Physiological controls of large-scale patterning in planarian regeneration: a molecular and computational perspective on growth and form

Planaria are complex metazoans that repair damage to their bodies and cease remodeling when a correct anatomy has been achieved. This model system offers a unique opportunity to understand how large‐scale anatomical homeostasis emerges from the activities of individual cells. Much progress has been made on the molecular genetics of stem cell activity in planaria. However, recent data also indicate that the global pattern is regulated by physiological circuits composed of ionic and neurotransmitter signaling. Here, we overview the multi‐scale problem of understanding pattern regulation in planaria, with specific focus on bioelectric signaling via ion channels and gap junctions (electrical synapses), and computational efforts to extract explanatory models from functional and molecular data on regeneration. We present a perspective that interprets results in this fascinating field using concepts from dynamical systems theory and computational neuroscience. Serving as a tractable nexus between genetic, physiological, and computational approaches to pattern regulation, planarian pattern homeostasis harbors many deep insights for regenerative medicine, evolutionary biology, and engineering.

Keywords: Anatomy, bioelectricity, computation, gap junctions, ion channels, morphogenesis, morphology, planaria, regeneration

Planaria are free‐living tripoblastic animals whose bodyplan (Martín‐Durán et al. 2010) exhibits three major axes of polarity: dorsal/ventral, anterior/posterior (AP), and medial/lateral (with a cryptic left/right asymmetry) (Nogi et al. 2005). Their complex anatomies include musculature of two distinct types (Kobayashi et al. 1998), digestive system (Newmark & Alvarado 2002), and reproductive system (Hyman 1951) complete with germ cells (Wang et al. 2010). Moreover, they have a true centralized brain (Sarnat 1985; Pagán 2014), which produces a continuous brain wave frequency as observed by electroencephalogram (Aoki et al. 2009), and central nervous system (CNS) (Cebrià 2008). Planaria exhibit complex behaviors, including decision‐making (Inoue et al. 2015) and lateralization (Corning 1964). They also have robust sensory capabilities and organs (Hyman 1951), mediated by photoreceptors (Carpenter et al. 1974) and various receptors in their auricles (MacRae 1967; Asano et al. 1998). Aside from chemical and mechanical cues, they also have the ability to sense electrostatic (Brown 1962), radioactive (Brown & Park 1964), and magnetic aspects (Brown 1962, 1966) of their environment.

The most unique aspect of this model species is that they are true champions of regeneration, able to replace any body part that is amputated (Morgan 1898) while recapitulating proper organ size (Hill & Petersen 2015). They also continuously remodel their bodies, maintaining proportions suitable to available food supply (Oviedo et al. 2003; González‐Estévez & Saló 2010; Forsthoefel et al. 2011; Beane et al. 2013), and appear to have solved the problem of aging by continuous regeneration of their soma. While the implications of this for human regenerative medicine and stem cell biology have been expertly discussed (Sanchez Alvarado 2007; Moraczewski et al. 2008; Rossi et al. 2008; Gentile et al. 2011), we focus here on another aspect highlighted by these remarkable creatures: the control of large‐scale shape.

A fuller appreciation of the major gaps in our knowledge can be gained by taking an engineering approach: how would we build a robot that exhibited the observed repair and remodeling properties? It becomes immediately apparent that knowing the genes necessary for regeneration to occur (and their interactions) is not sufficient. A planarian body must recognize damage, and harness individual cells to rebuild exactly what is missing (in the right place, of the appropriate scale, and correctly oriented; Fig. 1A−A″). Most important, although not often discussed in the pursuit of initiating therapeutic regeneration, is how cells know when to stop. A crucial part of the planarian regenerative response is that each worm has a specific target morphology that, when achieved, causes rapid proliferation and remodeling to cease. A thought experiment (Fig. 1B−E) reveals the fact that, despite recent molecular insights, none of our models really address how target morphology is specified to make (even incorrect) predictions about situations in which this property is directly challenged. Importantly, these issues have implications well beyond planaria, as understanding the relationship between cellular growth control and large‐scale anatomical metrics is central to mammalian regeneration, cancer, and bioengineering of synthetic constructs (Doursat et al. 2013; Lobo et al. 2014b).

