Slide 1.
Bioelectricity
Section 1 Make Plans,
talk about Bioelectricity and introduce
the core-conductor model
Slide 1-2
Section 1-2 What is the question?
Slide 1.3
A question to answer the
question
Why is this picture
our course icon?
Jack, how old are you?
Slide 1.4
The question for this course:
Slide 1.5
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 their
destination.
These pulses carry information from one site to
another.
Why this question?
Slide 1.7
Bioelectricity in nerves, the part of bioelectricity
studied in this course, is a good place to start.
Historically it was first and famous.
It is the foundation for understanding bioelectric
events in other systems, such as the brain, or in
muscles, including the heart.
Slide 1.7
Duke University Union Walkway
A picture of Duke and North Carolina ends each section.
Slide 1-8
Section 1 -3 About Bioelectricity
Slide 1.9
About Bioelectricity
What is Bioelectricity?
Bioelectricity involves the electrical voltages
and currents that are present in living tissue,
their causes, and their consequences.
When did the study of
Bioelectricity begin?
Slide 1.10
Answer: In the 1700s, in Italy,
with Galvani and with Volta,
in conflict.
Slide 1.11
What was the Galvani-Volta
conflict about?
One conflict was that Galvani thought that animal
electricity was a different kind of electricity than
the heat electricity of Volta.
Though we now know that Galvani incorrect, why does
his idea seem reasonable, even today?
Slide 1.12
How is electricity in living tissue different
from the ordinary electricity of batteries,
wires, radios and computers?
What happens
when you throw a
standard battery
into the ocean?
What happens when you
throw a fish in the ocean?
Slide 1.13
Fish does fine.
;
This ray does too .
Slide 1.14
Duke Chapel at Duke University, Durham, NC, USA
Slide 1.15
Section 1 -4 Major sections of the course
Section 1 (right now)
Slide 1.16
Bioelectricity
1. Make Plans
Bioelectricity background
Rectification of Names
Electricity in Solutions
Railroad
1. Make Plans
Section 2
Slide 1.17
Bioelectricity
2. Energy, to get Vm
Membrane patch
Membrane resistance
Membrane capacitance
Ion pump
Nernst Vm
Railroad
2. Sell Tickets, to get money
Section 3
Slide 1.18
Bioelectricity
3. Channels
Sodium ion
Potassium ion
Leakage
Railroad
3. Engines
Section 4
Slide 1.19
Bioelectricity
4. Action potentials
The Hodgkin-Huxley model
Different kinds of channels
cooperating to create voltage
pulses (action potentials)
Railroad
4. Train cars
Section 5
Slide 1.20
Bioelectricity
5. Currents
within the
tissue structure
Axial current and
trans-membrane
current as
determined by the
tissues structure
Railroad
5. Track
Section 6
Slide 1.21
Bioelectricity
6. Propagation
Bringing together channels,
action potentials, and
structure so that electrical
signals (action potentials)
move along a fiber
Railroad
6. Train is moving
What are the Sections of the course?
Slide 1.22
Bioelectricity
Railroad analogy
Slide 1.23
Duke University Chapel
Slide 1.24
Section 1-5 Rectification of Names
Rectification of Names
Slide 1.25
The Rectification of Names: The phrase is taken
from the Confucian doctrine that social harmony
is achieved by using the proper designations for
things.
Bioelectricity deals with invisible objects, a big
problem. Some conventions have been adopted
to name the abstract things that are its elements.
Membranes
Slide 1.26
The lipid bilayer is a thin material
around cells. It is made of two layers of
lipid molecules. One end (circles) is
hydrophilic. The middle (lines) is
hydrophobic.
The lipid bilayer is thin in comparison
to a cell diameter. In this illustration,
the cell diameter is 200,000 Angstroms,
while the lipid bilayer is only 80A.
Channels and Pumps
Slide 1.27
Channels are tiny tunnels through the membrane. They
are important electrically because charged ions pass
through channels.
Pumps are structures in the membrane that use food
energy to move ions uphill across the membrane.
Channels and pumps may be selective, meaning only
one kind of ion can pass through, e.g. Na+ but not K+
Important: In the membrane itself, not inside it.
Transmembrane Voltage
Slide 1.28
Transmembrane
Voltage Vm is the
potential at point B
minus the potential
at point A
The same Vm is often called Transmembrane Potential as a short form
of Transmembrane Potential Difference.
Slide 1.29
Positive membrane voltage &
positive membrane current
This sign convention is always used.
Slide 1.30
Passive versus Active:
same as dead versus alive?
Passive means that the same properties, such as resistance, are
maintained over time without change.
Active means that, due to some trigger, properties such as resistance may
change their value as time passes.
Slide 1.31
Passive versus Active:
same as dead versus alive?
Dead material is passive.
Living tissue (such as electrically active membrane) is sometimes
passive but active at other times.
Think of a resistor that is a million Ohms, but then changes to be a
thousand, and then changes back. That is what is meant by active.
Slide 1.32
Duke University Chapel Steps
Slide 1.33
Section 1-6 Ions in Solutions *
Electricity in Solutions
The Big 5
Slide 1.34
The arrows
signify that
each quantity
can be found
from the one
before
(including
number 1 from
number 5.
