Table 6.
Characteristics of models for calcium mechanisms or simplified intracellular processes.
| Type | Model | Inputs | Compartments | VGICs | LGICs | Molecules and mechanisms |
|---|---|---|---|---|---|---|
| LTP | Canepari and Vogt (2008) | ICa | 1 dendritic | No | No | CD28k, FF, and PV buffers, PMCA pump |
| LTP | Cornelisse et al. (2007) | JVGCC | Several dendritic and spine compartments | No | No | CaM, CD28k, OGB-1, and PV buffers, 1-D diffusion of Ca2+ and some of the buffers, PMCA pump |
| LTP, Elect. | De Schutter and Bower (1993) | ΔIm or ΔVm | Neuron with 1192 compartments | No | NMDAR, non-NMDAR | Buffer, 1-D Ca2+ diffusion, PMCA pump |
| LTP, Elect. | Franks et al. (2001) | ΔIm or ΔVm | 1 spine | CaL, CaT | NMDAR | CaM and other buffers, 3-D Ca2+ diffusion, PMCA pump |
| LTP, Elect. | Gamble and Koch (1987) | Isyn | 1 dendritic, 2 spine-head, 2 spine-neck | Ca2+, KM | No | CaM buffer, CaN, 1-D Ca2+ diffusion, PMCA pump |
| LTP, Elect. | Gold and Bear (1994) | ΔIm or ΔVm | 1 dendritic, 4 spine-head, 3 spine-neck | No | NMDAR | Buffer, 1-D Ca2+ diffusion, PMCA pump |
| LTP, Elect. | Holmes and Levy (1990) | ΔIm or ΔVm | Neuron with several 4-compartment dendrites, 4304 spines with 4 spine-head and 3 spine-neck, 1–115 synapses | No | NMDAR, non-NMDAR | Buffer, 1-D Ca2+ diffusion, PMCA pump |
| LTP, Elect. | Holmes (1990) | ΔIm or ΔVm | Neuron with several 4-compartment dendrites, 3 spines with 5 spine-head and 3 spine-neck, 96 synapses | No | NMDAR, non-NMDAR | Buffer, 1-D Ca2+ diffusion, PMCA pump |
| LTP, Elect. | Holmes and Levy (1997) | ΔIm or ΔVm | Neuron with several 12-compartment dendrites, several spines with 4 spine-head and 4 spine-neck, several synapses, 1 axonal, 1 somatic | Ca2+, KA, KCa, Nafast | GABAAR, NMDAR, non-NMDAR | CaM and other buffers, 1-D Ca2+ diffusion, PMCA pump |
| LTP, Elect. | Holmes (2000) | ΔIm or ΔVm | Neuron with several 12-compartment dendrites, several spines with 4 spine-head and 4 spine-neck, several synapses, 1 axonal, 1 somatic | Ca2+, KA, KCa, Nafast | NMDAR, non-NMDAR | CaM buffer, CaMKIIa, CaN, 1-D Ca2+ diffusion, PMCA pump |
| LTP, Elect. | Kitajima and Hara (1990) | ΔIm or ΔVm | 1 somatic, 1 spine-head, 1 spine-neck | No | NMDAR, non-NMDAR | CaM buffer, CaMKIIb |
| LTP, Elect. | Li and Holmes (2000) | ΔIm or ΔVm | Neuron with several 12-compartment dendrites, several spines with 4 spine-head and 4 spine-neck, several synapses, 1 axonal, 1 somatic | Ca2+, KA, KCa, Nafast | NMDAR, non-NMDAR | CaM buffer, CaMKIIa, CaN, 1-D–3-D Ca2+ and Glu diffusion, PMCA pump |
| LTP | Markram et al. (1998) | ICa | 1 or 25 dendritic | No | No | Buffer, 1-D Ca2+ diffusion, PMCA pump |
| LTP | Migliore and Ayala (1993) | Presyn. stimulus | 1 pre-, 1 postsynaptic | No | No | Simplified intracellular processesc |
| LTP, Elect. | Santucci and Raghavachari (2008) | ΔIm or ΔVm | 1 pre-, 1 postsynaptic | No | AMPAR, NMDAR | CaM buffer, CaMKIId, CaN, 3-D Glu diffusion, I1, PKA, PP1, 2 vesicles |
