Figures and data in A unified computational model for cortical post-synaptic plasticity

Version of Record: January 28, 2021
Version of Record: August 13, 2020
Accepted Manuscript: July 30, 2020

Download
A two-part list of links to download the article, or parts of the article, in various formats.
Downloads (link to download the article as PDF)
- Article PDF
- Figures PDF
Open citations (links to open the citations from this article in various online reference manager services)
- Mendeley
Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)
Tuomo Mäki-Marttunen

Nicolangelo Iannella

Andrew G Edwards

Gaute T Einevoll

Kim T Blackwell

(2020)
A unified computational model for cortical post-synaptic plasticity

eLife 9:e55714.

https://doi.org/10.7554/eLife.55714
- Download BibTeX
- Download .RIS
Cite
Share
CommentOpen annotations (there are currently 0 annotations on this page).

438 downloads

Figures
Tables

11 figures and 4 tables

Figures

Figure 1

Download asset Open asset

Signalling pathways included in the model.

The PKA-pathway-related proteins and signalling molecules are highlighted by blue, PKC-pathway molecules by yellow, and CaMKII-pathway molecules by green colours. Reactions associated with a …

Figure 2

Download asset Open asset

Ca²⁺ activates CaMKII, PKA, and PKC pathways.

(A) Illustration of the stimulus protocols with Ca²⁺ flux amplitudes 150 (green), 200 (cyan), and 250 (purple) particles/ms. (**B–F**) Time courses of Ca²⁺ (in nM) bound to buffers (B), pumps (C), …

Figure 3 with 4 supplements

Download asset Open asset

4xHFS activates CaMKII, PKA, and PKC pathways and leads to LTP (A–R), while LFS activates the PKC pathway and leads to LTD (S–U).

(A) Total synaptic conductance in response to 4xHFS, determined by the numbers of membrane-inserted GluR1s and GluR2s — see Equation 5. The stimulation starts at 40 s and lasts until 53 s. (**B–C**) …

Figure 3—figure supplement 1

Download asset Open asset

Both GluR1 and GluR2 are needed for bidirectional plasticity.

(A) When GluR1 subunits are absent, 4xHFS induces LTD instead of LTP. (B) When GluR2 subunits are absent, LFS does not lead to changes in synaptic conductance. (C) When GluR1 subunits are absent, …

Figure 3—figure supplement 2

Download asset Open asset

An alternative dimers-of-like-dimers rule of tetramer formation reproduces the HFS-induced LTP, LFS-induced LTD, and STDP predictions obtained with the default tetramer formation rule.

(A) Plasticity induced by HFS and LFS. The y-axis shows the total synaptic conductance, and the x-axis shows the time. The 4xHFS stimulation lasts from 40 to 53 s, and the LFS stimulation from 40 to …

Figure 3—figure supplement 3

Download asset Open asset

The biochemical signalling network model, given the NMDAR-conducted Ca²⁺ inputs from the multicompartmental neuron model of layer 2/3 pyramidal cell under 1.3 mM extracellular [Mg²⁺], predicts LTP for 6xHFSt and LTD for LFS-1Hz.

The 6xHFSt protocol lasts from 0 to 60 s, while the LFS-1Hz protocol lasts from 0 to 1800s (data shown until 500 s). See Materials and methods, section '*Modelling the Ca²⁺ inputs and neuromodulatory …*

Figure 3—figure supplement 4

Download asset Open asset

The biochemical signalling network model robustly predicts LTP for HFS and LTD for LTP with altered durations of neuromodulatory inputs.

In the control case, the pre-synaptic input-associated fluxes of β-adrenergic and cholinergic ligands were 10 and 20 particles/ms, respectively, and the duration of each pulse was 3 ms. Here, the …

Figure 4

Download asset Open asset

4xHFS-induced LTP is dependent on β-adrenergic ligands and LFS-induced LTD is dependent on activation of mGluRs or cholinergic receptors.

(**A–D**) 4xHFS-induced LTP in the control case (dark purple), without Ca²⁺ inputs (blue), without β-adrenergic ligands (green), and under blockade of PKC pathway-activation (mGluRs or cholinergic …

Figure 5 with 1 supplement

Download asset Open asset

Layer 2/3 pyramidal cell plasticity in response to STDP protocol depends on neuromodulatory state and pairing interval.

(A) Layer 2/3 pyramidal cell morphology (grey, thin), locations of synaptic input highlighted (black, thick). Inset: Illustration of the inputs (black) and the recorded synaptic intracellular Ca²⁺ …

Figure 5—figure supplement 1

Download asset Open asset

Ca²⁺ fluxes predicted by the multicompartmental layer 2/3 pyramidal cell model depend on the inter-stimulus interval (ISI).

(**A–D**) The Ca²⁺ flux time course during the pairing protocol (from 100 ms before to 900 ms after the pre-synaptic stimulus) entering the post-synaptic spine through NMDA receptors when the onset of …

Figure 6 with 1 supplement

Download asset Open asset

The STDP curve of layer 2/3 pyramidal cells is affected by the number of post-synaptic stimulus pulses associated with the pre-synaptic input.

(A) The STDP curves of Figure 5M when the number of spikes per post-synaptic burst was 1 (yellow), 2 (green), 3 (blue), or 4 (as in Figure 5; dark purple). Inset: relative concentrations of …

Figure 6—figure supplement 1

Download asset Open asset

The post-STDP synaptic conductance is weakly correlated with the peak of the Ca²⁺ input but strongly correlated with the mean Ca²⁺ input during the inter-stimulus interval.

The y-axis shows the post-STDP synaptic conductance (in presence of β-adrenergic and cholinergic neuromodulation) relative to baseline as in Figure 5M. (A) The x-axis shows the peak Ca²⁺ input (in …

Figure 7 with 1 supplement

Download asset Open asset

The fraction of GluR1s, number of Ca²⁺ extrusion proteins, and the concentrations of PKA and PKC-pathway proteins in the post-synaptic spine determine the type of LTP/LTD in the post-synaptic spine.

