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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, 2 nd ed, C Koch and I Segev, eds (MIT Press)
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Stochastic models of channels Single channels are stochastic, described by kinetic equations for probabilities of being in different states
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Stochastic models of channels Single channels are stochastic, described by kinetic equations for probabilities of being in different states Example: the HH K channel:
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HH K channel Kinetic equations:
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HH K channel Kinetic equations: Open probability: n = p 5
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HH Na Channel
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But in this picture, inactivation only when activation gate is open:
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Na channel: Patlak model
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V -independent k 1, k 2, k 3 Fits fast data a bit better than stochastic HH model
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Synapses
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Conductances gated by presynaptic activity:
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Synapses Conductances gated by presynaptic activity:
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Synapses Conductances gated by presynaptic activity:
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Synapses Conductances gated by presynaptic activity:
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Synapses Conductances gated by presynaptic activity: ~ deterministic (many channels) on postsynaptic side, stochastic on presynaptic side
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Synapses Conductances gated by presynaptic activity: ~ deterministic (many channels) on postsynaptic side, stochastic on presynaptic side Receptors: ionotropic and metabotropic
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Synapses Conductances gated by presynaptic activity: ~ deterministic (many channels) on postsynaptic side, stochastic on presynaptic side Receptors: ionotropic and metabotropic
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Synapses Conductances gated by presynaptic activity: ~ deterministic (many channels) on postsynaptic side, stochastic on presynaptic side Receptors: ionotropic and metabotropic
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Transmitters and Receptors Main transmitters:
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Transmitters and Receptors Main transmitters: glutamate (excitatory)
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Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA ( -aminobutyric acid, inhibitory)
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Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA ( -aminobutyric acid, inhibitory) ACh (neuromuscular junction)
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Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA ( -aminobutyric acid, inhibitory) ACh (neuromuscular junction) Noradrenaline (modulatory)
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Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA ( -aminobutyric acid, inhibitory) ACh (neuromuscular junction) Noradrenaline (modulatory) Receptor types (named after pharmacological agonists):
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Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA ( -aminobutyric acid, inhibitory) ACh (neuromuscular junction) Noradrenaline (modulatory) Receptor types (named after pharmacological agonists): Glutamate receptors (both ionotropic) :
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Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA ( -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)
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Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA ( -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
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Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA ( -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 GABA A (ionotropic, Cl) GABA B (metabotropic, K)
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Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA ( -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 GABA A (ionotropic, Cl) GABA B (metabotropic, K) Ach receptors:
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Transmitters and Receptors Main transmitters: glutamate (excitatory) GABA ( -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 GABA A (ionotropic, Cl) GABA B (metabotropic, K) Ach receptors: nicotinic (ionotropic) muscarinic (metabotropic)
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Postsynaptic conductance (AMPA receptor) Kinetic equation:
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Postsynaptic conductance (AMPA receptor) Kinetic equation:
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Postsynaptic conductance (AMPA receptor) Kinetic equation: Transmitter: s constant for a short time, s >> s
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Postsynaptic conductance (AMPA receptor) Kinetic equation: Transmitter: s constant for a short time, s >> s
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Postsynaptic conductance (AMPA receptor) Kinetic equation: Transmitter: s constant for a short time, s >> s Then =0, decay:
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Postsynaptic conductance (AMPA receptor) Kinetic equation: Transmitter: s constant for a short time, s >> s Then =0, decay:
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Postsynaptic conductance (AMPA receptor) Kinetic equation: Transmitter: s constant for a short time, s >> s Then =0, decay: s = 0.93/ms s = 0.19/ms
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Other receptors excitatory inhibitory
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Other receptors excitatory inhibitory commonly fit by
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Other receptors excitatory inhibitory commonly fit by limit
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Other receptors excitatory inhibitory commonly fit by limit “ -function”
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NMDA receptors Conductance is voltage-dependent (raising voltage knocks out Mg ions that block channel at low V )