| LTP, Elect. | Schiegg et al. (1995) | ΔIm or ΔVm | Neuron with 8 dendritic, 1 somatic, 3 spine-head, 3 spine-neck | No | AMPAR, NMDAR | CaM buffer, CaN, CICR, 1-D Ca2+ diffusion, Na+/Ca2+ exchanger, PMCA pump, Ca2+ store |
| LTP, Elect. | Volfovsky et al. (1999) | JCa, ΔIm or ΔVm | Several multi-compartment spines and dendrites | Ca2+ | No | CaM and CG-1 buffers, CaN, CICR, 3-D Ca2+ and CG-1 diffusion, PMCA and SERCA pumps, Ca2+ store |
| LTP, Elect. | Zador et al. (1990) | ΔIm or ΔVm | Neuron with 28 compartments | No | NMDAR, non-NMDAR | CaM buffer, 1-D Ca2+ diffusion, 2 PMCA pumps |
| LTD | Hellgren Kotaleski and Blackwell (2002) | Ca2+ | 1 spine | No | IP3R | Buffer, 1-D Ca2+ diffusion, IP3, PMCA pump |
| LTD | Hernjak et al. (2005) | JCa | 1–32 1-compartment spines, 2 dendritic | No | IP3R | CD28k, CG-1, and PV buffers, 1-D and 2-D diffusion of all molecules, IP3, PMCA and SERCA pumps, Ca2+ store |
| LTD, Elect. | Holthoff et al. (2002) | ΔIm or ΔVm | 1 dendritic, 1 spine-head, 1 spine-neck | CaL | No | CG-1 and other buffers, 1-D Ca2+ diffusion, PMCA and SERCA pumps |
| LTD | Schmidt et al. (2007) | ICa | 1 or 7 1-compartment spines, 1 or 7 dendritic | No | No | CaM, CD28k, OGB-1, and PV buffers, 1-D–3-D diffusion of all molecules, PMCA pump |
| LTD | Schmidt and Eilers (2009) | ICa | 1 spine, 1 dendritic | No | No | CaM, CD28k, OGB-1, and PV buffers, 1-D diffusion of all molecules, PMCA pump |
| Dual, Elect., STDP | Abarbanel et al. (2002) | Synaptic stimulus | 1 pre-, 1 postsynaptic | Noe | Simplified processes | Simplified intracellular processesc |
| Dual, Elect., STDP | Abarbanel et al. (2003) | ΔIm or ΔVm | Neuron with 1 compartment | CaT, K+, Na+ | AMPAR, NMDAR | Phosphorylation, dephosphorylation |
| Dual, Elect., STDP | Abarbanel et al. (2005) | ΔIm or ΔVm | 2 neurons with 1 presynaptic and 1 2-compartment postsynaptic | Ca2+, K+, KA, KM, Na+ | AMPAR, NMDAR | Phosphorylation, dephosphorylation |
| Dual, Elect., STDP | Badoual et al. (2006) | ΔIm or ΔVm | Neuron with 1 spine, 1 axonal, 1 dendritic, 1 somatic | CaL, KCa, KDR, KM, Na+ | AMPAR, NMDAR | 1-D Ca2+ diffusion, PMCA pump, 3 enzymes |
| Dual, Elect., STDP | Cai et al. (2007) | Synaptic stimulus | 1 pre-, 1 postsynaptic | No | NMDAR | Simplified intracellular processes, vesicle |
| Dual, Elect. | Castellani et al. (2001) | ΔIm or ΔVm | 1 spine | No | AMPAR, NMDAR | 2 kinases, 2 phosphatases |
| Dual | Castellani et al. (2009) | CaMKII | 1 postsynaptic | No | AMPAR | CaMKII, PKA, PP1c |
| Dual, Elect. | Clopath et al. (2008) | ΔIm | Neuron with 1 compartment, 100 synapses | Nof | Simplified processes | Protein synthesisc |
| Dual, Elect. | Coomber (1997) | ΔIm or ΔVm | Neuron with 149 compartments | CaL, KA, KAHP, KCa, KDR, KM, Na+ | AMPAR, NMDAR | Buffer, 1-D Ca2+ diffusion, PMCA pump |
| Dual, STDP | Gerkin et al. (2007) | Synaptic stimulus | 1 pre-, 1 postsynaptic | No | No | Simplified intracellular processesc |
| Dual, Elect., STDP | Helias et al. (2008) | Synaptic stimulus | Neuron with 1 compartment, max 10000 synapses | Nog | NMDAR | CaMKII |
| Dual | Holcman et al. (2004) | JNMDAR | 4-compartment spine | No | No | CaM buffer, CaN, 2-D Ca2+ diffusion, PMCA pump |