(A) The LTP/LTD curves for all 16 classes. Four values of Ca²⁺ input amplitude were considered: 0, 50, 150, and 250 particles/ms (x-axis; repeated and overlaid for space). The y-axis shows the …

Figure 7—figure supplement 1

Download asset Open asset

The PKC-pathway parameter distributions differ between clusters separated by their response to low (50 particles/ms) Ca²⁺ input.

Here, the experiment of Figure 7 is repeated by clustering the parameters sets based on the relative synaptic conductance after a steady-state Ca²⁺ flux of 50 particles/ms (250 particles/ms in Figure…

Figure 8

Download asset Open asset

The model predictions of LTP and LTD are robust to small changes in model parameters.

Values of initial concentrations (47 parameters) or reaction rates (223 parameters) were changed one at the time by −10% or +10%, and the resulting synaptic conductance 16 min after LFS (A) or 4xHFS …

Figure 9 with 11 supplements

Download asset Open asset

The model can be fit to LTP/LTD data from different cortical areas.

(A) The model could be fit to LTP/LTD data from data sets EC-1 (top), EC-2, PFC-1, PFC-2, BC, ACC, PFC-3, AuC-1, and AuC-2 (bottom). The curves represent the model predictions of the best-fit …

Figure 9—figure supplement 1

Download asset Open asset

Parameters for data set EC-1.

Ranges of each parameter among the accepted parameter sets from the fitting of Figure 9. All parameters are linearly scaled between 0 and 1, which represent the minimal and maximal value of the …

Figure 9—figure supplement 2

Download asset Open asset

Parameters for data set EC-2.

See Figure 9—figure supplement 1 for details.

Figure 9—figure supplement 3

Download asset Open asset

Parameters for data set PFC-1.

See Figure 9—figure supplement 1 for details.

Figure 9—figure supplement 4

Download asset Open asset

Parameters for data set PFC-2.

See Figure 9—figure supplement 1 for details.

Figure 9—figure supplement 5

Download asset Open asset

Parameters for data set BC.

See Figure 9—figure supplement 1 for details.

Figure 9—figure supplement 6

Download asset Open asset

Parameters for data set ACC.

See Figure 9—figure supplement 1 for details.

Figure 9—figure supplement 7

Download asset Open asset

Parameters for data set PFC-3.

See Figure 9—figure supplement 1 for details.

Figure 9—figure supplement 8

Download asset Open asset

Parameters for data set VC-1.

See Figure 9—figure supplement 1 for details.

Figure 9—figure supplement 9

Download asset Open asset

Parameters for data set VC-2.

See Figure 9—figure supplement 1 for details.

Figure 9—figure supplement 10

Download asset Open asset

Parameters for data set AC-1.

See Figure 9—figure supplement 1 for details.

Figure 9—figure supplement 11

Download asset Open asset

Parameters for data set AC-2.

See Figure 9—figure supplement 1 for details.

Figure 10

Download asset Open asset

The models describing plasticity in different cortical areas predict diverse responses to modified stimulation protocol and stimulation under chemical blockers.

(A) The predicted responses of the 20 best models in each data set to HFS (100 pulses at 100 Hz) stimulation. (**B–D**) The predicted responses of the 20 best models in each data set to the applied …

Figure 11 with 2 supplements

Download asset Open asset

Calibration of the model.

Black curves represent the final model, while grey lines represent predictions of models where previous model components or tentative parameter values were used. (A) Concentration of …

Figure 11—figure supplement 1

Download asset Open asset

1 hr of simulation without inputs is sufficient to obtain a steady state.

The model was run for 4040 s without inputs. The absolute values of the time derivatives for each molecular species were determined, and the black curve shows the sum of these derivatives (nM/sec) …

Figure 11—figure supplement 2

Download asset Open asset

The model STDP model is robust to changes in AMPA conductance but sensitive to changes in NMDA condutance in the multicompartmental layer 2/3 pyramidal cell model.

The model of Figure 5 was simulated with altered AMPAR (A) or NMDAR (B) conductances, and the effects on STDP curves were measured. See Figure 5 for details. (A) Half (blue) or double (red) the …

Tables

Table 1

Pathways contributing to cortical synaptic plasticity.

(A) Experimental evidence on the requirement of various molecular species for specific types of synaptic regulation in different cortical areas. (B) Model components needed for describing the modes …

