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

The information required to determine anatomical identity is not local: upon bisection, the two pieces' blastemas must make a head or a tail respectively, despite the fact that the wound cells were adjacent neighbors before the cut and thus at the same location in the worm. The same positional information gives rise to two distinct anatomical outcomes, based on the cells’ context (the rest of the fragment). Thus, knowing local (positional) information is not sufficient―a blastema needs cues from the rest of the body (Where am I located? Which way am I facing? What else already exists in the fragment and does not need to be re‐created?). Targeting mechanisms that can underlie such long‐range tissue coordination, our laboratory examined the role of GJs (Levin 2007; Yamashita 2010) in planarian regeneration (Nogi & Levin 2005).

GJ proteins are conductive channels within the cell membrane that allow for intercellular communication and signaling via ions and very small molecules (Phelan 2005; Scemes et al. 2007). Signaling mediated by GJs has been shown to support the proliferative abilities of both embryonic and somatic stem cells (Wong et al. 2008), including planaria (Oviedo & Levin 2007). GJ genes (innexins and connexins) are widely expressed during development, establishing electrically‐isopotential cell compartments (Lo & Gilula 1979; Pitts et al. 1988). GJs are required for the physiological maintenance of many mammalian tissues (Maeda & Tsukihara 2011), regeneration of retina (Umino & Saito 2002) and zebrafish fins (Hoptak‐Solga et al. 2008), and patterning of the left−right axis (Levin & Mercola 1998, 1999; Chuang et al. 2007).

Invertebrates form functional GJ channels using innexins (Phelan et al. 1998). Innexins are expressed throughout the planarian and are classified into three functional groups as determined by their expression pattern: the first in the gut, the second in the nervous system or blastema, and the third in the parenchyma or protonephridia (Nogi & Levin 2005). When GJC was inhibited pharmacologically (Nogi & Levin 2005) or via RNAi (Oviedo et al. 2010) in D. japonica, a re‐specification of AP polarity occurred and viable two‐headed planaria resulted (Fig. 4A). Interesting differences reveal themselves when this outcome is compared to the above‐described alteration of head shape in GD worms.

In GDs, the regeneration of other species’ heads is a two‐phase process: the heads regenerate with new shapes in the normal timeframe (<10 days), but within the next 30 days they remodel back to a GD‐specific shape (Fig. 4C). This is strikingly similar to what happens in salamanders when a tail blastema is grafted to the flank: initially, a tail grows, but some months later it remodels into a limb―a structure more appropriate to its new global position (Farinella‐Ferruzza 1953, 1956). This temporary shift into a different stable attractor by GJ (electrical synapse) somatic networks has a clear parallel in neural networks: attractors in state space of neural networks represent individual memories (Fuster 1998; Wills et al. 2005). Depending on the strength of the attractor state, memories can have different degrees of permanence.

The middle third fragments from two‐head animals, derived from GJC inhibition, continue to regenerate as two‐headed in subsequent amputations without any further GJ blockade (Fig. 6B). Likewise, two‐head animals result when just one of the heads is removed in plain water from a two‐head worm. This is permanent, months after the initial GJ blocker exposure (which was shown to leave tissues within 24–48 h) (Oviedo et al. 2010). On the one hand, this is quite reasonable given that GJs are one of the ways plasticity (memory) is implemented in the CNS: GJs serve as versatile transistors, able to “freeze” transient physiological stimuli into stable, permanent changes of network topology (Palacios‐Prado & Bukauskas 2009; Pereda et al. 2013). On the other hand, it is remarkable that a brief, transient, physiological perturbation can permanently alter a complex metazoan's target morphology (the shape to which an animal regenerates, and the morphology that, once reached, signals an end to massive remodeling).

This two‐head permanence has many potential implications, not the least of which arises from the fact that it is stable across the animal's most common reproductive mode (fission) (unpublished observations). First, it impacts the relationship between genomic sequence and bodyplan structure. This would become sharply apparent if the two‐head worms were allowed to reproduce in the wild (assuming they could compete with wild‐type animals and survive). One can imagine wanting to sequence the genomes of one‐head and two‐head worms, looking for the mutations that drove this speciation event resulting in significant morphological diversity. The key difference here is not provided by the genomic sequence, and reminds us that real‐time physiomic profiling must be added to proteomics and genomics if we are to understand and predict large‐scale shape.

