Detection of M-sequences from spike sequence in neuronal networks

Abstract

In circuit theory, it is well known that a linear feedback shift register (LFSR) circuit generates pseudorandom bit sequences (PRBS), including an M-sequence with the maximum period of length. In this study, we tried to detect M-sequences known as a pseudorandom sequence generated by the LFSR circuit from time series patterns of stimulated action potentials. Stimulated action potentials were recorded from dissociated cultures of hippocampal neurons grown on a multielectrode array. We could find several M-sequences from a 3-stage LFSR circuit (M3). These results show the possibility of assembling LFSR circuits or its equivalent ones in a neuronal network. However, since the M3 pattern was composed of only four spike intervals, the possibility of an accidental detection was not zero. Then, we detected M-sequences from random spike sequences which were not generated from an LFSR circuit and compare the result with the number of M-sequences from the originally observed raster data. As a result, a significant difference was confirmed: a greater number of "0-1" reversed the 3-stage M-sequences occurred than would have accidentally be detected. This result suggests that some LFSR equivalent circuits are assembled in neuronal networks.

Figure 1

3-stage LFSR circuit, the operation at the ring sum is an exclusive-OR such as 1 + 0 = 1 and 1 + 1 = 0. (a) A basic circuit with feedback [2, 3] generates an M-sequence as 10111001011100…(basic pattern). (b) A mirror circuit of (a) with feedback [1, 3] generates a time course of reversed-order M-sequence, as 11101001110100….

Figure 2

Micrograph of cultured hippocampal neurons in an MEA black rectangles are electrodes. The size of each electrode is 50 × 50 μm and the electrode spacing was 150 μm.

Figure 3

Stimulated spike response and results of M-sequence detection for culture 1. (a) The raw recording spike data (0-1 s). A stimulated spike response was observed from 5 ms (applied stimuli) to 150 ms on channels 2 and 3. (b) The raster plot and detected M-sequences on channels 8, 9, and 10.

Figure 4

Number of detected M-sequences for (a) Culture 1, (b) Culture 2, (c) Culture 3, (d) Culture 4, (e) Culture 5, and (f) Culture 6.

Figure 5

Process of interval shuffle (a) original raster plot data (b) shuffled raster plot data.

Figure 6

Mean number of detected M3 patterns. Error bar shows the standard deviation of the number of detected M3 patterns for each culture. (a) Rev. M3 from spike data. There were significant differences between the original and interval shuffle data in all cultures except culture 2 (P < 0.05). (b) Rev. M3 from random noise data. Noise 1 is the raster plots obtained by detecting peaks from recorded noise responses of medium (without cell cultures) with threshold 0.01[mV]. Noise 2 is random sequence data created from random numbers. (c) non-Rev. M3 from Spike data (d) non-Rev. M3 from Noise data.

Figure 7

An equivalent 3-stage LFSR. (a) Model 1: spikes of multiple neurons in a neuron group propagate to another neuron group like synfire chain. Although we assume that neurons in the same neuron group evoke simultaneously and all pair of neurons are equal in their synaptic delay, there is a possibility that an equivalent LFSR circuit is assembled when the spike timing delay of each neuron in a same neuron group and synaptic delay between neuron groups are coordinated even if pair of neurons are not equal in their synaptic delay. (b) Model 2: the framework of LFSR is constructed by “mainneurons” and “sub neurons” are connected with “mainneurons” to excite them. Although, we omit a XOR function in both figures, some XOR circuit models constructed by neurons are already shown in previous study.