Electrical Signaling Beyond Neurons Open Access

When a neuron spikes, what is it saying? Do its action potentials (APs) only have meaning as constituents of some broader “neural code”? Or does each AP have meaning on its own? For decades, theoretical neuroscience has debated several conflicting interpretations of neural APs as signal encoders and/or computational primitives (Perkel & Bullock, 1968; Brette, 2019, 2015; Kumar et al., 2010). Rate coding theory asserts that the frequency of APs in time encodes stimulus information (Adrian, 1954; Barlow, 1972; Rossum et al., 2002; London et al., 2010). Spike timing contends that the timing of individual APs in a spike train contains more information about stimuli than their frequency of occurrence (Victor & Purpura, 1996; Rullen & Thorpe, 2001; Johansson & Birznieks, 2004; Gollisch & Meister, 2008). The Bayesian brain hypothesis considers APs as noisy measurements that update an animal’s beliefs about its environment (Pouget et al., 2003; Knill & Pouget, 2004; Jazayeri & Movshon, 2006). Population coding argues that individual neurons and their APs are so unreliable that nervous systems are only sensible to study at the level of systems or networks (Georgopoulos et al., 1986; Quiroga & Panzeri, 2009; Churchland et al., 2012). Some studies propose that different brain regions communicate with different neural codes (O’Keefe & Burgess, 2005; Knutsen & Ahissar, 2009; Smith et al., 2019), which affects communication between them (Kumar et al., 2010). Others question whether neural codes exist at all (Brette, 2019). One of the most fundamental questions in theoretical neuroscience is understanding how nervous systems use APs to represent the world and make decisions. There is no consensus answer to this question.

One reason that neural APs are difficult to interpret is that their relationships to stimuli and behavior are obscured by the complexity of neurons and nervous systems. A neuron’s spiking response to a stimulus depends not only on the stimulus, but also on its own spiking history (Benda & Herz, 2003; Benda et al., 2005, 2010), intrinsic plasticity (Paz et al., 2009; Monk et al., 2016; Shim et al., 2018; Monk et al., 2018), and ion channel distribution (Lörincz et al., 2002; Hossain et al., 2005; Zhuchkova et al., 2013) for example. That relationship is also affected by the spiking of other neurons, and therefore neural diversity, network structure, synaptic weights, feedback, inhibition, and countless other factors (Maass et al., 2002; Buonomano & Maass, 2009; Moroz & Romanova, 2022). The relationship between a neuron’s spiking and animal behavior is also obscured for the same reasons. One way to sidestep this complexity is to observe that APs are not unique to neurons. Many nonneural organisms transduce stimuli into APs that directly affect their behavior. So we can study the ecological and computational purposes of APs in simpler organisms with simpler behaviors, without a nervous system complicating our observations.

Figure 1 shows that biological cells throughout all domains of life exhibit transient pulses in their membrane potentials, often in response to stimuli. Figure 1A presents a phylogenetic tree from the Interactive Tree of Life with LUCA at its root. To see individual species’ names in the tree, visit https://itol.embl.de (a fantastic website) or view this paper online. We colored the major domains of life as indicated by the legend below panel A. In particular, the pink section of the circle is the animal kingdom. Figure 1B displays the major clades of animals, including those that develop nervous systems (gray-shaded background) and those that do not (white background) (Kristan, 2016; Moroz & Romanova, 2022). The specific orders and times of branching in either tree do not matter for our purposes. The colored and numbered triangles in panels A and B mark some known lineages that use cellular membrane potentials to electrically signal given particular environmental conditions. The disparity of these lineages, from bacteria to chickens, strongly suggests that cellular electrical signaling is as old as cells themselves (Wan & Jékely, 2021; Burkhardt & Jékely, 2021).

Figure 1C shows 10 intra- or extracellular recordings of membrane potentials recorded from the lineages marked by triangles in panels A and B. The numbers next to each trace correspond to the numbers in the triangles. We intentionally omit the time and voltage axes of each trace to highlight their similarities. Traces 1 and 7 are extracellular recordings from neuron-less animals given electrical stimuli (Leys & Mackie, 1997; Romanova, Smirnov, et al., 2020). Trace 2 is an intracellular recording from a filamentous fungus (Olsson & Hansson, 1995). Trace 3 is from an auditory nerve fiber in a chicken (Oline et al., 2016). Trace 4 is an intracellular recording from an alga in salty artificial pond water (Kisnieriene et al., 2019). Trace 5 is an extracellular recording from a rhythmic potential neuron in a jellyfish (Dupre & Yuste, 2017). Traces 6 and 10 are inverse fluorescences of dyes in bacterial cells whose brightnesses are inversely related to membrane potentials (Prindle et al., 2015; Jin et al., 2023). Trace 6 is the (inverse) collective brightnesses of all bacterial cells at the periphery of a biofilm (Prindle et al., 2015), and trace 10 is the (inverse) brightness of dye in a single bacterial cell (Jin et al., 2023). Trace 8 is an intracellular recording from an Opalina protozoan after transferring it to a new medium (Nakatani, 1972). Trace 9 is a whole-cell patch clamp of a giant antennal mechanosensory descending neuron in Drosophila (Mu et al., 2014). An untrained eye could mistake some of these nonneural spike trains as neural APs and vice versa, especially when we omit timescale information. Maybe neural APs are just one variant of the ancient and pervasive practice of cellular electrical signaling.

Some of the nonneural APs in Figure 1C have simple and direct interpretations. For example, sponges periodically pause their water pumping under adverse conditions, e.g., when their pores get clogged by sediment in the water (Grant et al., 2018). Each individual glass sponge AP (trace 1, panel C) pauses the sponge’s pumping in some part of its body for some period of time (Leys & Mackie, 1997; Leys et al., 1999; Leys & Anderson, 2015). The biological processes behind this signal transduction and its resultant effect on behavior are complex and fascinating. Yet from a signal processing or computational perspective, these sponge APs are trivial to interpret. Each individual AP represents the sponge’s detection of adverse pumping conditions at that time (e.g., a clog), so it pauses pumping for awhile. There is no need to debate whether or how glass sponges encode sediment stimulus information in a spike train (because they don’t). Nor do we need to debate whether the sponge’s individual APs are relevant to behavior (because they are). Of course, neural APs are not so easy to interpret. They have some different properties with respect to nonneural APs, presumably because they are specialized for different sensory and decision-making tasks. But by specifying what those different properties are and inferring how those tasks are different, we gain valuable context to interpret neural APs as signaling and decision-making elements. Maybe neural and nonneural electrical signaling are not fundamentally disparate phenomena. Instead, maybe they are conceptually analogous, but with some different properties to address different selection pressures. If so, then we could offer a parsimonious framework to interpret both neural and nonneural electrical signaling while accounting for those different properties.

We review examples of nonneural electrical signaling from five domains of life typically neglected by neuroscience: bacteria, protozoans, plants, fungi, and neuron-less animals. This is the first comparative review of electrical signaling across all of those domains. Our definition of electrical signaling is a stimulus-induced change in a cell’s membrane potential, either via a net flow of ionic charge across the membrane or the release of ions from intracellular stores.¹ Where applicable, we report the signal’s amplitude, frequency, duration, refractory period, and ionic basis. We pay particular attention to the ecological relevance of the electrical signal and the behavioral response that it actuates. We compare properties of neural and nonneural electrical signals and offer a parsimonious computational interpretation of cellular stimulus transductions. We infer selection pressures that neural APs satisfy and identify neural computation hypotheses from the literature that are consistent with those pressures. Those hypotheses each imply that the electrophysiology of a neuron’s membrane is related to the spiking statistics of its inputs. Nervous systems are not necessary for organisms to sense their surroundings, make decisions, or electrically signal. All living things perform these tasks, and the vast majority of them do not have a nervous system (Moroz et al., 2021). Nervous systems just seem specialized to accomplish these tasks under evolutionary pressures that could be unique to higher animals.

Like all living organisms, bacterial cells maintain a membrane potential and use it as a source of free energy to do chemical and mechanical work (Krasnopeeva et al., 2019; Jin et al., 2023; Bavaharan & Skilbeck, 2022). Examples of that work include pH regulation, membrane transport, flagellar motion, irradiance resistance, antibiotic resistance, forming a colony, and cell reproduction (Benarroch & Asally, 2020; Sirec et al., 2019; Blee et al., 2020; Masi et al., 2015; Miller & Koshland, 1980; Ng & Bassler, 2009; Yang et al., 2020). Once thought to be static, bacterial membrane potentials are dynamic (Kralj et al., 2011; Yang et al., 2022), tightly regulated (Benarroch & Asally, 2020), and energetically expensive to maintain (Stratford et al., 2019). Both bacteria and archaea possess genes that express a surprisingly wide variety of ligand- and voltage-gated ion channels (Jones & Larkin, 2021; Martinac et al., 2008, 2013) permeable to sodium (Ren et al., 2001), potassium (Akabuogu et al., 2022), calcium (Nava et al., 2020), and chloride (Iyer et al., 2002). In principle, all bacteria could use these familiar channels and ions to transduce stimuli and communicate with each other (Reguera, 2011). This section reviews examples of bacterial communicative electrical signaling in Bacillus subtilis colonies and transductive electrical signaling in individual Escherichia coli cells.

Due to their small size, bacteria are very difficult to patch clamp (Martinac et al., 2013). So instead of electrophysiological recordings, we present the fluorescences of intracellular dyes whose luminance depends on bacterial membrane potentials (Vassae & Culling, 1959).

Many species of bacteria can form sticky, sessile colonies called biofilms on wet surfaces (Liu et al., 2015). Figure 2A shows an example biofilm comprising millions of cells from the species B. subtilis. The spatial organization, signaling, and behavior of biofilms are complex (Waters & Bassler, 2005; Ben-Jacob, 2009; Larkin et al., 2018; Masi et al., 2015), and they have even been proposed as precursors to eukaryotic tissues (Costerton et al., 1995). For example, Figure 2A shows channels in a B. subtilis biofilm that presumably facilitate efficient transport of substances. Biofilms can help bacteria survive adverse environmental conditions such as nutrient scarcity (Costerton et al., 1999) or antibiotic presence (Shrout et al., 2011). But they also introduce competitive pressures for their constituent cells. Peripheral cells are exposed to the environment, so they are more susceptible to dangers (e.g., changes in pH, predation, or antibiotics) but enjoy first access to nutrients. Interior cells are more protected from environmental dangers, but can be starved if peripheral cells consume too many nutrients. Biofilms are simultaneously pressured to grow while ensuring the survival of interior cells.

Biofilms address these conflicting pressures by periodically pausing their growth (Prindle et al., 2015; Martinez-Corral et al., 2019; Liu et al., 2015; Nunes-Alves, 2015; Liu et al., 2017; Humphries et al., 2017; Beagle & Lockless, 2015; Bavaharan & Skilbeck, 2022; Liu et al., 2015). Bacterial membrane potentials govern these periodic pauses in B. subtilis biofilms (Prindle et al., 2015). B. subtilis (and most microorganisms) combines glutamate and ammonium to produce glutamine (Gunka & Commichau, 2012), which serves as a nitrogen source and an amino acid for protein synthesis (Satomura et al., 2005). B. subtilis imports glutamate with pumps that depend on the membrane potential for free energy (Martinez-Corral et al., 2019). As the cell depolarizes, glutamate entry into the cell is reduced, and vice versa. When an interior cell experiences metabolic stress, it releases intracellular potassium ions into its local environment (Prindle et al., 2015; Nunes-Alves, 2015; Lee et al., 2017). This extracellular potassium depolarizes its neighbors (see equation S18 in Martinez-Corral et al., 2019), which in turn reduces their ability to uptake glutamate (Bavaharan & Skilbeck, 2022). So those neighbors experience metabolic stress, release their own stores of potassium ions, and a potassium wave is propagated from the interior cells to the peripheral cells (Prindle et al., 2015). When the peripheral cells reduce their glutamate uptake, the biofilm’s growth is temporarily paused, and more glutamate becomes available to the starving interior cells. The potassium wave then dissipates into the medium (Humphries et al., 2017; Liu et al., 2017) or is pumped back into cells to replenish their potassium reserves (Prindle, 2023). Biofilm growth resumes until the cycle repeats.

Figure 2B shows how the membrane potentials of the biofilm’s peripheral cells oscillate in time (Prindle et al., 2015). Specifically, it shows the brightness of a fluorescent dye called thioflavin T (ThT) (Vassae & Culling, 1959) in arbitrary units (a.u., $y$-axis label). ThT fluorescence is inversely related to membrane potential (Lee et al., 2019; Liu et al., 2017; Prindle et al., 2015), so spikes in ThT fluorescence correspond to periods of hyperpolarization for peripheral cells. Therefore spikes in ThT fluorescence indicate periods of metabolic stress, since releasing intracellular potassium under nutrient scarcity hyperpolarizes the membrane potential. The thick cyan trace is the mean of 30 individual measurements (thin gray traces; see Figure 2B). Hyperpolarization periods (i.e. periods of metabolic stress) appear to endure for one to two hours.

Figure 2C shows oscillations of cells’ membrane potentials across the entire B. subtilis biofilm via ThT fluorescence (Prindle et al., 2015). These pictures are representative images taken from over 75 different and independent biofilms. The small square in the center is a cell trap. From left to right, Figure 2C shows cyclical potassium waves starting in the biofilm’s interior and spreading to peripheral cells. Notice that all peripheral cells fluoresce at approximately the same time and that fluorescence does not appear to degrade with distance. These observations suggest that the potassium signal is actively propagated through the biofilm (and not passively diffused), and the timing of its arrival to peripheral cells is synchronized. Active propagation of the potassium wave was confirmed in further experiments that investigated the fluorescence of a chemical dye that measures extracellular potassium concentration (Prindle et al., 2015). Notice also that the biofilm grows in size from left to right in Figure 2C. B. subtilis cells actively propagate an electrical signal in biofilms to indicate their metabolic state and influence the metabolism of their neighbors.

Potassium-mediated electrical signals in B. subtilis biofilms extend beyond its peripheral cells and into its medium (Humphries et al., 2017; Liu et al., 2017). Therefore two or more independent biofilms can alternate their growth periods when nutrients are particularly scarce (Liu et al., 2017). Potassium signals can also alter the membrane potentials of distant motile cells and direct their swimming behavior (Humphries et al., 2017; Lee et al., 2017). Figure 2D shows motile (i.e., free-swimming) B. subtilis cells that were attracted to a biofilm’s periphery by the potassium waves it generated (Humphries et al., 2017). Motile cells (and not biofilm cells) expressed a fluorescent protein called mKate2 (pseudocolored in red), while peripheral biofilm cells again contained ThT (cyan). The left plot in Figure 2E compares the fluorescence (in a.u.) of motile B. subtilis cells (red, left $y$-axis) with ThT fluorescence of peripheral cells in the biofilm (cyan, right $y$-axis). During periods of hyperpolarization, the density of motile cells increases, and vice versa. The mechanism of attraction and repulsion is that extracellular potassium waves change the membrane potential of motile cells, which in turn affects their tumbling frequency. The swimming paths of motile bacteria are realizations of biased random walks up a potassium gradient while the biofilm is electrically active. This electrically mediated attraction also applies to evolutionarily distant species. The right plot in Figure 2E compares the fluorescence of motile P. aeruginosa cells (magenta, left $y$-axis) with ThT fluorescence of B. subtilis peripheral biofilm cells (cyan, right $y$-axis). Again, we see that periods of hyperpolarization in the B. subtilis biofilm attract motile P. aeruginosa cells that could then be incorporated into the biofilm. B. subtilis and P. aeruginosa probably diverged over 2 billion years ago (Feng et al., 1997), so similar electrical signaling strategies could be widespread in bacteria.

Bacteria do not need to form colonies to generate electrical signals.