Thus, we take an information processing perspective to reverse engineering the planarian's robust pattern memory (Lobo et al. 2012) and abstract from the details of molecular pathways to ask: what control algorithms do individual cells and cell networks use to correctly integrate their activities toward a complex outcome with high reproducibility? What information is stored, processed, and communicated among which regions, to drive correct dynamical patterning and termination of regeneration? What measurements are being made in this system (size, shape, topology) and at what scales to enable precise coordination of three‐dimensional anatomy? What head shape will hybrid bodies make? How many heads will appear on circular fragments (one continuous wound all around the periphery) in worms treated with various reagents? Answers to these questions are not available from existing data, because we still largely lack the conceptual tools to integrate genetic and functional data into multi‐scale models that describe not only pathways but emergent patterning decision‐making. However, a number of recent studies shed light on aspects of this long‐term goal.

Here, we first briefly review what is known about the biochemical cues that regulate patterning. Then, we focus on recent data involving several novel pathways that are beginning to provide experimental access to questions about target morphology and large‐scale pattern control: ion channels, gap junctions (GJs) (electrical synapses), and neurotransmitters (Fig. 2). We discuss the potential implications of the fact that the prodigious information processing required to implement the planarian's feats make use of precisely the same basic molecular components by which brains implement memory, decision‐making, and distributed control of biochemical events to the service of higher‐level goal states. Finally, we discuss the need for generative, algorithmic models of patterning, and highlight recent efforts to harness computer science and artificial intelligence toward helping human scientists extract understanding from the ever‐growing deluge of data.

The first step in any regenerative process is to detect that damage has occurred―that the current shape is not the correct shape. Within 30 min of cutting, a planarian initiates closure of the wound (Rink 2013) and begins regulation of the gene expression and physiological signaling required for proper patterning of the regenerating worm (Wenemoser et al. 2012). This wound response is potentially triggered by reactive oxygen species which burst within minutes of wounding (Pirotte et al. 2015), a damage signal conserved across regenerative organisms (Erler & Monaghan 2015). At 3 h runt‐1 is expressed in neoblasts allowing for neoblast specification, and between 3 and 12 h genes expressing patterning factors are expressed subepidermally (Wenemoser et al. 2012). This gene expression is coupled with a wound‐specific, apoptotic response that occurs between 1 and 4 h (Pellettieri et al. 2010). Between 6 and 12 h, in the epidermis, extracellular matrix remodeling proteins are expressed, as well as an activator of the Notch signaling pathway (Wenemoser et al. 2012). At this time, fst is also expressed, which is required for the initiation of regeneration of lost tissue (Gaviño et al. 2013). Alongside the required gene expression, the regenerating planarian also experiences two peaks of mitotic activity, the first being across the entire body in response to injury and the second involving a recruitment of neoblasts to the wound site (Wenemoser & Reddien 2010). Once a blastema is formed, cells begin differentiation. The transition of the neoblasts to enter their differentiating state has been determined to be extracellular‐signal‐related kinase (ERK) dependent (Tasaki et al. 2011) and their differentiation according to axial polarity is regulated by epidermal growth factor receptor (Fraguas et al. 2014) and JNK signaling (Almuedo‐Castillo et al. 2014; Tejada‐Romero et al.

2015).

Subsequent control mechanisms begin determining neoblast fate (Umesono 2014) and the eventual tissue specification of stem cell progeny. After an amputation, neoblasts migrate to the wound site to develop a blastema through proliferation, which is, in part, regulated via PTEN through TOR signaling (Oviedo et al. 2008). SMG‐1 acts to keep growth in response to injury in check as mTOR signaling drives the process forward (Gonzalez‐Estevez et al. 2012). Some neoblasts express specific, lineage restricted transcription factors during regeneration and remodeling (Scimone et al. 2014), thus suggesting that neoblasts are specialized to a particular fate before they produce undifferentiated blastema cells with particular identities that they will adopt (Reddien 2013).

