ELECTRICAL CONDUCTANCE AND RESISTANCE

1
ELECTRICAL CONDUCTANCE AND RESISTANCE
WHEN CHARGED PARTICLES ARE SUBJECT TO ELECTRICAL
FORCE, THEIR ABILITY TO MOVE FROM POINT A TO B IS
INFLUENCED BY CONDUCTIVE PROPERTY OF MATERIAL
CONDUCTANCE (g) unitssiemens,S measure of
materials ease in allowing movement of charged
particles RESISTANCE (R) unitsOhms,W measure
of materials difficulty in allowing electrical
conduction
Resistance is the INVERSE of Conductance. I.e.
1 g
1 R
g
R
OR
2
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
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 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 gt 0 means net flow of positive charge I
lt 0 means net flow of negative charge
3
OHMS LAW
The amount of current flow is directly
proportional to both the voltage differential and
the conductance
I DV x g
I DV / R DV I x R
OR
WATER PRESSURE ANALOGY
SCHEMATIC DIAGRAM
VALVE
I
FLOW RATE
PA
VA
VB
PB
R
Water Pressure is analogous to Voltage
Differential Valve Resistance is analogous to
Electrical Resistance Flow Rate is analogous to
Electrical Current
DV VA - VB IR I DV / R
Flow Rate Water Pressure / RVALVE
4
THE I-V PLOT OHMS LAW
I DV x g
CONDUCTANCE ( g ) is SLOPE of line in I - V PLOT
In a simple resistive circuit, the relationship
between current and voltage is LINEAR
WEAKER CONDUCTANCE
HIGH CONDUCTANCE
5
BEHAVIOR OF A SIMPLE RESISTIVE CIRCUIT
SWITCH OPEN AT t 0 sec
SWITCH CLOSED AT t 5 sec
I
I
R (10 W )
R (10 W )
10 V
10 V
DV
DV
CIRCUIT PROPERTIES
10
1
I (Amps)
DV (volts)
0
0
0 5
0 5
t (sec)
t (sec)
6
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 ----gt Larger charge
stored A material that has capacitance is
called a capacitor. The schematic symbol for a
capacitor is
C
7
RELATIONSHIP OF CAPACITANCE AND CURRENT
AS DESCRIBED BEFORE
q C x DV
I dq /dt
SINCE
dq/dt I C x dDV/dt
I.e. As current flows into a capacitor, the
voltage across it increases
8
CIRCUIT WITH CAPACITANCE RESISTANCE IN SERIES
( REMEMBER After switch closed, DVA DVB
DVTOTAL 10 V )
CIRCUIT PROPERTIES
10
10
2
DVA (volts)
DVB (volts)
I (amps)
0
0
0
-5 0 5 10
-5 0 5 10
-5 0 5 10
t (sec)
t (sec)
t (sec)
9
CIRCUIT WITH CAPACITANCE RESISTANCE IN SERIES
CONTROL OF CURRENT FLOW BY SIZE OF R AND C
THE LARGER THE RESISTANCE (R) ----gt 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) ----gt 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 (W) x C (F)
10
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
11


Vm Vin - Vout
- - - - - - - - - - - - - - - - - - - - - - - - -
-
In resting neuron
Vm - 60 to - 75 mV
- - - - - - - - - - - - - - - - - - - - - - - - -
-


Membrane potential is a BATTERY providing power
to drive currents when the cell is activated
12
MEASURING THE RESTING MEMBRANE POTENTIAL PATCH
PIPET IN WHOLE-CELL CONFIGURATION
Patch pipet filled with cytoplasm-like solution
is touched to cell membrane with negative
pressure, the pipet makes a very tight
cell-attached or on-cell seal onto membrane
(leak resistance gt 10 GW) Applying gentle
suction can break the membrane inside the pipet,
making pipet fluid continguous with the
cytoplasm. This is the whole-cell
configuration. When break is made into cell,
the pipet can record the membrane potential
13
TWO TYPES OF PROTEIN COMPLEXES CONTRIBUTE TO
ESTABLISHING THE RESTING MEMBRANE POTENTIAL
ION PUMP -- drives a specific ion or group of
ions from one side of
the plasma membrane to the other side
Pumps drive ions ONE-WAY and use energy from ATP
hydrolysis to make the process energetically
favorable
ION CHANNEL -- protein complex containing a small
pore which allows a
specific ion or group of ions to pass
Flow of ions through channels is PASSIVE and is
driven by the prevailing chemical and electrical
gradients A channel is an ion-specific resistor
with a certain conductance ( g ) For most
channels, the conductance is the same for ions
flowing IN or OUT Other channels allow ions to
pass with greater conductance in one
direction these are called RECTIFYING
CHANNELS e.g., a channel with greater
