A unified computational model for cortical post-synaptic plasticity

  1. Tuomo Mäki-Marttunen  Is a corresponding author
  2. Nicolangelo Iannella
  3. Andrew G Edwards
  4. Gaute T Einevoll
  5. Kim T Blackwell
  1. Simula Research Laboratory, Norway
  2. Department of Biosciences, University of Oslo, Norway
  3. Faculty of Science and Technology, Norwegian University of Life Sciences, Norway
  4. Department of Physics, University of Oslo, Norway
  5. The Krasnow Institute for Advanced Study, George Mason University, United States
11 figures and 4 tables

Figures

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 …

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
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
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
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
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
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 …

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
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
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
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
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
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
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…

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
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
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
Parameters for data set EC-2.
Figure 9—figure supplement 3
Parameters for data set PFC-1.
Figure 9—figure supplement 4
Parameters for data set PFC-2.
Figure 9—figure supplement 5
Parameters for data set BC.
Figure 9—figure supplement 6
Parameters for data set ACC.
Figure 9—figure supplement 7
Parameters for data set PFC-3.
Figure 9—figure supplement 8
Parameters for data set VC-1.
Figure 9—figure supplement 9
Parameters for data set VC-2.
Figure 9—figure supplement 10
Parameters for data set AC-1.
Figure 9—figure supplement 11
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.

(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
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
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
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 componentsType of neuronsType of regulationPre-/post-synapticReferences
CaMKIICingulate cortexEsophageal acid-induced sensitisationpost-syn.Banerjee et al., 2013
CaMKIIPrefrontal cortex, pyramidal neurons5-HT1-induced modulation of AMPA currentspost-syn.Cai et al., 2002
β-adr. receptors, PKAVisual cortex, layer 4 pyramidal cellsPotentiation of AMPA currentspost-syn.Seol et al., 2007
M1 receptors, PKCVisual cortex, layer 4 pyramidal cellsDepression of AMPA currentspost-syn.Seol et al., 2007
D1–PKAPrefrontal cortex, pyramidal neuronsPotentiation of AMPA currentspost-syn.Sun et al., 2005
β-adr. receptorsFrontal cortexPotentiation of field EPSPsn/aSáez-Briones et al., 2015
PKCCultured cortical neuronsInternalisation of AMPARspost-syn.Chung et al., 2000
ERKVisual cortexPotentiation of field EPSPsn/aDi Cristo et al., 2001
(B)
Molecular pathwayCell type and references
Ca2+ → CaM → CaMKIIHippocampal 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 S831pHippocampal CA1 neuron Jȩdrzejewska-Szmek et al., 2017
β-adrenergic receptors → cAMPHippocampal CA1 neuron Jȩdrzejewska-Szmek et al., 2017
cAMP → PKAHippocampal CA1 neuron Bhalla and Iyengar, 1999; Jȩdrzejewska-Szmek et al., 2017, cerebellar Purkinje
cells Gallimore et al., 2018
PKA → GluR1 S845pHippocampal CA1 neuron Jȩdrzejewska-Szmek et al., 2017
M1 receptors → PLCCerebellar Purkinje cells Gallimore et al., 2018
PLC → PKCHippocampal 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 S880pCerebellar 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 setReferencePathwayPre/postFreq.NpulsesExperiment10 min15 min20 minSD
EC-1Ma et al., 2008horizontalmostly100100control1.31.41.30.1
postCaMKII blocked1.051.020.950.07
without post-syn. Ca2+1.051.051.10.09
EC-2Ma et al., 2008ascendingmostly100100control1.61.61.60.11
postPKA blocked1.41.41.40.13
without post-syn. Ca2+1.31.41.40.13
PFC-1Sáez-Briones et al., 2015CC→PFCn/a312156control2.01.981.90.08
without β-adrenergic ligand1.341.41.360.09
PFC-2Flores et al., 2011CC→PFCn/a312156control1.71.61.640.12
without β−1-receptor agonist1.431.451.430.1
BCHardingham et al., 2003L4→L2/3n/a510 × 4control1.351.41.30.09
CaMKII mutant1.251.21.10.09
ACCSong et al., 2017L5/6 → L2/3post510 × 4control1.551.41.40.05
without s8451.11.051.050.07
without s8311.351.41.30.1
PFC-3Zhou et al., 2013L2/3 → L2/3mostly0.150control1.31.41.40.14
postwithout β−1-receptor agonist1.11.21.20.13
VC-1Kirkwood et al., 1997L4 → L3n/a510 × 4(CTR, HFS)1.31.261.260.07
(adult)(without CaMKII, HFS)1.021.021.020.02
5900*(CTR, LFS)n/a0.950.950.05
(without CaMKII, LFS)n/a0.880.930.03
VC-2Kirkwood et al., 1997L4 → L3n/a510 × 4(CTR, HFS)1.21.181.180.05
(4–5 w)(without CaMKII, HFS)1.071.091.080.03
5900*(CTR, LFS)n/a0.790.820.03
(without CaMKII, LFS)n/a0.820.890.03
AuC-1Kotak et al., 2007L6 → L5n/a125 × 5LTP-expressing cells1.981.581.930.19
AuC-2Kotak et al., 2007L6 → L5n/a125 × 5LTD-expressing cells0.770.680.670.09
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.
