Section1 Final Slides

8/10/2019 Section1 Final Slides

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BioelectricitySection 1 Make Plans,

talk about Bioelectricity and introduce

the core-conductor model

Slide 1.1


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Section 1-2 What is the question?

Slide 1-2


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Jack, how old are you?

Slide 1.4


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The question for this course:

How does Jacks communication system work? It is electrical, and it is fast. It creates its own voltages, generates pulses, and

propagates them from their source to theirdestination.

These pulses carry information from one site toanother.

Slide 1.5


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Why this question?

Bioelectricity in nerves, the part of bioelectricistudied in this course, is a good place to start.

Historically it was first and famous. It is the foundation for understanding bioelectr

events in other systems, such as the brain, or inmuscles, including the heart.

Slide 1.7


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Duke University Union WalkwayA picture of Duke and North Carolina ends each section.

Slide 1.7


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Section 1 -3 About Bioelectricity

Slide 1-8


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About Bioelectricity What is Bioelectricity?

Slide 1.9

Bioelectricity involves the electrical voltagesand currents that are present in living tissue,their causes, and their consequences.


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When did the study ofBioelectricity begin?

Answer: In the 1700s, in Italy,with Galvani and with Volta,in conflict.

Slide 1.10


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What was the Galvani-Voltaconflict about?

One conflict was that Galvani thought that animalelectricity was a different kind of electricity thanthe heat electricity of Volta.

Though we now know that Galvani incorrect, why doeshis idea seem reasonable, even today?

Slide 1.11


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How is electricity in living tissue differentfrom the ordinary electricity of batteries,

wires, radios and computers?

What happenswhen you throw astandard batteryinto the ocean?

Slide 1.12


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What happens when youthrow a fish in the ocean?

Fish does fine. This ray does too . ;

Slide 1.13


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Duke Chapel at Duke University, Durham, NC, USA

Slide 1.14


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Section 1 -4 Major sections of the course

Slide 1.15


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Section 1 (right now)

Railroad1. Make PlansBioelectricity1. Make Plans

Bioelectricity backgroundRectification of Names

Electricity in Solutions

Slide 1.16


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Section 2

Railroad2. Sell Tickets, to get moneBioelectricity2. Energy, to get Vm

Membrane patchMembrane resistance

Membrane capacitanceIon pumpNernst Vm

Slide 1.17


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Section 3

Railroad3. EnginesBioelectricity3. Channels

Sodium ionPotassium ionLeakage

Slide 1.18


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Section 4

Railroad4. Train cars

Bioelectricity4. Action potentials

The Hodgkin-Huxley model

Different kinds of channelscooperating to create voltagepulses (action potentials)

Slide 1.19


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Section 5Railroad5. TrackBioelectricity

5. Currentswithin thetissue structure

Axial current andtrans-membranecurrent asdetermined by thetissues structure

Slide 1.20


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Section 6

Railroad6. Train is moving

Bioelectricity6. Propagation

Bringing together channels,action potentials, andstructure so that electricalsignals (action potentials)move along a fiber

Slide 1.21


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What are the Sections of the course?

Railroad analogy

Bioelectricity

Slide 1.22


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Duke University Chapel

Slide 1.23


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Section 1-5 Rectification of Names

Slide 1.24


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Rectification of Names The Rectification of Names: The phrase is t

from the Confucian doctrine that social harmonis achieved by using the proper designations fothings.

Bioelectricity deals with invisible objects, a bigproblem. Some conventions have been adoptedto name the abstract things that are its elements

Slide 1.25


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MembranesThe lipid bilayer is a thin materialaround cells. It is made of two layers oflipid molecules. One end (circles) ishydrophilic. The middle (lines) ishydrophobic.

The lipid bilayer is thin in comparisonto a cell diameter. In this illustration,the cell diameter is 200,000 Angstroms,while the lipid bilayer is only 80A.