conductance of inward current is called an
inwardly rectifying channel
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Na/K ATPase PUMP
Na/K ATPase USES ENERGY FROM ATP HYDROLYSIS TO
PUMP SODIUM IONS OUT OF CELL POTASSIUM IONS
INTO CELL AT A 3 Na 2 K RATIO CONSEQUENCES
OF PUMP ACTIVITY K in gtgt K out Na
in ltlt Na out Net positive charge pumped
out of cell causes a matching amount of permeable
chloride anions to move out passively through
channels Cl- in ltlt Cl- out
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POTASSIUM CHANNELS FAVOR A NEGATIVE MEMBRANE
POTENTIAL
Potassium channels are the most abundant leak
channels in neurons. Because the Na/K pump makes
Kin gtgt Kout , potassium ions move
outwards through channels due to the chemical
driving potential, EK . (EK can be thought of as
a potassium battery) Net outward ion flow
continues until opposed by a membrane potential,
Vm , of equal force built up in the membrane
capacitor.
AT EQUILIBRIUM When Vm EK, zero net K flux
When Vm 0, large K efflux
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CIRCUIT REPRESENTATION OF POTASSIUM
CONDUCTANCE, POTASSIUM BATTERY, AND MEMBRANE
CAPACITANCE
When Vm 0, large K efflux
When Vm EK, zero net K flux
gK
gK
IK
IK 0
_ _ _
CM
CM
VM 0
VM EK


EK
EK
-
-
What is the strength of the potassium battery EK
???
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THE NERNST EQUATION
The cytoplasmic and extracellular concentrations
of an ion determine the chemical driving force
for that ion and the equilibrium membrane
potential if this is the ONLY ion that is
permeable through the membrane
Nernst Equation
Where EX is the chemical potential and z is the
charge of ion X
z 1
Kin 130 mM
Kout 5 mM
For potassium
5
58 mV
log
EK
- 82 mV
1
130
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RESTING POTENTIAL SET BY RELATIVE
PERMEABILITIES OF K, Na, Cl- IONS
Nernst Potential Relative Permeability
(P)
EK - 82.1 mV 1.0 ENa
84.8 mV 0.02 ECl -
80.1 mV 0.2
Resting membrane potential reflects the relative
permeabilities of each ion and the Nernst
potential of each ion
When the resting membrane potential is achieved,
there is ongoing influx of sodium and a matching
efflux of potassium. Na/K ATPase is continually
needed to keep the ion gradients from running
down over time
19
INCREASING SODIUM PERMEABILITY UNDERLIES SODIUM
INFLUX AND MEMBRANE DEPOLARIZATION DURING ACTION
POTENTIAL
During action potential, the number of open
sodium channels increases dramatically
Rest During Action Potential
- 72 mV
36 mV
GOLDMAN EQUATION-PREDICTED Vm
When sodium channels open, sodium ions flow in
rapidly because of the negative membrane
potential and the strong inward sodium
battery Inward sodium current depolarizes
membrane and moves it towards the positive
potential predicted by Goldmans equation (this
positive potential is never fully achieved due to
additional channel dynamics)
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LEAK CHANNELS GATED CHANNELS
Channels that are always open called leak
channels. Gated channels can switch between open
and closed states. THERE IS ONLY ONE OPEN STATE
(CONDUCTANCE) FOR A GATED CHANNEL!!! Gating
mechanisms voltage, extracellular ligand,
intracellular signaling
Channels can have the same ion specificity, but
different gating mechanisms. Eg. There are
leak, voltage-gated, and calcium-activated
potassium channels
21
THERE IS ONLY ONE OPEN STATE FOR A GATED CHANNEL
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STEPS OF TRANSMISSION AT CHEMICAL SYNAPSES
Chemical synaptic transmission has a 0.3 - 5 msec
delay, depending upon type of post-synaptic
receptor Chemical synaptic transmission can
depolarize or inhibit depolarization, depending
upon type of post-synaptic receptor Sub-threshold
presynaptic depolarizations are not
transmitted Depolarization in postsynaptic site
called Excitatory Post-Synaptic Potential
(EPSP) Inward current driving depolarization
called Excitatory Post-Synaptic Current (EPSC or
IEPSP)
23
WHY DOES CURRENT FLOW IN AT ACTIVATED EXCITATORY
SYNAPSES?