IDReactionRateRateIDReactionRateRate
1Ca + PMCA ⇌ PMCACa5e-050.00771GluR1𝐗22 + 𝐘22 ⇌ GluR1𝐙222.78e-080.002
2PMCACa ⇌ PMCA + CaOut0.00350.072GluR1𝐗23 ⇌ GluR1 𝐘23𝐙230.00050
3Ca + NCX ⇌ NCXCa1.68e-050.011273GluR1𝐗24 + PKAc ⇌ GluR1𝐙244e-060.024
4NCXCa ⇌ NCX + CaOut0.00560.074GluR1𝐗25 + PP1 ⇌ GluR1𝐙258.7e-070.00068
5CaOut + Leak ⇌ CaOutLeak1.5e-060.001175GluR1𝐗26 ⇌ GluR1 𝐘26 + PP10.000170
6CaOutLeak ⇌ Ca + Leak0.00110.076GluR1𝐗27 + PP1 ⇌ GluR1𝐙278.75e-070.0014
7Ca + Calbin ⇌ CalbinC2.8e-050.019677GluR1𝐗28 ⇌ GluR1 𝐘28 + PP10.000350
8L ⇌ LOut0.00052e-0978GluR1𝐗29 + PP2BCaMCa4 ⇌ GluR1𝐙292.01e-060.008
9L + R ⇌ LR5.555e-060.00579GluR1𝐗30 ⇌ GluR1𝐘30 + PP2BCaMCa40.0020
10LR + Gs ⇌ LRGs6e-071e-0680GluR1𝐗31 ⇌ GluR1_memb𝐗312e-078e-07
11Gs + R ⇌ GsR4e-083e-0781GluR1_S845𝐗32
12GsR + L ⇌ LRGs2.5e-060.0005⇌ GluR1_memb_S845𝐗323.28e-058e-06
13LRGs ⇌ LRGsbg + GsaGTP0.020.082PDE1 + CaMCa4 ⇌ PDE1CaMCa40.00010.001
14LRGsbg ⇌ LR + Gsbg0.080.083PDE1CaMCa4 + cAMP ⇌ PDE1CaMCa4cAMP4.6e-060.044
15𝐗1 + PKAc ⇌ PKAc𝐗18e-070.0044884PDE1CaMCa4cAMP ⇌ PDE1CaMCa4 + AMP0.0110.0
16PKAc𝐗2 ⇌ p𝐗2 + PKAc0.0010.085AMP ⇌ ATP0.0010.0
17ppLR + PKAc ⇌ PKAcppLR1.712e-050.0044886PDE4 + cAMP ⇌ PDE4cAMP2.166e-050.0034656
18pppLR + PKAc ⇌ PKAcpppLR0.0017120.0044887PDE4cAMP ⇌ PDE4 + AMP0.0172330.0
19ppppLR + Gi ⇌ ppppLRGi0.000150.0002588𝐗33 + 𝐘33 ⇌ PKAc 𝐙332.5e-078e-05
20ppppLRGi ⇌ ppppLRGibg + GiaGTP0.0001250.089PKAc𝐗34 ⇌ pPDE4𝐘34 + PKAc2e-050.0
21pppp𝐗3 ⇌ pppp𝐘3 + Gibg0.0010.090pPDE4 ⇌ PDE42.5e-060.0
22𝐗4𝐗42.5e-060.091pPDE4 + cAMP ⇌ pPDE4cAMP0.0004331750.069308
23pp𝐗5 ⇌ p𝐗52.5e-060.092pPDE4cAMP ⇌ pPDE4 + AMP0.34466740.0
24R + PKAc ⇌ PKAcR4e-080.0044893PKAcAMP4 ⇌ PKAr + 2*PKAc0.000242.55e-05
25pR + PKAc ⇌ PKAcpR4e-070.0044894Ca + fixedbuffer ⇌ fixedbufferCa0.000420.0
26ppR + PKAc ⇌ PKAcppR4e-060.0044895Glu ⇌ GluOut0.00052e-10
27pppR + PKAc ⇌ PKAcpppR0.00040.0044896Ca + PLC ⇌ PLCCa4e-070.001
28ppppR + Gi ⇌ ppppRGi7.5e-050.00012597GqaGTP + PLC ⇌ PLCGqaGTP7e-070.0007
29ppppRGi ⇌ ppppRGibg + GiaGTP6.25e-050.098Ca + PLCGqaGTP ⇌ PLCCaGqaGTP8e-050.04