Figure 3A shows brief, spontaneous flashes of fluorescence from a membrane potential sensor in a single E. coli cell (Jin et al., 2023). Yellow dots measure the change in fluorescence (relative to absolute fluorescence) in 1 second intervals, and the cyan line fits the raw data. Like ThT, this sensor’s fluorescence is inversely related to a cell’s membrane potential, so these flashes indicate hyperpolarizing “spikes.” These spikes have a duration of a few seconds and are caused by a rapid, transient efflux of cytoplasmic potassium. Their presence and frequency depend strongly on the type of salt in the bacteria’s medium (Jin et al., 2023). They could signal the bacteria’s metabolic state, which apparently regulates ion flux across the membrane. They also enhance E. coli’s efflux activity, which could improve its antibiotic tolerance (Jin et al., 2023)—or not (Lee et al., 2019).

Figure 3B shows typical E. coli hyperpolarization spikes measured in 100 ms intervals (Jin et al., 2023). Again, yellow dots represent raw fluorescence data, and the cyan trace fits those dots. Notice that the amplitudes and durations of the spikes can differ, even in the same cell. They are also heterogeneous between cells (Jin et al., 2023). These spikes do not exhibit the all-or-nothing hallmark of neural APs. But they do show that single bacteria are capable of producing transient electrical signals, with cations common to neurons, that depend on their environment.

Figure 3C shows that individual E. coli can also quickly depolarize their membrane potentials (Bruni et al., 2017), as reported elsewhere (Kralj et al., 2011; Jin et al., 2023). Red traces show fluorescence changes (relative to absolute fluorescence) of the PROPS voltage sensor for a single E. coli cell. Blue traces show simultaneous fluorescence changes in GCaMP6f, a genetically encoded calcium sensor. Collectively, these traces show that rapid membrane potential depolarizations (on the order of seconds) can be followed by calcium influx into a single bacterial cell (Bruni et al., 2017). Figure 3D shows that those depolarizations and calcium influx are the cell’s response to mechanical contact, specifically being squeezed under an aragose pad (Bruni et al., 2017). Mechanosensation is an important ecological stimulus for bacteria, as mechanical pressure and shear forces are potential triggers for motile cells to adhere to surfaces (Dufrêne & Persat, 2020; Koch et al., 2022; Sawers, 2021; Masi et al., 2015; Vrabioiu & Berg, 2022). Current evidence strongly suggests that E. coli uses calcium as a second messenger to affect its behavior in response to mechanical stimuli. More broadly, calcium regulates many more bacterial processes than mechanosensation and in many more bacterial species than E. coli (Jones & Larkin, 2021; King et al., 2020; Luder et al., 2021; Iyer et al., 2002; Nava et al., 2020). Neural learning and memory are reportedly facilitated by depolarization (i.e., an AP), subsequent calcium influx, and ensuing morphological or functional changes (e.g., synaptic weights change). That core blueprint is as old as bacteria.

Over a century ago, many prominent protozoologists suggested that unicellular eukaryotes (e.g., protozoans) could inform our understanding of nervous systems in higher lineages (Doughty & Dryl, 1981). Articles about Paramecium sensing, learning, and behavior were published in neurology and psychology journals (Jennings, 1908, 1899; Smith, 1908). Some researchers from that era even believed that protozoans must possess a tiny neuromotor system (Taylor, 1920; Sharp, 1914; Yocom, 1918; Rees, 1922; Parker, 1929). While that belief is untrue, we can acknowledge its appeal by observing the rich repertoire of protozoan sensory and social behaviors (Jennings, 1904b, 1939, 1940; Byrne & Byrne, 1978). Protozoans are equipped with a deeper arsenal of ion channels, mitochondria, cilia/pseudopodia, endomembranes, and often a larger size than prokaryotic bacteria and archaea (Wan & Jékely, 2021). The complexity, speed, and accuracy of protozoan electrical signaling and behavior vastly outperform those of prokaryotes (Wan & Jékely, 2021). APs are rare in bacteria but prevalent in protozoans, often in association with their sensorimotor cilia (Brunet & Arendt, 2016). So protozoans can quickly detect stimuli and react to them by temporarily changing their swimming behavior. We review two examples of this phenomenon in ciliate protozoans: light avoidance in Stentor coeruleus and mechanoreception in the genus Paramecium.

Figure 4A depicts a typical Stentor specimen anchored by its holdfast (lower-left corner, panel A) to feed. Anchored Stentor cells can reach 2 mm in length and are deeply pigmented, so they are visible to the naked eye (Song, 1999; Reiff & Marshall, 2015). Its size, regenerative capabilities, and range of behaviors have attracted the attention of developmental biologists for over a century (Morgan, 1901; Mast, 1906; Jennings, 1904b). Stentor can select food, recoil, avoid light, and even habituate to repetitive stimuli (Fabczak, 2000; Wood, 1973, 1977, 1982, 1988, 1970; Rajan et al., 2023). Figure 4B is a close-up of Stentor’s anterior end with its two cilia types (Stentor is a heterotrich, i.e., “mixed hair”) and pigmentation pattern visible. One cilia type circumscribes their anterior end and beats synchronously to feed and/or swim (Wood, 2001). The other cilia type forms rows down the entire length of the cell (Wood, 2001). Figure 4B shows these cilia rows (lighter stripes) alternating with blue-green stripes down the cell (Reiff & Marshall, 2015; Sobierajska et al., 2006; Iwatsuki & Yumi, 1991; Prusti et al., 1984). Those blue-green stripes contain stentorin, a pigment molecule unique to this genus (Song, 1999; Song et al., 1980a; Kim et al., 1984; Tao et al., 1993; Fabczak, 2000; Iwatsuki & Song, 1985; Wood, 1976; Møller, 1962). Stentorin contains hypericin, a chromophore that makes Stentor photosensitive (Kim et al., 1984; Iwatsuki & Yumi, 1991; Walker et al., 1979; Song et al., 1980b; Tao, 1994; Prusti et al., 1984; Häder & Häder, 1991; Prusti, 1987).

Figure 4C illustrates one type of photosensitivity in Stentor (Song, 1999). The cell typically swims with speed of about 250 $μ$m/s in a reasonably straight line (top arrow, panel C), rotating slowly about its anterior-posterior axis (Reiff & Marshall, 2015; Song, 1981; Fabczak et al., 1994). When it enters an illuminated region (yellow circle, panel C), the cilia abruptly stop beating with a delay between 100 and 500 ms (exclamation points, panel C), depending on the light intensity (Song et al., 1980b; Fabczak et al., 1993; Fabczak, 2000; Wood, 1976). Viscous drag then stops the cell (Wood, 2001), and it can wait for another 200 ms (Song et al., 1980b). If the light intensity is not particularly high, the cell can proceed swimming forward (Wood, 2001; Song et al., 1980b). But if the light intensity is high, then the power stroke of cilia rows reverses, anterior cilia point ahead, and the cell swims backward, reorients, and swims forward in a new direction (curved arrow, panel C; Prusti et al., 1984; Song et al., 1980b; Sobierajska et al., 2006; Wood, 2001; Fabczak, 2000). This photophobic response takes between 1 and 2 seconds. If the light is laterally incident on the cell, then the cell orients and swims away from the light source (i.e., negative phototaxis) (Song et al., 1980a; Song, 1981; Prusti, 1987; Kim et al., 1984; Fabczak, 2000; Sobierajska et al., 2006). Stentor avoids intense light because stentorin is a photodynamic sensitizer, that is, light oxidizes critical cell components and kills it (Prusti, 1987; Häder & Häder, 1991; Song, 1981). It seems paradoxical that the pigment Stentor uses to sense light is itself phototoxic. Perhaps stentorin serves some other useful purpose besides its photosensing capability, for example, screening ultraviolet light (Wood, 2001), generating ATP (Prusti, 1987), or deterring predation with its toxicity (Fabczak, 2000).

Figures 4D to 4F are strong evidence that the membrane potential of a Stentor cell controls its photophobic response (Wood, 2001). Each panel reports intracellular electrode recordings from individual Stentor cells. Panel D shows that Stentor transduces light into membrane potential depolarization with a delay of a few hundred milliseconds (Fabczak et al., 1993). The resting potential of Stentor is typically between $-$45 and $-$60 mV (see Figures 4D to 4F) (Song, 1999; Fabczak et al., 1993; Song, 1981; Wood, 1982) and is established primarily by a potassium concentration gradient (Fabczak, 2000; Prusti et al., 1984; Kim et al., 1984; Fabczak, 1983; Wood, 1982) When it absorbs light (yellow shaded area, panel D), stentorin dissociates free protons to the cytoplasm that depolarize the membrane potential (Fabczak, 2000; Wood, 1976; Kim et al., 1984; Sobierajska et al., 2006; Walker et al., 1981; Häder & Häder, 1991; Song, 1981; Song et al., 1981). Therefore, the photosensitivity of Stentor is sensitive to changes in pH (Prusti et al., 1984; Song, 1981; Walker et al., 1981). Detailed chemical characterizations of stentorin’s proton dissociation are available (Tao, 1994; Song, 1981; Song et al., 1981). Figure 4D suggests that the amplitude and duration of the photoreceptor potential depend on the intensity of light incident on Stentor (Fabczak et al., 1993). If the photoreceptor potential exceeds a threshold about 15 mV above rest (Fabczak et al., 1993; Wood, 1982), then Stentor generates an AP (peach trace, panel D). A sufficiently strong pH gradient either directly or indirectly opens calcium channels in the membrane, and calcium influx forms the depolarization phase of the AP (Song, 1999; Song et al., 1981; Song, 1981; Kim et al., 1984; Prusti et al., 1984; Prusti, 1987; Tao, 1994). A high intracellular calcium concentration then closes calcium channels, opens potassium channels, and potassium efflux repolarizes the cell (Wood, 1982; Kim et al., 1984; Prusti et al., 1984; Prusti, 1987; Koprowski et al., 1997). The cell does not appear to hyperpolarize after the AP (Wood, 1982; Tao, 1994) but instead can remain depolarized for an extended period of time (Fabczak et al., 1993). The refractory period of the AP probably depends on the duration of this afterdepolarization, but is reported to be 1 to 3 seconds (Song et al., 1980b; Song, 1981).

Figure 4E suggests a relationship between the irradiance of a light stimulus and the duration of the post-AP depolarization period (Fabczak et al., 1993). The shaded yellow area in panel E indicates when a Stentor cell (the same cell for all traces) was stimulated by white light but at four different irradiances (see the caption). We vertically offset the traces in panel E to aid visibility, but the resting potential for all traces was $-$55 mV. Figure 4E shows that the amplitudes and durations of this Stentor AP is around 42 mV (⁠$y$-axis values, panel E) and 0.5 s respectively (see Wood, 2001), and both quantities appear insensitive to the irradiance of light incident on the cell. But the latency of the AP with respect to stimulus onset noticeably reduces as irradiance increases (Fabczak et al., 1993). The duration of post-AP depolarization also increases as irradiance increases (Fabczak et al., 1993). Figures 4F reports analogous results to panel E, but the duration of the light stimulus varied instead of its irradiance (legend, shaded yellow areas, panel F; Fabczak et al., 1993). The cyan and orange numbers on the $y$-axis of panel F indicate the amplitudes of those two respective APs. Again, the post-AP depolarization period was significantly longer as the stimulus duration increased. The durations and latencies of the APs appeared unaffected by stimulus duration (Fabczak et al., 1993).

The timing of an AP and changes in swimming behavior are tightly correlated in Stentor and almost certainly causal (Fabczak et al., 1993; Fabczak, 2000). Ciliary beating in Stentor (and other ciliates) depends on its membrane potential (Tao, 1994), and particularly the calcium concentration inside the cell (Song, 1999). Cilia (and flagella) have cytoskeletons called axonemes that allow them to flex (Song, 1981). Calcium in a Stentor cell probably binds to calmodulin, which then binds to axonemes, changes their physical structure, and ultimately reverses their power stroke (Wood, 2001; Song, 1999). Since calcium influx forms the AP depolarization phase and reverses ciliary power strokes, it is unsurprising that Stentor’s stop response to light is so tightly correlated with the timing of its AP. It is also unsurprising that disrupting calcium concentrations or blocking calcium channels inhibits or abolishes Stentor’s photosensitive response (Prusti, 1987). Interestingly, the duration of the post-AP depolarization (Figures 4E and 4F) is correlated with how much time Stentor spends swimming backward (Fabczak et al., 1993). The specific mechanisms by which calcium affects ciliary beating in Stentor are still open research topics, but are probably analogous to those of more thoroughly studied ciliates like Paramecium (Song, 1981; Eckert, 1972a).

Paramecium could be the most-studied unicellular organism in the literature (Wichterman, 1986; Görtz, 1988). Its diverse repertoire of behaviors has drawn the attention of biologists since at least the late 19th century (Jennings, 1897). Paramecium exhibits chemotaxis (Van Houten, 1978), gravitaxis (Roberts, 2010), phototaxis (Matsuoka & Nakaoka, 1988), temperature sensitivity (Nakaoka & Oosawa, 1977), and social behaviors (Jennings, 1897), as recently reviewed by Brette (2021).

Figure 5A (left) is a scanning electron microscopy image of a Paramecium caudatum specimen (Ishida et al., 2023). Paramecium cells vary in size from 50 to 300 $μ$m, depending on the species in the genus (Fokin, 2010). Their bodies are covered with around 4000 cilia that metachronously beat to propel them through the water (Valentine et al., 2023). Figure 5A (right) is a blown-up image of the cilia from the box in the left image (Ishida et al., 2023). Many of the cell’s observed behaviors are primarily changes in the beating of these cilia given certain stimuli, and by extension changes in their swimming behavior. Here we review two ways that Paramecium transduces mechanical stimuli to change its ciliary beating, depending on where its membrane is touched.

Figure 5B is a schematic of obstacle avoidance by a Paramecium cell. Paramecium typically swims forward at about 1 mm/s in a tight spiral (red arrow, panel B), tumbling slowly about its anterior-posterior axis (Brette, 2021; Elices et al., 2023). When it bumps (exclamation marks, panel B) into an obstacle (pink square) or encounters undesirable chemicals, it abruptly changes its swimming behavior. Similarly to Stentor, the cell briefly swims backward (black arrow, panel B), tumbles to reorient itself, then resumes swimming forward (green arrow), perhaps avoiding the obstacle with its new swimming direction (Jennings, 1904a). This behavior is effectively a trial-and-error strategy that allows Paramecium to navigate complex environments (Jennings, 1931; Brette, 2021). This change in swimming behavior appears to depend on how hard the cell bumps into the obstacle, that is, the strength of the stimulus. If Paramecium bumps into an obstacle that provides some cushion (e.g., fibrous material), then the cell’s reaction might be different. It can enter a feeding mode where it stops swimming, but its oral cilia become more active (Jennings, 1897). Figure 5C is another schematic of a different mechanosensitive ability in Paramecium. When the posterior end of the cell is bumped (exclamation marks, panel C), for example, by a potential amoeba predator, its swimming velocity temporarily increases to escape possible danger (Roesle, 1902; Jennings, 1904a). Remarkably, this single cell disambiguates stimuli on its anterior and posterior end and exhibits different behaviors accordingly.

Figure 5D shows that Paramecium disambiguates anterior and posterior stimuli with its membrane potential, as beautifully illustrated by Naitoh and Eckert (1969). Single Paramecium caudatum cells were immobilized in solutions rich in potassium and calcium ions. The resting potential of Paramecium cells is usually between $-$30 and $-$20 mV (Naitoh & Eckert, 1968; Elices et al., 2023), established primarily by a strong potassium concentration gradient (Naitoh & Eckert, 1969; Brette, 2021). A recording electrode was inserted, and the cell was mechanically stimulated by a crystal-driven glass stylus that indented its membrane on its anterior or posterior end. When the anterior end was indented, the cell depolarized (blue traces, panel D). But when the posterior end was indented, it hyperpolarized (yellow traces, panel D). This hyperpolarization is also accompanied by a contraction of the posterior pole (Nakaoka & Iwatsuki, 1992). The time courses and amplitudes of the membrane potential depended not only on where the stimulus occurred on the cell, but also the strength of the stimulus (solid and dashed traces, panel D; Naitoh & Eckert, 1968, 1969). Notice that the posterior voltage traces are less sensitive to stimulus strength than the anterior voltage traces are. This observation suggests that the posterior end of the cell is more sensitive to weak stimuli because its maximum response amplitude is achieved at lower stimulus intensities (Naitoh & Eckert, 1969). These results are independent of the recording electrode’s position in Paramecium (Naitoh & Eckert, 1969) because the cell is isopotential (Eckert & Naitoh, 1970; Dunlap, 1977; Satow & Kung, 1979). Similar results were reported with current injection stimuli instead of mechanical perturbations (Eckert, 1972b).