(A)
Pathway components	Type of neurons	Type of regulation	Pre-/post-synaptic	References
CaMKII	Cingulate cortex	Esophageal acid-induced sensitisation	post-syn.	Banerjee et al., 2013
CaMKII	Prefrontal cortex, pyramidal neurons	5-HT1-induced modulation of AMPA currents	post-syn.	Cai et al., 2002
$β$ -adr. receptors, PKA	Visual cortex, layer 4 pyramidal cells	Potentiation of AMPA currents	post-syn.	Seol et al., 2007
M1 receptors, PKC	Visual cortex, layer 4 pyramidal cells	Depression of AMPA currents	post-syn.	Seol et al., 2007
D1–PKA	Prefrontal cortex, pyramidal neurons	Potentiation of AMPA currents	post-syn.	Sun et al., 2005
$β$ -adr. receptors	Frontal cortex	Potentiation of field EPSPs	n/a	Sáez-Briones et al., 2015
PKC	Cultured cortical neurons	Internalisation of AMPARs	post-syn.	Chung et al., 2000
ERK	Visual cortex	Potentiation of field EPSPs	n/a	Di Cristo et al., 2001
(B)
Molecular pathway	Cell type and references
Ca²⁺ → CaM → CaMKII	Hippocampal CA1 neuron Bhalla and Iyengar, 1999; Jȩdrzejewska-Szmek et al., 2017, generic Hayer and Bhalla, 2005,
	cerebellar Purkinje cells Gallimore et al., 2018, striatal spiny projection neuron Blackwell et al., 2019
CaMKII → GluR1 S831p	Hippocampal CA1 neuron Jȩdrzejewska-Szmek et al., 2017
$β$ -adrenergic receptors → cAMP	Hippocampal CA1 neuron Jȩdrzejewska-Szmek et al., 2017
cAMP → PKA	Hippocampal CA1 neuron Bhalla and Iyengar, 1999; Jȩdrzejewska-Szmek et al., 2017, cerebellar Purkinje
	cells Gallimore et al., 2018
PKA → GluR1 S845p	Hippocampal CA1 neuron Jȩdrzejewska-Szmek et al., 2017
M1 receptors → PLC	Cerebellar Purkinje cells Gallimore et al., 2018
PLC → PKC	Hippocampal CA1 neuron Bhalla and Iyengar, 1999, striatal spiny projection neuron
	Kim et al., 2013; Blackwell et al., 2019
	cerebellar Purkinje cells Kotaleski et al., 2002; Gallimore et al., 2018
PKC → GluR2 S880p	Cerebellar Purkinje cells Gallimore et al., 2018

Table 2

List of LTP/LTD experiments in the cortex.

The first column labels the experimental data set and names the underlying study. The second column shows the considered synaptic pathway and the third column shows whether the observed LTP/LTD had …

Data set	Reference	Pathway	Pre/post	Freq.	N_pulses	Experiment	10 min	15 min	20 min	SD
EC-1	Ma et al., 2008	horizontal	mostly	100	100	control	1.3	1.4	1.3	0.1
			post			CaMKII blocked	1.05	1.02	0.95	0.07
						without post-syn. Ca²⁺	1.05	1.05	1.1	0.09
EC-2	Ma et al., 2008	ascending	mostly	100	100	control	1.6	1.6	1.6	0.11
			post			PKA blocked	1.4	1.4	1.4	0.13
						without post-syn. Ca²⁺	1.3	1.4	1.4	0.13
PFC-1	Sáez-Briones et al., 2015	CC→PFC	n/a	312	156	control	2.0	1.98	1.9	0.08
						without $β$ -adrenergic ligand	1.34	1.4	1.36	0.09
PFC-2	Flores et al., 2011	CC→PFC	n/a	312	156	control	1.7	1.6	1.64	0.12
						without $β$ −1-receptor agonist	1.43	1.45	1.43	0.1
BC	Hardingham et al., 2003	L4→L2/3	n/a	5	10 × 4	control	1.35	1.4	1.3	0.09
						CaMKII mutant	1.25	1.2	1.1	0.09
ACC	Song et al., 2017	L5/6 → L2/3	post	5	10 × 4	control	1.55	1.4	1.4	0.05
						without s845	1.1	1.05	1.05	0.07
						without s831	1.35	1.4	1.3	0.1
PFC-3	Zhou et al., 2013	L2/3 → L2/3	mostly	0.1	50	control	1.3	1.4	1.4	0.14
			post			without $β$ −1-receptor agonist	1.1	1.2	1.2	0.13
VC-1	Kirkwood et al., 1997	L4 → L3	n/a	5	10 × 4	(CTR, HFS)	1.3	1.26	1.26	0.07
(adult)						(without CaMKII, HFS)	1.02	1.02	1.02	0.02
				5	900*	(CTR, LFS)	n/a	0.95	0.95	0.05
						(without CaMKII, LFS)	n/a	0.88	0.93	0.03
VC-2	Kirkwood et al., 1997	L4 → L3	n/a	5	10 × 4	(CTR, HFS)	1.2	1.18	1.18	0.05
(4–5 w)						(without CaMKII, HFS)	1.07	1.09	1.08	0.03
				5	900*	(CTR, LFS)	n/a	0.79	0.82	0.03
						(without CaMKII, LFS)	n/a	0.82	0.89	0.03
AuC-1	Kotak et al., 2007	L6 → L5	n/a	1	25 × 5	LTP-expressing cells	1.98	1.58	1.93	0.19
AuC-2	Kotak et al., 2007	L6 → L5	n/a	1	25 × 5	LTD-expressing cells	0.77	0.68	0.67	0.09

Table 3

List of model reactions.

(A) The reaction-rate units are in 1/ms, 1/(nMms), 1/(nM²ms), 1/(nM³ms), or 1/(nM⁴ms), depending on the number of reactants. Reactions are grouped by similar modes of action and identical forward …