30GsaGTP ⇌ GsaGDP0.010.099GqaGTP + PLCCa ⇌ PLCCaGqaGTP0.00010.01
31GsaGDP + Gsbg ⇌ Gs0.10.0100PLCCa + Pip2 ⇌ PLCCaPip23e-080.01
32GiaGTP ⇌ GiaGDP0.0001250.0101PLCCaPip2 ⇌ PLCCaDAG + Ip30.00030.0
33GiaGDP + Gibg ⇌ Gi0.001250.0102PLCCaDAG ⇌ PLCCa + DAG0.20.0
34GsaGTP + AC1 ⇌ AC1GsaGTP3.85e-050.01103PLCCaGqaGTP + Pip2 ⇌ PLCCaGqaGTPPip21.5e-050.075
35AC1 𝐗6 + CaMCa4 ⇌ AC1 𝐙66e-060.0009104PLCCaGqaGTPPip2 ⇌ PLCCaGqaGTPDAG + Ip30.250.0
36𝐗7 + ATP ⇌ 𝐙71e-052.273105PLCCaGqaGTPDAG ⇌ PLCCaGqaGTP + DAG1.00.0
37AC1GsaGTPCaMCa4ATP106Ip3degrad + PIkinase ⇌ Ip3degPIk2e-060.001
⇌ cAMP + AC1GsaGTPCaMCa40.028420.0107Ip3degPIk ⇌ PIkinase + Pip20.0010.0
38𝐗8 + 𝐘8 ⇌ AC1Gsa𝐙86.25e-050.01108PLC𝐗35 ⇌ PLC𝐘35 + GqaGDP0.0120.0
39𝐗9 ⇌ cAMP + 𝐙90.0028420.0109GqaGTP ⇌ GqaGDP0.0010.0
40AC1GiaGTPCaMCa4ATP110GqaGDP ⇌ Gqabg0.010.0
⇌ cAMP + AC1GiaGTPCaMCa40.00056840.0111Ca + DGL ⇌ CaDGL0.0001250.05
41AC1CaMCa4ATP ⇌ cAMP + AC1CaMCa40.0056840.0112DAG + CaDGL ⇌ DAGCaDGL5e-070.001
42AC8 + CaMCa4 ⇌ AC8CaMCa41.25e-060.001113DAGCaDGL ⇌ CaDGL + 2AG0.000250.0
43CaM + 2*Ca ⇌ CaMCa21.7e-080.035114Ip3 ⇌ Ip3degrad0.010.0
44𝐗10 + Ca ⇌ 𝐙101.4e-050.2281152AG ⇌ 2AGdegrad0.0050.0
45𝐗11 + Ca ⇌ 𝐙112.6e-050.064116DAG + DAGK ⇌ DAGKdag7e-080.0008
46CaM + Ng ⇌ NgCaM2.8e-050.036117DAGKdag ⇌ DAGK + PA0.00020.0
47CaM + PP2B ⇌ PP2BCaM4.6e-061.2e-06118Ca + PKC ⇌ PKCCa1.33e-050.05
48CaMCa𝐗12 + PP2B ⇌ PP2B𝐙124.6e-051.2e-06119PKCCa + DAG ⇌ PKCt1.5e-080.00015
49PP2BCaM + 2*Ca ⇌ PP2BCaMCa21.7e-070.35120Glu + MGluR ⇌ MGluR_Glu1.68e-080.0001
50CaMCa4 + CK ⇌ CKCaMCa41e-050.003121MGluR_Glu ⇌ MGluR_Glu_desens6.25e-051e-06
512*CKCaMCa4 ⇌ Complex1e-070.01122Gqabg + MGluR_Glu ⇌ MGluR_Gqabg_Glu9e-060.00136
52CKpCaMCa4 + CKCaMCa4 ⇌ pComplex1e-070.01123MGluR_Gqabg_Glu ⇌ GqaGTP + MGluR_Glu0.00150.0
53CK𝐗13 + Complex ⇌ CK𝐗13 + pComplex1e-070.0124GluR2𝐗36 + PKC𝐘36 ⇌ GluR2𝐙364e-070.0008
542*Complex ⇌ Complex + pComplex1e-050.0125GluR2𝐗37 ⇌ GluR2𝐘37 + PKC𝐙370.00470
55Complex + pComplex ⇌ 2*pComplex3e-050.0126GluR2𝐗38 + PP2A ⇌ GluR2𝐙385e-070.005