The second important aspect is the relationship to “epigenetics.” Bioelectric properties, and their permanence, are certainly a kind of epigenetics in the original full sense of the concept (Jablonka 2012). While it is possible that some aspect of chromatin modification (today's main focus of epigenetics) is involved, and indeed has been shown to be involved in neoblast regulation (Hubert et al. 2013; Robb & Sanchez Alvarado 2014), it must be kept in mind that the “reprogrammed” abnormal head blastema is discarded at each round of cutting (Oviedo et al. 2010). Only trunk fragments are taken, showing the holographic (distributed) nature of this pattern change: headless fragments from two‐head worms have been reprogrammed to work towards a two‐headed outcome upon regeneration (Fig. 4A, 6C). Thus, a truly explanatory model of this phenomenon will need not only to identify molecular targets required for two‐head persistence memory, but to explain how the proposed signaling is sufficient to specify the right number of heads for each fragment in each case. We are currently analyzing models of realistic bioelectric circuits that exhibit the necessary patterning and memory behavior. While editing of target morphology has been seen before in crabs and deer antlers (reviewed in Lobo et al. 2014b), it is clear that the planarian model system is by far the most molecularly tractable example and will greatly facilitate the study of pattern memory.

Ultimately, the building blocks of regeneration are sure to include biochemical, bioelectrical, and physical forces. Each will require an appropriate paradigm (gene regulatory networks, mechanical models of stresses and tensions, bioelectrical circuit dynamics and neural‐like networks). However, the final product must be not only a list of components required for regeneration to occur, nor even a highly detailed interactome or regulatory diagram. The ultimate end‐game for this field is the development of constructivist, algorithmic models that specify exactly what is going on at each step, and explain why these steps are sufficient to give rise to the correct shape from different starting conditions (the robust shape regulation that is observed in planaria). Such models can then be used to infer external modulations that can alter shape to desired outcomes or induce regenerative repair in biomedical settings. Modeling is also necessary because the stable and stochastic behaviors of chemical and physical pathways are often highly nonlinear and emergent. Here, we discuss recent efforts to glean insight into patterning homeostasis in planaria.

In order to understand the mechanisms of planarian regeneration, mathematical and computational models have been proposed that allow us to mechanistically explain and predict the regenerative dynamics of the worm (Fig. 7). The first models proposed to explain planarian regeneration were descriptive. Morgan, inspired by the correlation between the regenerative capacity of flatworms and the AP location level of the amputation (Sivickis 1931; Brøndsted 1955), suggested the existence of a substance concentration gradient signaling the regeneration of a head versus a tail (Adell et al. 2010). This idea was further developed in a series of historical models, including Child's gradient model (Child 1941), Spemann's organizer concept (Spemann & Mangold 2001), and Wolpert's positional information theory (Wolpert 1969). Similar gradient models have been suggested for explaining planarian regeneration, including morphogen concentration gradients (Adell et al. 2010; Schiffmann 2011) and mitotic activity gradients (Oviedo & Levin 2007). However, these descriptive models based on gradients do not represent a mechanism for which a given tissue can decide to regenerate either a head or a tail: the cells on either side of a transversal cut through the middle of the worm will essentially have the same gradient or positional information, yet one side will regenerate a head while the other will regenerate a tail.

