Spike Code Flow in Cultured Neuronal Networks

Abstract

We observed spike trains produced by one-shot electrical stimulation with 8 × 8 multielectrodes in cultured neuronal networks. Each electrode accepted spikes from several neurons. We extracted the short codes from spike trains and obtained a code spectrum with a nominal time accuracy of 1%. We then constructed code flow maps as movies of the electrode array to observe the code flow of "1101" and "1011," which are typical pseudorandom sequence such as that we often encountered in a literature and our experiments. They seemed to flow from one electrode to the neighboring one and maintained their shape to some extent. To quantify the flow, we calculated the "maximum cross-correlations" among neighboring electrodes, to find the direction of maximum flow of the codes with lengths less than 8. Normalized maximum cross-correlations were almost constant irrespective of code. Furthermore, if the spike trains were shuffled in interval orders or in electrodes, they became significantly small. Thus, the analysis suggested that local codes of approximately constant shape propagated and conveyed information across the network. Hence, the codes can serve as visible and trackable marks of propagating spike waves as well as evaluating information flow in the neuronal network.

Figure 1

(Upper) Micrograph of cultured hippocampal neurons in a microelectrode array. Black rectangles indicate electrodes. (Lower) Illustration of a vertical section. Each electrode catches spikes from several neurons. We can observe spike trains containing code such as “1011.” Each bit (“1” or “0”) is considered from different neuron for short time length (short bit width) code, since it takes more time for the same neuron to fire twice than the refractory period.

Figure 2

Spike trains on 8 × 8 multielectrodes between 0 and 18 ms (horizontal axis) after the stimulation pulse is given at time 0 from the electrode marked with a star. The red ellipse shows code “1011,” and the green ellipse shows “1101,” with each having a bit width more than 0.6 ms.

Figure 3

Average number of “1011” and “1101” codes that were observed per trial from 64 electrodes during the first 200 ms after stimulation versus the bit width of the code. We can see the bit width of the codes detected is mainly less than 2-3 ms.

Figure 4

Code “1101” detected with bit width 0.6 ms.

Figure 5

Spectrum of the detected codes with bit widths of 0.6–2.0 ms. We can see that the major component of the code spectrum is that of three bits (code number 1-21). Four bits or more codes (code number 22-120) are far less than that. Random train has flat spectrum within three-bit codes while the original train has its own shape. Interval shuffled and electrode shuffled spike trains show intermediate spectrum profiles.

Figure 6

Code flow map for Samples A and B (Org). The serial images are from right to left and top to bottom, and “1011” and “1101” codes are expressed in red and green, respectively. Yellow indicates a mixed code. These spots are blurred to smoothen the movies. The frame interval is 5 ms and elapsed time is shown at upper right.

Figure 7

Code flow map, which is the same as that in Figure 6(a), but for a different trial. The appearance is noticeably different from that in Figure 6(a). The maximum brightness is normalized to 1 in the image.

Figure 8

Movies in the three trials of code flow of Sample A. The code flows for the original, interval shuffled, and random spike trains in each trial are shown (http://www.nbl-technovator.jp/NBL_Tech/paper/CodeFlowFig8.pdf).

Figure 9

Maximum cross-correlation of a pixel with a 5 ms time difference (frame interval). For example, 20N (0.2–0.6) indicates that the “1011” (or “1101”) code with a 0.2–0.6 ms bit width had the maximum cross-correlation with some electrode within 20 neighbors in the next frame. The results are averages of “1011” and “1101.” From (b), we can see that the original train has clearly the code flow characteristic.

Figure 10

Maximum cross-correlation Φ_N(C) in 8 neighbors (8N) and 20 neighbors (20N) for 14 major codes of Sample A. The frame width is 2 ms, and the bit width is between 0.6 and 2.0 ms.

Figure 11

Maximum cross-correlation Φ_N(C) that is normalized by the code duration for 14 major codes of Sample A. The p values are calculated from the EShuf/Org ratios of each code. This graph can be considered as another spectrum concerning the flow property of major codes. We can see that the normalized spectrum has flat (white) characteristic. That is, each major code can be considered as relatively independent. Though the values of 20N itself are larger than 8N, flow property difference between the original train and shuffled one of 8N is significantly larger than that of 20N as seen from p value.