Evoking a prescribed spike train in vivo

i.e. the inverse of eq.(4.3):

µ_†=f_µ⁻¹(r_†), (4.13)

σ†=σ0. (4.14)

Using the inverse firing-rate-vs-input-current relation is again an approximation because the calculated stimulus, s†,G,fc(t), is colored noise and the noise color can affect the firing rate (Brunel and Sergi, 1998). In the following, we will writes†(t) instead ofs†,G,fc(t) for the converged stimulus, to ease the notation.

Because we derived s_†(t) under strong approximations (eq.(4.8)) and performed some nonlinear transformations (eq.(4.9) and eq.(4.11)) that have been introduced in a very ad hoc way, we need to test to which extend the stimulus is able to evoke the desired spike trainx†(t).

4.5. Evoking a prescribed spike train in vivo

We have tested our procedure to evoke prescribed spike trains in real cortical neurons in vivo. For these experiments we restricted us to the case of prescribed statistics that match the reference statistics, i.e. C_V†=CV0 and r†=r0. These values and the dynamic susceptibility χ0 at the reference point have been estimated from white Gaussian noise stimulations as explained in ch.4.2. To this end, we generated 10 white noise stimuli of which each stimulus has been applied 10 times and lasted for 1 s. Between each stimulus representation a 1s gap was introduced such that the total number of 100 stimulations was applied within less than 4 minutes. From these data, we also calculated the intrinsic reliability, Γ^refee, of the neuron by averaging the coincidence measure (eq.(1.26)) over pairs of spike trains that belong to the same stimulus. We then applied our procedure and injected the resulting stimulus into the very same neuron. We made recordings of five cells from which two cells have been stimulated with two stimulation intensities. Therefore, in total we generated seven data sets with 50-140 trials.

In Fig.4.3, the basic prescribed statistics, rate and CV, are compared to the statistics of the spike trains that have been evoked by our stimulus. The evoked and the prescribed firing rates are shown in Fig.4.3A. Data points are distributed along the diagonal (which would indicate a perfect agreement between prescribed and evoked rate) and show only minor deviations for most cases. Also for the CV a correlation between prescribed and evoked values can be observed (see Fig.4.3B), but most deviations from the optimal value on the diagonal tend towards larger evoked CVs. However, from our small data set it is

A B

Figure 4.3.: Spike train statistics of the prescribed and the evoked spike trains (experi-mental data, in vivo). A) Scatter plot of the firing rate. B) Scatter plot of the Coefficient of variation (CV). The same symbol in A and B belong to the same data sets. In total, seven data sets out of 5 different neurons are shown. An optimal agreement would be achieved for values on the diagonal (gray line).

hard to judge whether this bias is a reliable observation.

In Fig.4.4, the coincidence measures are used to quantify to which extent the specific AP timing could be achieved. We compare three different values to each other: Γ^refee, the intrinsic reliability (i.e. the similarity between evoked spike trains) that has been estimated by white noise stimulation at the reference point; Γee, the intrinsic reliability resulting from stimulation with the colored noise that comes out of our procedure; and Γde which is the similarity between prescribed and evoked spike trains.

The intrinsic reliability for the reference stimulation, Γ^refee, is plotted along the x-axis, while Γee (blue symbols) and Γde (red symbols) are given on the y-axis. The first obser-vation that we can make is that all data points are systematically above the diagonal.

This means that our colored noise stimulus could generate reproducible spike trains with larger reliability as for the white noise case. The second observation is that the similarity between evoked and prescribed spike train, Γde, is larger than the intrinsic reliability for the same data set (red symbols are above blue symbols). Note that in this figure different data sets are separated by their intrinsic reliability along the x-axis such that vertically aligned symbols belong to the same data set. Thus, the similarity between the colored noise evoked spike trains and the target spike train was even higher than the similarity within the evoked spike trains. This is the case because the prescribed spike train lacks the

4.5. Evoking a prescribed spike train in vivo

Figure 4.4.: Prescribed spike times can be evoked reliably in vivo. The trial-to-trial reliability in response to the colored noise (Γee, blue triangles) and the similarity between prescribed spike trains and evoked trials (Γde, red circles) are plotted against the trial-to-trial reliability in response to white noise stimulation (Γ^ref_ee). The colored noise evoked spike trains even more reliable than stimulation with white noise. The similarity between trials and desired spike train (Γde) exceeds the trial-to-trial reliability Γee.

A

B

Figure 4.5.:A) Example stimulus calculated to evoke a desired spike train in a particular cell. B) Raster plot of spike trains (black dashes) generated by stimulation with the current shown in A. The desired spike times are marked as blue stripes in the raster plot and mostly agree well with the evoked spike times.

intrinsic noise of the individual trials and the evoked APs are jittered around the desired spike time.

A less abstract example of the performance is given in Fig.4.5. Panel A shows the stimulus and panel B the corresponding raster plot for one example cell, for which the spikes (black dots) appeared with high precision close to the prescribed times (blue lines).

However, at around 200 ms and 610 ms the cell systematically generated APs that are not part of the prescribed spike train. It is likely that these systematic outliers are introduced by the constraints that we imposed on the stimulus.

Despite the finite intrinsic reliability and the weak systematic deviations from the pre-scribed spike train, we can conclude that this method has the ability to evoke prepre-scribed spikes in a precise and reliable manner using juxtacellular stimulation in vivo in cortical neurons.