Figure 5D also shows that Paramecium can generate an AP when mechanically stimulated with sufficient intensity on its anterior end (blue solid trace). The amplitude and half-height duration of this AP are around 40 mV and 40 ms, respectively (Naitoh & Eckert, 1969). A more recent study suggests a similar amplitude value but a shorter half-height duration of less than 10 ms (Elices et al., 2023). APs and passively conducted electrical signals spread at a speed of around 10 cm/s in the cell (Eckert & Naitoh, 1970). The generation of the AP involves voltage-gated (L-type) calcium channels present on the cilia and delayed rectifier potassium channels located in the somatic membrane (Eckert, 1972b; Machemer & Ogura, 1979). Upon a voltage step, the cell experiences a rapid influx of calcium ions and a slower efflux of potassium ions (Saimi & Kung, 1987; Brette, 2021). The calcium influx (and not the increase in voltage) quickly inactivates calcium channels within a few milliseconds (Brehm & Eckert, 1978; Eckert & Brehm, 1979; Brehm et al., 1980; Eckert & Chad, 1984). That calcium-dependent calcium inactivation typically lasts between a few tens to a hundred milliseconds (Naitoh et al., 1972; Brehm et al., 1980) and is commonly observed in neurons (Brette, 2021). The potassium current is also voltage-gated and acts as a delayed rectifier, activating within a few milliseconds and inactivating within seconds (Eckert & Brehm, 1979; Satow & Kung, 1980; Saimi et al., 1983).

Figure 5E illustrates the ionic basis of the mechanoreceptor potential in Paramecium tetraurelia (Satow et al., 1983). To isolate the cell’s mechanoreceptor potential from other currents, the traces in panel E were measured from pawn mutant cells that do not exhibit APs or voltage-gated calcium influx (Satow et al., 1983). Pawn mutants were immersed in a calcium solution with (right plot) or without (left plot) a potassium channel blocker (TEA$+$⁠). Pawn cell membranes were then indented with a glass stylus, analogous to the experiments in panel D. Comparing the two plots in panel E, we see that TEA$+$ almost abolishes hyperpolarization, strongly suggesting that hyperpolarization is caused by potassium efflux (Satow et al., 1983). Further experiments showed a high dependence of depolarization amplitudes on calcium concentration in the bath, implicating calcium as the principal depolarizing ion of the mechanoreceptor potential (not shown) (Satow et al., 1983). Figures 5D and 5E collectively suggest that mechanical stimulation causes a hyperpolarizing potassium efflux or a depolarizing calcium influx, depending on the anterior/posterior location of the stimulus. Overlapping spatial gradients of calcium and potassium channels in the membrane cause the mechanosensitive currents to gradually change from depolarizing to hyperpolarizing as we move down the anterior-posterior axis (Ogura & Machemer, 1980; Satow et al., 1983; Brette, 2021).

Figures 5F and 5G show that the swimming behavior of Paramecium depends on the cell’s membrane potential and internal calcium concentration. Panel F shows how the average beating frequency of cilia over five independent cells (pink trace, left $y$-axis) changes as a function of an external voltage applied via voltage clamp (blue trace, right $y$-axis; Machemer & Eckert, 1975). The holding potential was set to equal the resting potential of the cell, so the blue right $y$-axis is labeled with respect to the cell’s resting potential (i.e., 0 is the resting potential). When the membrane potential abruptly hyperpolarizes (at 0 s, panel F), the ciliary beating frequency noticeably increases within a fraction of a second (solid pink trace, panel F). The increase in beating frequency is probably caused by a calcium influx specifically activated by that hyperpolarization (Nakaoka & Iwatsuki, 1992; Preston et al., 1992). Then as the membrane potential increases, ciliary beating slows (solid pink trace, panel F) until a small depolarization was achieved by the voltage clamp (just after 3 s; Machemer & Eckert, 1975). Then the cilia reorient and reverse their beating direction with increasing speed as the membrane potential continues to rise (dashed pink trace; Machemer & Eckert, 1975). Presumably the depolarization opens voltage-gated calcium channels, and calcium influx causes the cilia to reorient (Naitoh et al., 1972; Naitoh, 1972). The exact depolarization threshold for cilia reorientation depends on the concentration of cyclic nucleotides (cAMP and cGMP) in the cell (Nakaoka & Machemer, 1990). When the voltage drops to rest (just before 6 s), the reversed ciliary beating slows, and the cilia switch back to their original orientation (Machemer, 1976). Figure 5G demonstrates a similar relationship between ciliary beating frequency, orientation, and the intracellular calcium concentration (Nakaoka et al., 1984). At low internal calcium concentrations, ciliary beating frequency gradually increases as the calcium concentration does (solid pink trace, panel G). Then at a critical calcium concentration level, the ciliary beating orientation reverses (dashed pink trace, panel G) and beats faster in reverse as the calcium concentration continues rising.

Figure 5 outlines how a Paramecium cell can transduce mechanical stimuli differently to initiate a particular reaction, depending on where the stimulus occurred on its membrane (Naitoh & Eckert, 1969). Most recently, these responses have been electrophysiologically modeled and coupled to a kinematic model of Paramecium (Elices et al., 2023). When a Paramecium cell bumps into an obstacle, its anterior membrane distorts. That distortion increases calcium permeability via a mechanosensitive channel, and calcium influx forms the depolarization phase of an AP. Analogous to Stentor, increasing the internal calcium concentration in Paramecium reverses the power stroke of its cilia (Naitoh et al., 1972; Naitoh, 1972). So the cell swims backward and tumbles until potassium efflux repolarizes the cell and calcium is buffered and/or pumped out (Brette, 2021; Machemer & Eckert, 1973). Then the cell resumes its forward swimming behavior, but in a new direction. This sequence of events forms the ionic basis of obstacle avoidance in Paramecium. But when the posterior end of the cell’s membrane is deformed, potassium efflux hyperpolarizes the membrane potential. This hyperpolarization induces a different calcium influx, which increases the beating frequency of cilia (see the solid pink trace, panel F, soon after 0 s), but is insufficient to change the direction of their power stroke. Potassium efflux is the ionic basis of the escape response of Paramecium. Nervous systems are not necessary for organisms to disambiguate stimuli and initiate different responses with high temporal precision. A single eukaryotic cell can accomplish these tasks and has probably been doing so at least since Paramecium branched from its ancestor approximately 600 million years ago (Long et al., 2023).

Most plants seem like passive organisms at the mercy of their environments. Instead, they are dynamic organisms capable of sensing and responding to a variety of stimuli. For example, plant roots require mechanosensation to grow in soils of different hardnesses (Nakagawa et al., 2007), grow around barriers (Fasano et al., 2002; Shih et al., 2014; Monshausen & Gilroy, 2009), and detect gravity (Haswell, 2007; Fasano et al., 2001) and even sound (Rodrigo-Moreno et al., 2017). They respond to nutrient, light, and chemical gradients not only by directing their growth but also by actively bending and turning themselves (Trewavas, 2005). Electrical signaling mediates many aspects of plant sensation. Perhaps the oldest recording of electrical signaling in a plant is from the carnivorous Venus flytrap (D. muscipula), published in 1873 (Burdon-Sanderson, 1873). Many other pioneering studies followed (Pickard, 1973), reporting voltage transients in fast-moving plants (Bose & Vines, 1914; Biedermann, 1898; Bose, 1907; Houwink, 1935; Sibaoka, 1953), sessile plants (Houwink, 1937; Montemartini, 1970; Auger, 1928; Umrath, 1959), and even algae (Osterhout & Harris, 1928; Blinks, 1930; Brooks, 1939; Gaffey & Mullins, 1958; Beilby & Coster, 1979). Today, the literature recognizes that many (if not all) plant species transduce different stimuli into different types of electrical signals. One category of plant electrical signals is APs, characterized by active propagation, an all-or-nothing response, and fast propagation speed between 2 mm/s and 20 cm/s, often in response to nondamaging stimuli (Hafke & van Bel, 2012; Pickard, 1973; Mousavi et al., 2013; Huber & Bauerle, 2016; Robinson & Draguhn, 2021; Sukhov et al., 2019; Gallé et al., 2015; Stahlberg et al., 2006; Mudrilov et al., 2021). Another category is variation potentials, characterized by signal attenuation, variable temporal waveforms, and slower propagation speed, often generated by damaging stimuli like cutting or burning (Hafke & van Bel, 2012; Pickard, 1973; Mousavi et al., 2013; Huber & Bauerle, 2016; Robinson & Draguhn, 2021; Sukhov et al., 2019; Gallé et al., 2015; Stahlberg et al., 2006; Mudrilov et al., 2021). Here we review examples of both signal categories in the two model plants Zea mays and Arabidopsis thaliana. Even sessile plants that do not demonstrate quick macroscopic movements coordinate responses to environmental changes with electrical signals.

Like all other multicellular plants, Z. Mays (i.e., maize, corn) has tissues that can conduct electrical signals to coordinate behaviors over distance (Hafke & van Bel, 2012; Canales et al., 2018; Pickard, 1973; Gallé et al., 2015; Fromm et al., 2013). The most prevalent example of a conductive tissue in higher plants (e.g. maize) is its phloem.

Figure 6A is a schematic of a vascular plant’s phloem (Robinson & Draguhn, 2021; Hedrich et al., 2016). The phloem is a chain of elongated cells called sieve elements (panel A). The phloem transports nutrients, hormones, RNA, and signals throughout the plant (Kalmbach & Helariutta, 2019). Transport is facilitated by sieve plates with pores that are permeable to ions and reduce resistance to mass flow (Bel et al., 2014; Hafke & van Bel, 2012; Gallé et al., 2015). The electrical properties of the phloem can be modeled as a cable (red circuit, Figure 6A) (Hedrich et al., 2016). This same model is also applied to electrically passive dendrites in cable theory (e.g. the ball-and-stick neuron; Tuckwell, 1988). The ions principally involved in current flow are potassium, chloride, and calcium (sodium is toxic to most plant cells; Bel, 2003; Volk & Franceschi, 2000; Lacombe et al., 2000; Fromm & Spanswick, 1993; Ward et al., 2009; Felle & Zimmermann, 2007; Vodeneev et al., 2015; Lautner et al., 2005). A proton gradient or another ion type (⁠$×$⁠, panel A) can also be included in this model. Figure 6B shows the concentrations of these ions in the sieve element cytoplasms from two maize leaves (Fromm & Bauer, 1994). One leaf was electrically stimulated with a 10 volt, 4 second pulse every minute for 30 minutes (red bars). The other was left alone as a control (blue bars). The dramatic change in ion concentrations strongly suggests that electrical stimulation affects voltage-gated ion channels in the phloem (Fromm & Bauer, 1994).

Figure 6C illustrates the ionic bases of electrical potential wave propagation in the phloem (Robinson & Draguhn, 2021). APs and variation potentials (VPs) are initiated and propagated by different mechanisms. For APs, a stimulus depolarizes the membrane potential of a sieve element by triggering calcium influx (top gray circles, red arrows, panel C). This influx can trigger the release of intracellular calcium stores in the endoplasmic reticulum (peach color, panel C) (Thiel et al., 2003; Hafke & van Bel, 2012; Sukhov et al., 2019; Huber & Bauerle, 2016; Reddy et al., 2011). Calcium influx activates chloride efflux and deactivates proton pumps, which forms the depolarization phase of the AP (Ward et al., 2009; Felle & Zimmermann, 2007; Mudrilov et al., 2021; Lunevsky et al., 1983). Voltage-gated potassium channels and proton pumps activate near the reversal potential of chloride ions, repolarizing the membrane potential (Thiel et al., 1997; Hafke & van Bel, 2012; Trebacz et al., 2006). The net effect of these ion fluxes is a depolarization wave accompanying a calcium wave through sieve elements or their neighboring parenchyma cells (PPC, Figure 6 panel C; Huber & Bauerle, 2016).

Higher plants elicit VPs in response to local damage (Vodeneev et al., 2015; Farmer et al., 2020; Sukhov et al., 2019; Gallé et al., 2015; Stahlberg & Cosgrove, 1996), for example, cutting maize root tips during growth (Meyer & Weisenseel, 1997) or herbivore grazing (Zimmermann et al., 2016). The exact mechanism that elicits and propagates VPs in the phloem (and xylem) is under debate (Hlavinka et al., 2012; Stahlberg et al., 2006; Sukhov et al., 2019; Malone et al., 1994; Vodeneev et al., 2015). One hypothesis is that damage increases water pressure, creating a hydraulic wave in a plant’s xylem (XV; see Figure 6C) (Robinson & Draguhn, 2021; Sukhov et al., 2019; Huber & Bauerle, 2016; Stahlberg & Cosgrove, 1997, 1996) that attenuates with distance from the source as the xylem leaks water (Stahlberg et al., 2006; Stahlberg & Cosgrove, 1997, 1996). Water flows through parenchyma cells (PPC, panel C) and companion cells (CC, panel C) into sieve elements, which activates mechanosensitive or ligand-gated calcium channels (H$2$O and Ca$2+$ channels, blue arrows, panel C). Again, calcium influx activates anion channels and inhibits proton pumps, leading to depolarization of the VP (Vodeneev et al., 2011; Stahlberg & Cosgrove, 1997, 1996). VP depolarization loses amplitude and gains lag with increasing distance from a wound due to attenuation of the hydraulic pressure wave (Stahlberg et al., 2006). The VP’s repolarization time course varies depending on the species and stimulus (Huber & Bauerle, 2016; Mudrilov et al., 2021; Sukhov et al., 2019; Vodeneev et al., 2015) and can even vary between applications of the same stimulus on the same plant (Vodeneev et al., 2011). In principle, this variation in waveform could allow higher plants to locate damage (Stahlberg et al., 2006) and modify its response depending on the cause (Bricchi et al., 2010).

Figure 6D demonstrates one ecological purpose of electrical signaling in maize phloem (Fromm & Fei, 1998). The red trace is a time series of the potential difference between two electrodes. One electrode was attached on the top surface of a mature leaf and the other on the shoot surface 10 to 20 cm away. The maize plant was watered just before the experiment, then experienced a 96 hour drought as indicated by the soil water content (cyan trace, panel D). Transient hyperpolarizations of approximate amplitude 50 mV and duration 30 min were observed on every change between dark (shaded areas, panel D) and light periods (white areas, panel D). For the first two days of drought, the potential difference gradually depolarized during dark periods and hyperpolarized during light periods. This rhythm and the hyperpolarization pulse amplitudes diminished as the drought progressed. After the plant was watered at 96 hours (vertical dashed trace, panel D), the electrodes measured an AP with approximate amplitude of 50 mV soon after, and soil water content returned to predrought levels. Figure 6D also plots changes in the CO$2$ concentration (green trace) and transpiration (i.e., exhalation of water vapor, blue trace) rates as measured on the same leaf with a porometer (Fromm & Fei, 1998). Unsurprisingly, both rates plummet during dark periods, but notice how both also depreciate by the fourth day of drought. The AP immediately precedes a recovery in both CO$2$ and transpiration rates when the drought ends (Serna, 2022). These measurements suggest that roots can detect the end of a drought and send an electrical signal to the leaves to reactivate photosynthesis.

