models of synaptic transmission (1)

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


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


Chemical synapses


Chemical synapses


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


[Meinrenken et al. J 2003; Sudhof 2004]

β/][ 2+Mg

Simplified mathematical description


)( ∆−−+→ spijii ttVV ε

)()( / teat mt

m

Θ= − τ

τεe.g.

Summation of postsynaptic inputs


)( ∆−−+→ spijii ttVV ε

)()( / teat mt

m

Θ= − τ

τεe.g.

V(t)Vrest

V(t)

Vrest

Chemical synapses


)()( / 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


)()()( 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


)()()( synsyn EVtgtI −⋅=

Excitatory neurons

• AMPA ( ) )(273.1)( // teegt ttAMPA Θ−⋅= ↑↓ −− ττα

ms09.0=↑τ

ms5.1=↓τ

pSg AMPA 720=

Chemical synapses


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]



facilitation

depression


Amplitude of postsynaptic response can also change from spike to spike

presynaptic train


Depending on Ca2+-concentration, depression and facilitation can be expressed at the same calyx synapse

Mouse calyx of Held synapse, P16H.Taschenberger



Synaptic depresssion and facilitation can be expressed at the same synapse(reponses to 100Hz trains of stimuli):

[von Gersdorff and Borst, 2002]


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


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.


)()( tItI A α⋅=


qpxNI A ⋅⋅⋅=depression




)()( tItI A α⋅=


facilitation



qpxNI A ⋅⋅⋅=

)()( tItI A α⋅=


receptor desensitization



qpxNI A ⋅⋅⋅=Postsynaptic current amplitude:

)()( tItI A α⋅=


[Tsodyks and Markram 1997]

3-state model of a synapse:• readily releasable• active• recovering

Depression



1=++ zyx


2-state model of a synapse:• readily releasable• active• recovering

Depression




• Depletion of single synaptic pool at each spike

• Exponential recovery from depression with rate k

Depression




• Increase of release probability p at each spike

• Exponential decrease of release probability to the basal level with time constant τf

Facilitation



• 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]



Short-term depression: consequences for rate coding

Pyramidal cells in rat somatosensory cortex[Tsodyks and Markram, 1997]



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



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


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



4-state model [Schneggenburger and Neher 2000]

allosteric model [Lou et al, 2005]



[Lou et al, 2005]


Calcium-dependent recovery

Recovery depends on the integral of the intracellular calcium in the presynaptic terminal

[Hosoi et.al., 2007]


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


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


models of synaptic transmission (1)

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