56CKpCaMCa4 ⇌ CaMCa4 + CKp8e-071e-05127GluR2𝐗39 ⇌ GluR2𝐘39 + PP2A0.000150
57CKp𝐗14 + PP1 ⇌ CKp𝐙144e-090.00034128GluR2𝐗40 ⇌ GluR2_memb𝐗400.000245450.0003
58CKp𝐗15 ⇌ PP1 + CK𝐙158.6e-050.0129GluR2_S880𝐗41 ⇌ GluR2_memb_S880𝐗410.00550.07
59PKA + 4*cAMP ⇌ PKAcAMP41.6e-156e-05130ACh + M1R ⇌ AChM1R9.5e-080.0025
60Epac1 + cAMP ⇌ Epac1cAMP3.1e-086.51e-05131Gqabg + AChM1R ⇌ AChM1RGq2.4e-050.00042
61I1 + PKAc ⇌ I1PKAc1.4e-060.0056132Gqabg + M1R ⇌ M1RGq5.76e-070.00042
62I1PKAc ⇌ Ip35 + PKAc0.00140.0133ACh + M1RGq ⇌ AChM1RGq3.96e-060.0025
63Ip35 + PP1 ⇌ Ip35PP11e-061.1e-06134AChM1RGq ⇌ GqaGTP + AChM1R0.00050.0
64Ip35𝐗16 + PP2BCaMCa4 ⇌ Ip35PP2B𝐙169.625e-050.33135ACh ⇌0.0060
65Ip35PP2B𝐗17 ⇌ I1 + PP2B𝐗170.0550.0136Ca + PLA2 ⇌ CaPLA26e-070.003
66PP1PP2BCaMCa4 ⇌ PP1 + PP2BCaMCa40.00150.0137CaPLA2 + Pip2 ⇌ CaPLA2Pip22.2e-050.444
67GluR1𝐗18 + PKAc ⇌ GluR1𝐙184.02e-060.024138CaPLA2Pip2 ⇌ CaPLA2 + AA0.1110.0
68GluR1𝐗19 ⇌ GluR1𝐘19 + PKAc0.0060139AA ⇌ Pip20.0010.0
69GluR1𝐗20 + CK𝐘20 ⇌ GluR1𝐙202.224e-080.0016140PKCt + AA ⇌ PKCp5e-091.76e-07
70GluR1𝐗21 ⇌ GluR1𝐘21 + CK𝐙210.00040
(B)
𝐗1 ∈ {LR, pLR}(𝐗23, 𝐘23, 𝐙23) ∈ { (_CKpCam, _S831, CKpCaMCa4), (_PKCt,
𝐗2 ∈ {LR, pLR, ppLR, pppLR, R, pR, ppR, pppR}_S831, PKCt), (_PKCp, _S831, PKCp), (_S845_CKpCam, _S845_S831,
(𝐗3, 𝐘3) ∈ { (LRGibg, LR), (RGibg, R) }CKpCaMCa4), (_S845_PKCt, _S845_S831, PKCt), (_S845_PKCp,
𝐗4 ∈ {LR, R, pR}_S845_S831, PKCp), (_memb_CKpCam, _memb_S831, CKpCaMCa4),
𝐗5 ∈ {LR, pLR, ppLR, pR, ppR}(_memb_PKCt, _memb_S831, PKCt), (_memb_PKCp, _memb_S831, PKCp),
(𝐗6, 𝐙6) ∈ { (GsaGTP, GsaGTPCaMCa4), (GsaGTPGiaGTP,(_memb_S845_CKpCam, _memb_S845_S831, CKpCaMCa4),
GsaGTPGiaGTPCaMCa4), ({}, CaMCa4) }(_memb_S845_PKCt, _memb_S845_S831, PKCt), (_memb_S845_PKCp,
(𝐗7, 𝐙7) ∈ { (AC1GsaGTPCaMCa4, AC1GsaGTPCaMCa4ATP),_memb_S845_S831, PKCp) }
(AC1GsaGTPGiaGTPCaMCa4, AC1GsGiCaMCa4ATP), (AC1GiaGTPCaMCa4,(𝐗24, 𝐙24) ∈ { (_S831, _S831_PKAc), (_memb_S831,
AC1GiaGTPCaMCa4ATP), (AC1CaMCa4, AC1CaMCa4ATP), (AC8CaMCa4,_memb_S831_PKAc) }
AC8CaMCa4ATP) }(𝐗25, 𝐙25) ∈ { (_S845, _S845_PP1), (_memb_S845,