(A)		Forw.	Backw.			Forw.	Backw.
ID	Reaction	Rate	Rate	ID	Reaction	Rate	Rate
1	Ca + PMCA ⇌ PMCACa	5e-05	0.007	71	GluR1 $𝐗_{22}$ + $𝐘_{22}$ ⇌ GluR1 $𝐙_{22}$	2.78e-08	0.002
2	PMCACa ⇌ PMCA + CaOut	0.0035	0.0	72	GluR1 $𝐗_{23}$ ⇌ GluR1 $𝐘_{23}$ + $𝐙_{23}$	0.0005	0
3	Ca + NCX ⇌ NCXCa	1.68e-05	0.0112	73	GluR1 $𝐗_{24}$ + PKAc ⇌ GluR1 $𝐙_{24}$	4e-06	0.024
4	NCXCa ⇌ NCX + CaOut	0.0056	0.0	74	GluR1 $𝐗_{25}$ + PP1 ⇌ GluR1 $𝐙_{25}$	8.7e-07	0.00068
5	CaOut + Leak ⇌ CaOutLeak	1.5e-06	0.0011	75	GluR1 $𝐗_{26}$ ⇌ GluR1 $𝐘_{26}$ + PP1	0.00017	0
6	CaOutLeak ⇌ Ca + Leak	0.0011	0.0	76	GluR1 $𝐗_{27}$ + PP1 ⇌ GluR1 $𝐙_{27}$	8.75e-07	0.0014
7	Ca + Calbin ⇌ CalbinC	2.8e-05	0.0196	77	GluR1 $𝐗_{28}$ ⇌ GluR1 $𝐘_{28}$ + PP1	0.00035	0
8	L ⇌ LOut	0.0005	2e-09	78	GluR1 $𝐗_{29}$ + PP2BCaMCa4 ⇌ GluR1 $𝐙_{29}$	2.01e-06	0.008
9	L + R ⇌ LR	5.555e-06	0.005	79	GluR1 $𝐗_{30}$ ⇌ GluR1 $𝐘_{30}$ + PP2BCaMCa4	0.002	0
10	LR + Gs ⇌ LRGs	6e-07	1e-06	80	GluR1 $𝐗_{31}$ ⇌ GluR1_memb $𝐗_{31}$	2e-07	8e-07
11	Gs + R ⇌ GsR	4e-08	3e-07	81	GluR1_S845 $𝐗_{32}$
12	GsR + L ⇌ LRGs	2.5e-06	0.0005		⇌ GluR1_memb_S845 $𝐗_{32}$	3.28e-05	8e-06
13	LRGs ⇌ LRGsbg + GsaGTP	0.02	0.0	82	PDE1 + CaMCa4 ⇌ PDE1CaMCa4	0.0001	0.001
14	LRGsbg ⇌ LR + Gsbg	0.08	0.0	83	PDE1CaMCa4 + cAMP ⇌ PDE1CaMCa4cAMP	4.6e-06	0.044
15	$𝐗_{1}$ + PKAc ⇌ PKAc $𝐗_{1}$	8e-07	0.00448	84	PDE1CaMCa4cAMP ⇌ PDE1CaMCa4 + AMP	0.011	0.0
16	PKAc $𝐗_{2}$ ⇌ p $𝐗_{2}$ + PKAc	0.001	0.0	85	AMP ⇌ ATP	0.001	0.0
17	ppLR + PKAc ⇌ PKAcppLR	1.712e-05	0.00448	86	PDE4 + cAMP ⇌ PDE4cAMP	2.166e-05	0.0034656
18	pppLR + PKAc ⇌ PKAcpppLR	0.001712	0.00448	87	PDE4cAMP ⇌ PDE4 + AMP	0.017233	0.0
19	ppppLR + Gi ⇌ ppppLRGi	0.00015	0.00025	88	$𝐗_{33}$ + $𝐘_{33}$ ⇌ PKAc $𝐙_{33}$	2.5e-07	8e-05
20	ppppLRGi ⇌ ppppLRGibg + GiaGTP	0.000125	0.0	89	PKAc $𝐗_{34}$ ⇌ pPDE4 $𝐘_{34}$ + PKAc	2e-05	0.0
21	pppp $𝐗_{3}$ ⇌ pppp $𝐘_{3}$ + Gibg	0.001	0.0	90	pPDE4 ⇌ PDE4	2.5e-06	0.0
22	p $𝐗_{4}$ ⇌ $𝐗_{4}$	2.5e-06	0.0	91	pPDE4 + cAMP ⇌ pPDE4cAMP	0.000433175	0.069308
23	pp $𝐗_{5}$ ⇌ p $𝐗_{5}$	2.5e-06	0.0	92	pPDE4cAMP ⇌ pPDE4 + AMP	0.3446674	0.0
24	R + PKAc ⇌ PKAcR	4e-08	0.00448	93	PKAcAMP4 ⇌ PKAr + 2*PKAc	0.00024	2.55e-05
25	pR + PKAc ⇌ PKAcpR	4e-07	0.00448	94	Ca + fixedbuffer ⇌ fixedbufferCa	0.0004	20.0
26	ppR + PKAc ⇌ PKAcppR	4e-06	0.00448	95	Glu ⇌ GluOut	0.0005	2e-10
27	pppR + PKAc ⇌ PKAcpppR	0.0004	0.00448	96	Ca + PLC ⇌ PLCCa	4e-07	0.001
28	ppppR + Gi ⇌ ppppRGi	7.5e-05	0.000125	97	GqaGTP + PLC ⇌ PLCGqaGTP	7e-07	0.0007
29	ppppRGi ⇌ ppppRGibg + GiaGTP	6.25e-05	0.0	98	Ca + PLCGqaGTP ⇌ PLCCaGqaGTP	8e-05	0.04
30	GsaGTP ⇌ GsaGDP	0.01	0.0	99	GqaGTP + PLCCa ⇌ PLCCaGqaGTP	0.0001	0.01
31	GsaGDP + Gsbg ⇌ Gs	0.1	0.0	100	PLCCa + Pip2 ⇌ PLCCaPip2	3e-08	0.01
32	GiaGTP ⇌ GiaGDP	0.000125	0.0	101	PLCCaPip2 ⇌ PLCCaDAG + Ip3	0.0003	0.0
33	GiaGDP + Gibg ⇌ Gi	0.00125	0.0	102	PLCCaDAG ⇌ PLCCa + DAG	0.2	0.0
34	GsaGTP + AC1 ⇌ AC1GsaGTP	3.85e-05	0.01	103	PLCCaGqaGTP + Pip2 ⇌ PLCCaGqaGTPPip2	1.5e-05	0.075
35	AC1 $𝐗_{6}$ + CaMCa4 ⇌ AC1 $𝐙_{6}$	6e-06	0.0009	104	PLCCaGqaGTPPip2 ⇌ PLCCaGqaGTPDAG + Ip3	0.25	0.0
36	$𝐗_{7}$ + ATP ⇌ $𝐙_{7}$	1e-05	2.273	105	PLCCaGqaGTPDAG ⇌ PLCCaGqaGTP + DAG	1.0	0.0