The new cells must then become appropriately arranged to establish correct polarity across all three of the body axes. Most of the work to date involves identifying the gene expression and signaling pathways necessary for this step, especially the Wnt signaling pathway. Knockdown of β‐catenin resulted in double‐headed or radial hypercephalized worms (Iglesias et al. 2008; Petersen & Reddien 2008) and upregulation of β‐catenin via APC‐1 and axin knockdown produced two‐tailed worms (Gurley et al. 2008; Iglesias et al. 2011). The bone morphogenetic protein signaling pathway largely mediates the dorsal/ventral axis as well as the dorsal planarian midline (Reddien et al. 2007) and, when disrupted, resulted in ectopic ventral sides of the planarian (Molina et al. 2007; Orii & Watanabe 2007). When proper axes are established via these signaling pathways, organs and structures need to be properly placed (Roberts‐Galbraith & Newmark 2015) and then in turn maintained homeostatically (Lin & Pearson 2014). Polarity determinants and those that pattern organ structures exhibit considerable crossover. For example, PBX/extradenticle is required for the proper patterning of several organ structures, but is also involved in the regulation of polarity genes such as notum and wnt1 (Blassberg et al. 2013).

A planarian constantly scales and remodels to maintain its appropriate morphology. Autophagy allows the animals to adapt to their environment in times of stress, regulated in part by Gtdap‐1 (González‐Estévez et al. 2007), whether it is due to injury or starvation. Regeneration after amputation also requires re‐sizing and scaling according to the new size of the planarian fragment. Alongside the initial apoptotic response at the blastema induced by wounding, there is a second apoptotic response that occurs systemically 3 days post‐amputation (Pellettieri et al. 2010). This is thought to allow for the worm to allometrically re‐scale according to its new size after tissue loss and is mediated by JNK activation (Almuedo‐Castillo et al. 2014). Whether it is induced by injury or an environmental factor requiring adaptive change, the ability to remodel existing tissues is crucial for the planarians’ pattern homeostasis.

It is clear that molecular details of cell signaling and stem cell specification are becoming ever more understood. How can we synthesize these reductive advances at the molecular level into predictive, systems‐level understanding of large‐scale planarian shape? Complexity, robustness, and emergence are some of the most difficult open problems in science today (Kauffman & Clayton 2006, Fernandez et al. 2013; Hoel et al. 2013). Fortunately, we have a possible roadmap: neuroscience has long faced the issue of functionally linking higher, emergent levels of system control to molecular pathways.

Most of the work in regeneration is focused on biochemical signals, such as secreted molecules and transcriptional networks. However, a number of classical studies in planaria have examined the role of biophysical signals in this process—in particular, those mediated by electrical forces (Hyman 1932; Marsh & Beams 1952; Bonaventure 1957; Lange & Steele 1978). More recent work on the instructive patterning roles of bioelectrical gradients in vertebrate regeneration, development, and cancer (reviewed in Stewart et al. 2007; Adams 2008; Adams & Levin 2013; Levin 2014b; Mustard & Levin 2014) has made use of molecular physiology to study the sources, consequences, and transduction mechanisms of endogenous ionic signaling in non‐excitable tissues (Fig. 3). This work is now being extended to planaria (Barghouth et al. 2015). The information processing capabilities of the planarian body exhibit robustness, distributed (long‐range) integration, decision‐making, and cellular activity that drives changes until the correct anatomical end‐state is reached. These properties suggested investigating possible roles of pathways used by the CNS to perform similar functions (e.g., memory and goal‐directed activity) (Pezzulo & Levin 2015). In the brain, adaptive, flexible programs are implemented by electrical circuits consisting of GJs, ion channels, and neurotransmitters.