Figure 6E shows these measurements in the half-hour after reirrigation (cyan shaded area, panel D; Fromm & Fei, 1998). The transpiration and CO$2$ uptake rates begin increasing about 10 and 15 minutes after watering, respectively. This low recovery latency suggests that slower signaling types, such as water ascent (Fromm & Fei, 1998) or chemical signaling (Huber & Bauerle, 2016), are too slow to mediate this response. Later experiments demonstrated that both a hydraulic and electrical signal are propagated independently in drought-stressed maize plants, and both affect gas exchange. Clever experimental design allowed Grams et al. (2007) to negate either the hydraulic or electrical signal to investigate their impacts on gas exchange rate independent of each other. Upon reirrigation, the hydraulic signal propagated through the xylem and appeared to increase the turgor of epidermal and guard cells, briefly closing the stomata (i.e., the leaf pores permitting gas exchange). Simultaneously, the electrical signal propagated through the phloem and triggered a prolonged increase in the gas exchange rates (Grams et al., 2007). Figures 6D and 6E and their follow-up experiments are strong evidence that electrical signaling conducted through the phloem plays a role in mediating photosynthetic processes in maize, depending on drought conditions. Analogous evidence has been demonstrated in other plant species (Huber et al., 2019; Kaiser & Grams, 2006; Lautner et al., 2005).

Figure 6F plots voltage responses of a maize leaf sieve element after stimulating the leaf with ice water (blue trace) or cutting off its tip (red trace) (Fromm et al., 2013). The former elicits an AP of approximate amplitude of 70 mV and propagation speed of 3 cm/s as measured 10 cm away from the stimulation site with an aphid stylet (Fromm et al., 2013). The latter elicits a VP exhibiting a brief depolarization followed by prolonged hyperpolarization and propagation speed of 0.5 cm/s (Fromm et al., 2013). Again, gas exchange rates were measured for a half-hour after applying the stimuli. The AP did not significantly affect CO$2$ uptake or transpiration during that time (not shown), though APs did inhibit phloem transport in the leaf away from the stimulation site. The VP halved both gas exchange rates after a half-hour (Fromm et al., 2013). Cutting the leaf tip generates a hydraulic wave in the whole leaf, which in turn creates ion flux in distant cells (recall Figure 6C). Once in the phloem, the resultant electrical signal can affect photosynthesis given the arrival of a damaging agent, even in cells distant from it.

Arabidopsis thaliana is a small flowering weed from the mustard family, native to western Eurasia. Historically considered useless (Curtis, 1777), Arabidopsis is now regarded as a fundamentally important model plant by the research community (Woodward & Bartel, 2018). It is easy, fast, and cheap to develop and experiment with them (Krämer, 2015). It is also conducive to genomic analysis due to its high rate of reproduction, self-fertility, and relatively small 132 Mbp genome (Arabidopsis Genome Initiative, 2000). It was the first flowering plant to have its entire genome sequenced (Arabidopsis Genome Initiative, 2000; Krämer, 2015), which is publicly available. These properties have spawned intense research interest in Arabidopsis, as it is the subject of twice as many publications as Drosophila this century (Woodward & Bartel, 2018). Some of these studies investigate how Arabidopsis transduces touch into electrical signals.

Figure 7A illustrates the importance of touch stimuli to plants (Chehab et al., 2008; Monshausen & Haswell, 2013). The left two plants in panel A show typical Arabidopsis plants after four weeks of development when left undisturbed (Chehab et al., 2012). The right two plants in panel A had their leaves gently moved back and forth two times per day over four weeks (Chehab et al., 2012). In the touch-stimulated plant, we observe stunted growth as measured by shorter flower stems, a smaller rosette radius, and delayed flowering. This response is termed thigmomorphogenesis (Jaffe, 1973), from the Greek thigma for touch. Arabidopsis presumably interprets daily mechanical movement of its leaves as wind. It responds by growing shorter stems, smaller leaves, strengthening their roots, reducing stomatal aperatures, and delaying flowering (Darwish et al., 2022). Figure 7B shows four knockout mutant plants subjected to the same experiment. These mutants lack a particular gene (allene oxide synthase, aos, panel B), so they cannot synthesize a key family of signaling hormones called jasmonates (Park et al., 2002). Among other roles (Acosta & Przybyl, 2019; Park et al., 2002), jasmonates mediate plant responses to both biotic (e.g., insect attack) and abiotic stresses (e.g., mechanical wounding, wind) (Devoto & Turner, 2003, 2005; Fonseca et al., 2009; Zhang et al., 2023; Lee & Seo, 2022). Panel B shows that Arabidopsis plants do not exhibit thigmomorphogenesis without jasmonate synthesis (Chehab et al., 2012).

Jasmonate synthesis is triggered by electrical signaling, at least in part (Farmer et al., 2020; Poretsky & Huffaker, 2022). Figure 7C shows a typical Arabidopsis rosette at 5 weeks old, with leaves numbered from oldest to youngest (Rufián et al., 2019). Only leaf 8 was wounded (W marks the wounded leaf in panel C), and surface electrodes on that leaf and others detected subsequent VPs (cyan-outlined boxes, panel C) (Mousavi et al., 2013). Panel D (top plot) shows those recorded VPs according to leaf number. The vertical cyan area marks the time that leaf 8 was wounded. The VPs look hyperpolarized when measured with surface electrodes, but intracellular recordings from aphid stylets show that they are depolarized signals (Mousavi et al., 2013; Kumari et al., 2019; Salvador-Recatalà et al., 2014). Panel D (bottom plot) shows one such intracellular recording from a separate but analogous experiment (Kumari et al., 2019), where leaf 8 was wounded with forceps (vertical cyan area, W), and an aphid stylet was in leaf 13. These depolarizing VPs can have amplitudes of approximately 70 mV latencies of tens of seconds after wounding, and durations of 1 to 3 minutes (Kumari et al., 2019; Salvador-Recatalà et al., 2014; Nguyen et al., 2018). They are propagated in the phloem and xylem via glutamate receptor-like channels (Nguyen et al., 2018; Poretsky & Huffaker, 2022; Jakšová et al., 2021) permeable to calcium (Meena et al., 2019). Within a minute, high cytosolic calcium levels are observed in the vasculature of the whole wounded leaf (Meena et al., 2019; Kiep et al., 2015) and other leaves connected by vasculature (Mousavi et al., 2013). Arabidopsis has enzymes called lipoxygenases that are activated by calcium and begin synthesis of jasmonates (Chehab et al., 2008; Chauvin et al., 2013; Gasperini et al., 2015; Farmer et al., 2020). The background colors of the number boxes in Figure 7C is a heat map of transcript levels for JAZ10, indicating jasmonate signaling levels (Mousavi et al., 2013). Darker shades of orange indicate high JAZ10 transcript levels (e.g., leaf 8, panel C), lighter shades indicate low transcript levels (e.g., leaf 11, panel C), and white indicates control transcript levels. Only leaves that share vascular connections with the wounded leaf show elevated JAZ10 expression levels (Mousavi et al., 2013). Proton pumps repolarize membrane potentials (Kumari et al., 2019), and calcium ATPases recover electrical excitability in case of a prolonged herbivore attack (Fotouhi et al., 2022).

Arabidopsis is also sensitive to gentler touches (Chehab et al., 2008; Howell et al., 2023; Paret, 2019). Figure 7E is a schematic of an electrophysiological experiment on an Arabidopsis leaf subjected to a nondamaging touch stimulus. Four dry (i.e., nonchloridized) silver electrodes were inserted into the main midrib of a single leaf (E1–E4, left panel E), and a fifth (E5, panel E) was inserted into the hypocotyl (i.e., the stem; Agosti, 2014). The leaf was gently stroked once in the middle of its blade, perpendicular to the rib, with a small number 8 painting pencil. The top plot in panel F plots the resultant potential difference between each (extracellular) electrode and a reference electrode inserted in the soil. The cyan-shaded area in panel F (top plot) indicates the time of the painting pencil touch stimulus. The electrodes detect an AP propagating past the first four electrodes (pink, green, orange, teal traces), but not reaching the fifth (red trace). Over 21 trials, its amplitude ranged from 27 to 45 mV, its duration ranged from 9 to 16 seconds, and its average propagation speed was 1.3 mm/s (Agosti, 2014). The blue arrow in panel F (top plot) shows that the AP’s amplitude increases with distance from the stimulus site, at least for leaf-tip-to-stem propagation (Agosti, 2014).

On some trials, those APs apparently reflected off the stem and traveled back up the rib toward the leaf tip. Figure 7E shows another experiment where only three silver electrodes were inserted into the midrib (E1–E3, bottom panel C) with a fourth in the hypocotyl (red E4, panel E) (Agosti, 2014). The lower plot in panel F is analogous to the top plot, but with four electrodes instead of five. Again, we see an AP with similar amplitude, duration, and speed traveling past the first three electrodes (but not the fourth). Again, the AP’s amplitude increases with distance from the stimulus site (green arrow, lower plot, panel F). But then a reflected AP traveling from stem to leaf tip, back toward the stimulus site, decreased in amplitude (red arrow, lower plot, panel F). Thus, the AP’s amplitude does not simply increase with distance propagated, but depends on acropetal or basipetal propagation (Agosti, 2014). The ecological utility of a reflected AP is unknown.

Mechanosensation is not restricted to Arabidopsis leaves. Broadly speaking, Arabidopsis transduces (internal or external) mechanical force into electrical signals via mechanosensitive ion channels (Basu & Haswell, 2017; Monshausen & Haswell, 2013; Fasano et al., 2002; Guerringue et al., 2018). These channels are present in Arabidopsis hypocotyl, leaves, and roots (Monshausen & Haswell, 2013; Haswell et al., 2008; Lewis & Spalding, 1998). Their presence suggests that the entire plant is mechanosensitive to some degree. Beyond Arabidopsis, all plant cells are probably able to sense and respond to externally or internally applied mechanical stimuli to some extent, as elegantly reviewed in Monshausen and Haswell (2013). Electrical signaling is central to translating those mechanical stimuli into behavioral responses throughout the plant kingdom.

Filamentous fungi are fascinating examples of complex, self-organizing systems (Adamatzky et al., 2023). They are a dynamic network of individual tubular cells called hyphae that collectively comprise a mycelium (Powers-Fletcher et al., 2016; Klein & Paschke, 2004). Hyphae can sense environmental stimuli and respond to them (Fischer & Glass, 2019; Bahn et al., 2007), leading to collective behavior of the whole mycelium (Adamatzky et al., 2021). Stimuli examples include light (Yu & Fischer, 2019; Carreras-Villaseñor et al., 2012), weight (Adamatzky et al., 2021), temperature (Xiao et al., 2022; Leach & Cowen, 2014; Zhang et al., 2016), gravity (Moore, 1991; Kern, 1999), electric fields (Lever et al., 1994; Brand & Gow, 2009), and chemicals (Turrà et al., 2016; Clark-Cotton et al., 2022). In particular, when a filamentous fungus finds a new food source, its mycelium thickens its cords, and the cytoplasm in it is actively transported in response (i.e., translocation; Klein & Paschke, 2004). Hyphae are also electrically active, as several disparate species pump protons through their tips, presumably to establish polarity (i.e., its growth axis; McGillviray & Gow, 1987; Gow, 1984). In addition to this steady electrical current, hyphae also generate calcium pulses as they extend their tips through the substrate (López-Franco et al., 1994; Takeshita et al., 2017; Nair et al., 2011; Smith, 1923), usually via turgor pressure (Roper & Seminara, 2019; Yafetto, 2018; Heaton et al., 2012; Lew et al., 2004; Bartnicki-Garcia et al., 2000)—but not always (Money & Harold, 1993). Therefore, we might expect to observe rich electrical behavior in filamentous fungi if we stick electrodes in them or fluoresce their calcium and stimulate them.

Figure 8A shows an electrode recording setup in the fruit bodies (i.e., above-ground hyphae that house spores; Maurice et al., 2021) of Pleurotus djamor, the pink oyster mushroom (Adamatzky, 2018). Three fruit bodies each had a pair of extracellular electrodes inserted in them, with a reference electrode in its cap and a recording electrode in its stem. The potential difference across the fruit body was recorded for two or three days, with no intentional stimulus applied to the mushroom (Adamatzky, 2018).

Figure 8B plots spontaneous electrical activity recorded by those three electrode pairs (green, black, and red traces) over approximately 14 hours (Adamatzky, 2018). We see a base potential slowly changing over a timescale of hours in each of the fruit bodies. On top of this slow drift of potential difference, we also observe trains of APs that lasted for hours. The insets in panel B are blow-ups of those trains. These insets exhibit some characteristics of neural spike trains, for example, periodic depolarizations above a baseline potential, slight overshoot of that baseline upon repolarization, and an apparent refractory period. Other characteristics differ; for example, spike amplitudes vary, the baseline potential varies (albeit slowly), and the timescale of these spikes is minutes instead of milliseconds (Adamatzky, 2018). These spike trains can be loosely grouped into high-frequency (averaging one spike per approximately 2.6 minutes see the upper-left black inset) or low-frequency categories (averaging one spike per approximately 14 minutes, for example, the black trace in the upper-right red inset; Adamatzky, 2018). Those categories exhibited refractory periods of 25 and 256 seconds for high- and low-frequency spike trains, respectively. AP amplitudes are typically 1–2 mV (measured extracellularly) with a standard deviation of 0.2 mV, and AP durations were about two minutes (Adamatzky, 2018). The very slow variations in base potential occur at a similar timescale as metabolite transport in other filamentous fungi (Tlalka et al., 2002; Adamatzky et al., 2023). Unfortunately there is no consensus on how to interpret the periodic, evenly spaced APs in the insets of Figure 8B.

Figure 8C shows electrical responses of the oyster fungus fruit bodies to various stimuli (Adamatzky, 2018). Fruit bodies were stimulated by applying 50 $μ$L of 40% ethanol, tapwater, and a silicone polymer on top of their caps. The vertical colored lines in panel C indicate the time that each stimulus was applied. Water prompted a spike of duration approximately 151 seconds, presumably due to a change in the capacitance of the stem. Ethanol prompted a smaller response of duration 51 seconds. The polymer did not elicit a noticeable response at all. Finally, one fruit body was burned at the edge of its cap with an open flame for 5 seconds; 103 seconds later, that fruit body registered a pulse that lasted 99 seconds. The inset of panel C shows simultaneous recordings from three fruit bodies (three $y$-axes and corresponding colored traces) near the time of thermal stimulation (Adamatzky, 2018). Interestingly, two unburned fruit bodies elicited signals a few minutes (peach and purple traces) before the burned fruit body did (teal trace; Adamatzky, 2018). This observation suggests that an electrical signal is propagated through the mycelium from damaged fruit bodies to undamaged ones, perhaps to expedite sporulation. We reviewed a similar effect in Arabidopsis leaves (see section 4.2).

Figure 8D shows a fungal electrical response to a nutrient source. Olsson and Hansson (1995) inserted an electrode into a single hypha of a wood decomposing fungus A. gallica (a.k.a. A. bulbosa), a honey mushroom (Yafetto, 2018). The resultant intracellular recordings demonstrated spontaneous (i.e., not intentionally stimulated) electrical signals resembling neural APs (Olsson & Hansson, 1995). The red trace at the upper-left of panel D is an example of those spontaneous APs. The baseline of the spikes remains relatively constant (at least on a seconds timescale), their duration is a fraction of a second, and they occur with a neurally plausible frequency of approximately 3 Hz. Then a small 5 mm$3$ block of beechwood was placed directly on the mycelium, 1–2 cm away from the electrode. When the wood was on the mycelium (green shaded areas, panel D), the spiking rate of the APs noticeably increased (orange bars, panel D). The green trace at the upper-right of panel D is an example of recorded APs when the wood was in contact with the mycelium. When the wood was absent (red shaded areas, panel D), the spiking rate declined back to its baseline of 3 Hz. A piece of perspex plastic of equal size and weight failed to elicit the same response, suggesting that the fungus was reacting to a new nutrient source (Olsson & Hansson, 1995).