37	AC1GsaGTPCaMCa4ATP			106	Ip3degrad + PIkinase ⇌ Ip3degPIk	2e-06	0.001
	⇌ cAMP + AC1GsaGTPCaMCa4	0.02842	0.0	107	Ip3degPIk ⇌ PIkinase + Pip2	0.001	0.0
38	$𝐗_{8}$ + $𝐘_{8}$ ⇌ AC1Gsa $𝐙_{8}$	6.25e-05	0.01	108	PLC $𝐗_{35}$ ⇌ PLC $𝐘_{35}$ + GqaGDP	0.012	0.0
39	$𝐗_{9}$ ⇌ cAMP + $𝐙_{9}$	0.002842	0.0	109	GqaGTP ⇌ GqaGDP	0.001	0.0
40	AC1GiaGTPCaMCa4ATP			110	GqaGDP ⇌ Gqabg	0.01	0.0
	⇌ cAMP + AC1GiaGTPCaMCa4	0.0005684	0.0	111	Ca + DGL ⇌ CaDGL	0.000125	0.05
41	AC1CaMCa4ATP ⇌ cAMP + AC1CaMCa4	0.005684	0.0	112	DAG + CaDGL ⇌ DAGCaDGL	5e-07	0.001
42	AC8 + CaMCa4 ⇌ AC8CaMCa4	1.25e-06	0.001	113	DAGCaDGL ⇌ CaDGL + 2AG	0.00025	0.0
43	CaM + 2*Ca ⇌ CaMCa2	1.7e-08	0.035	114	Ip3 ⇌ Ip3degrad	0.01	0.0
44	$𝐗_{10}$ + Ca ⇌ $𝐙_{10}$	1.4e-05	0.228	115	2AG ⇌ 2AGdegrad	0.005	0.0
45	$𝐗_{11}$ + Ca ⇌ $𝐙_{11}$	2.6e-05	0.064	116	DAG + DAGK ⇌ DAGKdag	7e-08	0.0008
46	CaM + Ng ⇌ NgCaM	2.8e-05	0.036	117	DAGKdag ⇌ DAGK + PA	0.0002	0.0
47	CaM + PP2B ⇌ PP2BCaM	4.6e-06	1.2e-06	118	Ca + PKC ⇌ PKCCa	1.33e-05	0.05
48	CaMCa $𝐗_{12}$ + PP2B ⇌ PP2B $𝐙_{12}$	4.6e-05	1.2e-06	119	PKCCa + DAG ⇌ PKCt	1.5e-08	0.00015
49	PP2BCaM + 2*Ca ⇌ PP2BCaMCa2	1.7e-07	0.35	120	Glu + MGluR ⇌ MGluR_Glu	1.68e-08	0.0001
50	CaMCa4 + CK ⇌ CKCaMCa4	1e-05	0.003	121	MGluR_Glu ⇌ MGluR_Glu_desens	6.25e-05	1e-06
51	2*CKCaMCa4 ⇌ Complex	1e-07	0.01	122	Gqabg + MGluR_Glu ⇌ MGluR_Gqabg_Glu	9e-06	0.00136
52	CKpCaMCa4 + CKCaMCa4 ⇌ pComplex	1e-07	0.01	123	MGluR_Gqabg_Glu ⇌ GqaGTP + MGluR_Glu	0.0015	0.0
53	CK $𝐗_{13}$ + Complex ⇌ CK $𝐗_{13}$ + pComplex	1e-07	0.0	124	GluR2 $𝐗_{36}$ + PKC $𝐘_{36}$ ⇌ GluR2 $𝐙_{36}$	4e-07	0.0008
54	2*Complex ⇌ Complex + pComplex	1e-05	0.0	125	GluR2 $𝐗_{37}$ ⇌ GluR2 $𝐘_{37}$ + PKC $𝐙_{37}$	0.0047	0
55	Complex + pComplex ⇌ 2*pComplex	3e-05	0.0	126	GluR2 $𝐗_{38}$ + PP2A ⇌ GluR2 $𝐙_{38}$	5e-07	0.005
56	CKpCaMCa4 ⇌ CaMCa4 + CKp	8e-07	1e-05	127	GluR2 $𝐗_{39}$ ⇌ GluR2 $𝐘_{39}$ + PP2A	0.00015	0
57	CKp $𝐗_{14}$ + PP1 ⇌ CKp $𝐙_{14}$	4e-09	0.00034	128	GluR2 $𝐗_{40}$ ⇌ GluR2_memb $𝐗_{40}$	0.00024545	0.0003
58	CKp $𝐗_{15}$ ⇌ PP1 + CK $𝐙_{15}$	8.6e-05	0.0	129	GluR2_S880 $𝐗_{41}$ ⇌ GluR2_memb_S880 $𝐗_{41}$	0.0055	0.07
59	PKA + 4*cAMP ⇌ PKAcAMP4	1.6e-15	6e-05	130	ACh + M1R ⇌ AChM1R	9.5e-08	0.0025
60	Epac1 + cAMP ⇌ Epac1cAMP	3.1e-08	6.51e-05	131	Gqabg + AChM1R ⇌ AChM1RGq	2.4e-05	0.00042
61	I1 + PKAc ⇌ I1PKAc	1.4e-06	0.0056	132	Gqabg + M1R ⇌ M1RGq	5.76e-07	0.00042
62	I1PKAc ⇌ Ip35 + PKAc	0.0014	0.0	133	ACh + M1RGq ⇌ AChM1RGq	3.96e-06	0.0025
63	Ip35 + PP1 ⇌ Ip35PP1	1e-06	1.1e-06	134	AChM1RGq ⇌ GqaGTP + AChM1R	0.0005	0.0
64	Ip35 $𝐗_{16}$ + PP2BCaMCa4 ⇌ Ip35PP2B $𝐙_{16}$	9.625e-05	0.33	135	ACh ⇌	0.006	0
65	Ip35PP2B $𝐗_{17}$ ⇌ I1 + PP2B $𝐗_{17}$	0.055	0.0	136	Ca + PLA2 ⇌ CaPLA2	6e-07	0.003
66	PP1PP2BCaMCa4 ⇌ PP1 + PP2BCaMCa4	0.0015	0.0	137	CaPLA2 + Pip2 ⇌ CaPLA2Pip2	2.2e-05	0.444
67	GluR1 $𝐗_{18}$ + PKAc ⇌ GluR1 $𝐙_{18}$	4.02e-06	0.024	138	CaPLA2Pip2 ⇌ CaPLA2 + AA	0.111	0.0
68	GluR1 $𝐗_{19}$ ⇌ GluR1 $𝐘_{19}$ + PKAc	0.006	0	139	AA ⇌ Pip2	0.001	0.0
69	GluR1 $𝐗_{20}$ + CK $𝐘_{20}$ ⇌ GluR1 $𝐙_{20}$	2.224e-08	0.0016	140	PKCt + AA ⇌ PKCp	5e-09	1.76e-07
70	GluR1 $𝐗_{21}$ ⇌ GluR1 $𝐘_{21}$ + CK $𝐙_{21}$	0.0004	0