The first mechanistic model proposed for planaria was Slack's serial threshold theory of regeneration (Slack 1980). This algorithmic explanation proposed the existence of a discrete set of territories dividing the worm along the AP axis, each of them containing an ordered coded sequence. After an amputation, neoblasts from the remaining territories migrate towards the wound site and then compare their original territory code with the territory code at the wound site. If the wound site has a higher code than the neoblasts, then the blastema adopts the maximum possible code; otherwise it adopts the minimum possible code. Regeneration proceeds by restoring the tissues corresponding to those codes that should be located between the wound and this new code in the blastema. In this way, this model specifies step by step the mechanisms that are sufficient to restore the morphological patterning of the worm. In a similar fashion, the intercalary regeneration model (Agata et al. 2003) hypothesizes that each region of the worm has a positional value, which is then used in an injury site to establish which regions are missing. This model can explain the regeneration of all the intermediate structures between two joined worm pieces, even if one of them is inverted, which produces the duplication of existent structures (Santos 1929; Slack 1980). However, certain predictions of these models based on positional information do not agree with specific experiments, such as the classic observation of the regeneration of a new pharynx and other structures from the old tissue, instead of from the blastema (Morgan 1898).

Inspired by Turing's reaction−diffusion mechanisms of biological pattern formation (Turing 1952), Meinhardt and Gierer proposed dynamical chemical systems based on properties of local self‐activation and long‐range lateral inhibition that control the generation (and regeneration) of specific patterns from near‐homogeneous states or perturbations (Gierer & Meinhardt 1972; Meinhardt 1982; Meinhardt & Gierer 2000). These dynamic models based on the self‐ and cross‐regulation of diffusible chemical species can explain the maintenance of polarity, the correct re‐patterning, and the scaling ability of planarian worms after surgical manipulations (Meinhardt 2009). Interestingly, a classic local activation and lateral inhibition model extended with an extra third diffusible molecule can account for the scaling of the self‐organized head−tail pattern to precisely match the variable worm length (Werner et al. 2015). Specific molecular components have been proposed for these dynamic mechanisms, such as cAMP and ATP, which can diffuse through GJs (Schiffmann 2011). Reaction−diffusion models still lack specific details to account for many knockdown experiments resulting in abnormal morphologies, dorsal−ventral joining experiments, the regeneration of multiple AP axes, or the mechanisms of neoblast migration and differentiation.

In addition to diffusion due to differences in concentration, models based on bioelectricity have been proposed to explain the transmission of long‐range signals during planarian regeneration (Lange & Steele 1978). Inspired by the effect of external electrical fields to reverse the polarity of the worm (Dimmitt & Marsh 1952; Marsh & Beams 1952), a negatively charged substance inhibiting the regeneration of brain tissue has been suggested to be produced by the brain itself, which then will electrically diffuse due to the global planarian bioelectrical field: negatively charged in the anterior region and positively charged in the posterior region. In this way, an amputation removing the brain will result in the charged molecule disappearing, which will trigger the formation of new brain tissue specifically at the most anterior side due to its lower concentration caused by the remaining global bioelectric field. This bioelectric model can account for the regeneration of double heads, or complete change of polarity after the application of external electric fields, which at different intensities can cause the charged molecule to stop electro‐diffusing or reverse its direction, respectively (Marsh & Beams 1947). A diffusion model has also been proposed for the control of serotonergic signals by bioelectric gradients during left−right patterning (Esser et al. 2006; Levin et al. 2006; Zhang & Levin 2009).

Models based on the theory of dynamical systems and differential equations represent one of the most useful approaches for mechanistically describing biological regulation of shape and form (Jaeger & Sharpe 2014). However, formulating the precise differential equations that can recapitulate the dynamics and behaviors of a given biological phenomenon is a very difficult task (Lobo et al. 2012), and indeed represents an inverse problem with no analytical solutions (Lobo et al. 2014b). Instead, heuristic computational methods have been proposed for the automatic construction of dynamic models directly from experimental data (Yeung et al. 2002; Bonneau et al. 2006; Schmidt & Lipson 2009; Sirbu et al. 2010). The reverse engineering of the regulatory network controlling the early patterning of the Drosophila embryo from one‐dimensional gene expression data represents one of the most successful applications of these heuristic methods (Reinitz et al. 1995, 1998; Jaeger et al. 2004; Perkins et al. 2006; Manu et al. 2009; Crombach et al. 2012; Becker et al. 2013).