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NMDA receptors Conductance is voltage-dependent (raising voltage knocks out Mg ions that block channel at low V )
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NMDA receptors Conductance is voltage-dependent (raising voltage knocks out Mg ions that block channel at low V )
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NMDA receptors Conductance is voltage-dependent (raising voltage knocks out Mg ions that block channel at low V )
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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)
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GABA B receptor kinetics Simplest model for a metabotropic receptor:
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GABA B receptor kinetics Simplest model for a metabotropic receptor: Transmitter binding activates receptor:
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GABA B receptor kinetics Simplest model for a metabotropic receptor: Transmitter binding activates receptor:
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GABA B receptor kinetics Simplest model for a metabotropic receptor: Transmitter binding activates receptor: Active receptor activates second messenger:
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GABA B receptor kinetics Simplest model for a metabotropic receptor: Transmitter binding activates receptor: Active receptor activates second messenger:
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GABA B receptor kinetics Simplest model for a metabotropic receptor: Transmitter binding activates receptor: Active receptor activates second messenger: Cooperative binding of second messenger to K channel opens it for current:
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GABA B receptor kinetics Simplest model for a metabotropic receptor: Transmitter binding activates receptor: Active receptor activates second messenger: Cooperative binding of second messenger to K channel opens it for current:
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Presynaptic kinetics: depression and facilitation
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depression (exc->exc synapses)
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Presynaptic kinetics: depression and facilitation depression (exc->exc synapses) facilitation (exc->inh synapses)
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Synaptic depression Dynamics of P rel controlled by depletion of synaptic vesicles:
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Synaptic depression Dynamics of P rel controlled by depletion of synaptic vesicles:
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Synaptic depression Dynamics of P rel controlled by depletion of synaptic vesicles: For presynaptic rate r(t),
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Synaptic depression Dynamics of P rel controlled by depletion of synaptic vesicles: For presynaptic rate r(t),
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Synaptic depression Dynamics of P rel controlled by depletion of synaptic vesicles: For presynaptic rate r(t), For stationary rate, stationary solution is
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Synaptic depression Dynamics of P rel controlled by depletion of synaptic vesicles: For presynaptic rate r(t), For stationary rate, stationary solution is
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Response to change in presynaptic rate expand:
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Response to change in presynaptic rate expand:
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Response to change in presynaptic rate expand:
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Response to change in presynaptic rate expand: Responds to change in input, not much to absolute level
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Synaptic facilitation P rel = P(vesicle) P(release|vesicle)
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Synaptic facilitation P rel = P(vesicle) P(release|vesicle) x y
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Synaptic facilitation P rel = P(vesicle) P(release|vesicle) x y Dynamics of x : depression (vesicle depletion)
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Synaptic facilitation P rel = P(vesicle) P(release|vesicle) x y Dynamics of x : depression (vesicle depletion) Dynamics of y : facilitation (need Ca influx to make release possible)
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Synaptic facilitation P rel = P(vesicle) P(release|vesicle) x y Dynamics of x : depression (vesicle depletion) Dynamics of y : facilitation (need Ca influx to make release possible)
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Synaptic facilitation P rel = P(vesicle) P(release|vesicle) x y Dynamics of x : depression (vesicle depletion) Dynamics of y : facilitation (need Ca influx to make release possible) For stationary rate:
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Synaptic facilitation P rel = P(vesicle) P(release|vesicle) x y Dynamics of x : depression (vesicle depletion) Dynamics of y : facilitation (need Ca influx to make release possible) For stationary rate:
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Combined model (Markram-Tsodyks)
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Facilitation as before:
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Combined model (Markram-Tsodyks) Facilitation as before:
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Combined model (Markram-Tsodyks) Facilitation as before: Depression is proportional to Prob(release|vesicle) after spike:
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Combined model (Markram-Tsodyks) Facilitation as before: Depression is proportional to Prob(release|vesicle) after spike:
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Combined model (Markram-Tsodyks) Facilitation as before: Depression is proportional to Prob(release|vesicle) after spike: With presynaptic rate r(t) :
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Combined model (Markram-Tsodyks) Facilitation as before: Depression is proportional to Prob(release|vesicle) after spike: With presynaptic rate r(t) :
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Combined model (Markram-Tsodyks) Facilitation as before: Depression is proportional to Prob(release|vesicle) after spike: With presynaptic rate r(t) :
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