Table 3.
Comparison of models for LTP and LTD.
| Short description and reference | Parameters | Experimental protocols | Classification in | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | Figure 1 | Figure 2 | ||
| Song et al. (2000): conventional nearest-neighbor exponential STDP (Pfister and Gerstner, 2006) | 2 TC, 2SF | f | n | h | n | n | n | n | n | 2 | 1, 4, 10 |
| Froemke et al. (2006): standard STDP model, with added pre and post suppression of spike efficacy. The efficacy of the pre spike is dependent on all the preceding spikes, while the post-spike depends only on the last preceding one (The model is an extension of Froemke and Dan, 2002) | Conventional STDP: 2 TC, 2 SF; suppression: 2 TC pre and post suppression, 1 SF post suppression | fc | h | fc | fc | f | n | n | n | 2 → 3 | 1, 3, 4, 7 |
| Pfister and Gerstner (2006): reduced triplet model: standard STDP model, with amplitude of LTP dependent on additional post spike trace | Conventional STDP: 2 TC, 2 SF, additional spike trace: 1 TC, 1 SF | f | f | f | f | u | n | f | n | 2 | 1, 4, 7, 10 |
| Benuskova and Abraham (2007): scaling constants of conventional STDP exponential functions are metaplastically changed according to mean over post-spike train | Conventional STDP: 2 TC, 2 SF; post mean for scaling: 1 TC, 1 SF | fc | u | hc | u | u | ? | u | n | 2 | 1, 3, 10 |
| Senn (2002): STDP modeling of neurotransmitter discharge probability, based on pre- and postsynaptic traces sampled at corresponding pulses, pre and post adaptation through secondary messengers | Receptors: 1 TC, 3 SF, secondary messengers: 1 TC, 2 SF, discharge prob.: 1 TC, 2 SF | f | h | f | fc | fc | fc | fc | ? | 3 → 1 | 1, 2, 3, 4, 7, 10 |
| Abarbanel et al. (2002): two ODEs describing pre neurotransmitter release and post voltage, disturbance functions representing pre and post action potentials. Weight derivation as a mixture of temporal competition and cooperation between processes | Pre- and post-ODEs: 2 TC, 2 SF (reduces to 1 SF for size (APpre) = size (APpost), weight combination: 2 SF | f | h | hc | u | u | ? | ? | hc | 2 → 3 | 1, 4, 5, 6, 10 |
| Badoual et al. (2006): biophysical model of realistic compartmental neuron and kinetic equations for separate LTP and LTD | LTP kinetics: 2 TC, LTD: 4 TC, AMPA/NMDA receptors: 2 TC, 3 SF, Calcium pump: 1 SF, 1 TC, ca. 20 TC/SF neuron model | f | f | h | u | ? | ? | ? | ? | 3 → 2 | 2, 3, 5, 6, 7, 8, 9 |
| Badoual et al. (2006): original suppression model of Froemke and Dan (2002) plus additional weight bounds | Conventional STDP: 2 TC; suppression: 2 TC pre and post suppression, weight scaling/bounds: 2 SF | f | n | f | f | f | u | u | n | 2 | 1, 3, 4, 7 |
| Lu et al. (2007): pulse transition governed model, three states: pre event, post event, resting. Transitions incorporate short term adaptation | Transitions: 2 TC, weight computation: 3 SF | f | ? | f | f | fc | hc | ? | n | 2 | 1, 3, 4, 7, 10 |
| Pfister et al. (2006): STDP curve based on neuron/PSC characteristics derived from supervised pattern classification task | STDP: 2 TC, 2SF; constraint: 1 SF | f | u | hc | u | u | u | u | n | 1 | 2, 5 |
| Shah et al. (2006): calcium based model with formulations of bAP and EPSP influence on Calcium dynamics, additional pre and post attenuation, weight dependent on Calcium amplitude and slope (The model is an extension of Shouval et al., 2002) | Ω: 5 SF; η/τ: 2 TC, 2 SF; Calcium: 1 TC; pre and post attenuation 2 SF, 2 TC | h | f | f | ? | fc | f | fc | fc | 3 | 1, 2, 3, 4, 5, 7, 8 |
| Clopath et al. (2010): triplet model of Pfister and Gerstner (2006) with additional voltage thresholds | LTD: 1TC, 2SF; LTP: 2TC, 2 SF; after-potential: 1 SF, 1 TC | f | f | fc | fc | ? | fc | fc | f | 2 | 1, 4, 6, 7, 10 |
| Sjöström et al. (2001): LTP behavior as a sigmoidal dependence on (measured) residual depolarization, LTD as single scaling, post nearest-neighbor interaction | LTP sigmoid: 3SF, 1TC, LTD: 1 SF, 1 TC, Frequency dependence of LTP: 2 SF | fc | f | hc | fc | fc | fc | f | hc | 2 → 3 | 1, 4, 6, 7 |
| Fusi et al. (2000): LTP and LTD probability dependent on post membrane potential at pre spike, probability governs transition of two-state synapse | 8 SF, 4 TC | f | f | hc | u | u | fc | fc | hc | 1 | 1, 5, 6, 10 |
| This paper, LCP with SRM: exponential decay for PSC; post membrane potential: spike response model; weight change: integral of the product of pre and post side; Voltage threshold for LTP/LTD, refractoriness-based attenuation of post pulses | 1 TC PSC; 1 TC, 2 SF post-spike response; 1 SF attenuation | f | h | f | f | n | n | f | h | 2 → 3 | 2, 5, 6, 7, 10 |
| This paper, LCP with LIAF: PSC as above; post side leaky integrate-and-fire neuron, PSC charges post neuron; attenuation and plasticity as above | same as above, one additional SF for UPSP | f | f | f | f | h | f | f | h | 2 → 3 | 2, 5, 6, 7, 9, 10 |
The numbers for the experimental protocols denote the experiments as listed in Table 1.
The evaluation of the models with respect to biological experiments employs the following symbols: “f” this experiment has been fully reproduced in literature using the respective model, “h” reproduction of one half of the experiment shown, “fc” has not been shown to work, but will likely be fully compatible based on the performance of similar models; “hc” has not been shown to work, but at least one half of the experiment will likely be compatible based on the performance of similar models; “u” we speculate that it is unlikely that this experiment can be reproduced with the model (for discussion, see Appendix); “n” it is shown in literature that this experiment can not be reproduced with the model; “?” there is no data/investigation to relate the model to this particular biological experiment. The last two categories provide a classification with respect to the mechanisms and model types shown in Figures 1 and 2.
TC, time constant; SF, scaling factor; pre, presynaptic; post, postsynaptic.