Recently, a novel heuristic computational method (Fig. 8) has been demonstrated for the reverse engineering of dynamic models of planarian regeneration patterning directly from resultant morphological perturbation experiments (Lobo & Levin 2015). The method takes as input a dataset of planarian experiments formalized with a specifically designed mathematical ontology (Lobo et al. 2013a, 2013b). Crucially, this formalization permits the unambiguous specification of precise surgical manipulations, genetic and pharmacological treatments and, using a mathematical graph representation (Lobo et al. 2011), the resultant planarian morphologies. The method then uses a whole‐organism simulator for testing the error of a given dynamic model with respect to the set of experiments formalized in the input dataset, scoring the models according to the level of similarity between the in vivo and in silico resultant morphologies. Based on the algorithmic techniques of evolutionary computation (Holland 1975), the method maintains a population of evolving models, iteratively crossing, mutating, and selecting the best ones for the next generation. When a model is found that can perfectly recapitulate all the experiments in the input dataset, the algorithm stops and the found model is returned.

This method was successfully validated by reverse engineering the most comprehensive dynamic model of planarian regeneration found to date (Lobo & Levin 2015). The input experimental dataset included the formalization of the most important head‐versus‐tail planarian experiments in the literature, including surgical, genetic, and pharmacological perturbations (Gurley et al. 2008; Iglesias et al. 2008; Petersen & Reddien 2008, 2009, 2011; Rink et al. 2009; Oviedo et al. 2010). After 42 h (using 256 cores in a computer cluster), the algorithm found a dynamic model (a set of differential equations) that, when simulated, could recapitulate all the experiments included in the input dataset. Importantly, the model predicted new regulatory interactions (such as the unexpected inhibition of wnt by notum recently validated in vivo) (Kakugawa et al. 2015), the existence of novel regulatory genes (unknown genes labeled a and b in the model and characterized as the Frizzled family of receptors [pending validation] and hnf4 [manuscript in preparation], respectively), and the specific phenotypes produced after novel perturbations (such as the ability of hnf4 to rescue abnormal phenotypes [manuscript in preparation]). Indeed, this methodology can readily assist in the definition of comprehensive models directly from the ever‐growing experimental datasets obtained at the bench, and hence accelerate our complete understanding of planarian regeneration. While the specific details of the model will continue to be tested and refined in planaria, this general scheme can be applied to many other models in regenerative biology (e.g., limb regeneration [Lobo et al. 2014a] and bioelectric induction of metastasis [Lobikin et al. 2015a]).

The planarian regeneration field is at an extremely exciting place, poised to contribute to our understanding of physiological networks in pattern formation and evolution, as well as drive regenerative medicine advances. A few specific areas for future focus include (1) the continued development of comprehensive databases of planarian results, encompassing functional and physiological data, going beyond protein/gene datasets toward a bioinformatics of shape, and a standardization that will facilitate new machine learning approaches (Lobo et al. 2013a; Brandl et al. 2015); (2) novel monitoring and functional modification techniques, especially for physiological pathways. The extension of optogenetics, a powerful tool for probing neural and bioelectric controls of regeneration (Bernstein et al. 2012; Adams et al. 2013, 2014), may need to wait until misexpression technology becomes available in planaria. However, recent drug‐only approaches to light control of ion channel activity (Chambers et al. 2006; Tochitsky et al. 2014) and immobilization techniques (Dexter et al. 2014) may offer a way around the current impasse. (3) Much more work is needed to unify bioelectric and biochemical signaling. In particular, bi‐directional regulatory loops between specific chemical pathways, chromatin state, and spatial voltage distributions need to be characterized. Physiological networks also need to start being incorporated into the advanced modeling platforms, which heretofore largely focus on gene regulatory networks and biochemical gradients (Lobo & Levin 2015; Werner et al. 2015). (4) The molecular investigation of additional species of planaria (Sheiman et al. 2010) will facilitate studies of the evolutionary implications of bioelectric signaling.

