Interaction of electrically evoked responses in networks of dissociated cortical neurons

In this work we describe the interaction of the responses of neuronal networks to pairs of electrical stimuli. For this we use networks of dissociated cortical neurons cultured on planar microelectrode arrays. We compare the response to pairs of stimuli with the response to a stimulus in isolation. To evaluate the influence of both stimuli we introduce a normalization of the root-mean square of the response. Furthermore we consider the response to a pair of stimuli as the linear superposition of the two constituents. The two methods combined show that the neuronal network strongly suppresses the second stimulus. At the same time we find a possible window of integration in which two stimuli from separate locations in the network can interact to form a new response.

Figure 1

Experimental design. (A) The time line of the different phases in the experiment. The test response on the primary and secondary electrode (vertical black lines) is recorded before and after each paired-stimulation (double white lines) recording. The vertically printed labels under the paired-stimulation phases give a possible, random ordering for this experiment. The sequence, i.e., spontaneous activity, paired stimulation and test stimulation, is repeated eight times; here only three are shown. The labels on the arrows illustrate for one particular phase of paired stimulation (two-site stimulation, ${\Delta }_{\text{PP}}=50\text{ms}$) from which phases the firing rate profiles $r\left(t\right)$ are computed that are used for the comparisons (see text). (B) Illustration of the difference between the single- and two-site protocols. Whereas in the single-site protocol both pulses are applied form the same electrode $(+)$, in the two-site protocol pulses are applied from the two separate electrodes (first $+$ then $x$).

Figure 2

Chronological ordering of the analyses of evoked activity from a two-site stimulation phase with ${\Delta }_{\text{PP}}=25\text{ms}$. The thick vertical lines indicate the arrival of the two stimuli. Data in panels A–D are from one representative electrode. (A) The raw recordings following the first 10 (of 60) pairs from $t=-10\dots 50\text{ms}$ relative to the first stimuli. This type of figure is of great help in assuring the proper functioning of stimulator, amplifier and peak detection algorithms. (B) The same data as in A after peak detection to visualize the functional effect of stimulation and reproducibility of the response. (C)–(E) The PSTH is a histogram of delays of spikes after a stimulus and can be transformed into an estimate of the instantaneous firing rate (IFR). The PSTHs are estimated from all 60 responses with a bin size of (C) 0.5 ms and [(D) and (E)] 5 ms. In panel C the dashed line indicates the threshold for detecting direct action potentials (see text). The population PSTH in panel E is obtained by pooling spikes from all electrodes to get an estimate of the array-wide firing rate (AWFR). Firing rates are referred to as $r\left(t\right)$ in the text with labels in sub- and superscript and $t$ relative to the stimulus as in these graphs.

Figure 3

Illustration of how responses from two separate electrodes might be combined for fictitious data from a two-site protocol with ${\Delta }_{\text{pp}}=50\text{ms}$. Panels A and B show the response at an electrode after stimulating in isolation the primary (a) and secondary (b) electrode, respectively. This is referred to as “test stimulation.” Panel C shows the response when the two electrodes are stimulated in close succession (paired stimulation). The gray bars below the horizontal axes depict the windows used for comparisons with the normalized rms (see text). Panel D illustrates the fitting method. The observed pair response in panel C is reconstructed as a linear combination of the test responses in panels A and B (see text).

Figure 4

Examples of changes of the response when applying paired pulses. The gray area indicates the range of values observed for the test responses before and after the pair response. The lower bound at time $t$ is the smaller one of $r_{\text{PRIM}}^{\text{PRE}}\left(t\right)$ and $r_{\text{PRIM}}^{\text{POST}}\left(t\right)$ while the upper bound is the larger one. The pair response itself is represented by the black trace. Under ${\text{H}}_1$ we expect that the black trace and the gray area overlap. Arrows indicate the arrival of the second stimulus. All data are from single electrodes (cf. panels 2C and 2D). (A) A typical pair response composed solely of the primary response in the single-site protocol at ${\Delta }_{\text{PP}}=25\text{ms}$. (B) The same response at higher time resolution; only the first 50 ms. The early response is clearly visible and is evoked by the second pulse in the pair as well. [(C) and (D)] Two responses to two-site stimulation from the same electrode and network at two different values for ${\Delta }_{\text{PP}}$. C: 10 ms and D: 50 ms. The trace in panel C is more different from the test response than is D. (E) After 1000 ms the network is again able to evoke activity. (F) A typical response from a rejected network where the response has become much elongated spanning 500 ms.

Figure 5

The normalized rms expresses the difference between the pair and test response as a multiple of the difference between the response from two subsequent phases of test stimuli. Panel A shows the results for the single-site protocol and (B) for the two-site protocol. The symbols represent outliers, mainly due to a small denominator for normalization. These are analyzed separately.

Figure 6

Quantitative analysis of the pair response composition. The two rows show the results for the single-site (panels A and B) and two-site (panels C and D) protocol, respectively. The leftmost panels show the values for $a_{\text{p}}$ (solid) and $a_{\text{s}}$ (dashed) representing the contribution of the first $\left(a_{\text{p}}\right)$ and second $\left(a_{\text{s}}\right)$ stimulus. The rightmost panels give the proportion of electrodes in which the reduced chi-square statistic indicated as $\epsilon$ for the naïve fit is larger than the reduced chi-square statistic under ${\text{H}}_1$, i.e., assuming $a_{\text{p}}$ is 1.0.

Figure 7

Ratio of the dAP’s reliability after the second stimulus in the pair and a stimulus in isolation. Panels A and B show the results for single- and two-site protocol, respectively. The traces show a very clear frequency effect, with the response returning to “normal” steadily when the interpulse interval exceeds the duration of the response. For the two-site protocol the effect shows slightly more spread but a very reliable return to baseline for ${\Delta }_{\text{PP}}=1000\text{ms}$. Error bars indicate the standard deviation over the experiments.