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