Slide 1.26


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Channels and Pumps Channels are tiny tunnels through the membrane. Th

are important electrically because charged ions passthrough channels.

Pumps are structures in the membrane that use foodenergy to move ions uphill across the membrane.

Channels and pumps may be selective, meaning onlyone kind of ion can pass through, e.g. Na+ but not K

Important: In the membrane itself, not inside

Slide 1.27


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Transmembrane VoltageTransmembraneVoltage Vm is thepotential at point B minus the potential

at point A

The same Vm is often called Transmembrane Potential as a short formof Transmembrane Potential Difference.

Slide 1.28

P i i b l &


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Positive membrane voltage & positive membrane current

This sign convention is always used.

Slide 1.29

P i A ti


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Passive versus Active:same as dead versus alive?

Passive means that the same properties, such as resistance, aremaintained over time without change.

Active means that, due to some trigger, properties such as resistance mchange their value as time passes.

Slide 1.30

Passive versus Active:


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Passive versus Active:same as dead versus alive?

Dead material is passive.

Living tissue (such as electrically active membrane) is sometimepassive but active at other times.

Think of a resistor that is a million Ohms, but then changes to bethousand, and then changes back. That is what is meant by active

Slide 1.31


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Duke University Chapel Steps

Slide 1.32


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Section 1-6 Ions in Solutions *

Slide 1.33

Electricity in Solutions


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Electricity in Solutions The Big 5

The arrowssignify thateach quantitycan be foundfrom the onebefore

(includingnumber 1 fromnumber 5.

Slide 1.34


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Current is the movement of ions

An ion is a atom or molecule with a charge, becauseits number of electrons differs from the number ofprotons.

The presence of ions gives a solution electricalconductivity because ions can move.

Slide 1.35


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Example of ions in solution

Ordinary table salt NaCl has no net charge. In water NaCl divides into sodium ions and chloride io

written in symbols as Na+ and Cl- .

Each ion is charged because Na+ has lost an electron aCl- has gained one.

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Ions and conductivity Ions carry charge and move. Conductivity is a measure of how many and how eas

charges move. The higher the concentrations of ions the greater the

conductivity, if ease of movement is unchanged. For electrophysiology, the concentrations of the ions

sodium, potassium, and chloride are particularlysignificant.

Slide 1.37


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Resistivity and sea water

In ocean water the resistivity is around abo25 Ohm-cm.

The conductivity is the reciprocal, 1/25

Siemens per cm.

Slide 1.38


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Slide 1.39


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Section 1-7 Core-conductor model of a nerve fiber

Slide 1.40


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Cylindrical geometrySlide 1.41

Core -conductor model --- geometrically simple model yet retains essential features

Uniform cylindrical surface of radius h, long length Here the axial direction is the direction of the x coordinate. Cross-sections drawn in green with separation L are mathematical surfaces, not real. s Letters a through f identify points interior, exterior. Assumed cylindrical symmetry, as suggested by the dotted line Used here for nerve, but most famously to analyze the trans-Atlantic telegraph cable.


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Slide 1.42

Resistivity and Conductivity

25 cm50 cm

e

i

1/ 25 0.04S/cm1/ 50 0.02S/cm

e

i

Ocean water has resistivity of about 25 Ohm-cm

Interior and exterior volumes are both conducting solutions.

Here values chosen as examples are:


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Slide 1.43

Axial Resistance a-to-b

i

x

R A

L 2

i L

h

We can use the standard formula to find resistance from resistivity


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Slide 1.44

Axial Resistance numbers 1

2

i R L

h

2

50 cm(100E-4cm(5E-4cm)

R

Notes1cm=10,000 mm E-4 means divided by 10,000


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Slide 1.45

Axial Resistance numbers 2

636,620 R 1wire R Compare to

Nerve model Copper or sliver wire

In terms of axial resistance, nerves are not like wires.


