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Lecture 7: Stochastic models of channels, synapses

Lecture 7: Stochastic models of channels, synapses. References: Dayan & Abbott, Sects 5.7, 5.8 Gerstner & Kistler, Sect 2.4 C Koch, Biophysics of Computation Chs 4,8 (13) A Destexhe, Z Mainen & T J Sejnowski, Ch 1 in

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Lecture 7: Stochastic models of channels, synapses

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  1. Lecture 7: Stochastic models of channels, synapses References: Dayan & Abbott, Sects 5.7, 5.8 Gerstner & Kistler, Sect 2.4 C Koch, Biophysics of Computation Chs 4,8 (13) A Destexhe, Z Mainen & T J Sejnowski, Ch 1 in Methods in Neuronal Modeling, 2nd ed, C Koch and I Segev, eds (MIT Press)

  2. Stochastic models of channels Single channels are stochastic, described by kinetic equations for probabilities of being in different states

  3. Stochastic models of channels Single channels are stochastic, described by kinetic equations for probabilities of being in different states Example: the HH K channel:

  4. HH K channel Kinetic equations:

  5. HH K channel Kinetic equations: Open probability: n = p5

  6. HH Na Channel

  7. HH Na Channel

  8. HH Na Channel But in this picture, inactivation only when activation gate is open:

  9. Na channel: Patlak model

  10. Na channel: Patlak model V-independent k1, k2, k3 Fits fast data a bit better than stochastic HH model

  11. Synapses

  12. Synapses Conductances gated by presynaptic activity:

  13. Synapses Conductances gated by presynaptic activity:

  14. Synapses Conductances gated by presynaptic activity:

  15. Synapses Conductances gated by presynaptic activity:

  16. Synapses Conductances gated by presynaptic activity: ~ deterministic (many channels) on postsynaptic side, stochastic on presynaptic side

  17. Synapses Conductances gated by presynaptic activity: ~ deterministic (many channels) on postsynaptic side, stochastic on presynaptic side Receptors: ionotropic and metabotropic

  18. Synapses Conductances gated by presynaptic activity: ~ deterministic (many channels) on postsynaptic side, stochastic on presynaptic side Receptors: ionotropic and metabotropic

  19. Synapses Conductances gated by presynaptic activity: ~ deterministic (many channels) on postsynaptic side, stochastic on presynaptic side Receptors: ionotropic and metabotropic

  20. Transmitters and Receptors Main transmitters:

  21. Transmitters and Receptors Main transmitters: glutamate (excitatory)

  22. Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA (g-aminobutyric acid, inhibitory)

  23. Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA (g-aminobutyric acid, inhibitory) ACh (neuromuscular junction)

  24. Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA (g-aminobutyric acid, inhibitory) ACh (neuromuscular junction) Noradrenaline (modulatory)

  25. Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA (g-aminobutyric acid, inhibitory) ACh (neuromuscular junction) Noradrenaline (modulatory) Receptor types (named after pharmacological agonists):

  26. Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA (g-aminobutyric acid, inhibitory) ACh (neuromuscular junction) Noradrenaline (modulatory) Receptor types (named after pharmacological agonists): Glutamate receptors (both ionotropic) :

  27. Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA (g-aminobutyric acid, inhibitory) ACh (neuromuscular junction) Noradrenaline (modulatory) Receptor types (named after pharmacological agonists): Glutamate receptors (both ionotropic) : AMPA (Na, K) NMDA (Na, K, Ca)

  28. Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA (g-aminobutyric acid, inhibitory) ACh (neuromuscular junction) Noradrenaline (modulatory) Receptor types (named after pharmacological agonists): Glutamate receptors (both ionotropic) : AMPA (Na, K) NMDA (Na, K, Ca) GABA receptors

  29. Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA (g-aminobutyric acid, inhibitory) ACh (neuromuscular junction) Noradrenaline (modulatory) Receptor types (named after pharmacological agonists): Glutamate receptors (both ionotropic) : AMPA (Na, K) NMDA (Na, K, Ca) GABA receptors GABAA (ionotropic, Cl) GABAB (metabotropic, K)

  30. Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA (g-aminobutyric acid, inhibitory) ACh (neuromuscular junction) Noradrenaline (modulatory) Receptor types (named after pharmacological agonists): Glutamate receptors (both ionotropic) : AMPA (Na, K) NMDA (Na, K, Ca) GABA receptors GABAA (ionotropic, Cl) GABAB (metabotropic, K) Ach receptors:

  31. Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA (g-aminobutyric acid, inhibitory) ACh (neuromuscular junction) Noradrenaline (modulatory) Receptor types (named after pharmacological agonists): Glutamate receptors (both ionotropic) : AMPA (Na, K) NMDA (Na, K, Ca) GABA receptors GABAA (ionotropic, Cl) GABAB (metabotropic, K) Ach receptors: nicotinic (ionotropic) muscarinic (metabotropic)

  32. Postsynaptic conductance (AMPA receptor) Kinetic equation:

  33. Postsynaptic conductance (AMPA receptor) Kinetic equation:

  34. Postsynaptic conductance (AMPA receptor) Kinetic equation: Transmitter: as constant for a short time, as >> bs

  35. Postsynaptic conductance (AMPA receptor) Kinetic equation: Transmitter: as constant for a short time, as >> bs

  36. Postsynaptic conductance (AMPA receptor) Kinetic equation: Transmitter: as constant for a short time, as >> bs Then a=0, decay:

  37. Postsynaptic conductance (AMPA receptor) Kinetic equation: Transmitter: as constant for a short time, as >> bs Then a=0, decay:

  38. Postsynaptic conductance (AMPA receptor) Kinetic equation: Transmitter: as constant for a short time, as >> bs Then a=0, decay: as = 0.93/ms bs = 0.19/ms

  39. Other receptors excitatory inhibitory

  40. Other receptors excitatory inhibitory commonly fit by

  41. Other receptors excitatory inhibitory commonly fit by limit

  42. Other receptors excitatory inhibitory commonly fit by limit “a-function”

  43. NMDA receptors Conductance is voltage-dependent (raising voltage knocks out Mg ions that block channel at low V)

  44. NMDA receptors Conductance is voltage-dependent (raising voltage knocks out Mg ions that block channel at low V)

  45. NMDA receptors Conductance is voltage-dependent (raising voltage knocks out Mg ions that block channel at low V)

  46. NMDA receptors Conductance is voltage-dependent (raising voltage knocks out Mg ions that block channel at low V)

  47. NMDA receptors Conductance is voltage-dependent (raising voltage knocks out Mg ions that block channel at low V) Opening requires both pre- and postsynaptic depolarization: Coincidence detector (important for learning)

  48. GABAB receptor kinetics Simplest model for a metabotropic receptor:

  49. GABAB receptor kinetics Simplest model for a metabotropic receptor: Transmitter binding activates receptor:

  50. GABAB receptor kinetics Simplest model for a metabotropic receptor: Transmitter binding activates receptor:

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