Excitatory receptors (AMPA or NMDA glutamate
receptors, Ach receptors) conduct both sodium and
potassium Since Naout Kout Nain
Kin , battery of these channels is 0
V Since resting potential of cell is negative,
opening of excitatory receptors causes net influx
of cations (Na) which depolarizes cell
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MOST EXCITATORY SYNAPSES ELICIT EPSP WITH
REVERSAL POTENTIAL OF 0 mV
IONOTROPIC RECEPTOR
ION PERMEABILITY
NEUROTRANSMITTER
GLUTAMATE AMPA GluR Na, K GLUTAMATE
Kainate GluR Na, K GLUTAMATE NMDA
GluR Na, K, Ca ACETYLCHOLINE Nicotinic
AChR Na, K ATP ATP Receptor Na, K,
Ca SEROTONIN 5-HT3 Receptor Na, K
Excitatory reversal potential, EEPSP, is near 0
mV, due to permeability of receptor to
both sodium and potassium
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NMDA AND NON-NMDA RECEPTORS FUNCTION DIFFERENTLY
AMPA
NMDA receptors open only when depolarization
precedes glutamate binding. Depolarization
releases Mg2 blocking particle from
ligand-binding site. NMDA receptors only open
with prolonged presynaptic activity. Calcium
entry through NMDARs induces signaling processes
that can modify synaptic behavior both short- and
long-term
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LECTURE 21 CELLULAR BASIS OF LEARNING MEMORY
REQUIRED READING Kandel text, Chapter 63, and
Assigned Review Articles
Research on cellular basis of learning memory
mainly performed in three animal systems
Aplysia Drosophila
Mouse
All neurons and synapses in behavioral circuits
are identified and can be recorded easily Ideal
for detailing mechanisms underlying implicit
learned motor responses
Capable of learned behaviors Amenable to
random mutagenesis and selection of mutants with
defective behaviors
Similar anatomy to human Amenable to study
of explicit memory Hippocampus amenable to
electrophysiology Behavior modification
of genetically modified mice
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LTP AT MOSSY FIBER--CA3 SYNAPSES IS DUE TO
PRESYNAPTIC CALCIUM INFLUX AND cAMP/PKA PATHWAY
28
LTP AT SCHAFFER COLLATERAL--CA1 SYNAPSES IS DUE
TO POSTSYNAPTIC CALCIUM INFLUX AND CAM KINASE
ACTIVITY
LTP at CA3-CA1 synapse is blocked by NMDAR
antagonist APV and by inhibitors of CAM kinase
29
SYNAPSES SENSITIVE TO NMDAR-MEDIATED LTP ARE ALSO
SENSITIVE TO NMDAR-MEDIATED LONG-TERM DEPRESSION
(LTD)
AXON STIMULATION PROTOCOL
AMPLITUDE OF EPSCS
300
LTP
Once per minute
Once per minute
10 Hz
200
EPSP Slope ( original)
20 min
1 m
60 min
100
60
20
40
80
TIME (min)
300
200
EPSP Slope ( original)
Once per minute
Once per minute
LTD
2 Hz
100
20 min
5 m
60 min
60
20
40
80
TIME (min)
30
LTD HAS A LOWER CALCIUM CONCENTRATION THRESHOLD
THAN LTP, BUT LTP IS DOMINANT
THETA- OR HIGH-FREQUENCY STIMULUS
TRAIN GREATER CALCIUM ENTRY ACTIVATION OF
CALCINEURIN AND CAMK AMPA RECEPTOR INSERTION
AND PHOSPHORYLATION LTP
LOW-FREQUENCY STIMULUS TRAIN LOW-LEVEL CALCIUM
ENTRY ACTIVATION OF CALCINEURIN AMPA