Figure 8E depicts an analogous experiment to panels A to C, but in the wild instead of a laboratory (Fukasawa et al., 2023). Panel E shows four pairs of electrodes inserted into the stem and cap of four fruit bodies of Laccaria bicolor. The reference electrode is in the stem, and the recording electrode is in the cap. Two more pairs were inserted into two other fruit bodies 28 cm away (not shown). In addition to the electrodes, the temperature and precipitation were simultaneously recorded at a nearby meteorological station. Electrode recording began on September 30, 2021, a day before typhoon Mindulle caused precipitation at the recording site in eastern Japan (Fukasawa et al., 2023). Very little precipitation was reported for the 12 days prior to recording (Fukasawa et al., 2023).

Figure 8F shows the recordings from all six electrode pairs (thick colored traces), as well as temperature (thin red trace, red right $y$-axis) and precipitation (blue bars, blue right $y$-axis) data. The gray and yellow shaded areas indicate night and day, respectively. We see that the typhoon caused the temperature to drop during the day of October 1, and 32 mm of rain fell throughout the whole day (Fukasawa et al., 2023). One hundred minutes after the rainfall started, the electrodes in fruit bodies 2 (yellow trace) and 5 (magenta trace) reported electrical activity. Electrodes in fruit bodies 3, 6, and 4 reported activity later, and fruit body 1 (gray trace) reported a negative spike about 6 hours after the rain started. Throughout the day, all fruit bodies generally reported positive electrical potentials, and fruit bodies 4 (light green trace), 5, and 6 (pink trace) remained strongly positive long into October 2, after the typhoon had passed. The authors of this study noted that further control experiments are necessary to eliminate possible artifacts as the source of these results (Fukasawa et al., 2023). For example, control experiments where water of various ionic concentrations is soaked directly into the ground would eliminate ions deposited on the fruit bodies by raindrops (Fukasawa et al., 2023). But considering Figures 8C, 8D, and 8F collectively, it seems that filamentous fungi electrically respond to water, especially after experiencing a drought. These results are reminiscent of our earlier observations in Z. mays (see section 4.1).

Calcium signaling mediates hyphal growth, responses to mechanical injury, and surface contact.

Figure 9A shows a calcium signal induced by cutting A. nidulans hyphae with a razor blade (Itani et al., 2023). The red calcium sensor R-GECO indicates intracellular calcium concentration via the strength of its fluorescence. The edge of the mycelium was cut parallel to hyphal growth (gray line, panel A) to determine whether and how the calcium signal is propagated to other hyphae. Panel B presents R-GECO’s fluorescence intensity (in a.u.) over time near the cut site (blue), far from it (red), or in between (green), as indicated by the colored lines in panel A. A calcium signal appeared soon after the cut within a radius of a half-millimeter, peaking 10 seconds later and fading after 2 minutes (Itani et al., 2023). Panel B shows that the signal’s amplitude quickly attenuates with distance, and no calcium signal was detected beyond 1 mm from the cut site (Itani et al., 2023). This observation contrasts with the actively propagated calcium signals in Arabidopsis (see section 4.2).

Figure 9C shows that the calcium signal propagated between different hyphae in close proximity to each other and the cut site (Itani et al., 2023). The large image in panel C is a blow-up of the dashed box in panel A. A small section of the cut site is still visible in the lower-right corner of the image (gray line). The images in the numbered and colored boxes below are pictures of the corresponding boxes above, taken at the time that the calcium signal arrived at that location (white numbers). Panel D shows fluoresence intensity over time in those colored boxes. Notice that the peak amplitude of the signal diminishes and the arrival of the calcium signal delays with distance from the cut site (colored numbers in the plot; Itani et al., 2023). The sharp decreases and/or increases in fluorescences at the cut time are artifacts caused by the razor blade appearing and disappearing from the field of view. This A. nidulans mycelium promptly responds to damage with a localized and transient calcium signal (Itani et al., 2023). Fantastic videos of this experiment (and others) are available as supplementary information available online (Itani et al., 2023).

Figure 9E presents a similar experiment as panels A to D, but with more focus on individual hyphae of T. atroviride (Medina-Castellanos et al., 2018). The six pictures on the left side of panel E are live-cell images of a single wild-type (left column) or calcium-chelated (BAPTA, right column) hypha before (top row) or after (bottom two rows) cutting it with a scalpel (Medina-Castellanos et al., 2018). The cell expressed the green fluorescent calcium sensor GCamP6 to observe its free intracellular calcium concentration. Injury induced a strong calcium signal in wild-type hyphae with a short latency of 2 seconds and a brief duration of around 10 seconds (three left images, panel E; Medina-Castellanos et al., 2018). The right three images in panel E show the same experiment, but after treating the cell with BAPTA for 15 minutes before injury. The plot in panel E shows post-injury traces of the fluorescence intensity (FI) for three wild-type hyphae (green) and three hyphae treated with BAPTA (red). In the wild-type hyphae, the calcium signal has a very short onset latency after the cut and a duration of 2 or 3 minutes (Medina-Castellanos et al., 2018). These durations are significantly longer than that of the hypha shown in the left three images of panel E. The calcium signal’s duration can vary significantly between trials, but the onset latency is reliably around a few seconds (Herrera-Estrella, private communication, 2023). The BAPTA-treated hyphae (red traces, panel E) did not produce detectable calcium signals.

Figure 9F illustrates a hypha’s eventual response to injuries like cutting. Panel F shows light microscopy images of single T. atroviride hyphae stained with lactophenol cotton blue, 1 hour after cutting them (Medina-Castellanos et al., 2018). The top image in panel F exemplifies a regenerative response of an injured hypha (the black arrow marks a regenerated tip). The middle image suggests that their regenerative ability is eliminated after treatment with BAPTA for 15 minutes before the cut (Medina-Castellanos et al., 2018). The bottom image shows that hypha regeneration is partially restored by adding 0.34 mM of calcium chloride after BAPTA exposure, that is, a source of extracellular calcium. The black arrow in the bottom image of panel F marks the formation of a thin new hyphal tip (Medina-Castellanos et al., 2018). Extracellular calcium influx presumably prompts the release of intracellular calcium stores that amplify the signal (Medina-Castellanos et al., 2018) to ensure that regeneration is initiated. These regenerated hyphae can also form conidiophores for asexual reproduction as a response to the injury (Hernández-Oñate et al., 2012; Hernández-Oñate & Herrera-Estrella, 2015; Medina-Castellanos et al., 2014). These results suggest that extracellular calcium influx is necessary for hyphae to elicit a calcium signal and regenerate themselves and/or asexually reproduce after injury.

Calcium signaling mediates other mechanosensory responses of hyphae—for example, tip growth (Takeshita et al., 2017; López-Franco et al., 1994) branching (Meyer et al., 2009), and polarity (Kim et al., 2012). Figure 9G shows typical thigmotropism (i.e., touch-directed growth) of C. albicans hyphae (Brand et al., 2007; Brand & Gow, 2009; Nelson et al., 2004). Hyphal tips change their growth direction (crooked red arrows, panel G) when encountering ridges (teal shaded areas, panel G) in a substrate (Watts et al., 1998; Gow, 2004; Brand & Gow, 2009). This mechanosensitivity helps fungal pathogens (e.g., C. albicans) recognize potential host cells and penetrate them where their membrane is weak or invaginated (Sherwood et al., 1992; Gow et al., 1994; Brand et al., 2008). Figure 9H shows how this behavior is mediated by calcium signaling (Brand et al., 2007). The membrane curvature of the hyphal cell changes when it bumps into an obstacle in the substrate (Kumamoto, 2008). This change opens the stretch-activated calcium channel Mid1p, permitting calcium influx (Brand et al., 2007; Iida et al., 1994). Then, via unknown effectors, that calcium influx acts on a bud site selection protein Rsr1 to initiate a new growth axis (Brand et al., 2007, 2008; Brand & Gow, 2009). Mutants with diminished capacity for calcium uptake and signaling exhibit impaired thigmotropic responses (Brand et al., 2007, 2008). Directed growth allows fungi to find valuable resources and avoid dangers. Calcium signaling mediates this ecologically crucial behavior.

The animal kingdom contains two phyla whose members never develop nervous systems at any stage of their lives (Monk & Paulin, 2014; Monk, 2014; Ryan & Chiodin, 2015). The first is the sponges (Leys & Anderson, 2015), and the second is the Placozoans (the “flat animals”) (Schierwater et al., 2021; Eitel, 2013). Due to their morphological simplicity, it was long thought that these animals are ancestral to all other neuron-developing descendants (Borchiellini et al., 2001; Nielsen, 2008). Modern molecular and chemical evidence is split on their ancestral status (Srivastava et al., 2010; Philippe et al., 2009; Sperling et al., 2009; Dellaporta et al., 2006; Schierwater et al., 2009; Pisani et al., 2015, 2016; Halanych et al., 2016; Ryan et al., 2013; Moroz et al., 2014; Moroz & Romanova, 2022, 2023; Moroz, Sohn, et al., 2020). Whichever phylum is ancestral, sponges and Placozoans have all of the necessary tools to electrically signal. Placozoans are probably the earliest-branching animal to possess all three major groups of voltage-gated calcium channels found in humans (Gauberg et al., 2020; Moran & Zakon, 2014; Senatore et al., 2016) and at least five types of voltage-gated sodium channels (Romanova, Smirnov, et al., 2020). In sponges, no voltage-gated sodium or potassium channels have been reported yet (Francis et al., 2017; Liebeskind et al., 2017; Moran et al., 2015; Leys & Hill, 2012; Leys & Anderson, 2015; Senatore et al., 2016). But they do have a voltage-gated calcium channel (Moran & Zakon, 2014; Moran et al., 2015; Srivastava et al., 2010) and both inward- and outward-rectifying potassium channels (Tompkins-Macdonald et al., 2009; Leys & Hill, 2012; Leys & Anderson, 2015; Carpaneto et al., 2003; Sakarya, 2007; Zocchi et al., 2001; Wells et al., 2012). These potassium channels could depolarize and repolarize cellular membrane potentials (Tompkins-Macdonald et al., 2009; Leys & Hill, 2012; Leys & Anderson, 2015; Nickel, 2010; Wells et al., 2012). Sponges also possess mechanosensitive, thermosensitive, pH-sensitive, ligand-dependent, and transient receptor potential cation channels (Nickel, 2010; Zocchi et al., 2001; Ludeman et al., 2014; Kenny et al., 2020; Leys & Anderson, 2015). Ion concentrations and/or channel blockers affect a variety of sponge behaviors—for example, contraction (Ludeman et al., 2014; Leys & Anderson, 2015), choanoderm function (Vernale et al., 2021), larval settlement (Conaco et al., 2012), metamorphosis (Nakanishi et al., 2015; Woollacott & Hadfield, 1996), and phototaxis (Wong et al., 2022). At least some sponges have a sealed, functional epithelium (Elliott & Leys, 2007) that maintains a membrane potential and regulates ion flow across it (Adams, 2010). Sponges and Placozoans show that animals do not require nervous systems to sense and respond to cues, exhibit goal-oriented behaviors, or electrically signal.

Sponges are remarkably diverse animals, with thousands of species currently recognized. They are divided into four classes: Demospongiae, Hexactinellida, Calcarea, and Homoscleromorpha (Soest, 2012). In terms of electrical signaling, sponges are divided into two groups: Hexactinellida (i.e., glass sponges) and everything else (i.e., cellular sponges). Glass sponges represent around 6% of all sponges with about 500 known species (Leys et al., 2007). They have a remarkable and unique syncytial tissue that permits electrical conduction (Leys & Anderson, 2015; Mackie et al., 1983; Leys et al., 1999). Cellular sponges (and all other animals) lack this syncytial tissue. Almost everything reported about sponge electrophysiology was recorded from a glass sponge. But we do have strong evidence that cellular sponge larvae use calcium signaling to control their swimming (Leys & Degnan, 2001; Renard et al., 2009; Wong et al., 2022) and initiate metamorphosis (Ueda et al., 2016; Nakanishi et al., 2015). Here we review electrical signaling in the adult glass sponges Rhabdocalyptus dawsoni and calcium signaling in larvae of the demosponge Amphimedon queenslandica.

Figure 10A is a picture of the adult glass sponge R. dawsoni. Glass sponges are potential model organisms for studying the origins of multicellular animals. Unfortunately, they are difficult to study in the wild as most inhabit the seafloor at depths of 300 to 600 meters (Tabachnick, 1991; Vacelet et al., 1994; Leys et al., 2007). Early laboratory observations depicted glass sponges as somewhat passive filter feeders, relying on water currents and their body structure to deliver nutrients and expel waste (Bidder, 1923). Flagellar beating was believed to facilitate water movement, but only locally in the body. Subsequent studies showed that glass sponges efficiently pump water using flagella-driven chambers, even in the absence of external water currents. Observations of R. dawsoni revealed intermittent pumping interrupted by spontaneous arrests, often triggered by extrinsic factors like sediment in the water (Leys, 1995; Leys & Tompkins, 2004; Tompkins-MacDonald & Leys, 2008; Grant et al., 2018, 2019), mechanical disturbance (Mackie, 1979; Lawn et al., 1981), or electrical stimulation (Mackie et al., 1983; Leys et al., 1999). Here we review evidence that these arrests in flagellar beating are mediated by electrical signaling in R. dawsoni.

Figure 10B shows the unique soft tissue that distinguishes glass sponges from all other animals (including other sponges). Most of a glass sponge’s body is effectively a single, gigantic, thin, multinucleated cell called the trabecular reticulum (Leys & Anderson, 2015; Mackie et al., 1983; Leys et al., 1999). The cytoplasm of all tissues in the glass sponge is continuous and streams through large microtubules (Leys et al., 2007). The blue dots in Figure 10B are individual nuclei in the trabecular reticulum, and the green lines show those microtubules (Leys & Anderson, 2015). This syncytial tissue is formed by the fusion of embryonic cells very early in development, creating a mix of multinucleate and cellular regions not seen in other animals (de Ceccatty, 1982; Leys, 1995, 1997, 1998). It transports nutrients (Leys, 1995) and could propagate electrical signals throughout the organism since it lacks cell membranes that would impede ion flow (Lawn et al., 1981; Leys & Mackie, 1997; Leys et al., 1999).

Electrical recordings from sponges are technically challenging because their tissues are extremely thin (1–20 $μ$m), porous sheets and filaments delicately draped over a spicule skeleton (Mackie et al., 1983; Leys & Mackie, 1997). Leys and Mackie addressed this fragility by dissociating some of a sponge’s tissue, aggregating it, and then grafting it back onto that sponge (Leys & Mackie, 1997). Figure 10C presents a schematic of an electrophysiological experiment with those grafts (Leys et al., 1999; Leys, 1997). The schematic shows two recording suction electrodes 1.55 cm apart (R1 and R2, panel C), attached by gently drawing lump tissue into their tips. Two chlorided silver wires (S, panel C) were inserted into the body wall 5 mm apart to deliver electrical stimuli 40 to 60 V in amplitude and 20 to 40 ms in duration (Leys et al., 1999). The suction electrodes R1 and R2 were 3.45 and 5 cm away from the stimulating electrodes, respectively. The graph at the bottom of panel C shows an electrical impulse (i.e., an AP) recorded by the (extracellular) suction electrodes in response to this stimulus. The colors of the electrodes in the schematic of panel C correspond to the colors of the traces and axes in the graph. The vertical shaded cyan area in panel C marks a stimulus artifact, that is, when the stimulus occurred. Soon after, R1 recorded an AP with amplitude of approximately 25 $μ$V (left black $y$-axis, measured extracellularly) and duration of approximately 5 s. Then R2 recorded an AP with amplitude of approximately 100 $μ$V (right red $y$-axis, measured extracellularly) and duration of approximately 5 s. From the impulse arrival times and the distance between electrodes, we can compute a conduction velocity of $v=0.28$ cm/s (at temperature $10∘$C). The amplitudes of the APs were sensitive to the quality of seal between the lump tissue and the suction electrodes, but generally did not exceed a few millivolts (Leys et al., 1999). They also exhibited a refractory period of 29 seconds (not shown).

