AP Conduction

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Lecture 12

• AP Conduction
• Cell-Cell Communication

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Review of Lecture 11

• Revised circuit model of membrane
• Hodgkin Huxley Model of AP

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Hodgkin-Huxley Equations

• Major equations used by Hodgkin-Huxley to
  mathematically model action potential
• CmdV/dt-36n4(V-VK)-120m3h(V-VNa)-0.3(V-VL)
• dm/dt am(Vm)(1-m)-bh(Vm)(m)
• dn/dtan(Vm)(1-n)-bn(Vm)(n)
• dh/dt ah(Vm)(1-h)-bh(Vm)(h)
• Four coupled ODEs with highly non-linear terms
• Cannot solve analytically
• Difficult to motivate solution in intuitive way

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Ion Channel Conductance

• Potassium channels
• gK36n4
• 4 open n gates which work together
• n is a time dependent probability that any one
  gate is open
• a,b ? voltage dependent rate constants
• dn/dt an(V)(1-n)-bn(V)(n)

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Ion Channel Conductance

• Sodium channels
• gNa120m3h
• Two types of gates
• Three m gates ? open
• One h gate ? close
• dh/dt ah(V)(1-h)-bh(V)(h)
• dm/dt am(V)(1-m)-bh(V)(m)

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HH Summary
http//biolpc22.york.ac.uk/hh/hh_excel.html
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Outline

• Propagation of Action Potentials
• Synapse
• Ion Channel Structure

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Outline

• Propagation of Action Potentials
• Synapse
• Ion Channel Structure

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Conduction of AP Along Neuron

• What if we remove the space clamp that we
  inserted last time?
• Now VV(x,t)
• Divide membrane into patches of length dx
• Set up model in terms of incremental variables

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Fig 3.6 Cellular Biophysics Electrical
Properties Weiss
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Derivation of Cable Equation

• Circuit diagram
• Step One
• KVL along inner/outer membrane
• Step Two
• KCL
• Cable Equation

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Fig 3.11 Cellular Biophysics Electrical
Properties Weiss
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(No Transcript)
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Outline

• Propagation of Action Potentials
• Synapse
• Ion Channel Structure

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Synapse

• Point at which neuron meets its target cell
• Three parts
• Axon terminal of pre-synaptic cell
• Synaptic cleft
• Membrane of post-synaptic cell
• Cell can from many synapses
• Average 10,000
• CNS 150,000
• Two types
• Electrical
• Chemical

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Fig 8.19 A chemical synapse Silverthorn 2nd
Ed
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Types of Synapses

• Electrical
• Pass electrical signal directly through gap
  junctions
• Uncommon, occur mostly in CNS
• Allow rapid signal conduction
• Chemical
• Vast majority of synapses
• Use neurotransmitter to carry information

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Chemical Synapses

• AP reaches axon terminal
• Voltage gated calcium channels in axon open
• Calcium moves into axon, binds to regulatory
  proteins and initiates exocytosis
• Exocytosis of neurotransmitter vesicles releases
  neurotransmitter into synaptic cleft
• Neurotransmitter diffuses across cleft and binds
  with membrane receptors on post-synaptic cell
• Initiates response in post-synaptic cell
• Excitatory (opens Na channels)
• Inhibitory (opens K channels)

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Fig 8.21 Synthesis and recycling of
acetylcholine at the synapse Silverthorn 2nd Ed
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Neurotransmitters

• Seven classes of neurotransmitters
• Acetylcholine
• Amino acids
• Amino acid derived amines
• Polypeptides
• Purines
• Gases
• Lipids

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Neurotransmitter Receptors

• Two types
• Ligand gated ion channels ? Fast
• G-protein linked receptors ? Activate 2nd
  messenger system which opens or closes ion
  channels ? Slow

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Fig 8.20 Events at the synapse Silverthorn
2nd Ed
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Fig 8.22 Fast and slow responses in
postsynaptic cells Silverthorn 2nd Ed
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Table 8.3 Major Neurocrines Silverthorn
2nd Ed
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Models of Synaptic Transmission

• Synaptic transmission has quantal nature
• Ach is packaged into discrete vesicles
• An integer number of vesicles are released
• Particularly apparent at low calcium concentration

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Fig 7.2 Mathematical Physiology Keener
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Models of Synaptic Transmission

• n ACh vesicles at presynaptic terminal, each
  with same amount of ACh
• p probability of 1 vesicle release
• Probability that k sites fire?

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Fig 7.4 Mathematical Physiology Keener
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Pre-Synaptic Voltage Gated Calcium Channels

• In synaptic transmission
• AP reaches nerve terminal
• Opens voltage gated calcium channels
• Influx of calcium
• Neurotransmitter release
• Voltage gated calcium channel
• Consists of n identical subunits
• Each can be open (Op) or shut (S)
• All subunits must be open to conduct calcium

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Fig 7.5 Mathematical Physiology Keener
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Outline

• Propagation of Action Potentials
• Synapse
• Ion Channel Structure

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2003 Nobel Prize in Chemistry

• The Atomic Basis of Selective Ion Conduction in
  Potassium Channels
• http//nobelprize.org/chemistry/laureates/2003/mac
  kinnon-lecture.html

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Summary

• Propagation of Action Potentials
• Synapse
• Ion Channel Structure

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Poem of the Day
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Due Dates

• Tuesday, October 12th
• HW6