General anesthesia reduces complexity and temporal asymmetry of the informational structures derived from neural recordings in Drosophila

We apply techniques from the field of computational mechanics to evaluate the statistical complexity of neural recording data from fruit flies. First, we connect statistical complexity to the flies' level of conscious arousal, which is manipulated by general anesthesia (isoflurane). We show that the complexity of even single channel time series data decreases under anesthesia. The observed difference in complexity between the two states of conscious arousal increases as higher orders of temporal correlations are taken into account. We then go on to show that, in addition to reducing complexity, anesthesia also modulates the informational structure between the forward- and reverse-time neural signals. Specifically, using three distinct notions of temporal asymmetry we show that anesthesia reduces temporal asymmetry on information-theoretic and information-geometric grounds. In contrast to prior work, our results show that: (1) Complexity differences can emerge at very short timescales and across broad regions of the fly brain, thus heralding the macroscopic state of anesthesia in a previously unforeseen manner, and (2) that general anesthesia also modulates the temporal asymmetry of neural signals. Together, our results demonstrate that anesthetized brains become both less structured and more reversible.

Figure 1

Evolution of experimental data from neural signals to $\epsilon \text{machines}$. (a) Representative schematic of D. melanogaster brain (modified from Ref. [50]) depicted with probe and approximate channel locations. Each channel $c\in [1,15]$ samples around a localised region in the brain, with numerical labels ordered from the central ($c=1$) to peripheral ($c=15$) regions. (b) Example reading of a processed local field potential (LFP) for a single channel. Points along the $x$ axis represent LFP measurements at each sampling time step. The median LFP measurement of the sample is shown as the gray line bisecting data. LFP binarization is determined via splitting over the median with the encoding scheme 0: LFP $\le$ Median, and 1: otherwise. The $\epsilon \text{machines}$ are inferred by using the binary string as the input to the CSSR algorithm. (c) Digraph representation of the CSSR-inferred $\epsilon \text{machine}$ for channel 1 readings of fly 1 under anesthesia (0.6 vol.% isoflurane) with $\sigma =0.005$ and $\lambda =3$. Graph vertices correspond to causal states. Vertex labels distinguishing causal states are assigned arbitrarily and do not imply state equivalence across multiple graphs. Directed edges correspond to transitions between causal states. Edge labels denote the probability (two significant figures) of a transition occurring, and edge color encodes the emitted symbol upon making the transition (1: Red, 0: Blue). The histories stored in the causal states for this $\epsilon \text{machine}$ are visualised in Fig. 6. (d) Digraph representation of $\epsilon \text{machine}$ for the wakeful (0 vol.% isoflurane) level of conscious arousal for the same channel, fly, $\sigma$, and $\lambda$ as in (c). We report the forward-time statistical complexities $C_{\mu }^a=1.88$ and $C_{\mu }^w=2.96$ for (c) and (d), respectively.

Figure 2

Colour map of statistical complexity response averaged over $(n=13)$ flies ${\langle C_{\mu }^{(+,\psi )}\rangle }_f$, (left) during wakefulness (0 vol.% isoflurane), and (right) anesthesia (0.6 vol.% isoflurane), over channel location and memory length $\lambda$, measured in milliseconds. Hatched cells on the right subfigure, show regions where $C_{\mu }$ did not decrease under anesthesia.

Figure 3

Statistical complexity differences $\mathrm{\Delta }{C}_{\mu }=C_{\mu }^w-C_{\mu }^a$ of $\epsilon \text{machines}$ between states of conscious arousal for: (Top) increasing memory length $\lambda$. Gray lines indicate complexity averages over channels per fly $(n=13), {\langle \mathrm{\Delta }{C}_{\mu }\rangle }_c$, while the blue line denotes the average over both channels and flies ${\langle \mathrm{\Delta }{C}_{\mu }\rangle }_{c,f}$. Error bars are $95\%$ confidence intervals of the population. (Bottom) maximum memory length $\lambda =11$ (in milliseconds), mapped throughout the fly brain (channels). Gray and red lines indicate the result per fly and the average over $(n=13)$ flies, ${\langle \mathrm{\Delta }{C}_{\mu }\rangle }_f$, respectively. Error bars corresponding to the $95\%$ confidence intervals over the sample of files.

Figure 4

Colour map of two-tailed paired $t$ scores over channel location and memory length $\lambda$ for (a) statistical complexity differences ${\langle \mathrm{\Delta }{C}_{\mu }^{+}\rangle }_f={\langle C_{\mu }^{(+,w)}-C_{\mu }^{(+,a)}\rangle }_f$; (b) causal irreversibility differences ${\langle \mathrm{\Delta }\mathrm{\Xi }\rangle }_f={\langle {\mathrm{\Xi }}^w-{\mathrm{\Xi }}^a\rangle }_f$; (c) crypticity differences ${\langle \mathrm{\Delta }d\rangle }_f={\langle d^w-d^a\rangle }_f$; and (d) the differences in KL divergence rate ${\langle \mathrm{\Delta }{\mathcal{D}}_{\text{KLS}}\rangle }_f={\langle {\mathcal{D}}_{\text{KLS}}^w-{\mathcal{D}}_{\text{KLS}}^a\rangle }_f$. The dotted lines indicate the memory length and channel locations that exceed $p<0.05$ (uncorrected). The color scale is consistent across all subplots.

Figure 5

Exemplary digraph representations of $\epsilon \text{machines}$ for wakeful (a–d) and anesthetized (e–g) conditions for forward-time (a, e), reverse-time (c, f), and bidirectional (d, g) analyses, all constructed from channel 5 in fly 7, at memory length $\lambda =3$. Panel (b) gives an example emission sequence and causal state sequence for forward and reverse-time $\epsilon \text{machine}$ pair (a) and (c). The vertex labeling denoting causal states in (a-d) is consistent to show composition of forward and reverse-time $\epsilon \text{machines}$ in the bidirectional $\epsilon \text{machine}$. The $\epsilon \text{machines}$ for the wakeful condition have statistical complexity of $C_{\mu }^{(+,w)}=1.76, C_{\mu }^{(-,w)}=1.50$, and $C_{\mu }^{(\pm ,w)}=3.25$. In this example the process is irreversible for all three quantities. The $\epsilon \text{machines}$ for the anesthetized condition have statistical complexity of $C_{\mu }^{(+,a)}=C_{\mu }^{(-,a)}=1.0$ and $C_{\mu }^{(\pm ,a)}=1.9989$. The process is causally and microscopically reversible but has finite crypticity.

Figure 6

$\epsilon \text{machine}$ for same channel, fly, conscious state as Fig. 1 but with histories stored in each causal state explicitly stated. The sequences after the asterisk $*$ represent the sequence of symbol observations with the most recent observed symbol on the far right. Sequences collected within a causal state (gray circle) warrant significantly different future statistics to observed sequences in other causal states. The red lines emit a “1” upon transition, and blue lines emit “0”s.