Interestingly, ion channels and the resulting bioelectrical gradients are evolutionarily far older than brains (Borgens 1982; Levin et al. 2006). Cells were using this versatile medium for communication and coupling physiology to cell behavior long before nervous systems evolved to optimize them for fast muscle control during behavior (Keijzer et al. 2013; Gao et al. 2015; Prindle et al. 2015). A now classic body of work in this field (Jaffe 1981; Nuccitelli et al. 1986; Borgens et al. 1989; Pullar 2011) has been augmented by modern molecular approaches in the last two decades showing that trans‐epithelial electric fields (Robinson & Messerli 1996; Yamashita 2013), ion currents (Smith & Trimarchi 2001; Reid & Zhao 2011), and resting potential gradients (Levin et al. 2002; Adams et al. 2006, 2016) within many tissue types serve as instructive signals for pattern regulation. Similar bioelectrical regulatory mechanisms have been shown in mammalian systems, both in vivo (Zhao et al. 2006; Lange et al. 2011; Leppik et al. 2015) and in vitro (Sundelacruz et al. 2008, 2013a, 2013b), and in a plethora of studies on aquatic vertebrate model species in the contexts of wound healing (Kucerova et al. 2011; Sebastian et al. 2015; Zhang & Bei 2015), regeneration (Adams et al. 2007, 2013; Monteiro et al. 2014), development (Dahal et al. 2012; Pai et al. 2012, 2015a; Perathoner et al. 2014; Lobikin et al. 2015b), and cancer (Chernet & Levin, 2013a, 2013b, 2014; Yang & Brackenbury 2013; Djamgoz et al. 2014). The intrinsic dynamics of bioelectric signaling (Cervera et al. 2014, 2015; Law & Levin 2015), the transduction machinery that allows voltage changes and ion flows to regulate gene expression and chromatin states (Carneiro et al. 2011; Tseng & Levin 2012a), and the downstream transcriptional targets of electrically mediated signaling (Pai et al.

2015b) have been extensively reviewed (McCaig et al. 2005; Stewart et al. 2007; Sundelacruz et al. 2009; Funk 2013; Bates 2015). Interestingly, the transduction of bioelectric states into downstream second messenger and nuclear events often involves neurotransmitters such as serotonin (Fukumoto et al. 2005b; Blackiston et al. 2011, 2015a; Lobikin et al. 2015a), but can also occur via clustering of RAS molecules (Zhou et al. 2015) and voltage‐sensitive phosphatases (Murata et al. 2005; Okamura & Dixon 2011). This biophysical layer of control not only guides individual cell functions like migration and differentiation, but also allows cellular networks to communicate and process global information for large‐scale patterning (Adams & Levin 2013; Levin 2013, 2014a, 2014; Mustard & Levin 2014). While endogenous electric fields provide long‐range guidance cues for a variety of galvanotactic cell types (Kucerova et al. 2011; Meng et al. 2011; Reid et al. 2011; Sun et al. 2013; Ozkucur et al. 2014), spatiotemporal patterns of resting potential regulate mitosis and differentiation (Cone & Cone 1976; Sundelacruz et al. 2008).

Together, these diverse modes of ionic signaling enable organ‐level control, setting size of appendages (Perathoner et al. 2014) and programming identity of tissues, such as converting gut tissues into an eye with a bioelectrical perturbation (Pai et al. 2012). Recently, we hypothesized that these neural‐like mechanisms and strategies are conserved―utilized by the planarian body in making decisions about growth and form (Pezzulo & Levin 2015). This hypothesis makes a number of predictions, which have been tested by recent work that has implicated all of these bioelectric signaling mechanisms in the regulation of global pattern in planaria (Fig. 4).

The first prediction of the brain analogy is the involvement of neurotransmitters in pattern regulation (not only in the control of behavior). Neurotransmitters and their receptors are widely present in flatworms (Ribeiro et al. 2005), and surveys have revealed numerous effects of neurotransmitter modulation on planarian regeneration (Villar & Schaeffer 1993). Indeed, recent work has shown that the dynamics of neurotransmitter signaling can alter regenerative morphology. A key study that was originally designed to develop sophisticated anti‐parasitic therapeutics now has implicated neurotransmitters as important factors in the regulation of polarity. Praziquantel, an anti‐parasitic, synthetic compound which increases the permeability of the tegument to Ca2+, induced bipolar phenotypes in planaria (Chan et al. 2014) and can be rescued with exogenous serotonin (Chan et al. 2015). A broad drug screen designed to identify other potential anti‐parasitic drugs like praziquantel also screened for patterning defects and found cholinergic, dopaminergic, and serotonergic drugs all induced changes in planarian regenerative polarity (Chan et al. 2014). This included but was not limited to pharmaceuticals that are commonly prescribed to human patients, such as the selective serotonin re‐uptake inhibitor fluoxetine, which induced a headless phenotype, and the antipsychotic dopamine antagonist haloperidol, which induced both double‐headed and headless phenotypes (Fig. 4A).

