models of synaptic transmission (1)
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Models of synaptic transmission
Dmitry Bibichkov Max Planck Institute for Biophysical Chemistry Göttingen, Germany
Bernstein Center for Computational Neuroscience Göttingen , Germany
Overview
09.08.2010 D. Bibichkov, AACIMP-2010
1. Basic principles of synaptic transmission2. Basic modelling of synaptic responses3. Dynamical properties of synapses. Short-term plasticity. 4. Phenomenological models of dynamic synapses5. Role of calcium in synaptic transmission6. Statistical models and experimental estimation of their parameters 7. Effects of synaptic dynamics on information transmission8. Effects of synaptic dynamics on neural network behavior9. Long term synaptic plasticity 10. Electric synapses, gap junctions
Synapses: communication devices for neurons
1. Chemical synapses: AP ---> Postsynaptic currents / potentials:
Excitatory: glu, ACh depolarization: - EPSC/EPSP
Inhibitory: GABA hyperpolarization: - IPSC/IPSP
2. Electric synapses: gap junctions: potential synchronization
09.08.2010 D. Bibichkov, AACIMP-2010
Synapses: communication devices for neurons
1. Chemical synapses: AP ---> Postsynaptic currents / potentials:
Excitatory: AMPA-receptors NMDA
Inhibitory: GABA-A GABA-B
2. Electric synapses: gap junctions: potential synchronization
09.08.2010 D. Bibichkov, AACIMP-2010
Chemical synapses
09.08.2010 D. Bibichkov, AACIMP-2010
Chemical synapses
09.08.2010 D. Bibichkov, AACIMP-2010
1. Action potential initiation at the presynaptic neuron
2. Action potential propagation along the axon3. Opening of voltage gated Ca channels at the
presynaptic terminal4. Ca-difusion and interaction with vesicle
release machinery5. Vesicle exocytosis and neurotransmitter
release into the synaptic cleft6. Neurotransmitter binding and activation of
postsynaptic receptors, channel opening7. Neurotransmitter uptake and vesicle recycling
Stages of synaptic transmission
Chemical synapses
09.08.2010 D. Bibichkov, AACIMP-2010
[Meinrenken et al. J 2003; Sudhof 2004]
β/][ 2+Mg
Simplified mathematical description
09.08.2010 D. Bibichkov, AACIMP-2010
)( ∆−−+→ spijii ttVV ε
)()( / teat mt
m
Θ= − τ
τεe.g.
Summation of postsynaptic inputs
09.08.2010 D. Bibichkov, AACIMP-2010
)( ∆−−+→ spijii ttVV ε
)()( / teat mt
m
Θ= − τ
τεe.g.
V(t)Vrest
V(t)
Vrest
Chemical synapses
09.08.2010 D. Bibichkov, AACIMP-2010
)()( / tet t Θ= ↓− τα
For models describing neuron voltage by a differential equation (e.g. I&F neuron)
)()()( synsyn EVtgtI −⋅=Esyn is the reversal potential of the synapse Excitatory Esyn ~0 mVInhibitory Esyn ~ -75 mV
Postsynaptic current
)()( tt δα =
Conductance change
)()( ∆−−⋅= ∑ spsp
synsyn ttgtg α
( ) )()( //max teeIt tt Θ−−
= ↑↓ −−
↑↓
ττ
ττα
Chemical synapses
09.08.2010 D. Bibichkov, AACIMP-2010
)()()( synsyn EVtgtI −⋅=
( ) )()( // tegegt fastfast tslow
tfast Θ+= −− ττα
τ= 5 ms, gsyn= 40 pS
)()( / tet t Θ= − τα
τfast= 5 ms, τslow= 50 ms
Inhibitory neurons
)(~)( ∆−− spsyn tttg α
Chemical synapses
09.08.2010 D. Bibichkov, AACIMP-2010
)()()( synsyn EVtgtI −⋅=
Excitatory neurons
• AMPA ( ) )(273.1)( // teegt ttAMPA Θ−⋅= ↑↓ −− ττα
ms09.0=↑τ
ms5.1=↓τ
pSg AMPA 720=
Chemical synapses
09.08.2010 D. Bibichkov, AACIMP-2010
Excitatory neurons• NMDA voltage-dependent Mg2+- block (removed at V > - 50 mV)
( ) )(])[,(358.1)( 2// tMgVgeegt ttNMDA Θ⋅⋅−⋅= +
∞−− ↑↓ ττα
)][1/(12
β
ε VeMgg−+
