Tsodyks-Markram model for short-term synaptic plasticity

[gabrevaya]

I need to implement a model similar to the one presented in Steiner et al., 2024. One of its key aspects currently missing in Neuroblox is a short-term synaptic plasticity mechanism through the Tsodyks-Markram model. Concisely, this model consist of:

• Equations:

1. Resource dynamics:

$$\frac{dr}{dt} = \frac{1 - r}{\tau_{\text{rec}}} - u(t) \cdot r(t) \sum_i \delta(t - t_i)$$

2. Utilization dynamics:

$$\frac{du}{dt} = -\frac{u}{\tau_{\text{facil}}} + U \cdot (1 - u) \sum_i \delta(t - t_i)$$

3. Postsynaptic current at each spike $t_i$:

$$\text{PSC}(t_i) = A \cdot u(t_i) \cdot r(t_i)$$

• Variables:

  • $r(t)$: Fraction of available resources.
  • $u(t)$: Release probability.

• Parameters:

  • $U$: Baseline increase in $u(t)$ per spike.
  • $\tau_{\text{rec}}$: Recovery time constant for $r(t)$.
  • $\tau_{\text{facil}}$: Decay time constant for $u(t)$.
  • $A$: Maximal synaptic efficacy.

Depression: $r(t)$ decreases with each spike and recovers over time with $\tau_{\text{rec}}$.
Facilitation: $u(t)$ increases with each spike by a factor of $U$ and decays over time with $\tau_{\text{facil}}$.

Note: In the paper (Steiner et al., 2024), there seem to be some errors in the equations of this model: in Eq. 1, the delta function term is missing, and in Eqs. 2 and 3, the expressions $r^{\delta (t-t_{sp})}$ should be factors rather than exponents.

I'm considering how to implement this within Neuroblox. Since synaptic plasticity could be a valuable feature beyond this particular model, I think it's worth discussing its design with the group to allow for generalization to other plasticity rules. I wonder if you have already been thinking of integrating such mechanisms to Neuroblox. @harisorgn @helmutstrey ?

The only plasticity rule that I noticed is the HebbianPlasticity but there might be others that I missed.
Should we implement this new plasticity model similarly? However in that case involved discrete changes, while in this case, the modulation is continuous in time. I think it might be more appropriate to handle it in the connection rules (BloxConnector), adding the $u$ and $r$ factors to the base connectivity weights. This would require adding 2 extra equations for each AbstractNeuronBlox.

Regarding the delta functions at the time of the spikes, should we set a threshold voltage for all AbstractNeuronBlox and add ContinuousCallbacks? While HH and Izhikevich neurons don't have such fixed thresholds, we could provide it as an optional parameter.

We can start with the plasticity framework for AbstractNeuronBlox while keeping in mind how to make it extensible for neural mass model plasticity in the future.

[gabrevaya]

During today's DBS meeting, we resolved to leave the short-term plasticity to a later stage and prioritize other aspects first. However, I leave this issue open for future discussions of this feature.