Lecture I' Principles of Membrane Excitability

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Lecture I. Principles of Membrane Excitability
Manoj K. Patel, Ph.D. Assistant Professor Dept.
Anesthesiology 924 9693 mkp5u_at_virginia.edu
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Outline

• Equivalent Electrical Circuit
• review of resting membrane potential
• passive membrane properties
• fundamentals of active signaling
• changes in ion conductance underlie changes in
  membrane potential
• The Action Potential
• action potential phenomenology
• threshold, all-or-none refractory periods
• voltage clamp analysis
• overview of Hodgkin Huxley formalism

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Intracellular and Extracellular ion concns
Nernst Equation Ek -61.5 log ( Ki / Ko )
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What Determines The Ion Movement?

• 1. Chemical or concentration gradient.
• Molecules will flow down concn gradient
• 2. Electrostatic gradient.
• Positive ions will move to negative charge.

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Electrochemical Driving Forces

• I gion(Vm-Eion)
• there is a different driving force for each ion
  at any given Vm
• the same Dg for different ions can give very
  different current magnitude
• changes in g for a given ion will drive Vm toward
  the equilibrium potential for that particular ion

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Resting membrane potential
so, EK -100 mV and ENa is 50 mV, but we know
that membrane potential (Em) is usually somewhere
in between (e.g. -75 mV). How can we get a
stable Em of -75 mV?
if Em is stable, then net current is 0, i.e., IK
INa 0
substitute gK (Em-EK) gNa (Em-ENa) 0
solve for Em Em (EK gK) (ENa
gNa) gNa gK
the membrane potential is between EK and ENa,
weighted by the relative membrane conductances
for K and Na
if gNagK 15, then Em (-100 5) (50
1) -450 -75 mV 5 1
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Equivalent electrical circuit model
with unequal distribution of ions and
differential resting conductances to those ions,
we can use the Nernst equation and Ohms law in
an equivalent circuit model to predict a stable
resting membrane potential of -75 mV, as is seen
in many cells
NB, this is a steady state and not an
equilibrium, since K and Na are not at their
equilibrium potentials there is a continuous
flux of those ions at the resting membrane
potential
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Changing extracellular K changes Vm
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Responses to Current Injection
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Passive membrane properties

• under current clamp, the passive response to
  current injection is a function of the RC
  characteristics of the membrane
• V IR (Ohms law) gives the steady state voltage
• t RC (gives the kinetics)
• under voltage clamp, the passive response
  includes
• capacitive current, which flows only at the step
  onset and offset
• resistive current (through leak channels), also
  given by Ohms law (I V/R)

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Passive cable properties length constant

• l v(rm/ri)
• ri is inversely proportional to cross sectional
  area
• bigger cables have lower ri, and therefore pass
  more axial current this strategy for increasing
  l is used to an extreme in the squid giant axon
• increased rm promotes more effective axial
  current flow by discouraging transmembrane current

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Myelination increases conduction velocity

• myelination increases conduction velocity by
• increasing rm and thereby increasing l
• decreasing capacitance and lowering Q (VQ/C)
• the net result is that less current will escape
  through the membrane resistance less current
  needed to charge the smaller capacitance

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Equivalent electrical circuit model

• more complete model
• provides energy-dependent pump to counter the
  steady flux of ions
• add voltage-gated K and Na channels for
  electrical signaling
• add ligand-gated (e.g. synaptic conductances)
• obviously, much greater complexity could be
  imagined

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Ion channels involved in action potentials
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The essence of electrical signaling
ENa
gKgNa 51
gKgNa 525
gKgNa 51
EK
(-1005)(501) 5 1 Em -75 mV
(-1005)(5025) 5 25 Em 25 mV
(-1005)(501) 5 1 Em -75 mV
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Action potential thresholds
CA1 hippocampal neuron
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Using the model to understand signaling
reaches AP threshold
doesnt reach threshold
add GluR agonist Erev 0, g 4
add GABAR agonist Erev -75, g 4
add both GluR and GABAR agonist
(-1005)(501)(40) 5 1 4 Em -45 mV
(-1005)(501)(4-75) 5 1 4 Em -75 mV
(-1005)(501)(40)(4-75) 5 1 4 4 Em
-54 mV
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Action potential phenomenology
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Action potential cardiac ventricular myocyte
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Squid Giant Axon Action potential
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Action potential stimuli refractory periods

• short duration pulses require high stimulus
  intensity to evoke an action potential
• rheobase is the current needed to generate spikes
  50 of the time
• this is influenced by input resistance and
  capacitance of the recorded cell
• recall VIR tRC

• refractory periods time domains during which
  action potentials can not be generated (absolute
  refractory period) or require greater strength
  and/or duration of current input (relative
  refractory period)

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Voltage Clamp the basic concept

• revolutionized analysis of cell excitability
• the approach is described in the text
• for our purposes, based on feedback/servo control

• conceptually similar to thermostat controlling
  the temperature in your house
• step membrane to some potential called the
  command potential
• if channels are activated by the voltage step,
  they generate a current that tends to move
  membrane potential (Vm) away from the command
  potential (Vc)
• this error signal is sensed by the feedback
  circuit, which injects current into the cell to
  correct the error
• that injected current is measured as the ionic
  current

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Voltage Clamp sample records

• voltage clamp records
• a 40 mV hyperpolarizing voltage step evokes only
  capacitive and leak currents
• a 40 mV depolarizing step, by contrast, evokes a
  time-dependent current in addition to capacitive
  and leak currents
• a subtraction protocol is often used to remove
  those currents and reveal the time-dependent
  current in isolation

capacitative
leak
represents current to charge membrane (Ic) and
through leak channels subtraction removes leak
and capacitive current, yielding
voltage-dependent currents
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Voltage clamp analysis of action potential
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Voltage clamp analysis of action potential
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Voltage clamp I-V curves
K current
Na current
Ix Gx (Vm-Ex)
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Na and K conductance in the AP

• Hodgkin Huxley used their empirical measures to
  model Na and K currents

• they developed an equation that predicts membrane
  potential based on the sum of capacitive and
  ionic currents

• the n4 term provides the pronounced delay in K
  current activation
• the h term equals 1 when there is no Na current
  inactivation
• the smaller exponent on the m term allows for
  faster Na current activation

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Na and K conductance in the AP
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Voltage dependent ion channels
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Structure-Function Relations in a
Voltage-Dependent Channel
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Molecular structure of a sodium channel






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Current voltage relationship
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Activation IV
G/Gmax I / Imax Where I max Vm b G/Gmax
I / (Vm b) Plot G/Gmax as a function of
Voltage
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Steady State Inactivation