| Dual | Ichikawa (2004) | JNMDAR | 3112-compartment spine | No | No | CaM buffer, CaMKII, CaN, 3-D diffusion of all molecules |
| Dual, Elect. | Ichikawa et al. (2007) | ΔIm or ΔVm | 1 spine, 1 dendritic | No | AMPAR, NMDAR | CaM and other buffers, CaMKII, CaN, 1-D Ca2+ diffusion, PMCA pump |
| Dual, Elect., STDP | Kalantzis and Shouval (2009) | ΔVm | 6 spine-head, 10 spine-neck | No | NMDAR | Buffer, 1-D Ca2+ diffusion, PMCA pump |
| Dual, Elect., STDP | Karmarkar and Buonomano (2002) | Synaptic stimulus | 2 1-compartment neurons | Ca2++h | AMPAR, NMDAR | Simplified intracellular processes |
| Dual, Elect., STDP | Karmarkar et al. (2002) | Synaptic stimulus | 2 1-compartment neurons | Noh | AMPAR, NMDAR | Simplified intracellular processes |
| Dual, Elect. | Keller et al. (2008) | ΔIm or ΔVm | 1 dendritic, 1 extracellular, 1 presynaptic, 1 spine-head | Ca2+ | AMPAR, NMDAR | CaM, CD28k, OGB-1, and other buffers, 3-D diffusion of all molecules, Na+/Ca2+ exchanger, PMCA pump |
| Dual, Elect. | Kitajima and Hara (1997) | Presyn. stimulus | Several spines with 1 spine-head and 1 spine-neck, 3 dendritic, 1 presynaptic | Ca2+ | AMPAR, GABAR, NMDAR | Kinase, phosphatase, PMCA pump, vesicle |
| Dual, Elect. | Kitajima and Hara (2000) | ΔIm or ΔVm | Neuron with 2 1-8-compartment dendrites, 1 spine, 1 axonal, 1 somatic | CaL, CaN, CaT, KA, KDR, Na+ | AMPAR, NMDAR | Phosphorylation, dephosphorylation |
| Dual, Elect., STDP | Kubota and Kitajima (2008) | ΔIm or ΔVm | Neuron with 2 4-7-compartment dendrites, 1 spine, 4800 synapses, 1 somatic | KA, KAHP, Nafast' | AMPAR, GABAR, NMDAR | Simplified intracellular processes |
| Dual, Elect. | Kubota et al. (2008) | ΔIm or ΔVm | 1 spine | No | NMDAR | CaM buffer, Ng |
| Dual | Migliore et al. (1995) | Presyn. stimulus | 1 pre-, 1 postsynaptic | No | No | Simplified intracellular processesc |
| Dual | Migliore et al. (1997) | Presyn. stimulus | Several synapses with 1 pre- and 1 postsynaptic | No | No | Simplified intracellular processesc |
| Dual, Elect. | Migliore and Lansky (1999b) | Presyn. stimulus | 1 pre-, 1 postsynaptic | Noj | No | Simplified intracellular processesc |
| Dual | Migliore and Lansky (1999a) | Presyn. stimulus | 1 pre-, 1 postsynaptic | No | No | Simplified intracellular processesc |
| Dual | Naoki et al. (2005) | INMDAR | 15-compartment spine | No | No | CaM and other buffers, 1-D diffusion of all molecules, Na+/Ca2+ exchanger, PMCA and SERCA pumps |
| Dual | Pi and Lisman (2008) | JNMDAR | 1 spine | No | AMPAR | Buffer, CaMKII, PP2A, AMPAR trafficking |
| Dual, Elect., STDP | Rubin et al. (2005) | ΔIm or ΔVm | Neuron with 1 spine (dendritic), 1 somatic | CaL, KA, KAHP, KDR, Na+ | AMPAR, NMDAR | Buffer, Ca2+ detectors, 1-D Ca2+ diffusion |
| Dual, Elect. | Saftenku (2002) | ΔIm or ΔVm | Neuron with several compartments | BKCa, CaN, KA, KDR, KIR, Kslow, Nafast, Nar, Naslow | AMPAR, NMDAR | Simplified intracellular processes |
| Dual, Elect., STDP | Saudargiene et al. (2005) | ΔIm or ΔVm | 1 dendritic | No | AMPAR, NMDAR | Simplified intracellular processes |