(𝐗8, 𝐘8, 𝐙8) ∈ { (GiaGTP, AC1GsaGTP, GTPGiaGTP), (GiaGTP,_memb_S845_PP1) }
AC1CaMCa4, GTPCaMCa4), (AC1GiaGTP, GsaGTP, GTPGiaGTP) }(𝐗26, 𝐘26) ∈ { (_S845_PP1, {}), (_memb_S845_PP1,
(𝐗9, 𝐙9) ∈ { (AC1GsGiCaMCa4ATP, AC1GsaGTPGiaGTPCaMCa4),_memb) }
(AC8CaMCa4ATP, AC8CaMCa4) }(𝐗27, 𝐙27) ∈ { (_S845_S831, _S845_S831_PP1), (_S831,
(𝐗10, 𝐙10) ∈ { (CaMCa2, CaMCa3), (PP2BCaMCa2,_S831_PP1), (_memb_S845_S831, _memb_S845_S831_PP1),
PP2BCaMCa3) }(_memb_S831, _memb_S831_PP1) }
(𝐗11, 𝐙11) ∈ { (CaMCa3, CaMCa4), (PP2BCaMCa3,(𝐗28, 𝐘28) ∈ { (_S845_S831_PP1, _S845), (_S845_S831_PP1,
PP2BCaMCa4) }_S831), (_S831_PP1, {}), (_memb_S845_S831_PP1, _memb_S845),
(𝐗12, 𝐙12) ∈ { (2, CaMCa2), (4, CaMCa4) }(_memb_S845_S831_PP1, _memb_S831), (_memb_S831_PP1,
𝐗13 ∈ {pCaMCa4, CaMCa4}_memb) }
(𝐗14, 𝐙14) ∈ { ({}, PP1), (CaMCa4, CaMCa4PP1) }(𝐗29, 𝐙29) ∈ { (_S845, _S845_PP2B), (_S845_S831,
(𝐗15, 𝐙15) ∈ { (PP1, {}), (CaMCa4PP1, CaMCa4) }_S845_S831_PP2B), (_memb_S845, _memb_S845_PP2B),
(𝐗16, 𝐙16) ∈ { ({}, CaMCa4), (PP1, P2BCaMCa4) }(_memb_S845_S831, _memb_S845_S831_PP2B) }
𝐗17 ∈ {CaMCa4, P2BCaMCa4}(𝐗30, 𝐘30) ∈ { (_S845_PP2B, {}), (_S845_S831_PP2B,
(𝐗18, 𝐙18) ∈ { ({}, _PKAc), (_memb, _memb_PKAc) }_S831), (_memb_S845_PP2B, _memb), (_memb_S845_S831_PP2B,
(𝐗19, 𝐘19) ∈ { (_PKAc, _S845), (_S831_PKAc, _S845_S831),_memb_S831) }
(_memb_PKAc, _memb_S845), (_memb_S831_PKAc,𝐗31 ∈ {{}, _PKAc, _CKCam, _CKpCam, _CKp, _PKCt, _PKCp,
_memb_S845_S831) }_S831, _S831_PKAc, _S831_PP1}
(𝐗20, 𝐘20, 𝐙20) ∈ { ({}, CaMCa4, _CKCam), ({}, p,𝐗32 ∈ {{}, _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),(𝐗33, 𝐘33, 𝐙33) ∈ { (PKAc, PDE4, PDE4), (PDE4cAMP, PKAc,
(_memb_S845, CaMCa4, _memb_S845_CKCam), (_memb_S845, p,_PDE4_cAMP) }
_memb_S845_CKp) }(𝐗34, 𝐘34) ∈ { (PDE4, {}), (_PDE4_cAMP, cAMP) }
(𝐗21, 𝐘21, 𝐙21) ∈ { (_CKCam, _S831, CaMCa4), (_CKp, _S831,(𝐗35, 𝐘35) ∈ { (GqaGTP, {}), (CaGqaGTP, Ca) }
p), (_S845_CKCam, _S845_S831, CaMCa4), (_S845_CKp, _S845_S831,(𝐗36, 𝐘36, 𝐙36) ∈ { ({}, 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),(𝐗37, 𝐘37, 𝐙37) ∈ { (_PKCt, _S880, t), (_PKCp, _S880, p),
