT DIAGRAM

R(10 )

+

-

I

V 10 V R(10 )

+

-

I

V 10 V

SWITCH OPEN AT t = 0 sec

SWITCH CLOSED AT t = 5 sec

BEHAVIOR OF A SIMPLE RESISTIVE CIRCUIT

CIRCUIT PROPERTIES

t (sec)0 5 t (sec)

0 5

V

(vo

lts)

0

10I

(Am

ps)

0

1

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 = V x C or V = 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:

CAPACITANCE

SOME MATERIALS CANNOT CONDUCT ELECTRICITY, BUT CAN ABSORB CHARGE WHEN SUBJECTED TO A CURRENT OR VOLTAGE

C

BEHAVIOR OF A SIMPLE CAPACITIVE CIRCUIT

C(10 F)

+

-

I

V 10 V +

-

I

V 10 V

SWITCH OPEN AT t = 0 sec


CIRCUIT PROPERTIES

t (sec)0 5 t (sec)

0 5

V

(vo

lts)

0

10

I (A

mp

s)

0

C(10 F)

t (sec)0 5

Q

(co

ulo

mb

s)

0

100

RELATIONSHIP OF CAPACITANCE AND CURRENT

q = C x V

AS DESCRIBED BEFORE:

SINCE I = dq /dt

dq/dt = I = C x dV/dt

I.e. As current flows into a capacitor, the voltage across it increases

CIRCUIT WITH CAPACITANCE & RESISTANCE IN SERIESIN SERIES

+

-

I

10 V


R(5 )

C(1 F)

VAR

(5 )

+

-

I

VA 10 V

SWITCH OPEN BEFORE t = 0

C(1 F)

VB VB

CIRCUIT PROPERTIES

t (sec)-5 0 5 10

VA

(vo

lts)

0

10

( REMEMBER: After switch closed, VA + VB = VTOTAL = 10 V )

t (sec)-5 0 5 10

VB

(vo

lts)

0

10

t (sec)-5 0 5 10

I (a

mp

s)0

2

LOGARHYTHMIC DECAY OF CURRENT THROUGH ACIRCUIT WITH CAPACITANCE & RESISTANCE IN SERIESIN SERIES

+

-

I

10 V

SWITCH CLOSED

AT t = 0 sec

R(5 )

C(1 F)

VAR(5 )

+

-

I

VA 10 V

SWITCH OPEN

BEFORE t = 0

C(1 F)

VB VB

I = C d VC

d tI = =

VTOT - VC

R

VR

REqu. A Equ. B

Combine equations A & B and integrate

VC (t) = VTOT (1 - e - t / RC )

VR (t) = VTOT (e - t / RC )

As capacitor charges, VR and I decay logarhythmically

CIRCUIT WITH CAPACITANCE & RESISTANCE IN SERIES IN SERIES CONTROL OF CURRENT FLOW BY SIZE OF R AND C

R +

-

I

VA

+

-

I

SWITCH OPEN

SWITCH CLOSED

C

R

C

VA

VB VB

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

t1/2-max (sec) = 0.69 x R () x C (F)

CIRCUIT WITH CAPACITANCE & RESISTANCE IN SERIES IN SERIES CHARGE AND DISCHARGE OF A CAPACITOR

R(5 )

I

+

-VA 10 V

CHARGE SWITCH CLOSED AT t = 0 sec

C(1 F)

VB

CHARGE SWITCH OPENED AT t = 10 sec

DISCHARGE SWITCH CLOSED AT t = 10 sec

CIRCUIT PROPERTIES

t (sec)0 5 10 15 20

VA

(vo

lts)

0

10

-10

t (sec)0 5 10 15 20

I (a

mp

s)

0

2

-2

t (sec)0 5 10 15 20

VB

(vo

lts)

0

10

-10

RESISTORVOLTAGE

CAPACITORVOLTAGE

CIRCUIT WITH CAPACITANCE & RESISTANCE IN PARALLEL IN PARALLEL

RB

(5 )

RA

(5 ) +

-

ITOT

10 V

SWITCH OPEN BEFORE t = 0 sec


C(1 F)

IBIC

ITOT

VA

VB

t (sec)-5 0 5 10

VA

(vo

lts)

0

10

5

t (sec)-5 0 5 10

VB

(vo

lts)

0

10

5

t (sec)-5 0 5 10

I C

(am

ps)

0

2

1

t (sec)-5 0 5 10

I B

(am

ps)

0

2

1

t (sec)-5 0 5 10

I T

OT

(am

ps)

0

2

1

CURRENT FLOWTHROUGHPARALLELRESISTOR

IS DELAYEDBY THE

CAPACITOR{

CIRCUITS WITH TWO BATTERIES IN PARALLEL IN PARALLEL

RB IB +

- VA

VB

+

-


t (sec)-5 0 5 10

I B

(am

ps)

0

VA = VB + IBRBIB = (VA - VB) / RB

or

RB IB

+

-VAVB

+

-

RA IA

VC

IC

In this circuit,what is VC at steady state?

IA = - IBtherefore, (eq.2)

VC = VA + IARA = VB + IBRB(eq.1)

IA + IB + IC = 0 IC = 0andalso

Combining eq. 1 & 2, and converting R to g

VC =VA gA + VB gB

gA + gB

VC is the weighted average of the two batteries,weighted by the conductance through each battery path

CONCLUSION:

RESISTANCES & CAPACITANCES ALONG AN AXON

MEMBRANE MEMBRANE ((CC))

IONIONCHANNEL (CHANNEL (gg))

CYTOSOL (CYTOSOL (gg))

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

RMRMRM

RAXON

CMCMCM

RAXON RAXON 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.

+

-

IA1 IA2

IM1 IC1

Axon current nearest the voltage source (IA1) does not all proceed down the axon (IA2). Some current is diverted through membrane conductance (IM1), and current propogation down axon is delayed by diversion into the membrane capacitance (IC1).

Next lecture: ION CHANNELS & THE RESTING MEMBRANE POTENTIAL

REQUIRED READING: Kandel text, Chapters 7, pgs 105-139

lecture 2: basic principles of electricity required reading: kandel text, appendix chapter i neurons...

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