| Dual, Elect., STDP | Shah et al. (2006) | Synaptic stimulus | 1 pre-, 1 postsynaptic | No | NMDAR | Simplified intracellular processes |
| Dual, Elect., STDP | Shouval et al. (2002a) | Synaptic stimulus | 1 synaptic | No | NMDAR | Simplified intracellular processes |
| Dual, Elect., STDP | Shouval et al. (2002b) | Synaptic stimulus | 1 pre-, 1 postsynaptic | No | AMPAR, NMDAR | 2 kinases, 2 phosphatases |
| Dual, Elect., STDP | Shouval and Kalantzis (2005) | Synaptic stimulus | 1 synaptic | No | NMDAR | Simplified intracellular processes |
| Dual, Elect., STDP | Yeung et al. (2004) | Synaptic stimulus | Neuron with 1 compartment, 120 synapses | Nog | NMDAR | Simplified intracellular processes |
| Dual, Elect., STDP | Yu et al. (2008) | Synaptic stimulus | Neuron with 1 compartment, 1000 synapses | Noi | NMDAR | Simplified intracellular processes |
Models are in alphabetical order by the first author and according to the publication month and year. First all LTP models are listed, then all LTD models, and finally all dual LTP and LTD models. Furthermore, electrophysiological (Elect.) models taking into account membrane voltage and spike-timing-dependent plasticity (STDP) models are indicated in the first column. Tabulated characteristics are the model inputs, compartments, voltage-gated ion channels (VGICs), ligand-gated ion channels (LGICs), as well as molecules and Ca2+ mechanisms modeled. ICa denotes in this study the Ca2+ current but dependency in membrane voltage is not modeled. INMDAR denotes in this study the Ca2+ current via NMDARs but dependency in membrane voltage and NMDAR kinetics are not modeled. Isyn denotes the synaptic current. JCa denotes the Ca2+ influx, JVGCC denotes the Ca2+ influx via VGCC, and JNMDAR denotes the Ca2+ influx via NMDARs. For complex CaMKII models, number of CaMKII subunits, number of states for each subunit, and specified threonine (Thr) residues of CaMKII that are phosphorylated are given. Molecules that are modeled as constants are also listed. All abbreviations are given in the list of abbreviations.
aTen CaMKII subunits/Thr-286, Thr-305/306 with five states: inactive, bound with CaMCa4, bound with CaMCa4 and autophosphorylated (trapped), CaMCa4 dissociated from the trapped form but remains phosphorylated (autonomous), and autonomous state secondary phosphorylated (capped).
bIt is not clearly stated in the publication how many CaMKII subunits are modeled but they have two states: inactive and phosphorylated.
cCa2+ is not included in the model.
dModel is by Miller et al. (2005), 12 CaMKII subunits/Thr-286/287 with two states: inactive and phosphorylated.
ePre- and postsynaptic membrane voltage are modeled.
fPostsynaptic neuron is described using adaptive exponential IF neuron model.
gPostsynaptic neuron is described using IF neuron model.
hPre- and postsynaptic neurons are described using IF neuron model.
iPostsynaptic neuron is described using LIF neuron model.
jPostsynaptic membrane voltage is modeled.