Serotonin signaling has been implicated in regulating cell activity and pattern in embryonic left−right asymmetry (Fukumoto et al. 2005a, 2005b), neural growth (Blackiston et al. 2015a), and metastasis (Blackiston et al. 2011). Interestingly, serotonin has been shown to regulate gap junctional communication (GJC) (Rorig & Sutor 1996; Orellana et al. 2013) whilst also being a GJ permeable morphogen (Levin 2006; Gairhe et al. 2012), which suggests the possibility of feedback loops with rich and complex behavior. Thus, the voltage−serotonin control cycle may function beyond the CNS, forming a second messenger pathway for the control of intracellular events by bioelectric signaling. With better techniques to help visualize cellular networks such as photo‐uncaging (Li & Zheng 2012; Rea et al. 2013) and neurotransmitter reporters (Balaconis & Clark 2012), exciting future discoveries no doubt await the characterization of neurotransmitter activity throughout the planarian regenerative process.

In the CNS, the function of bioelectric circuits triggers recall of specific compound memories and complex (modular) behaviors (Maisto et al. 2015). The brain offers a paradigm of how cellular signaling gives rise to integrated decision‐making and goal‐driven activity at the whole organism level. Thus, a second prediction is that modulation of ion‐channel‐dependent bioelectric states during regeneration should be able to specifically alter coherent (large‐scale) properties, such as anatomical re‐specification and scaling. An emerging theme in developmental bioelectricity studies is that, while cell migration is guided by electric fields (McCaig et al. 2005), anatomical specification appears to be determined in part by the spatial distribution of resting potentials of cells, V mem (Levin 2012a; Levin & Stevenson 2012), as has been shown for pre‐patterning of the face (Vandenberg et al. 2011) and brain (Pai et al. 2015a) and for induction of eyes (Pai et al. 2012) in vertebrate models. Involvement of bioelectric signaling in regeneration is reviewed by Levin (2009) and Stewart et al. (2007).

An inverse drug screen implicated the H,K‐ATPase in AP patterning; it was subsequently shown to underlie the planarian endogenous bioelectric gradient (Beane et al. 2011). This process appears to be conserved, since the H,K‐ATPase also regulates V mem in mammals for proper functionality of the gut and cochlea (Shibata et al. 2006; Kaufhold et al. 2008), biomineralization of the developing sea urchin skeleton (Schatzberg et al. 2015), and left−right patterning in embryonic frog, sea urchin, and chick (Levin et al. 2002; Duboc et al. 2005; Hibino et al. 2006; Aw et al. 2008; Morokuma et al. 2008).

Using the specific inhibitor of H,K‐ATPase, SCH28080 (SCH), a wide‐scale, relatively hyperpolarized bioelectric state across entire regenerating Dugesia japonica fragments was induced, eliminating the normal relative depolarization at the anterior blastema. When treated within the first 72 h of regeneration, this abolished formation of anterior structures and expression of anterior genes, and resulted in headless, one‐tailed phenotypes (Fig. 4A) (Beane et al. 2011), which are similar but not identical to those produced via perturbation of the Wnt pathway which produced headless, two‐tailed worms (Gurley et al. 2008; Iglesias et al. 2011). Investigation of epistasis between bioelectric control of patterning and known genetic elements showed that H,K‐ATPase inhibition blocked ectopic heads (Beane et al. 2011) normally formed by β‐catenin RNA interference (Gurley et al. 2008; Petersen & Reddien 2008). Thus, the details of the interactions between bioelectric gradients and canonical biochemical signaling pathways have begun to emerge. However, considering the bioelectric state as being entirely downstream of Wnt signaling is not the whole story. H,K‐ATPase function is also required to clear Wnt11 expression from anterior regions (Beane et al. 2013), suggesting a feedback loop between V mem and Wnt signaling. A similar bi‐directional loop has been described between Notch signaling and V mem gradients in vertebrate brain development (Pai et al. 2015a). Importantly, the suppression of genetically induced malformations (β‐catenin two heads or Notch‐mutation‐induced brain defects in frog) (Pai et al. 2015a) by exposure to drugs already approved for human use is a proof‐of‐principle for the strategic use of ion channel drugs (so‐called electroceuticals) to address mispatterning during birth defects (Masotti et al. 2015; Adams et al. 2016), regenerative repair (Tseng et al.