Figures 10D strongly suggests causality between the AP and pumping arrest. The diagram in panel D shows another experimental setup analogous to that of panel C. But this experiment uses one recording electrode (R, panel D) and a thermistor flow probe (T, panel D) to simultaneously measure APs and flagellar beating (Leys et al., 1999; Leys & Anderson, 2015). The APs measured by the electrode had a small amplitude of approximately 1 mV from peak to trough (measured extracellularly), though that amplitude is sensitive to the quality of the electrode’s seal (Leys et al., 1999). The pink traces at the bottom of panel D show that a single AP (thin pink trace) is sufficient to immediately and temporarily arrest water flow (thicker pink trace immediately below it). Two APs arriving 30 s (green, trace ii, panel D) or 60 s (orange, trace iii, panel D) apart prolonged arrest. When those APs were 90 s apart (blue, trace iv, panel D), flagellar beating stopped, briefly resumed, and then stopped again. These experiments strongly indicate that R. dawsoni uses an electrical conduction system to control water pumping (Leys et al., 1999; Leys & Anderson, 2015; Leys & Meech, 2006).

Figure 10E suggests the ionic basis of electrical signaling in R. dawsoni (Leys et al., 1999; Leys & Anderson, 2015). The top-right plot in panel E shows that a 75% reduction of sodium with respect to normal seawater has a relatively minor impact on the impulse. Reducing sodium (blue trace) slightly diminishes AP amplitude and slightly increases delay with respect to normal seawater (gray trace). The middle-left plot in panel E shows that application of the calcium channel blocker nimodipine (reversibly) attenuates and delays the impulse. Similarly, the bottom-right plot in panel E demonstrates a similar effect with application of the potassium channel blocker TEA. The middle and bottom plots in panel E show that high enough concentrations of potassium and calcium channel blockers can abolish the AP (light green and pink traces, respectively) (Leys et al., 1999; Leys & Anderson, 2015). These findings collectively suggest that AP generation requires calcium influx and subsequent repolarization of the membrane requires potassium efflux. Sodium ions apparently have little effect on APs.

Control of water pumping can benefit sponges under certain conditions. For example, if the temperature of the water is too low, then sponges could arrest beating to conserve energy as food availability is probably limited (Leys & Anderson, 2015; Leys et al., 1999; Leys & Meech, 2006). Or if the seawater contains too much sediment, then sponges could arrest pumping to prevent clogging. Sponges are broadly sensitive to changes in water flux through their oscula and, by extension, to clogging (Ludeman et al., 2014; Ellwanger & Nickel, 2006; Leys et al., 2019; Renard et al., 2009; Flensburg et al., 2022; Leys & Anderson, 2015). At least some adult sponges respond to these stimuli by arresting pumping and/or slowly contracting their bodies (Elliott & Leys, 2007, 2010; Flensburg et al., 2022; Nickel, 2010). In particular, R. dawsoni arrests pumping when particles are added to the water that they filter (Leys et al., 1999). Sponges widely control their pumping given certain environmental cues. Currently, only glass sponges are known to do so by transducing cues into electrical signals.

We know very little about the electrophysiology of cellular sponges. There are at least two reasons for this knowledge gap. First, juxtacrine and/or paracrine signaling might be more prevalent in cellular sponges than electrical signaling (Leys & Anderson, 2015; Elliott & Leys, 2010; Nickel, 2010). No gap junctions (Adams, 2010; Elliott & Leys, 2007; Renard et al., 2009) or voltage-gated sodium or potassium channels (Francis et al., 2017; Liebeskind et al., 2017; Moran et al., 2015; Leys & Hill, 2012; Leys & Anderson, 2015) have been identified in cellular sponges (Senatore et al., 2016). Second, intracellular recordings are technically difficult (Tompkins-Macdonald et al., 2009; Nickel, 2010; Leys & Meech, 2006) and require creative techniques to obtain (Leys & Mackie, 1997; Wells et al., 2012; Zocchi et al., 2001; Carpaneto et al., 2003). But we do have strong evidence for calcium signaling mediating a key stage in a cellular sponge’s life: its metamorphosis from larva to adult (Conaco et al., 2012).

Figure 11A shows the posterior pole of an A. queenslandica larva. They have a clear anterior-posterior axis and radial symmetry, and they are patterned by genetic pathways familiar to “higher” animals (Adamska, 2007). Larvae can actively swim by coordinating the beating of short cilia covering most of their bodies (Maldonado et al., 2003; Leys & Degnan, 2001; Degnan & Degnan, 2010), and they exhibit phototaxis (Maldonado, 2006; Ueda et al., 2016; Say & Degnan, 2020; Leys et al., 2019). Ciliary beating is affected by external potassium concentration and calcium channel inhibitors, suggesting its mediation by membrane potential depolarization and calcium influx into ciliary cells (Leys & Degnan, 2001; Renard et al., 2009; Wong et al., 2022). The cells responsible for A. queenslandica larval photosensitivity are located around their posteriors. A ring of pigment cells containing blue-light sensitive cryptochromes (and not opsins) surrounds their posterior pole (Leys & Anderson, 2015; Conaco et al., 2012; Mah & Leys, 2017; Say & Degnan, 2020; Rivera et al., 2012). Nearby long-ciliated cells (purple, panel A) change their configurations given light cues, collectively acting as a photosensitive rudder (Renard et al., 2009; Maldonado, 2006; Leys et al., 2019; Leys & Degnan, 2001). After release, larvae spend at least 4 hours (Ueda et al., 2016) in the water column before swimming or sinking to the seabed at twilight (Maldonado, 2006; Maldonado et al., 2003). So their photosensitivity biases larvae to metamorphose in the dark (Say & Degnan, 2020; Leys & Degnan, 2001; Renard et al., 2009; Degnan & Degnan, 2010).

On the substrate, algae produce a chemical cue that reliably induces larval metamorphosis (Conaco et al., 2012; Leys & Anderson, 2015; Say & Degnan, 2020; Ueda et al., 2016; Nakanishi et al., 2015). As they approach competency to metamorphose, larvae begin upregulating genes for calcium signaling and ion channels (Conaco et al., 2012; Gaiti et al., 2015). Then they crawl on the substrate, sometimes for days, searching for a dark, nutrient-rich location to colonize (Maldonado, 2006; Maldonado et al., 2003). At spots of interest, larvae stop swimming and slowly spin with their anterior pole touching the substrate, sometimes for hours (Maldonado, 2006; Ereskovsky, 2010). These observations suggest that larvae have (nonneural) sensory cells that detect some algal cue and transduce it to begin metamorphosis. They are probably located near the larva’s anterior pole.

Figure 11B shows one larval cell type implicated in this transduction. A. queenslandica larvae have a sparse cell type called flask cells with a single deep cilium, located mostly in the anterior third of their bodies (Nakanishi et al., 2015; Sakarya, 2007). Figure 11B shows flask cells near the anterior pole of a larva stained in red CM-DiI dye; white arrowheads indicate two cells in particular (Wong et al., 2022). These flask cells have morphological hallmarks of sensory-secretory cells, namely, a (probably) sensory cilium surrounded by F-actin, vesicles, and basal neurite-like processes (Nakanishi et al., 2015; Renard et al., 2009). They express the synaptic gene orthologs DLG, HOMER, GRIP, CRIPT, and GKAP more prominently than other cell types, suggesting that flask cells can form a proto-synaptic scaffold (Sakarya, 2007; Ryan & Grant, 2009). Flask cells apparently do not form a network with each other, but their neurite-like processes and expression of synaptic orthologs could permit intercellular communication with other neighboring cell types.

Figure 11C shows anterior-lateral flask cells near the epithelial surface of a larva within a half-hour of settlement (Nakanishi et al., 2015). They are labeled with a calcium indicator Fluo-4-AM (green). Flask cells (black arrowheads, panel C), and no other cell types, strongly label for cytosolic calcium (Nakanishi et al., 2015). The inset in panel C is a lateral view close-up of one labeled flask cell, with its (changing) apical process at the top (ap, inset panel C) (Nakanishi et al., 2015). This calcium-mediated signal was not observed in swimming larvae that had not settled yet (Nakanishi et al., 2015). Treating larvae with a calcium chelating agent, but not a general divalent cation chelating agent, severely reduced settlement rates (Nakanishi et al., 2015). No evidence suggested that the epithelium conducts ions in the form of a calcium wave (Nakanishi et al., 2015). But these observations demonstrate that flask cells transduce an algae-related chemical cue into an intracellular calcium signal.

Figure 11D suggests how a larva translates intracellular calcium signals in flask cells into metamorphosis. The larva in panel D is just beginning metamorphosis and is stained with a nitric oxide (NO) indicator DAF-FM (Ueda et al., 2016). NO is an ancient regulator of signaling and life cycle transitions from all kingdoms of life (Tao et al., 1997; Wilken & Huchzermeyer, 1999; He et al., 2004; Ueda et al., 2016), including “higher” animals (Castellano, 2014; Moroz, Romanova, et al., 2020; Jokura et al., 2023) and sponges (Colgren & Nichols, 2022; Leys & Anderson, 2015; Musser et al., 2021; Say & Degnan, 2020; Leys & Meech, 2006). Globular cells (bright green dots, panel D) show the highest levels of NO (among the visible surface cells at least) and express a nitric oxide synthase gene AqNOS similar to other animals (Ueda et al., 2016). Globular cells are unciliated and located almost everywhere near the larval surface (Ueda et al., 2016), but are more densely packed on the anterior end. They are located appositionally to flask cells and have been hypothesized to secrete mucus (Mah & Leys, 2017; Leys & Degnan, 2001). NO produced by globular cells then activates downstream (in this sponge) pathways that initiate metamorphosis (Ueda et al., 2016). Maybe globular cells’ mucus helps the sponge stick to the substrate during the process (Ereskovsky, 2010).

Figure 11E summarizes this algae-dependent signaling pathway in A. queenslandica larvae. A competent larva searching for a location to colonize touches its anterior end to the substrate (Maldonado, 2006) (bottom panel E). Anterior flask cells (fc, panel E), which resemble sensory cells (Sakarya, 2007; Nakanishi et al., 2015; Ryan & Grant, 2009; Renard et al., 2009), experience increased cytosolic calcium levels when they detect an (unknown) algal cue (Nakanishi et al., 2015) (red circles, panel E). Flask cells have basal neurite processes (Nakanishi et al., 2015; gray lines, panel E) and globular cells (Mah & Leys, 2017; gc, panel E) are located nearby. Some unidentified intercellular signal prompts the globular cells to synthesize NO (yellow dots, panel E; Ueda et al., 2016), and possibly mucus (Ereskovsky, 2010). NO diffuses through tissues (Colgren & Nichols, 2022), and the signal is strengthened by other cell types that synthesize NO in lower amounts (Ueda et al., 2016, brown cells, panel E). NO activates downstream kinase pathways necessary for metamorphosis to begin (Ueda et al., 2016). Interestingly, light can inhibit this pathway and bias larvae to metamorphose in the dark (Say & Degnan, 2020).

Reports of electrical signaling in cellular sponges are scarce. Maybe cellular sponges lost much of their ability to electrically signal, and these channels and genes are used for some other purpose. Or maybe alternative voltage measurement techniques (e.g., voltage-sensitive dyes) will reveal electrical activity in cellular sponges that electrodes cannot.

Figure 12A is an overhead view of the Placozoan (sp. Hoilungia hongkongensis). Placozoans are simple, small, disc-shaped blobs that inhabit shallow tropical and subtropical oceans (Srivastava et al., 2008). They possess almost no extracellular matrix, do not develop tissues (Schulze, 1883; Schierwater et al., 2021), and exhibit only very basic dorsal-ventral patterning. At least six cell types have been recognized in Placozoans (Mayorova et al., 2021), though more types could soon be acknowledged (Romanova et al., 2021), and the organization of those cells is rudimentary (Smith et al., 2014). Figure 12B illustrates those six cell types and their approximate locations in the Placozoan body plan. Their lifestyle is apparently dominated by crawling on a substrate, searching for algae and cyanobacteria to eat (Varoqueaux et al., 2018; Mayorova et al., 2019; Smith & Mayorova, 2019; Romanova, Heyland, et al., 2020; Romanova et al., 2021).

Placozoan cells are tiny and fragile, so it is difficult to record a patch of a Placozoan cell with a whole cell electrode (Romanova, Smirnov, et al., 2020). We only have indirect evidence that calcium signaling is prevalent in Placozoans. For example, removing calcium from the water stops Placozoans from gliding, implicating it in their movement control (A. Senatore, private communication, 2023).

Figures 12C and 12D illustrate the highly unusual feeding strategy of Placozoans. Unlike almost all other animals, Placozoans do not have a gut (Smith et al., 2015). They digest their food outside their bodies on a substrate (Smith & Mayorova, 2019). Their ventral epithelium contains gland cells (see Figure 12B), which presumably chemosenses algae under the animal (Senatore et al., 2017; Smith & Mayorova, 2019; Romanova, Heyland, et al., 2020). Lipophil cells (see Figure 12B) contain granules of digestive enzymes (panel C) that are locally secreted (panel D) around detected algae to lyse them (yellow-green colors, panel C; Senatore et al., 2016; Smith & Mayorova, 2019). The magenta arrowheads in panel D indicate two faint, swollen granules that turned green after release due to uptake of a green lipophilic dye. Placozoans’ ventral surface then develops an invagination around the lysed algae and the animal “churns” to absorb nutrients (see the videos in Smith et al., 2015). The process of detecting, lysing, and absorbing algae takes around 5 minutes (Smith et al., 2015), so the animal needs to remain stationary during this time.

Placozoans search for algae by walking on ventral cilia to “glide” on a substrate (Mayorova et al., 2019). Since they lack strong intercellular junctions (Eitel et al., 2018; Srivastava et al., 2008; Moroz & Kohn, 2016; Smith & Reese, 2016; Smith & Mayorova, 2019) their cells are only bound by adherens junctions. Therefore, when Placozoans find algae, they need to pause the beating of all their ventral cilia lest they risk tearing themselves apart (Armon et al., 2018). Since they have no neurons or muscles (Nikitin et al., 2023), Placozoans must use alternative means to coordinate ciliary pauses and subsequent enzyme release (Smith & Mayorova, 2019).

Figure 12E shows immunostained gland cells located on the periphery of the ventral epithelium (Smith et al., 2017). The green tips of the cells (see panel E, left) reveal that the cells’ ventral ends express a T-type calcium channel TCa$V3$⁠. The red-stained cell bodies (see panel E, center) show that those gland cells also label for complexin, indicating that these cells are secretory (Lin et al., 2013; Smith et al., 2017). Double-staining these cells (see panel E, right) confirms that the same cells expressing TCa$V3$ label for complexin. Granules inside the cells label for a peptide implicated in the control of ciliary beating (Senatore et al., 2017; Conzelmann et al., 2011). Gland cells could also express receptors for the peptides that they secrete (Senatore et al., 2017; Smith & Mayorova, 2019), so a small number of gland cells detecting algae could initiate a chain reaction releasing peptides throughout the whole animal. This mechanism offers an explanation for why the feeding behavior in one Placozoan can affect the feeding behaviors of others (Smith et al., 2015; Senatore et al., 2017; Romanova et al., 2022).

Calcium probably plays a wider role in Placozoan behavior beyond their foraging strategy. Figure 12F shows filamentous cells in the interior of a Placozoan stained for TCa$V2$⁠. These cells are morphologically consistent with Placozoan fiber cells (Mayorova et al., 2021), which is their only cell type that contacts both dorsal and ventral cells (DuBuc et al., 2019). Fiber cells could mediate Placozoan immunity responses like phagocytosis and wound healing (Mayorova et al., 2021), and they form rudimentary proto-synaptic contacts with all five other cell types (Smith et al., 2014). Dorsal peripheral cells also express TCa$V2$ channels (Gauberg et al., 2020), which could implicate calcium signaling in their rapid contraction and expansion cycles (Armon et al., 2018). Occasional contractile waves have been observed moving across the animal, and the speed of the wave front is comparable to calcium wave propagation (Armon et al., 2018). If technically possible, live calcium imaging of intact Placozoans would reveal fascinating insights into their signaling and behavior.