(B)
$𝐗_{1}$ ∈ {LR, pLR}				( $𝐗_{23}$ , $𝐘_{23}$ , $𝐙_{23}$ ) ∈ { (_CKpCam, _S831, CKpCaMCa4), (_PKCt,
$𝐗_{2}$ ∈ {LR, pLR, ppLR, pppLR, R, pR, ppR, pppR}				_S831, PKCt), (_PKCp, _S831, PKCp), (_S845_CKpCam, _S845_S831,
( $𝐗_{3}$ , $𝐘_{3}$ ) ∈ { (LRGibg, LR), (RGibg, R) }				CKpCaMCa4), (_S845_PKCt, _S845_S831, PKCt), (_S845_PKCp,
$𝐗_{4}$ ∈ {LR, R, pR}				_S845_S831, PKCp), (_memb_CKpCam, _memb_S831, CKpCaMCa4),
$𝐗_{5}$ ∈ {LR, pLR, ppLR, pR, ppR}				(_memb_PKCt, _memb_S831, PKCt), (_memb_PKCp, _memb_S831, PKCp),
( $𝐗_{6}$ , $𝐙_{6}$ ) ∈ { (GsaGTP, GsaGTPCaMCa4), (GsaGTPGiaGTP,				(_memb_S845_CKpCam, _memb_S845_S831, CKpCaMCa4),
GsaGTPGiaGTPCaMCa4), ( ${}$ , CaMCa4) }				(_memb_S845_PKCt, _memb_S845_S831, PKCt), (_memb_S845_PKCp,
( $𝐗_{7}$ , $𝐙_{7}$ ) ∈ { (AC1GsaGTPCaMCa4, AC1GsaGTPCaMCa4ATP),				_memb_S845_S831, PKCp) }
(AC1GsaGTPGiaGTPCaMCa4, AC1GsGiCaMCa4ATP), (AC1GiaGTPCaMCa4,				( $𝐗_{24}$ , $𝐙_{24}$ ) ∈ { (_S831, _S831_PKAc), (_memb_S831,
AC1GiaGTPCaMCa4ATP), (AC1CaMCa4, AC1CaMCa4ATP), (AC8CaMCa4,				_memb_S831_PKAc) }
AC8CaMCa4ATP) }				( $𝐗_{25}$ , $𝐙_{25}$ ) ∈ { (_S845, _S845_PP1), (_memb_S845,
( $𝐗_{8}$ , $𝐘_{8}$ , $𝐙_{8}$ ) ∈ { (GiaGTP, AC1GsaGTP, GTPGiaGTP), (GiaGTP,				_memb_S845_PP1) }
AC1CaMCa4, GTPCaMCa4), (AC1GiaGTP, GsaGTP, GTPGiaGTP) }				( $𝐗_{26}$ , $𝐘_{26}$ ) ∈ { (_S845_PP1, ${}$ ), (_memb_S845_PP1,
( $𝐗_{9}$ , $𝐙_{9}$ ) ∈ { (AC1GsGiCaMCa4ATP, AC1GsaGTPGiaGTPCaMCa4),				_memb) }
(AC8CaMCa4ATP, AC8CaMCa4) }				( $𝐗_{27}$ , $𝐙_{27}$ ) ∈ { (_S845_S831, _S845_S831_PP1), (_S831,
( $𝐗_{10}$ , $𝐙_{10}$ ) ∈ { (CaMCa2, CaMCa3), (PP2BCaMCa2,				_S831_PP1), (_memb_S845_S831, _memb_S845_S831_PP1),
PP2BCaMCa3) }				(_memb_S831, _memb_S831_PP1) }
( $𝐗_{11}$ , $𝐙_{11}$ ) ∈ { (CaMCa3, CaMCa4), (PP2BCaMCa3,				( $𝐗_{28}$ , $𝐘_{28}$ ) ∈ { (_S845_S831_PP1, _S845), (_S845_S831_PP1,
PP2BCaMCa4) }				_S831), (_S831_PP1, ${}$ ), (_memb_S845_S831_PP1, _memb_S845),
( $𝐗_{12}$ , $𝐙_{12}$ ) ∈ { (2, CaMCa2), (4, CaMCa4) }				(_memb_S845_S831_PP1, _memb_S831), (_memb_S831_PP1,
$𝐗_{13}$ ∈ {pCaMCa4, CaMCa4}				_memb) }
( $𝐗_{14}$ , $𝐙_{14}$ ) ∈ { ( ${}$ , PP1), (CaMCa4, CaMCa4PP1) }				( $𝐗_{29}$ , $𝐙_{29}$ ) ∈ { (_S845, _S845_PP2B), (_S845_S831,
( $𝐗_{15}$ , $𝐙_{15}$ ) ∈ { (PP1, ${}$ ), (CaMCa4PP1, CaMCa4) }				_S845_S831_PP2B), (_memb_S845, _memb_S845_PP2B),
( $𝐗_{16}$ , $𝐙_{16}$ ) ∈ { ( ${}$ , CaMCa4), (PP1, P2BCaMCa4) }				(_memb_S845_S831, _memb_S845_S831_PP2B) }