2010), and cancer (Arcangeli et al. 2009; Gupta et al. 2009; House et al. 2010; Lobikin et al. 2012; Chernet & Levin 2013b; Villanueva et al. 2015).

V mem patterns can be manipulated readily, using many pharmacological reagents under the guidance of the Goldman equation; this is particularly useful in planaria, where drug‐induced ion channel opening is a convenient method for gain‐of‐function perturbation. Ivermectin drives changes in V mem by activating glutamate‐gated chloride (GluCl) channels (Shan et al. 2001) and can depolarize or hyperpolarize cells based on the concentration of extracellular chloride. Manipulating V mem using ivermectin has been shown to induce regeneration in non‐regenerative (refractory age) tail stumps in Xenopus (Tseng & Levin 2012a), and to promote head regeneration in non‐regenerative fragments of Macrostomum lignano (Simanov et al. 2012). In Dugesia japonica flatworms, ivermectin exposure created a wide‐scale depolarization across regenerating fragments with two regions of high relative depolarization at both anterior and posterior blastemas. Upon regeneration, posterior blastemas were anteriorized, resulting in mature worms with a double‐headed phenotype (Fig. 4A). Raising external chloride to hyperpolarize the worms blocked ectopic anteriorization, suggesting that V mem changes, rather than some other function of GluCl or an off‐target effect of ivermectin, are the key early step in determining AP polarity in regenerating planaria (Beane et al. 2011).

Advancements in regenerative medicine will require induction of not only correct anatomical identity of new structures, but also their correct size and proportion. Planaria have the striking ability to allometrically scale their organs and tissues in order to maintain their proper proportions after regeneration (Oviedo et al. 2003). Although many aspects of morphallaxis (Morgan 1901) remain mysterious, recent findings in planaria suggest that V mem plays a role in these processes, as it does in size control in vertebrates (Perathoner et al. 2014). Upon H,K‐ATPase knockdown, worms lost their relative depolarization at the anterior blastema and became relatively hyperpolarized across the entire fragment, causing the regeneration of small shrunken heads (Fig. 4B) with incomplete neural tissue and reduced expression of anterior genes (Beane et al. 2013). Correspondingly, expression of posterior genes extended ectopically toward the anterior region of the worm; moreover, the size and location of the pharynx was unable to scale according to the new size of the worm, and any anterior tissues were made using new tissue rather than remodeling the old, suggesting a failure to execute proper morphallaxis. Regeneration in a variety of systems requires some level of remodeling or dedifferentiation to successfully promote the regenerative process (Jopling et al. 2011). If the process of remodeling old tissue to make way for new tissue can be induced by simple manipulation of ion transporters, regeneration in currently non‐regenerative tissues may be more accessible in the future. What cell‐level behaviors mediate the ability of bioelectric gradients in coordinating cell growth across three dimensions?

Regeneration in many species involves an apoptotic response (Ryoo & Bergmann 2012), including in planaria (Hwang et al. 2004; Almuedo‐Castillo et al. 2014), allowing for proper size and scaling to maintain proportion. Indeed, regeneration requires a correct amount of apoptosis (Tseng et al. 2007; Chera et al. 2009). Planarians experience two waves of apoptosis during regeneration, the first being specifically at the wound site 1−4 days post‐amputation (dpa) and the second being at 3 dpa which occurs throughout the animal (Pellettieri et al. 2010). Inhibiting apoptosis in planaria with M50054 (Tsuda et al. 2001) resulted in regenerates with relatively small heads and large pharynxes, a phenotype very similar to that seen with H,K‐ATPase inhibition (Beane et al. 2013). Consistently, after Smed‐H,K‐ATPase RNA interference, the second wave of apoptosis at 3 dpa to drive remodeling essential for proper regeneration was inhibited. This implies that the role of bioelectric signaling in planarian remodeling is specifically involved in the apoptotic response that is necessary for proper size, shape, and proportion of tissues after regeneration.