∞ +=
[Gabbiani et.al 1994]
-1 0 0 -5 0 0 5 0 1 0 00
0 . 1
0 . 2
0 . 3
0 . 4
0 . 5
0 . 6
0 . 7
0 . 8
0 . 9
1
V
g∞
[ M g 2 + ] = 1 . 2 m M
[ M g 2 + ] = 0 . 2 m M
[ M g 2 + ] = 2 5 m M
nSgNMDA 2.1=
Dynamic changes of postsynaptic responses
facilitation
depression
[Markram, et. al. 1998]
09.08.2010 D. Bibichkov, AACIMP-2010
Dynamic changes of postsynaptic responses
facilitation
depression
09.08.2010 D. Bibichkov, AACIMP-2010
Amplitude of postsynaptic response can also change from spike to spike
presynaptic train
Dynamic changes of postsynaptic responses
Depending on Ca2+-concentration, depression and facilitation can be expressed at the same calyx synapse
Mouse calyx of Held synapse, P16H.Taschenberger
09.08.2010 D. Bibichkov, AACIMP-2010
Dynamic changes of postsynaptic responses
Synaptic depresssion and facilitation can be expressed at the same synapse(reponses to 100Hz trains of stimuli):
[von Gersdorff and Borst, 2002]
09.08.2010 D. Bibichkov, AACIMP-2010
Neurotransmitteraccumulation
Postsynaptic receptordesensitization & saturation
Ca++ accumulation, changes in release probability
facilitation
Depletion of vesicles
depression
(Ca++ - dependent) changes in recycling and refilling of vesicles
Synaptic transmission scheme
09.08.2010 D. Bibichkov, AACIMP-2010
Postsynaptic current amplitude:
Total pool size Navailable pool fraction xrelease probability pquantal size q
Phenomenological model of synaptic dynamics
qpxNI A ⋅⋅⋅=
Quantal hypothesis [Del Castillo, B.Katz, 1954] : The neurotransmitter is released in discrete packets (vesicles) or quanta, and each quantum evoke a nearly constant postsynaptic response. The number of released quanta after each action potential is a random number.
09.08.2010 D. Bibichkov, AACIMP-2010
)()( tItI A α⋅=
Total pool size Navailable pool fraction xrelease probability pquantal size q
qpxNI A ⋅⋅⋅=depression
Phenomenological model of synaptic dynamics
09.08.2010 D. Bibichkov, AACIMP-2010
Postsynaptic current amplitude:
)()( tItI A α⋅=
Postsynaptic current amplitude:
facilitation
Phenomenological model of synaptic dynamics
09.08.2010 D. Bibichkov, AACIMP-2010
qpxNI A ⋅⋅⋅=
)()( tItI A α⋅=
Total pool size Navailable pool fraction xrelease probability pquantal size q
receptor desensitization
Phenomenological model of synaptic dynamics
09.08.2010 D. Bibichkov, AACIMP-2010
qpxNI A ⋅⋅⋅=Postsynaptic current amplitude:
)()( tItI A α⋅=
Total pool size Navailable pool fraction xrelease probability pquantal size q
[Tsodyks and Markram 1997]
3-state model of a synapse:• readily releasable• active• recovering
Depression
Phenomenological model of synaptic dynamics
09.08.2010 D. Bibichkov, AACIMP-2010
1=++ zyx
[Tsodyks and Markram 1997]
2-state model of a synapse:• readily releasable• active• recovering
Depression
Phenomenological model of synaptic dynamics
09.08.2010 D. Bibichkov, AACIMP-2010
[Tsodyks and Markram 1997]
• Depletion of single synaptic pool at each spike
• Exponential recovery from depression with rate k
Depression
Phenomenological model of synaptic dynamics
09.08.2010 D. Bibichkov, AACIMP-2010
[Tsodyks and Markram 1997]
• Increase of release probability p at each spike
• Exponential decrease of release probability to the basal level with time constant τf
Facilitation
Phenomenological model of synaptic dynamics
09.08.2010 D. Bibichkov, AACIMP-2010
• Depletion of receptor pool at each spike transmission.