(_memb_S845_CKp, _memb_S845_S831, p) }(_memb_PKCt, _memb_S880, t), (_memb_PKCp, _memb_S880, p) }
(𝐗22, 𝐘22, 𝐙22) ∈ { ({}, CKpCaMCa4, _CKpCam), ({},(𝐗38, 𝐙38) ∈ { (_S880, _S880_PP2A), (_memb_S880,
PKCt, _PKCt), ({}, PKCp, _PKCp), (_S845, CKpCaMCa4,_memb_S880_PP2A) }
_S845_CKpCam), (_S845, PKCt, _S845_PKCt), (_S845, PKCp,(𝐗39, 𝐘39) ∈ { (_S880_PP2A, {}), (_memb_S880_PP2A,
_S845_PKCp), (_memb, CKpCaMCa4, _memb_CKpCam), (_memb, PKCt,_memb) }
_memb_PKCt), (_memb, PKCp, _memb_PKCp), (_memb_S845, CKpCaMCa4,𝐗40 ∈ {{}, _PKCt, _PKCp}
_memb_S845_CKpCam), (_memb_S845, PKCt, _memb_S845_PKCt),𝐗41 ∈ {{}, _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.

SpeciesConc. (nM)SpeciesConc. (nM)SpeciesConc. (nM)
CaOutextracell. Ca2+1900000AMPadenosine monophosphate980Pip2phosphatidylinositol 4,5-bisphosphate24000
Leakleak channels2000Ngneurogranin20000PIkinasephosphatidylinositol kinase290
Calbincalbindin150000CaMcalmodulin60000Ip3degPIkIp3-bound PI kinase400
CalbinCCa2+-bound calbindin15000PP2Bprotein phosphatase 2B2300PKCprotein kinase C15000
LOutextracell. β-adr. ligand2500000CKCaMKII23000DAGdiacylglycerol90
Epac1Epac1500PKAprotein kinase A6400DAGKDAG kinase300
PMCACa2+ pump22000I1inhibitor-12200DGLDAG lipase1600
NCXCa2+ exchanger540000PP1protein phosphatase 11600CaDGLCa2+-bound DAG lipase250
Lβ-adrenergic ligand10GluR1AMPAR subunit type 1180DAGCaDGLCa2+-and DAG-bound DAG lipase90
Rβ-adrenergic receptor1600GluR1_membmembrane-inserted GluR190Ip3degraddegraded Ip3600
GsS-type G-protein13000PDE4phosphodiesterase type 4670GluR2AMPAR subunit type 214
GiI-type G-protein2600fixedbufferimmobile buffer500000GluR2_membmembrane-inserted GluR2256
AC1adenylyl cyclase type 1430.0mGluRmetab. glutamate receptor800PP2Aprotein phosphatase 2A500
ATPadenosine triphosphate2000000GluOutextracell. glutamate1000000M1Racetylcholine receptor M1450
AC8adenylyl cyclase type 8370GqabgQ-type G-protein1400PLA2phospholipase A21000
PDE1phosphodiesterase type 112000PLCphospholipase C250

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