$𝐗_{17}$ ∈ {CaMCa4, P2BCaMCa4}				( $𝐗_{30}$ , $𝐘_{30}$ ) ∈ { (_S845_PP2B, ${}$ ), (_S845_S831_PP2B,
( $𝐗_{18}$ , $𝐙_{18}$ ) ∈ { ( ${}$ , _PKAc), (_memb, _memb_PKAc) }				_S831), (_memb_S845_PP2B, _memb), (_memb_S845_S831_PP2B,
( $𝐗_{19}$ , $𝐘_{19}$ ) ∈ { (_PKAc, _S845), (_S831_PKAc, _S845_S831),				_memb_S831) }
(_memb_PKAc, _memb_S845), (_memb_S831_PKAc,				$𝐗_{31}$ ∈ { ${}$ , _PKAc, _CKCam, _CKpCam, _CKp, _PKCt, _PKCp,
_memb_S845_S831) }				_S831, _S831_PKAc, _S831_PP1}
( $𝐗_{20}$ , $𝐘_{20}$ , $𝐙_{20}$ ) ∈ { ( ${}$ , CaMCa4, _CKCam), ( ${}$ , p,				$𝐗_{32}$ ∈ { ${}$ , _CKCam, _CKpCam, _CKp, _PKCt, _PKCp, _S831,
_CKp), (_S845, CaMCa4, _S845_CKCam), (_S845, p, _S845_CKp),				_PP1, _S831_PP1, _PP2B, _S831_PP2B}
(_memb, CaMCa4, _memb_CKCam), (_memb, p, _memb_CKp),				( $𝐗_{33}$ , $𝐘_{33}$ , $𝐙_{33}$ ) ∈ { (PKAc, PDE4, PDE4), (PDE4cAMP, PKAc,
(_memb_S845, CaMCa4, _memb_S845_CKCam), (_memb_S845, p,				_PDE4_cAMP) }
_memb_S845_CKp) }				( $𝐗_{34}$ , $𝐘_{34}$ ) ∈ { (PDE4, ${}$ ), (_PDE4_cAMP, cAMP) }
( $𝐗_{21}$ , $𝐘_{21}$ , $𝐙_{21}$ ) ∈ { (_CKCam, _S831, CaMCa4), (_CKp, _S831,				( $𝐗_{35}$ , $𝐘_{35}$ ) ∈ { (GqaGTP, ${}$ ), (CaGqaGTP, Ca) }
p), (_S845_CKCam, _S845_S831, CaMCa4), (_S845_CKp, _S845_S831,				( $𝐗_{36}$ , $𝐘_{36}$ , $𝐙_{36}$ ) ∈ { ( ${}$ , t, _PKCt), ( ${}$ , p, _PKCp),
p), (_memb_CKCam, _memb_S831, CaMCa4), (_memb_CKp, _memb_S831,				(_memb, t, _memb_PKCt), (_memb, p, _memb_PKCp) }
p), (_memb_S845_CKCam, _memb_S845_S831, CaMCa4),				( $𝐗_{37}$ , $𝐘_{37}$ , $𝐙_{37}$ ) ∈ { (_PKCt, _S880, t), (_PKCp, _S880, p),
(_memb_S845_CKp, _memb_S845_S831, p) }				(_memb_PKCt, _memb_S880, t), (_memb_PKCp, _memb_S880, p) }
( $𝐗_{22}$ , $𝐘_{22}$ , $𝐙_{22}$ ) ∈ { ( ${}$ , CKpCaMCa4, _CKpCam), ( ${}$ ,				( $𝐗_{38}$ , $𝐙_{38}$ ) ∈ { (_S880, _S880_PP2A), (_memb_S880,
PKCt, _PKCt), ( ${}$ , PKCp, _PKCp), (_S845, CKpCaMCa4,				_memb_S880_PP2A) }
_S845_CKpCam), (_S845, PKCt, _S845_PKCt), (_S845, PKCp,				( $𝐗_{39}$ , $𝐘_{39}$ ) ∈ { (_S880_PP2A, ${}$ ), (_memb_S880_PP2A,
_S845_PKCp), (_memb, CKpCaMCa4, _memb_CKpCam), (_memb, PKCt,				_memb) }
_memb_PKCt), (_memb, PKCp, _memb_PKCp), (_memb_S845, CKpCaMCa4,				$𝐗_{40}$ ∈ { ${}$ , _PKCt, _PKCp}
_memb_S845_CKpCam), (_memb_S845, PKCt, _memb_S845_PKCt),				$𝐗_{41}$ ∈ { ${}$ , _PP2A}
(_memb_S845, PKCp, _memb_S845_PKCp) }

