Figures and data in Competition for synaptic building blocks shapes synaptic plasticity

Version of Record: October 11, 2018
Accepted Manuscript: September 17, 2018

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Jochen Triesch

Anh Duong Vo

Anne-Sophie Hafner

(2018)
Competition for synaptic building blocks shapes synaptic plasticity

eLife 7:e37836.

https://doi.org/10.7554/eLife.37836
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Figures
Tables
Additional files

8 figures, 4 tables and 1 additional file

Figures

Figure 1

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Architecture of the model.

(A) Sketch of the architecture of the model. Neurotransmitter receptors, e.g. AMPA receptors, are trafficked through the dendrite and bind to ‘slots’ inside of dendritic spines. The efficacy of a …
https://doi.org/10.7554/eLife.37836.002

Figure 2

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Synaptic filling fraction.

(A) Filling fraction $F$ as a function of the removal ratio $(β δ) / (α γ)$ . (B) Example empirical cumulative distribution functions (CDFs) of the numbers of receptors bound in individual synapses for fixed …
https://doi.org/10.7554/eLife.37836.004

Figure 3

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Filling fraction $F^{*}$ in the short-term approximation of constant receptor number as a function of the ratio of transition rates $ρ = β / α$ for different combinations of $R$ and $S$ .

(A) $F^{*}$ for a fixed number of $S = 10 000$ slots and three different receptor numbers as a function of $ρ$ . (B) For fixed number of $R = 10 000$ receptors and three different numbers of slots. Note that $F^{*}$ reacts …
https://doi.org/10.7554/eLife.37836.006

Figure 4

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Effect of sudden change of the pool size $p$ on synaptic efficacies.

(A) After 2 min, the pool size is either doubled (solid curves) or set to zero (dotted curves). In response, the synaptic efficacies are scaled multiplicatively as receptors are redistributed …
https://doi.org/10.7554/eLife.37836.007

Figure 5

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Induction of transient heterosynaptic plasticity.

(A) Illustration of transient heterosynaptic plasticity. After 2 min, the number of slots in synapses 1 and 3 is increased instantaneously. The system quickly reaches a new (transient) equilibrium, …
https://doi.org/10.7554/eLife.37836.008

Figure 6

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Model of homosynaptic LTP accompanied by heterosynaptic LTD.

After 2 min, LTP is induced in synapses 2 and 3. This entails a transient synapse-specific change in the insertion rate $α$ of these synapses and a gradual change in their slot numbers. (A) Time …
https://doi.org/10.7554/eLife.37836.009

Figure 7

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Illustration of long-term behavior under the separation of time scales assumption.

Parameters were: $β = 1 / 43 s^{- 1}$ , $δ = 1 / 14 {m i n}^{- 1}$ . The desired relative pool size was set to $ϕ = 2.67$ and the desired filling fraction to $F = 0.9$ . The production rate $γ$ and attachment rate $α$ were calculated according to Equation 12 …
https://doi.org/10.7554/eLife.37836.010

Figure 8

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Quantification of spontaneous synaptic efficacy fluctuations due to the fast exchange of receptors between synapses and the receptor pool.

(A) Example simulation of a piece of dendrite with 7 synapses during 10 min of simulated time. The number of receptor slots in each synapse is given in the legend. The relative pool size was set to $ϕ = 2.67$ and the filling fraction was set to $F = 0.5$ by choosing the binding rate to receptor slots $α$ via Equation 13. (B) Same as A. but for a higher filling fraction of $F = 0.9$ . (C) Size of synaptic efficacy fluctuations as measured by the coefficient of variation (CV) as a function of the steady state number of receptors in each synapse, which is given by the product of the filling fraction $F$ and the number of slots $s_{i}$ in synapse $i$ . The relative pool size was set to $ϕ = 2.67$ . Data points represent averages over 10 simulations of 30 min simulated time each. Lines represent linear fits through the data points in double log space. (D) CV as a function of steady state number of receptors for different relative pool sizes $ϕ$ achieved by holding the binding rate to receptor slots $α$ fixed and varying the externalization rate $γ$ .

https://doi.org/10.7554/eLife.37836.011

Tables

Table 1

Standard parameters of the model.

https://doi.org/10.7554/eLife.37836.003

	Value	Description	Reference
$β$	${(43 s)}^{- 1}$	unbinding rate from slots	Henley and Wilkinson (2013); Henley and Wilkinson (2016)
$δ$	${(14 min)}^{- 1}$	internalization rate	Ehlers et al. (2007)
$ϕ$	2.67	relative pool size	M. Renner, personal communication
$F$	unknown	filling fraction	set by hand to {0.5, 0.7, 0.9}
$γ$	unknown	externalization rate	set via Equation 12 to achieve desired $ϕ$
$α$	unknown	binding rate to slots	set via Equation 13 to achieve desired $F$

Table 2

Summary of model predictions.

Further predictions are mentioned in the Discussion.

https://doi.org/10.7554/eLife.37836.005

Prediction	Explanation
Filling fraction	Synapses in a local group have identical filling fractions in the basal state.
Pool Size	Manipulation of local pool size scales synapses multiplicatively.
Sensitivity	Filling fraction is most sensitive when pool size matches slot numbers.
Heterosynaptic I	High pool size and filling fraction reduce heterosynaptic plasticity.
Heterosynaptic II	Heterosynaptic plasticity is only transient.
Homosynaptic	Pool size and filling fraction modulate homosynaptic plasticity.
Fluctuations	Spontaneous efficacy fluctuations are bigger for small synapses.

Table 3

Fitting results from the stochastic version of the model, cf. Figure 8C.

The externalization rate $γ$ and the attachment rate of receptors to slots $α$ are set to obtain different filling fractions while maintaining a relative pool size of $ϕ = 2.67$ . Parameters $β$ and $δ$ are as …

https://doi.org/10.7554/eLife.37836.012

$F$	$α [{min}^{- 1}]$	$γ [{min}^{- 1}]$	Scale factor $a$	Exponent $b$
0.5	0.0056	12.1	71.4	−0.52
0.7	0.0093	9.4	55.6	−0.51
0.9	0.0278	6.7	31.8	−0.50

Table 4

Fitting results from the stochastic version of the model, cf. Figure 8D.

The attachment rate of receptors to slots is chosen as $α = 0.0093 min^{- 1}$ to obtain a filling fraction of $0.7$ for a relative pool size of $ϕ = 2.67$ . Parameters $β$ and $δ$ are as in Tab. 1. $γ$ is varied to obtain different …