Modeling somatic and dendritic spike mediated plasticity at the single neuron and network level

Synaptic plasticity is thought to be the principal neuronal mechanism underlying learning. Models of plastic networks typically combine point neurons with spike-timing-dependent plasticity (STDP) as the learning rule. However, a point neuron does not capture the local non-linear processing of synaptic inputs allowed for by dendrites. Furthermore, experimental evidence suggests that STDP is not the only learning rule available to neurons. By implementing biophysically realistic neuron models, we study how dendrites enable multiple synaptic plasticity mechanisms to coexist in a single cell. In these models, we compare the conditions for STDP and for synaptic strengthening by local dendritic spikes. We also explore how the connectivity between two cells is affected by these plasticity rules and by different synaptic distributions. Finally, we show that how memory retention during associative learning can be prolonged in networks of neurons by including dendrites.


Supplementary Figures
Input rate [Hz]  (a) The same simulation as in Figure 2f is repeated, but for all rates between 1 and 15Hz and with steps of 1Hz. The traces for all individual distal compartments shown in Figure 1a are plotted (red), and reveal synaptic depression at lower activation rates than those leading to potentiation. The mean over all compartments (black) somewhat obscures this fact, due to the strong potentiation compared to depression. (b,d) Five synapses connected distally evoke an NMDA spike (b), leading to synaptic potentiation (d). (c,e) Using the same activation as in panel (b) with the addition of five inhibitory synapses fails to evoke an NMDA spike (c), leading to synaptic depression (e).  Location-dependent spike thresholds   15  16  17  18  19  20  21  22  23  24  25  26  27  28  29   28  27  26  25  24  23  22  21  20  19  18  17  16  15  14  13  12  11  10  9  8  7  6  5  4 NMDA spike Som at ic spike Locat ion-dependent spike thresholds AMPA to NMDA ratio: 0.5 to 1 AMPA to NMDA ratio: 2 to 1  (See Figure 1, but now for a layer 2/3 neuron morphology) (      (Analogous to Figure 4, but both the AMPA and NMDA components of the synapses are plastic)

Inputs:
Proximal locations (Analogous to Figure 6, but both the AMPA and NMDA components of the synapses are plastic)

Supplementary Methods
Supplementary Figure 1a: The distal compartments shown in Figure 1a are connected with 10 synapses each, all with an initial weight of 0.5. The 10 synapses are activated using a Poisson process with the same average rate, lasting 2s. This protocol is repeated with rates between 1Hz to 15Hz with steps of 1Hz. The red lines represent all individual compartments, the black line is the mean over these compartments.
Supplementary Figure 1b-e: Five excitatory and five inhibitory synapses are connected to the same distal compartment. The excitatory synapses have plastic AMPA components (g max = 1500nS) and fixed NMDA components (g NMDA = 1500nS). The inhibitory synapses are not plastic (g GABA = 1000nS) and an activated inhibitory synapse will result in an instantaneous rise of GABA conductances by an amount of g GABA . This is followed by an exponential decay with a time constant of 10ms. The current flowing through GABA receptors is modelled by For the detailed model, we used a mean of 100pA and a standard deviation of 300pA. We remind the reader that these values, especially in the reduced model, are abstract parameters and do not necessarily represent realistic values, but were chosen in order to reproduce a certain behaviour. In panels (g,h), a step current of 3000pA was injected in the soma of our reduced model during 3ms. A step current of 1000pA was injected during 3ms in the soma of our full model. No other stimulation was used and the membrane voltage in the soma, proximal (blue) and distal (red) compartments as shown in (a,b) were stored. In panel (i), the same protocol as in Figure 2b was reproduced in our reduced model. Figure 2b is shown as panel (j) for reference.
Supplementary Figures 6 to 10: We refer to the methods of Figures 2 to 6, with the following differences: The simulations in the main text were performed with a plastic AMPA component and a fixed NMDA component of synapses. Therefore, the NMDA component was able to contribute to a neuron's depolarisation, even when the AMPA component reached its minimum weight. However, experimental results have shown that long-lasting changes in neuronal activity maintain the ratio of AMPA to NMDA across a neuron [1]. To account for this plasticity of synaptic NMDA receptors, we performed simulations with both AMPA and NMDA component plastic. These gave qualitatively similar results.
The axonal sodium channel densities are: for the initial two segments, 8000 and 7000 pS µm −2 , for the rest of the axon, 5000 pS µm −2 .
The maximal AMPA conductance is 1.5nS and the maximal NMDA conductance is 3nS.
Supplementary Figure 7a-d: 20 synaptic connections are made instead of 15.
Supplementary Figure 8: the maximum weight is reduced to 0.65, the minimum weight is increased to 0.55.
Supplementary Figure 9: the coloured noisy current has standard deviation σ noise = 10pA, mean µ noise = 115pA. An activation event consists of Poisson-distributed spikes at an average rate of 30Hz at the member synapses during 350ms. Two subsequent activations are separated by a 150ms interval. Every 10 activations (i.e. 5 for each pool), both pools are activated simultaneously.
Supplementary Figure 10: the parameter A inhib has the value 750pS for panels 10b-c and 600pS for panels 10e-i