Placozoans can also generate electrical signals mediated by sodium channels. Figure 13A presents a rare example of a direct electrophysiological recording from an intact Placozoan H. hongkongensis. An extracellular glass microelectrode was placed in contact with its cells. No spontaneous APs were recorded (Romanova, Smirnov, et al., 2020). But stimulation with a step current of 150 nA lasting 2 seconds (square wave, panel A) induced a burst of spikes, each with a duration of about 2 ms. Similar bursts of brief spikes were observed in four tested Placozoan species (Romanova, Smirnov, et al., 2020).

These electrical signals were identified as a class of regenerative electrical signals (Romanova, Smirnov, et al., 2020). Figure 13B presents an averaged signal (black trace) from 911 individual spikes (gray traces). The timing of some individual APs (gray traces) resembles spike frequency adaptation (red arrows, Figure 13B), with the initial spike occurring at a repeatable time after stimulus onset and subsequent spikes occurring with progressive delays. These similarities do not imply that these signals are analogous to neural APs. But their existence shows that Placozoans can generate fast electrical signals given the right stimulus (Romanova, Smirnov, et al., 2020).

The brevity of the average recorded signal (⁠$∼1$ ms, panel B) suggests that these spikes are generated with sodium channels. Figures 13C and 13D confirm this suspicion. Placozoans were placed in artificial seawater with (red trace, panel C) or without (blue trace, panel C) sodium. Upon stimulation, electrical signals were detected only with sodium present in the solution (or in the electrode). Panel D is a bar plot showing the mean number of spikes from 14 animals during one current stimulus in the presence (red) or absence (blue) of sodium. A students’ paired $t$-test on these data shows strong statistical significance with $p<0.0001$⁠. Subsequent molecular analysis revealed between five and seven types of voltage-gated sodium channels in the Placozoan genus Hoilungia, depending on the species (Romanova, Smirnov, et al., 2020).

The ecological purpose of these sodium spikes is unknown. They could help Placozoans defend against toxins (Romanova, Smirnov, et al., 2020). They could also be involved in regulating spatial orientation and geotaxis. One of Placozoans’ six cell types is a crystal cell. Crystal cells are located around the periphery of the animal and oriented to face its epithelium (Mayorova et al., 2018). Their eponym is a small (⁠$∼8μ$m$3$⁠), rhomboid-shaped, calcium aragonite crystal that acts as a statolith (i.e., a gravity sensor; Mayorova et al., 2018). The positions of crystals within their cells depend on the force of gravity, which in turn affects the crawling behavior of Placozoans. Sodium spikes were observed in these rare crystal cells (Romanova, Smirnov, et al., 2020), and they make (nonsynaptic) connections with fiber and epithelial cells (Smith & Mayorova, 2019; Mayorova et al., 2019, 2021). Crystal cells and their sodium spikes might mediate fast control of spatial orientation and movement given the direction of gravity. The problem with this hypothesis is that the force of gravity moves crystals within cells on a timescale of minutes (Mayorova et al., 2018). It is unclear why Placozoans would generate electrical signals on a millisecond timescale when their crystal cells require many orders of magnitude more time to detect gravity.

Many of the electrical signals that we reviewed are very easy to interpret from a sensory processing and/or decision-making perspective. When a B. subtilis cell in a biofilm starves, it releases potassium ions to slow the metabolism of its neighbors. When an E. coli cell is mechanically squeezed, its membrane potential depolarizes and induces colonization on the substrate. When Stentor is illuminated, membrane potential depolarization and calcium influx change its swimming direction. When Paramecium is bumped on its posterior, potassium efflux and calcium influx initiate an escape response. When Z. mays roots detect the end of a drought, they send an electrical signal to the leaves to restart photosynthesis. When Arabidopsis leaves are wounded, the plant sends an electrical signal to initiate defense hormone production. When A. nidulans hyphae are cut, the fungus sends a local calcium signal to begin regeneration. When H. hongkongensis detects algae to lyse, a calcium signal coordinates a pause in ciliary beating and animal movement (probably). When R. dawsoni detects reduced excurrent water flow (and implicitly sediment clogging its pores), an electrical signal pauses water pumping. When A. queenslandica larvae detect algae on the seabed, a calcium signal initiates metamorphosis (in the dark). These organisms are transducing a stimulus, and that transduction actuates a behavioral response.

These electrical signals are timing an organism’s response to some environmental change (i.e., the onset of a stimulus). The presence or absence of these electrical signals implies the presence or absence of the stimulus, and vice versa. None of these organisms are “encoding stimulus information” via some statistic of their spiking activity, for example, a spiking rate, interspike interval, or active population subset (Quiroga & Panzeri, 2009; London et al., 2010). They simply actuate some behavioral or physiological change whenever a stimulus is transduced. We are not claiming that electrical signals are exclusively used for this purpose. Electrical signals have other utilities that are independent of environmental sensing and decision making, for example, during development and regeneration (Harris, 2021). Conversely, organisms can time responses to stimuli with nonelectrical mechanisms, such as second messengers (Agostoni & Montgomery, 2014; Newton et al., 2016). We are only observing that cellular stimulus transductions often represent an organism’s detection of a stimulus at that moment in time, so a behavior is actuated.

We wonder if neural APs should be interpreted analogous to the nonneural electrical signals that we reviewed. If so, then a neuron’s AP is its (correct or incorrect) assertion that it has detected something important at that moment in time. In this framework, neurons are not “encoding stimulus information” via some statistic of their spiking activity. Its spiking rate is the rate at which it makes detection assertions. Its interspike intervals are the waiting times between detection assertions. A population of neurons that spiked at some time is the collection of those neurons that detected something then. These quantities may contain information about stimuli in a rigorous information-theoretic sense. But they do not represent or “encode” anything. Instead, spikes have a direct causal role in the activity of the nervous system (Brette, 2015). Like the nonneural cells we reviewed, whenever a neuron spikes, it is saying “right now.” We could offer one parsimonious interpretation of a cell’s stimulus transductions, regardless of whether that cell is a neuron.

One could object that neurons have some key anatomical or functional differences from the cells that we reviewed, so this reductionist approach to interpreting neural APs is invalid. We would offer three counterarguments to this objection. First, the cells that we reviewed also exhibit significant anatomical and functional differences from each other. For example, maize phloem cells and Stentor cells are wildly divergent, yet our interpretation of the signals that they generate and/or propagate remains the same. Second, cellular stimulus transductions have the same interpretation across five domains of life. Interpreting neural APs differently implies that neurons are exceptional and unique in their exceptionalism. A parsimonious interpretation of cellular stimulus transductions should be strongly preferred over exceptionalist arguments without compelling evidence to the contrary. Third, both nervous systems and nonneural cells transduce stimuli to time reactions. Since they both solve the same ancient and ubiquitous problem, those transductions are probably not disparate phenomena with unrelated computational interpretations. Instead, anatomical or functional differences between them might reflect that they solve variations of the same problem under different selection pressures.

We next compare the properties of neural and nonneural stimulus transductions. Our goal is to infer differences in the selection pressures that have shaped stimulus transductions in neural and nonneural cells. Then we can infer how those differences should affect our interpretation of neural APs. We will argue that nervous systems were strongly pressured to detect and react to very weak stimuli under enormous time pressure. Spiking neurons are not unique as cells that can transduce stimuli extremely quickly. Nor are they unique as cells that exhibit extraordinary sensitivity to very weak stimuli. We will offer examples of nonneural cells that accomplish one task or the other. Then we will observe that neurons can accomplish both tasks simultaneously. They do so with extremely sensitive ion channels that generate very fast APs and have opening thresholds near the limit of thermal noise. One consequence of this sensitivity is that ion channels can be opened by random chance, so a neuron can generate an AP without any stimulus present. Spiking neurons are effectively sacrificing the specificity of their stimulus transductions for sensitivity and speed. In this framework, both neural and nonneural APs are a cell’s assertion that it has detected something important at that moment in time. Those assertions just have different signal-to-noise ratios.

Table 1 overviews key characteristic quantities of many electrical signals that we reviewed. We list the amplitudes, refractory periods, durations, and propagation speeds of those electrical signals. We also list the ionic bases and ecological purposes of those electrical signals. Entries with “n/a” denote a nonapplicable quantity, and a question mark denotes an unmeasured quantity. For example, we do not know the amplitude of electrical signals that were measured extracellularly or with fluorescent dyes instead of electrodes. For comparison, we also include typical values of those quantities for a neuron in the bottom row (Brunel, 2000; Potjans & Diesmann, 2014).

Table 1 shows that the refractory periods, durations, and propagation speeds of electrical signals vary by several orders of magnitude across the tree of life. One important function of electrical signals is to time behavioral responses to stimuli. So this variance in the temporal properties of electrical signals suggests that different organisms need to detect and react to their environments on different timescales. Table 1 suggests that the relevant timescale for neurons is milliseconds.

Neural APs are the fastest electrical signal listed in Table 1 in terms of their refractory periods, durations, and propagation speeds. They are often the fastest signal by at least an order of magnitude in each category. Neurons and nervous systems must have been pressured to detect and react to stimuli on the millisecond timescale (Liu & Fetcho, 1999; Stewart et al., 2013; Gaudry et al., 2013; Gonzalez-Bellido et al., 2013). Table 1 shows that non-neural organisms often sense and respond to their environments on timescales of seconds to hours. Exceptions to this observation have been documented, particularly in protozoans. APs in Paramecium and Odontella sinensis have durations of around 10 ms and 1 ms, respectively (Elices et al., 2023; Taylor, 2009). Therefore neurons are not strictly necessary to permit very quick detection, responses, or electrical signaling. But we did not find examples of organisms responding to stimuli at faster timescales (for example, microseconds or nanoseconds). So apparently neurons (and some protozoans) have experienced strong selection pressures to detect and react to stimuli very quickly.

Predator-prey interactions impose extreme selection pressures for animals to detect and react to stimuli with millisecond temporal precision (Monk & Paulin, 2014; Monk, 2014; Monk et al., 2015; Ackels et al., 2021). This selection pressure on animals is 550 million years old (Hua et al., 2003; Bengtson & Zhao, 1992). The fossil record shows that the evolution of the first predatory animal sparked a frantic evolutionary arms race for weapons and armor. Over the next 20 million years, we see the first fossil appearances of shells, teeth, claws, spines, plates, drills, skeletons, and jaws (Monk & Paulin, 2014; Monk, 2014; Monk et al., 2015; Hua et al., 2003; Bengtson & Zhao, 1992; Erwin et al., 2011). The earliest recognizable nervous systems also appear in the fossil record at around this time (Clarkson et al., 2006; Yang et al., 2016), suggesting that they evolved for combat. Suddenly, animals needed to detect other nearby animals and quickly decide to attack, defend, or flee. Making these decisions a few milliseconds too early or too late can be fatal (Liu & Fetcho, 1999; Stewart et al., 2013; Gaudry et al., 2013; Gonzalez-Bellido et al., 2013). Maybe predator-prey interactions drove animals to evolve nervous systems (Monk & Paulin, 2014; Kristan, 2016) (independently and simultaneously in several phyla (Moroz, 2021)). Or maybe predator-prey interactions repurposed nervous systems that had already evolved for some other reason (Keijzer et al., 2013; Jékely, 2010; Jékely et al., 2015). Either way, modern nervous systems achieved their speed and temporal precision over a half-billion years of the animal kingdom being at war with itself.

Table 1 suggests that organisms achieve the reaction speed required to satisfy their selection pressure but not more. For example, Arabidopsis also suffers from predation by herbivores, including caterpillars (Body et al., 2019; Farmer et al., 2003). Its signal to start defense hormone production contains valuable information about its environment. Yet the timing of that signal does not require millisecond precision to ensure the plant’s survival. The electrical signal from a wounded leaf arrives at other leaves after around a minute (Mousavi et al., 2013; Kumari et al., 2019). Arabidopsis survives despite that delay costing it a minute of being grazed before initiating a response. The timing of detecting and reacting to certain stimuli is important to all living organisms to some degree. For example, if Arabidopsis did not initiate a defense response to herbivores for days or weeks, then the entire plant could be consumed. The timescale of minutes is apparently acceptable for it (Mousavi et al., 2013). In principle, Arabidopsis would benefit from initiating defense hormone production within milliseconds instead of minutes to reduce herbivore grazing. The observation that it doesn’t implies that fast reactions incur some kind of cost that requires sufficiently strong selection pressures to justify (Herculano-Houzel, 2012; Laughlin, 2001; Niven & Laughlin, 2008; Niven & Farris, 2012). In “higher” animals (and some protozoans; Wan & Jékely, 2021), the selection pressure for fast detection and reaction is so extreme that this cost is met down to the timescale of milliseconds.

Many of the nonneural transductions that we reviewed were caused by significant physical distortions of cellular membranes. E. coli cells were mechanically squeezed between an aragose pad and a substrate (Bruni et al., 2017). Paramecium had its membrane indented with a glass stylus (Naitoh & Eckert, 1969). Z. mays root cells increased their turgor pressure when watered after a drought, and their membranes were suddenly stretched (Fromm et al., 2013). Arabidopsis leaves were physically clipped (Mousavi et al., 2013). T. atroviride and A. nidulans hyphae were sliced with a scalpel (Medina-Castellanos et al., 2018; Itani et al., 2023). C. albicans hyphae changed their membrane curvatures when they bumped into an obstacle (Brand et al., 2007). In each example, significant physical changes in cellular membrane structure open ion channels and permit ion flow. This transduction of touch is probably pervasive in all domains of life.

For sufficiently strong membrane distortions, both the sensitivity and specificity of this transduction are usually very high. It is rare to observe these electrical signals without the stimulus or vice versa. For example, we observe one depolarizing spike in Z. mays leaves when a drought ends and no spikes before that. We did not see reports of calcium signals in fungal hyphae unless they were injured. Nor did we see reports of Arabidopsis generating APs or VPs unless it was mechanically stimulated. One notable counterexample is obstacle avoidance in Paramecium, which can spike and change swimming direction without bumping into anything (Nakaoka et al., 2009). Interestingly, this phenomenon is not caused by stochastic ion channels opening and closing, but rather a regulated positive feedback loop of calcium influx (Nakaoka et al., 2009). So the cell’s occasional random changes in swimming direction appear to be an intentional behavioral strategy rather than false detections of an obstacle, perhaps to more efficiently explore space or avoid capture. Generally it is easy for cells maintaining ion gradients to reliably transduce stimuli that bend, stretch, compress, shear, or rupture their membranes.

These mechanotransductions and reactions occur across a wide range of timescales. For Arabidopsis, transduction and propagation between leaves take a minute (Mousavi et al., 2013). T. atroviride hyphae respond to injury within a few seconds (Medina-Castellanos et al., 2018). Mechanical transduction in both Stentor and Paramecium has latencies within tens of milliseconds (Newman, 1972; Fabczak, 2000; Naitoh & Eckert, 1969; Brette, 2021; Elices et al., 2023). These protozoans demonstrate that neurons are not necessary for cells to quickly and reliably detect stimuli, at least if the stimulus is a significant physical distortion of their membrane.

Other nonneural transductions that we reviewed were caused by stimuli that did not appreciably distort cellular membranes. B. subtilis cells released potassium ions when their glutamate uptake was impaired (Prindle et al., 2015). Stentor cells depolarized and spiked when they were illuminated (Fabczak et al., 1993). A. queenslandica larvae transduced a chemical cue from algae into an intracellular calcium signal (Nakanishi et al., 2015). Placozoans could perform a similar transduction (Senatore et al., 2017). Other examples exist in the literature that we did not review. E. coli performs chemotaxis by comparing attractant or repellent concentrations over time (Berg & Purcell, 1977), which affects the cell’s membrane potential (Szmelcman & Adler, 1976). Paramecium transduces extremely small pressure differences induced by gravity across the cell (Gebauer et al., 1999; Häder et al., 2017). Nonneural cells from all domains of life can also transduce stimuli other than touch.