Table 4

List of initial concentrations of molecular species.

All non-mentioned species have an initial concentration of 0 nM.

Species		Conc. (nM)	Species		Conc. (nM)	Species		Conc. (nM)
CaOut	extracell. Ca²⁺	1900000	AMP	adenosine monophosphate	980	Pip2	phosphatidylinositol 4,5-bisphosphate	24000
Leak	leak channels	2000	Ng	neurogranin	20000	PIkinase	phosphatidylinositol kinase	290
Calbin	calbindin	150000	CaM	calmodulin	60000	Ip3degPIk	Ip3-bound PI kinase	400
CalbinC	Ca²⁺-bound calbindin	15000	PP2B	protein phosphatase 2B	2300	PKC	protein kinase C	15000
LOut	extracell. β-adr. ligand	2500000	CK	CaMKII	23000	DAG	diacylglycerol	90
Epac1	Epac1	500	PKA	protein kinase A	6400	DAGK	DAG kinase	300
PMCA	Ca²⁺ pump	22000	I1	inhibitor-1	2200	DGL	DAG lipase	1600
NCX	Ca²⁺ exchanger	540000	PP1	protein phosphatase 1	1600	CaDGL	Ca²⁺-bound DAG lipase	250
L	β-adrenergic ligand	10	GluR1	AMPAR subunit type 1	180	DAGCaDGL	Ca²⁺-and DAG-bound DAG lipase	90
R	β-adrenergic receptor	1600	GluR1_memb	membrane-inserted GluR1	90	Ip3degrad	degraded Ip3	600
Gs	S-type G-protein	13000	PDE4	phosphodiesterase type 4	670	GluR2	AMPAR subunit type 2	14
Gi	I-type G-protein	2600	fixedbuffer	immobile buffer	500000	GluR2_memb	membrane-inserted GluR2	256
AC1	adenylyl cyclase type 1	430.0	mGluR	metab. glutamate receptor	800	PP2A	protein phosphatase 2A	500
ATP	adenosine triphosphate	2000000	GluOut	extracell. glutamate	1000000	M1R	acetylcholine receptor M1	450
AC8	adenylyl cyclase type 8	370	Gqabg	Q-type G-protein	1400	PLA2	phospholipase A2	1000
PDE1	phosphodiesterase type 1	12000	PLC	phospholipase C	250

Share this article

Cite this article

Signalling pathways included in the model.

Ca2+ activates CaMKII, PKA, and PKC pathways.

4xHFS activates CaMKII, PKA, and PKC pathways and leads to LTP (A–R), while LFS activates the PKC pathway and leads to LTD (S–U).

Both GluR1 and GluR2 are needed for bidirectional plasticity.

An alternative dimers-of-like-dimers rule of tetramer formation reproduces the HFS-induced LTP, LFS-induced LTD, and STDP predictions obtained with the default tetramer formation rule.

The biochemical signalling network model, given the NMDAR-conducted Ca2+ inputs from the multicompartmental neuron model of layer 2/3 pyramidal cell under 1.3 mM extracellular [Mg2+], predicts LTP for 6xHFSt and LTD for LFS-1Hz.

The biochemical signalling network model robustly predicts LTP for HFS and LTD for LTP with altered durations of neuromodulatory inputs.

4xHFS-induced LTP is dependent on β-adrenergic ligands and LFS-induced LTD is dependent on activation of mGluRs or cholinergic receptors.

Layer 2/3 pyramidal cell plasticity in response to STDP protocol depends on neuromodulatory state and pairing interval.

Ca2+ fluxes predicted by the multicompartmental layer 2/3 pyramidal cell model depend on the inter-stimulus interval (ISI).

The STDP curve of layer 2/3 pyramidal cells is affected by the number of post-synaptic stimulus pulses associated with the pre-synaptic input.

The post-STDP synaptic conductance is weakly correlated with the peak of the Ca2+ input but strongly correlated with the mean Ca2+ input during the inter-stimulus interval.

The fraction of GluR1s, number of Ca2+ extrusion proteins, and the concentrations of PKA and PKC-pathway proteins in the post-synaptic spine determine the type of LTP/LTD in the post-synaptic spine.

The PKC-pathway parameter distributions differ between clusters separated by their response to low (50 particles/ms) Ca2+ input.

The model predictions of LTP and LTD are robust to small changes in model parameters.

The model can be fit to LTP/LTD data from different cortical areas.

Parameters for data set EC-1.

Parameters for data set EC-2.

Parameters for data set PFC-1.

Parameters for data set PFC-2.

Parameters for data set BC.

Parameters for data set ACC.

Parameters for data set PFC-3.

Parameters for data set VC-1.

Parameters for data set VC-2.

Parameters for data set AC-1.

Parameters for data set AC-2.

The models describing plasticity in different cortical areas predict diverse responses to modified stimulation protocol and stimulation under chemical blockers.

Calibration of the model.

1 hr of simulation without inputs is sufficient to obtain a steady state.

The model STDP model is robust to changes in AMPA conductance but sensitive to changes in NMDA condutance in the multicompartmental layer 2/3 pyramidal cell model.

Pathways contributing to cortical synaptic plasticity.

List of LTP/LTD experiments in the cortex.

List of model reactions.

List of initial concentrations of molecular species.

Ca²⁺ activates CaMKII, PKA, and PKC pathways.

The biochemical signalling network model, given the NMDAR-conducted Ca²⁺ inputs from the multicompartmental neuron model of layer 2/3 pyramidal cell under 1.3 mM extracellular [Mg²⁺], predicts LTP for 6xHFSt and LTD for LFS-1Hz.

Ca²⁺ fluxes predicted by the multicompartmental layer 2/3 pyramidal cell model depend on the inter-stimulus interval (ISI).

The post-STDP synaptic conductance is weakly correlated with the peak of the Ca²⁺ input but strongly correlated with the mean Ca²⁺ input during the inter-stimulus interval.

The fraction of GluR1s, number of Ca²⁺ extrusion proteins, and the concentrations of PKA and PKC-pathway proteins in the post-synaptic spine determine the type of LTP/LTD in the post-synaptic spine.

The PKC-pathway parameter distributions differ between clusters separated by their response to low (50 particles/ms) Ca²⁺ input.