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Slide 1.46


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Section 1-8 Potential and voltages in the nerve fiber

Slide 1.47

P t ti l Fi ld


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Potential Field Slide 1.48

Expoo a -b c

d e f at

One gets a potential field by keeping the negative lead in oneplace and moving the positive lead to all points of interest. Onecan do so experimentally and also conceptually.

T b d i l lt g


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Transmembrane and axial voltages Slide 1.49

( 20) ( 1)

19mV

m a

m

d

m

V

V

V

f f -

- - -

-

( 20) ( 60) 40mVab a bV f f - - - -

Transmembrane a-d:

Axial a-b:


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Slide 1.50


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Section 1-9 Axial currents in the nerve fiber

Slide 1.51

Axial current by Ohms law


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Axial current by Ohm s law

Assume current is uniform Use Ohms law Ix = Vab / R . Vab = 40mV, and R=636,620 Ohms Substitute and get: Ix = 62.8nA

Slide 1.52

1nA is 1E-is one billiof an Amp

Axial current from the electric field


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Assume current density is uniform from a to b The electric field is the (change in potential) / (change in position)

Note that Ex has a direction Vba = -40mV and L=100 mm, so Ex=4V/cm in the +x direction. The presence of Ex implies forces on charges F=Eq

Slide 1.53

( ) / ( ) / x b a b a ab x x V E Lf f - - -

Axial current density, and the axial current


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y,

Slide 1.54

280mA/cm x i x

x x x

J

I

E

J A

i

2A 7.854E-7cm

62.8nA x

x I

Here the direction of Jx and Ix is the same as that of Ex.


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Slide 1.54


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Section 1-10: Membrane Resistance

Slide 1.55

Membrane Resistance 1


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Slide 1.57

The direction of interest is now perpendicular to the axial direction In membranes there are significant voltages and currents between the

volumes internal and external to the membrane. What is the membrane resistance for the segment drawn in red? The membrane segment is centered and has length L.



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Slide 1.58

At rest the membrane resistivity is (approximately) Rm=1500 Ohm-cm2. Thus the membrane resistance for the segment can be computed if one

knows the surface area of the segment. Membrane resistance R=(membrane resistivity) / (Surface area)



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Slide 1.59

R=(membrane resistivity) / (Surface area) As = surface area = (Pi * 2h * L) = 3.14E-5 = 0.0000314 cm2 (approximat R = 1500 / As = about 48 Million Ohms (MOhms), approximately. So nerve membrane resistance R is less than R for most wire insulation,

which is possibly 1000 Mohms or more.


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Slide 1.60


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Section 1-11: Membrane Current, Failure & Mystery

Slide 1.61

Membrane Current 1


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Slide 1.62

Membrane Current Im has, by convention, a positive sign when outward. Suppose the trans-membrane voltage is -50mV at a, b, and c. In the previous subsection the membrane resistance Rmem was found to be

about 48 million Ohms. Lets give Ohms law a try.


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Membrane Current Mystery 1


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Slide 1.64

Im computed with Ohms law was about 1nA inward.

With Vm of -50mV, Im might be 1nA inward, or it might not. Im in fact could have higher or lower magnitude, and even might

be outward instead of inward.

Membrane Current Mystery 2


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Slide 1.65


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Slide 1.66


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Section 1-12: Section in Review

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Summary, continued


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y,

5. The core-conductor is a simple yet powerful nerve model. It includes the

essential elements--- inside, outside, axial, trans-membrane.6. Axial resistance is much higher in the cylindrical model than in a wire, thoug

in both cases axial current can be found using Ohms law.

7. Membrane resistance is millions of ohms, less in nerve than in wire.

8. In nerve, axial current follows Ohms law, but trans -membrane current dnot. Current may even be in the opposite direction.

Why and how Im does what it does is so far a mystery.

Slide 1.69

Following these lectures, please answerh


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Section 1.70

Please follow up the lectures byanswering the questions in set A(concepts) and then set B(mathematical and numerical).Experience shows that doing thequestions is fun and rewarding.

the questions.


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Section1 Final Slides

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