# Estimation of Synaptic Activity during Neuronal Oscillations
## 4 Discussion
We found the exponential integrate-and-fire model (EIF) to be a convenient base model: on the one hand, its oscillation period can be well approximated by means of the semi-analytical formula (6); on the other, there are examples in the literature showing that its \(f-I\) curve can fit \(f-I\) curves of neural data. Our procedure has been applied first to a representative computational model driven by a prescribed input conductance trace. We verify that the use of the \(f-g_{syn}\) curve brings excellent predictions of the \(g_{syn}\) fluctuations along the prescribed trace, see Figure 3. We also observe better estimations when the synaptic conductances change on a time-scale longer than the mean interspike interval. We also analyze the effects of the discretization and the measurement noise, see Tables 2 and 3. In particular, we observe that levels of noise below \(1\) mV do not compromise the estimations in a substantial way since the MSE of the estimations is very low (MSE \(<10^{-6}\)) in all cases. In Section 3.1.3, we explore the goodness of the estimations under the assumption that the EIF (base) model provides a good fit to the neural data. By using a model for a noisy pyramidal cell to generate the data, we again observe excellent estimations of the synaptic conductance (MSE \(<10^{-6}\)), see Figure 5. We conclude that we could reasonably estimate the synaptic conductances from other neural data to which the EIF could be fitted. We next study potential difficulties that can be found in more realistic scenarios. First, in Section 3.1.4, we cope with the problem of estimating synaptic conductances when there is no base model that decently fits the data. We propose a procedure to come up with an approximation of the \(T-g_{syn}\) curve and apply it to data generated by a computational model. Again, we achieve good estimations (MSE \(<10^{-6}\)), see Table 4. For real cells, the dynamic-clamp technique allows obtaining the period \(T\) from a \(g_{syn}\) value, and therefore it would be interesting to design a protocol so that it was feasible to obtain the \(T-g_{syn}\) curve. As our method is mainly addressed to the spiking regime,the second potential difficulty is the presence of interspersed short subthreshold periods. We show (see Figure 8) that these short subthreshold periods do not contaminate the estimation of synaptic conductances and provide results with small errors. In order to check the robustness of the estimation procedure for other types of neurons, we have also considered the stellate cell model (see Section 3.1.2), to which the quadratic integrate and fire model (QIF; see [30]) has been fitted. Results (not shown) reveal that the estimation procedure can also be used in cases where the fitting is not as perfect as those obtained for the pyramidal cell model. Our method is related in spirit to the firing-clamp method presented in [25], where the authors also consider a point neuron and, by calibrating its activity, they experimentally build up an approximated function to describe the changes in both the membrane potential threshold and the amplitude of the spiking regime (instead of the spiking frequency). Their model is able to discern between excitatory and inhibitory conductances; however, as their calibration is purely experimental, errors could arise from the measurement noise because of repetitive trials.