The sensitivity and specificity of these transductions are again very high. Stentor cells almost never actuate their photophobic response in the dark (Fabczak et al., 1994). A. queenslandica larvae are overwhelmingly more likely to settle near live algae than not (Nakanishi et al., 2015). Some of these transductions demonstrate remarkable sensitivity to stimuli that we might not expect from organisms without nervous systems. E. coli chemotaxis operates at the theoretical limit of sensitivity imposed by the diffusion of molecules at tiny spatial scales (Berg & Purcell, 1977). Gravity sensing by a single Paramecium cell is among the most sensitive transductions found in biology (Gebauer et al., 1999). Neurons are not necessary for cells to reliably transduce extremely weak stimuli.

While the sensitivity of some nonneural cells is remarkable, the speed of these transductions seems limited. The photophobic response of Stentor occurs on the timescale of seconds (Song, 1981). A. queenslandica larvae can spend hours choosing their settlement location (Maldonado, 2006). E. coli compares chemical concentrations around a second apart in time to bias its swimming up or down a gradient (Berg & Purcell, 1977). Gravity-induced membrane potential changes in Paramecium occur with a latency of around 20 seconds (Gebauer et al., 1999; Brette, 2021). There is no obvious time pressure for these cells to transduce their respective non-touch stimuli more quickly. For example, a free-swimming cell’s fitness is practically unaffected if it ascends a chemical or gravity gradient a half-second faster or slower. Animals with nervous systems do not enjoy this luxury of time.

For higher animals with nervous systems, the timescale of seconds is almost always two or three orders of magnitude too slow (Liu & Fetcho, 1999; Stewart et al., 2013; Gaudry et al., 2013; Gonzalez-Bellido et al., 2013). Like some nonneural cells, the sensitivity of sensory neurons can approach their relevant physical limits (Hardie, 2012). Sharks have ampullae of Lorenzini that detect electric fields of less than 1 nanovolt per centimeter (Newton et al., 2019). Barn owls detect sounds as low as $-$14 dB sound pressure levels throughout their hearing range (Dyson et al., 1998). Drosophila detects pheromones at the physical limit of single molecules (Ronderos & Smith, 2009). Unlike the nonneural cells that we discussed, these extraordinarily weak signals are detected within milliseconds.

Sensory neurons can accomplish this task with ion channels that generate all-or-none APs and whose opening or closing thresholds approach the limit of thermal noise. So extremely weak stimuli reliably open those ion channels, and the sensory neuron generates quick APs to assert the stimulus onset with millisecond precision. One consequence of this sensitivity is that those ion channels can also be opened by random chance, without any stimulus (Häusser et al., 2004; Uddin, 2020). For example, shark ampullae of Lorenzini spike at rates around tens of hertz without any electrical stimulus (Neiman & Russell, 2004; Newton et al., 2019). Some barn owl auditory nerve fibers spike at rates exceeding 100 hz in silence (Köppl, 1997). Drosophila olfactory receptor neurons spontaneously spike at a rate between 1 and 15 hz (de Bruyne et al., 2001). Like the nonneural cells that we reviewed, the sensitivity of these transductions is high. But unlike our examples, their specificities are low. These sensory neurons are effectively sacrificing stimulus specificity for sensitivity and speed. It does not necessarily follow that we should consider neural and nonneural electrical signals as fundamentally different phenomena. We interpret both as a cell’s assertion that it has detected something important at that moment in time. Those assertions just have different signal-to-noise ratios and temporal resolution requirements.

The interpretation and treatment of spontaneous APs is a major point of contention between neural computation proposals (Schölvinck et al., 2015; Uddin, 2020; Cowley et al., 2020). Some proposals argue that spontaneous APs are a feature of neural coding that can be exploited by nervous systems (Vreeswijk and Sompolinsky, 1996; Brunel, 2000). For example, it has been argued that shark ampullae of Lorenzini maintain a nonzero spontaneous spiking rate so that they can “encode” electric fields of opposite polarities by spiking at a faster or slower rate. We accept that sharks can detect opposite electric field polarities and that their ampullae’s spiking rates behave in this manner (Newton et al., 2019). But we disagree with the interpretation of their spontaneous rate as a clever feature that can be exploited. Fungi also detect electric fields with different polarities (Brand & Gow, 2009) and do not require sensors that spike 30 times per second to do so. From an information-theoretic perspective, there is negative benefit to unstimulated sensory neurons spiking at nothing. From an energetic efficiency perspective, this practice is wasteful (Laughlin, 2001; Niven & Laughlin, 2008). Other proposals cast spontaneous APs as noisy spikes but treat that noise differently. Rate coding averages it out by integrating APs over some time window and/or populations of neurons (Shadlen & Newsome, 1998; London et al., 2010; Pouget et al., 2000; Quiroga & Panzeri, 2009). Bayesians consider each sensory AP as a noisy measurement of some world state (Knill & Pouget, 2004; Weiss et al., 2002; Jékely, 2021; Seilheimer et al., 2014; Alais & Burr, 2019; Shaikh, 2022; Beierholm et al., 2007; Gardner & Martin, 2000). Spike timing does not propose how to filter noise at all (Abeles et al., 1993; Izhikevich, 2006; Brette, 2012). If APs are a neuron’s assertion that it has detected something important at that moment, then spontaneous neural APs are false-positive detection assertions. They are an unavoidable consequence of sensory neurons trying to detect extremely weak stimuli on the millisecond timescale.

The nonneural electrical signals that we reviewed directly activate an effector. From an information-theoretic perspective, this observation is not surprising. If a transduction contains almost-perfect information about a stimulus, then there is no need to perform any computations on or with the transduction. It is easier, faster, and cheaper for that transduction to activate the appropriate effector directly. This sensory-effector strategy falls apart when transductions are noisy. An animal cannot activate effectors every time one of its noisy sensory neurons spikes. It can address this problem with another neuron that integrates and thresholds those noisy sensory APs.

Consider a single sensory neuron and a single downstream thresholded neuron connected by an excitatory synapse. Say the downstream neuron’s threshold is larger than the excitatory postsynaptic potential (EPSP) it receives when the sensory neuron spikes. Then the downstream neuron needs to receive at least two EPSPs from the sensory neuron in order to spike. Thresholding the downstream neuron downsamples the sensory spikes by at least half (and likely much more). This downsampling incurs a steep cost of delayed detection time. Say the downstream neuron actuates some effector when it spikes. The waiting time to observe two (or more) sensory APs is longer than it is for one. So the effector will be actuated later than if it was actuated directly by sensory spikes. This delay can be reduced by connecting $k>1$ sensory neurons to the same downstream neuron. The waiting time to observe some number of spikes from $k>1$ sensory neurons is less than it is from $k=1$ sensory neuron. By adjusting synaptic weights, thresholds, and $k$⁠, an animal can balance the cost of detection delay with the benefit of filtering spontaneous APs.

The auditory pathway of barn owls exemplifies this trade-off. The first neurons in that pathway are auditory nerve fibers that can spike at a rate of 100 Hz without a sound stimulus (Köppl, 1997). Up to $k=4$ nerve fibers synapse onto one downstream nucleus magnocellularis neuron that spikes at a spontaneous rate of around 150 Hz (Köppl, 1997; Carr & Boudreau, 1991). Nucleus magnocellularis neurons downsample false-positive input spikes from 400 Hz (four nerve fibers, each spiking at 100 Hz) to 150 Hz. Then given a sound stimulus, auditory nerve fibers and nucleus magnocellularis neurons can spike at faster rates of 300 Hz and 400 Hz, respectively (Peña et al., 1996). The detection delay of the sound (i.e., the average waiting time until the first spike) is $1/(4·300$⁠) s = 0.83 ms for four independent and identical auditory nerve fibers. For the nucleus magnocellularis neuron, the average detection delay increases to $1/400$ s = 2.5 ms.

Neurons are not unique as integrators and thresholders of discrete sensory events. One (rare) counterexample is the Venus flytrap, which famously requires mechanoreceptive hairs to be triggered twice within 10 to 30 seconds for its trap to close (Böhm et al., 2016). We suggest that the Venus flytrap performs this operation for the same reason as neurons: filtering false-positive detections. If a trigger hair is activated once, it does not necessarily follow that an insect occupies the plant’s trap. Trigger hairs can be activated by abiotic events like a raindrop or debris falling in the trap. But two activations occurring close together in time are much more likely to have been caused by a crawling insect. By requiring two activations in a time window, the plant filters out false-positive detections of a crawling insect. We suggest that this computational strategy is directly analogous to a neuron receiving noisy sensory APs as input.

Our review suggests that the purpose of cellular stimulus transductions is to time an organism’s behavioral response to environmental changes. The presence or absence of the transduction represents the presence or absence of some world state. This interpretation is agnostic to whether a cell is a neuron or not. Neural APs are extremely fast, highly sensitive, but unspecific variants of cellular stimulus transductions. Nervous systems address the low specificity of neural APs (i.e., false-positive stimulus detections) by integrating and thresholding them in downstream neurons. Collectively, this comparative analysis suggests that nervous systems evolved to detect extremely weak signals from noisy sensory data under enormous time pressure.

We conclude by discussing how this interpretation of neural APs can shape our understanding of neural computation. We identify some proposals of neural computation from the literature that are consistent with this framework. Those proposals imply that the electrophysiological properties of a neuron’s membrane are related to the statistics of its input spikes. Describing that relationship is key to understanding how neurons and nervous systems represent sensory information and time decisions.

The purpose of stimulus transductions is to time reactions to environmental changes. Therefore, the computational output of a neuron is the millisecond-precise time that it spiked given its inputs (Douglas & Martin, 2007; Stimberg et al., 2019). A neuron implements this computation by comparing its input-dependent membrane potential at its axon hillock with a threshold. The propagation, amplification, and attenuation of postsynaptic potentials down dendrites and into the soma are critical to determining the threshold crossing time. Electrophysiological properties of a neuron’s membrane (e.g., its ion channel distribution and dendritic topology) determine the output of its computation. These properties must be highly regulated over a variety of timescales (Turrigiano, 2011; Titley et al., 2017; Zenke & Gerstner, 2017). This framework casts neurons as analog, online computing units. Their computing medium is their analog membrane potential.

Neurons are often considered analog in the sense that some statistic of their output spike train can assume a continuous range of values (such as its firing rate; Gabbiani & Koch, 1998). When we hypothesize that neurons are analog computational units, that is not our meaning. We mean that each neural AP is the output of an analog computation, executed with the subthreshold membrane potential, that determined its timing. We do not need to define a continuously valued statistic of a neuron’s output spike train to consider them as analog. They already have a built-in analog membrane potential that is updated by its inputs as they are observed or not.

One prominent class of neural computation theories is that neurons represent stimulus information as a function of their spiking activities. For example, rate coding requires an instantaneous measure of firing rate, and population coding proposes pooling activities across neurons (Quiroga & Panzeri, 2009; London et al., 2010). These proposals do not explain any subthreshold computations occurring between a neuron’s spikes that determined their precise timings. They only observe the output of those subthreshold computations. So they miss the rich dynamics that are critical to making threshold-crossing decisions on the millisecond timescale (Desmaisons et al., 1999; Koch, 1998).

It might seem counterintuitive that neurons should determine millisecond-precise threshold crossing times when their inputs can be very noisy. But several statistics disciplines offer thresholded algorithms that make precisely timed decisions given incoming streams of noisy measurements. Examples of these algorithms include sequential analysis and change-point detection (Tartakovsky, 2014; Basseville & Nikiforov, 1993). They work by accumulating evidence from noisy measurements and comparing it to one or more thresholds. They define evidence as some test statistic of their inputs—for example, a likelihood ratio, its logarithm (Wald, 1945; Page, 1954), a recursive residual (James et al., 1987; Brown et al., 1975), or some general Radon-Nikodym derivative. That test statistic is updated online as noisy measurements are observed or not observed. When the evidence crosses a threshold, the algorithm asserts some detection or decision at that time. These assertions can have valuable optimality properties, such as minimizing error probabilities (Wald & Wolfowitz, 1948) or minimizing long detection delays for a given fault tolerance (Lorden, 1971; Moustakides, 2004). Some of these algorithms look strikingly neural.

Several studies have shown that neural membrane potentials can represent a test statistic, at least for simple neuron models. Deneve (2008) showed that the membrane potential of a leaky integrate-and-fire (LIF) neuron approximates the log-likelihood ratio for two homogeneous Poisson processes. Paulin and van Schaik (2014) showed that the membrane potentials of an array of LIF neurons can collectively represent the Bayesian posterior of a Poisson input rate. Ratnam et al. (2003) noticed that LIF neurons resemble change-point detectors, whose membrane potentials represent a decision variable (i.e., a test statistic) of their inputs. Yu (2006) made a similar observation for change-point detection subjected to a cost function. Gold and Shadlen (2007) reviewed how neurons might represent an analog test statistic for hypothesis testing (though they did not explicitly state that membrane potentials could be that representation). By comparing a test statistic to a threshold, a neuron can make statistically optimal assertions the instant that it has received sufficient evidence to declare a decision or detection (Wald, 1945; Wald & Wolfowitz, 1948; Page, 1954; Lorden, 1971; Moustakides, 2004). It represents its assertion with an AP.

Say a neuron’s membrane potential represents an analog, online test statistic of their inputs. Then we infer that the electrophysiology of an efferent neuron’s membrane must be related to spiking statistics of its afferent input(s). Examples of this relationship have been reported by the studies we referenced earlier. Deneve (2008) related a LIF neuron’s synaptic weights to input spiking statistics generated from a hidden Markov model. Paulin and van Schaik (2014) related a LIF neuron’s time constant to a single point on the Bayesian posterior of a Poisson input rate. Ratnam et al. (2003) via his change-point detection formulation relates the LIF neuron’s time constant to the input rates of the change-point problem. The specific form of this afferent-efferent relationship is different for different problems. Measuring that relationship (assuming it exists) would suggest which types of analog, online statistics problems neurons could solve.

Computational neuroscience has a long history of modeling the statistics of neural spike trains (Perkel et al., 1967; Gabbiani & Koch, 1998). It also has a long history of electrophysiologically modeling spiking neurons (Koch, 1993; D’Angelo & Jirsa, 2022). We suggest that those models should be related for afferent-efferent neuron pairs connected by a synapse. For example, say we have a slice preparation of a barrel cortex from a mouse (Shlosberg et al., 2012; Buskila et al., 2014; Buskila, Crowe, et al., 2013) and we execute the experimental protocol outlined in Buskila and Amitai (2010). Specifically, we insert an electrode into a dendrite of a neuron from layer 2/3. Then we use another stimulating electrode to drive the spiking of a neuron in layer 4, which feeds inputs to layer 2/3. Move the stimulating electrode around layer 4 until we observe postsynaptic potentials in the dendrite of layer 2/3. Then we know that the driven and recording neurons are connected by a synapse. As we change the spiking behavior of the layer 4 neuron, the layer 2/3 neuron’s membrane should change its electrophysiological properties (Buskila, Morley, et al., 2013). Maybe as the spiking rate of the layer 4 neuron increases, the (somatic and/or dendritic) time constant of the layer 2/3 neuron decreases. Or maybe the resonance frequency of the layer 2/3 neuron will increase. If animals are making decisions under enormous time pressure, then the efferent layer 2/3 neuron will adapt to changes in its inputs from layer 4 very quickly, perhaps within seconds. This experiment could provide strong evidence that neurons are not noisy devices whose APs must be averaged over time or populations. Instead they are thresholded, analog electrical circuits that implement sophisticated statistical computations on their inputs in real time.

We thank Yossi Buskila, Joel Kralj, Arthur Prindle, Alfredo Herrera-Estrella, and Adriano Senatore for useful discussions. We thank Yu Fukasawa, Giancarlo Bruni, and Ding Xuejing for generously sharing data. We thank Sally Leys, Robert Degli Agosti, and Edward Farmer for granting us permissions to reproduce figure panels.