These 5
quantities are
referred to,
later on, as the
big 5
Current is the movement of ions
Slide 1.35
An ion is a atom or molecule with a charge, because
its number of electrons differs from the number of
protons.
The presence of ions gives a solution electrical
conductivity because ions can move.
Example of ions in solution
Slide 1.36
Ordinary table salt NaCl has no net charge.
In water NaCl divides into sodium ions and chloride ions,
written in symbols as Na+ and Cl- .
Each ion is charged because Na+ has lost an electron and
Cl- has gained one.
Ions and conductivity
Slide 1.37
Ions carry charge and move.
Conductivity is a measure of how many and how easily
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 of
sodium, potassium, and chloride are particularly
significant.
Resistivity and sea water
Slide 1.38
In ocean water the resistivity is around about
25 Ohm-cm.
The conductivity is the reciprocal, 1/25
Siemens per cm.
Slide 1.39
Duke Chapel at Duke University, Durham, NC, USA
Slide 1.40
Section 1-7 Core-conductor model of a nerve fiber
Slide 1.41
Cylindrical geometry
L=100mm
h=5mm
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.
Resistivity and Conductivity
Slide 1.42
Interior and exterior volumes are both conducting solutions.
Here values chosen as examples are:
e 25cm
i 50cm
e 1/ 25 0.04S/cm
i 1/ 50 0.02S/cm
Ocean water has resistivity of about 25 Ohm-cm
Axial Resistance a-to-b
Slide 1.43
We can use the standard formula to find resistance from resistivity
i L
Ax
i L
2
h
Axial Resistance numbers 1
Slide 1.44
i L
R 2
h
50cm(100E-4cm)
R
(5E-4cm) 2
Notes
1cm=10,000mm
E-4 means divided by 10,000
Axial Resistance numbers 2
Slide 1.45
Nerve model
R 636, 620
Copper or sliver wire
Compare to
In terms of axial resistance, nerves are not like wires.
Rwire 1
Slide 1.46
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Slide 1.47
Section 1-8 Potential and voltages in the nerve fiber
Potential Field
Slide 1.48
One gets a potential field by keeping the negative lead in one
place and moving the positive lead to all points of interest. One
can do so experimentally and also conceptually.
Examples of
potentials f at
o 0mV
a -20mV
b - 60mV
c - 62mV
d -1mV
e +2mV
f +0mV
at one moment
Transmembrane and axial voltages
Slide 1.49
Transmembrane a-d:
Vm fa - fd
Vm (-20) - (-1)
Vm -19mV
Axial a-b:
Vab fa - fb (-20) - (-60) 40mV
Slide 1.50
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Slide 1.51
Section 1-9 Axial currents in the nerve fiber
Axial current by Ohms law
Slide 1.52
Assume current is uniform
Use Ohms law Ix = Vab / R .
Vab = 40mV, and R=636,620 Ohms
Substitute and get: Ix = 62.8nA
1nA is 1E-9A so
is one billionth
of an Ampere
Axial current from the electric field
Slide 1.53
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=100mm, so Ex=4V/cm in the +x direction.
The presence of Ex implies forces on charges F=Eq
Ex (fb - fa ) / ( xb - xa ) -Vab / L
Axial current density, and the axial current
Slide 1.54
i 0.02S/cm
J x i Ex 80mA/cm 2
A x 7.854E-7cm 2
I x J x Ax
I x 62.8nA
Here the direction of Jx and Ix is the same as that of Ex.
Slide 1.54
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Slide 1.55
Section 1-10: Membrane Resistance
Membrane Resistance 1
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.
Membrane Resistance 2
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)
Membrane Resistance 3
Slide 1.59
R=(membrane resistivity) / (Surface area)
As = surface area = (Pi * 2h * L) = 3.14E-5 = 0.0000314 cm2 (approximately)
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.
Slide 1.60
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Slide 1.61
Section 1-11: Membrane Current, Failure & Mystery
Membrane Current 1
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.
Membrane Current 2
Slide 1.63
By Ohms Law we expect Im = Vm / Rmem = -50mV/48E6 Ohms
So by Ohms Law Im is approximately -1nA in this segment
That is, Im computed with Ohms law is about 1nA inward.
Membrane Current Mystery 1
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
Slide 1.65
Slide 1.66
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Slide 1.67
Section 1-12: Section in Review
Summary
Slide 1.68
1. Galvani was wrong. Electricity is fundamentally the same thing in living
tissue, dead materials, and ordinary experience. Electricity is unified.
2. Galvani was right. The manifestations and rules are so different, such as the
difference between a radio battery and the fish in the sea, that one thinks
differently about electricity in living systems.
3. The conductivity of biological solutions comes from ions.
4. Bioelectricity depends on excitable membranes made of thin lipids. They have
special pumps and channels used to move ions from one side to the other.
Summary, continued
Slide 1.69
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, though
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 does
not. Current may even be in the opposite direction.
Why and how Im does what it does is so far a mystery.
Following these lectures, please answer
the questions.
Section 1.70
Please follow up the lectures by
answering the questions in set A
(concepts) and then set B
(mathematical and numerical).
Experience shows that doing the
questions is fun and rewarding.
Slide 1.71
Goodbye for
section 1.
Talk to you
again soon.
Duke Chapel at Duke University, Durham, NC, USA