Alongside organ identity and scaling, correct shape is also crucial for successful regeneration. Since bioelectric distributions guide and pre‐pattern the morphology of complex structures such as the face and brain (Vandenberg et al. 2011; Pai et al. 2012), it has been shown that direct modulation of voltage states in vivo can alter morphogenesis via the control of numerous downstream patterning genes (Pai & Martyniuk 2015). However, bioelectric circuits operate within cells connected by electrical synapses, also known as GJs (Cooper 1984; Palacios‐Prado & Bukauskas 2012). Recently, we asked two questions: (1) could modification of overall bioelectric network connectivity give rise to coherent patterning changes during regeneration, and (2) is it possible to obtain evolutionarily relevant patterns. The results suggested that shifting among different regions of planarian morphospace (Stone 1997) is possible by physiological perturbation alone (Emmons‐Bell et al. 2015).

When GJC was disrupted in Girardia dorotocephala (GD), it induced a finer‐grain V mem regionalization among the endogenous bioelectric network and worms regenerated heads with an altered shape morphology that quantitatively resembles that of multiple other flatworm species (Fig. 4C) (Emmons‐Bell et al. 2015). This resemblance is more than skin deep: the external shape of the head not only was converted to the shapes of distant planarian relatives, but also was extended to changes to other species‐specific brain morphologies and neoblast distributions. The exact same treatment of a cohort of GD worms produced four types of worm heads in characteristic frequencies (proportional to their evolutionary distance from GD). It is not yet known whether this stochastic property is a consequence of the still relatively crude method of network topology perturbation, or whether it is an intrinsic aspect of the dynamics of this system. The ability to induce a different species’ head shape in a genetically wild‐type worm is fascinating, and suggests that the bioelectric network is a profound regulator of species‐specific morphology. It remains to be seen whether changes in the dynamics of bioelectrical circuits have been widely exploited by evolution to explore variations of anatomical structure.

How to infer the large‐scale outcomes (which kind of head, how many heads, etc.) from cell‐level properties and signals? This question has been addressed for gene regulatory networks (Fig. 5A), using dynamical state spaces built to describe transcriptional circuits that have been used to map complex system behavior (Huang et al. 2009; Huang 2011; Halley et al. 2012). More directly relevant to physiological networks, similar approaches (Fig. 5B) have been used to understand global behaviors of electrical activity in neural networks during decision‐making (Wong & Wang 2006). Importantly, in planarian regeneration, as in the brain, circuit dynamics are not directly revealed from ion channel expression data but are complex and nonlinear. Such dynamics must be modeled quantitatively to understand their emergent properties (Cervera et al. 2015; Law & Levin 2015). One possibility is that different anatomical outcomes correspond to specific attractors in the dynamical state space of the bioelectric network formed by the planarian body; in this paradigm, bioelectric perturbations can shift the system from a default (genome‐specified) attractor to another nearby one (Fig. 6). We are currently working to computationally model this process, to quantitatively map stable attractors to underlying physiological details, and thus to gain more control over the resulting shapes.

How do bioelectrical events become transduced into transcriptional readouts and chromatin modification? In the brain, this job is performed by calcium signaling: calcium channels and a set of calcium‐sensitive receptor pathways convert electrical activity into biochemical and genetic responses. Not surprisingly, voltage‐gated calcium channels (CaV) have been shown to transduce V mem signals into growth cone attraction in Xenopus (Nishiyama et al. 2008), transcriptional patterning in Xenopus by instructing the development of the eye (Pai et al. 2012), and the development and maturation of mammalian neurons (Nakanishi & Okazawa 2006). In planaria, similar to the phenotype observed by treatment with ivermectin, treatment with praziquantel, a CaV activator, resulted in a double‐headed phenotype upon regeneration (Nogi et al. 2009; Chan et al. 2013). Analogously, the CaV inhibitor nicardipine induced a headless phenotype. Normally, calcium is upregulated in anterior blastemas; this became disrupted upon hyperpolarization of regenerating fragments with H,K‐ATPase inhibitors. These data suggest that calcium signaling could be involved in translating V mem signals into anterior gene expression in planaria (Beane et al. 2011) probably involving Hedgehog signaling for proper cell differentiation (Zhang et al. 2011). Ever‐finer dissection of the mechanistic details of voltage transduction on a single cell level complements efforts to synthesize signaling into large‐scale patterning behavior.