(5) Work on transplantation (Nodono & Matsumoto 2012), currently a technique only mastered in very few laboratories, will be essential to test questions of target morphology (Fig. 1), as well as to understand the relative contributions of neoblasts versus surrounding soma for specification of pattern. (6) A major question concerns the persistence of morphologies (such as two‐head forms). Aberrant forms are rarely re‐cut in studies, and it is unclear currently which of the many phenotypes exhibited in the literature are in fact permanent, or what mechanisms mediate the permanence. (7) The role of the CNS in regeneration is well known (Kumar & Brockes 2012), although the fact that it can be instructive for shape and not merely permissive (Mondia et al. 2011) is less often mentioned. In planaria, ventral nerve cord integrity synergizes with GJC to determine whether a head forms at a wound (Oviedo et al. 2010); this interaction is currently not understood but is probably a gateway to understanding the relationship between neural and non‐neural bioelectric signaling in pattern control. (8) Planaria are an emerging model for cancer (Oviedo & Beane 2009); interestingly, anterior regeneration has the ability to cure posterior tumors (Seilern‐Aspang & Kratochwil 1965), exhibiting another example of long‐range patterning influence. Given the recent advances in bioelectrics as a functional regulator of cancer (Lobikin et al. 2012; Chernet & Levin 2013a; Yang & Brackenbury 2013; Huang & Jan 2014), planaria may well be a very fruitful context in which to understand the physiological inputs into the tension between robust patterning morphostasis and the patterning disorganization of tumorigenesis. (9) Planarian behavioral capabilities extend far past sensory systems and even extend into learning and memory (McConnell 1965; Nicolas et al. 2008).

Planaria demonstrate classical conditioning, instrumental learning, and can be preference trained (Thompson & McConnell 1955; Best & Rubenstein 1962; Wells 1967; Abbott & Wong 2008). Indeed, planaria are a unique model species in which memory and brain regeneration can be done in the same animal. This gives unprecedented opportunity to study the dynamics of memories during brain regeneration (McConnell et al. 1959; Shomrat & Levin 2013; Blackiston et al. 2015b).

One of the major areas for future development, in addition to specific techniques and datasets, is advances in conceptual integration of molecular data and algorithmic understanding of the regenerating body as a computational distributed system (Couzin 2007). Having seen the molecular conservation of information processing machinery (ion channels, GJs, and neurotransmitters) between brain function and planarian regeneration, it may be conjectured that some of the algorithms by which cell networks make decisions could also be conserved (Pezzulo & Levin 2015). We are currently testing this hypothesis by attempting to link realistic cell‐level electrophysiological simulation (Law & Levin 2015) to models of emergent patterning (Bessonov et al. 2015; Tosenberger et al. 2015) and dynamic systems descriptions of anatomical attractors (Friston et al. 2015), attempting a multi‐scale understanding of the planarian's remarkable shape homeostasis.

The planarian system is teaching us crucial lessons about how self‐repairing structures can be implemented via crosstalk between the genome and physical forces. Much of what we have seen in this model is highly conserved to bioelectric controls in vertebrate (Levin 2014a, 2014b) and even mammalian (Zhao et al. 2006; Lange et al. 2011) systems; these advances will suggest transformative roadmaps for biomedicine. Moreover, this invertebrate will teach us not only about this specific example of cell biology but more broadly about how communication among networks of agents implements adaptive pattern control (Levin 2012b). The impact of physiological studies in planaria, by revealing new ways to achieve guided self‐assembly of complex self‐repairing shapes, will probably impact artificial life, robotics, unconventional computation platforms, and the design of hybrid artificial agents (Doursat 2006; Doursat et al. 2013; Doursat & Sanchez 2014).

We thank the members of the Levin laboratory and many researchers in the planarian regeneration community for useful discussions. We also gratefully acknowledge support from the Paul G. Allen Family Foundation, National Institutes of Health (1R01HD081326, AR055993), the G. Harold and Leila Y. Mathers Charitable Foundation, the NSF (IGERT DGE‐1144591, CDI EF‐1124651 and EBICS CBET‐0939511), and the Templeton World Charity Foundation (TWCF0089/AB55).