• Power law relationship between amount of desensitization and neurotransmitter release.
• Exponential recovery from desensitization with rec. time τq
Receptor desensitization
[Brenowitz and Trussell 2001]
Phenomenological model of synaptic dynamics
09.08.2010 D. Bibichkov, AACIMP-2010
Short-term depression: consequences for rate coding
Pyramidal cells in rat somatosensory cortex[Tsodyks and Markram, 1997]
09.08.2010 D. Bibichkov, AACIMP-2010
Short-term depression: consequences for rate coding
Steady state response decreases as 1/f
Pyramidal cells in rat somatosensory cortex[Tsodyks and Markram, 1997]
Integrated steady state response (summed EPSP/C over time) saturates below the limiting frequency ~k/p
09.08.2010 D. Bibichkov, AACIMP-2010
Short-term depression: consequences for rate coding
Steady state response decreases as 1/f
Transient response to abrupt rate change ~ Δf/f
This corresponds to the Weber-Fechner law in psychophysics
0 0 . 2 0 . 4 0 . 6 0 . 8
5 0
5 5
6 0
0 0 . 2 0 . 4 0 . 6 0 . 8
0 . 2 8
0 . 3
0 . 3 2
0 0 . 2 0 . 4 0 . 6 0 . 81 3
1 4
1 5
1 6
1 7
09.08.2010 D. Bibichkov, AACIMP-2010
f
x
<I>
∞∞∫= pxfdttIT
I ~)(1
fx /1~∞
ffxfI /~~ ∆∆∆ ∞
Calcium-dependent release
• Calcium influx is the trigger for fast evoked transmitter release
• An elevation in intracellular calcium concentration is an absolute requirement for transmitter release. Na+ and K+ ions not necessary for release.
• Release probability is a nonlinear function of calcium concentration in the active zone
09.08.2010 D. Bibichkov, AACIMP-2010
Calcium-dependent release
4-state model [Schneggenburger and Neher 2000]
allosteric model [Lou et al, 2005]
09.08.2010 D. Bibichkov, AACIMP-2010
Calcium-dependent release
[Lou et al, 2005]
09.08.2010 D. Bibichkov, AACIMP-2010
Calcium-dependent recovery
Recovery depends on the integral of the intracellular calcium in the presynaptic terminal
[Hosoi et.al., 2007]
09.08.2010 D. Bibichkov, AACIMP-2010
Activity-dependent recovery
0 . 2 0 . 5 1 2 5 1 0 2 0 5 0 1 0 0 2 0 00
1
2
3
4
5
6
7
8
i n p u t f r e q u e n c y f , H z
reco
very
rat
e k
, H
z
Effective recovery rate:mean recovery rate over an ISI
09.08.2010 D. Bibichkov, AACIMP-2010
Calcium accumulates during the trains of action potentials and leads to increased recovery rates during high-frequency stimulation
Activity-dependent recovery
Calyx of Held[Weis et.al. 1999]
Activity-dependent recovery increases the range of characteristic frequencies towards the maximal recovery rate
climbing fiber to Purkinje cell synapse[Dittmann and Regehr 1998]
activity dependenceno activity dependence
09.08.2010 D. Bibichkov, AACIMP-2010
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