RECEPTOR INTERNALIZATION LTD
31
STRUCTURAL AND FUNCTIONAL FEATURES OF AMPA-TYPE
GLUTAMATE RECEPTORS
AMPA receptors are homo- or hetero-tetramers Restr
iction of calcium entry mediated by GluR2
tetramers containing gt1 GluR2 subunit conduct
only Na/K AMPA receptors encoded by different
genes or by alternative splicing have different
C-terminal tails. Receptor tails contain
phosphorylation sites for different protein
kinases and binding sites for PDZ-domain-containin
g proteins Receptors containing only
GluR2(short) and/or GluR3 subunits are delivered
constitutively from vesicles to synapse Retention
at synapse mediated by complex with Glutamate
Receptor Interacting Protein (GRIP) Receptors
containing at least one GluR1(long) subunit are
stored in intracellular vesicles near
synapse During LTP, GluR1-containing tetramers
are added to the synapse
32
NMDAR-INDUCED CAMK ACTIVITY ACTS ON AMPA
RECEPTORS IN TWO WAYS TO PROMOTE LTP
STG GRIP PSD-95
CAMK phosphorylates an unknown protein, enabling
a PDZ-protein that interacts with long tail on
GluR1 to deliver receptor TO EXTRASYNAPTIC
SITE Delivered receptors migrate
(randomly?) into post-synaptic density, where
interactions of receptor- associated GRIP and STG
and the major postsynaptic matrix protein PSD-95
anchor receptor to synapse Newly delivered
GluR1-containing AMPA receptors can be
phosphorylated directly by CAMK, which increases
unitary conductance of the receptor
GRIP PSD-95
CAMK PDZ-protein
Calcineurin
Calcineurin activation promotes
internalization of AMPA receptors containing
only short-tail subunits, thereby promoting LTD
WHEN HIGH CALCIUM ENTRY ACTIVATES BOTH
CALCINEURIN AND CAMK, CAMK-MEDIATED
GluR1-CONTAINING AMPAR EXOCYTOSIS EXCEEDS
CALCINEURIN-MEDIATED SHORT TAIL-ONLY AMPAR
ENDOCYTOSIS
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HIGH CAMK ACTIVITY INDUCED DURING LATE LTP IS
ALSO MEDIATED BY NEW CAM KINASE PROTEIN SYNTHESIS
NEAR THE SYNAPSE
Most mRNAs have 3 polyA tail, which is necessary
for initiation of the mRNAs translation Neurons
contain some mRNAs that are not polyadenylated,
are not translated, and are transported along
dendrites to areas near dendritic spines NMDA
receptor activation and calcium entry activates a
protein kinase called AURORA Aurora kinase
activates translation of nearby dormant
mRNAs ONE OF THESE DORMANT RNAs ENCODES CAM
KINASE Because of its dendritic localizaation,
new CAMK synthesis is restricted to the synapse
undergoing LTP The dendritic localization of
dormant CAMK RNA and its activation during LTP
are mediated by Cytoplasmic Polyadenylation
Element Binding (CPEB) protein
34
HOW DOES CPEB PROTEIN CONTROL RNA DORMANCY AND
ACTIVATION IN NEURONS?
PolyA is needed for assembly of 5 translation
initiation complex
CPEB protein binding to 3 CPE helps mask RNA 5
end
CPEB phosphorylation by Aurora allows for
recruitment of polyA polyermerase
(PAP) Polyadenylation of dormant RNA allows
assembly of 5 translation initiation complex