Neural control of body-plan axis in regenerating planaria

Discussion
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The model is able to account for regeneration outcomes resulting from 10 different, major perturbations to the underlying molecular regulatory network (Fig 2A), and furthermore, makes accurate predictions regarding the expected incidence of heteromorphoses for different fragments cut along the anterior-posterior axis for different manipulations (Fig 4). The model is capable of predicting steady-state morphogen gradients consistent with regeneration outcomes of, not only cuts perpendicular to the anterior-posterior axis of 1H worms and complex cutting scenarios (Fig 5), but also the non-obvious regenerative outcomes of various localized sections of 2H worms (Fig 7). Furthermore, the incidence of 2H outcomes with cAMP inhibition and 0H outcomes with cAMP enhancement (Table 3), corroborates the previously suggested role for cAMP acting downstream of G-protein coupled receptor (GPCR) signaling through an abundantly-expressed 5HT7-like serotonin receptor [42]. This further highlights the role that neurotransmitters such as dopamine and serotonin, signaling through GPCRs, may play in specifying regenerated body-plan axis [25, 42], and suggests a potential additional signaling role for neural activity in the control of regeneration.

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Importantly, the model also suggested a test to cleanly distinguish between two hypotheses: control of regenerative polarity by pre-existing morphogen gradients versus by the directionality of net innervation of a fragment. Our new experimental data confirmed the remarkable prediction of 90° rotation of the regenerated anterior-posterior axis in small VNC-free fragments, indicating that average neural axon polarity in a fragment is the dominant driver of anatomical polarity via the directional transport of morphogens with respect to nerve polarity (Fig 6). This fact is not apparent from fragments containing VNC as typically used in most studies, because the large nerves of the VNC dominate transport, thereby leading to morphogen transport and stable gradients aligned with the original anterior-posterior axis. However, in fragments lacking VNC, their axial polarity is dominated by the commisural nerves and lateral branches, which are directed at right angles to the anterior-posterior axis, and their regenerative anatomy corresponds to the neural directionality, not to that of the original anatomical polarity. This is, to our knowledge, the first case were anterior-posterior polarity is predictably changed during regeneration without molecular or chemical manipulations, and therefore presents a strong confirmation of our model and a new avenue in which the re-establishment of polarity can be studied in a new context in planaria.

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An additional important current knowledge gap concerns mechanistic explanations for permanent rewriting of target morphology: planaria exposed to brief modulators of physiological state produce 2-headed (bipolar) regenerates, which continue to re-create two-headed anatomy upon future rounds of regeneration, with no further manipulation [79, 80]. The ability to permanently alter the pattern to which the animal regenerates, without genomic editing, is a novel example of large-scale epigenetics and has not been addressed by existing molecular pathway models. Here we show that the existence of a bipolar nervous system determines subsequent regeneration outcomes dependent on the portion of nervous system map cut from the whole: fragments containing significant bipolarity regenerate as 2H, whereas fragments cutting a monopolar portion out of the neural network regenerate with 1H morphology (Fig 7). Thus, we provide further evidence that target morphology outcomes may be encoded by the net polarity of nerves in a regenerating fragment.

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These data have implications beyond planarian regeneration. It has long been known that the nervous system is required for proper appendage regeneration [122, 123]. However, a mechanistic explanation for this dependence has not been available; nor was it known whether the influence of the neurons is permissive or instructive for patterning, although experiments in tadpole tails [124], developing frog embryos [125], and non-planarian worms [81] have provided tantalizing suggestions to this effect. Our model proposes a specific mechanism by which neural growth patterns can control large-scale whole body patterning. This work in bilaterian regeneration is consistent with observations in nematode development [126], which suggest that neural control of Wnt signaling profiles is a highly conserved mechanism for body pattern control, conserved among taxa with widely divergent body-plans, developmental modes, and regenerative abilities. More broadly, these data suggest new hypotheses, to be tested in future work, about the evolutionary dynamics of nervous systems, ectodermal polarity pathways, and Hh and Wnt signaling pathways [40].

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Ultimately, our model provides a context for understanding target morphology in terms of both an embedded vector transport field (augmenting the positional information concept with that of a directional information flow map) and the complex system established by interacting molecular entities. Within this context, the regenerating organism utilizes the inherent system dynamics to maintain body-plan homeostasis under normal circumstances by maintaining steady-state concentration profiles of various substances, yet naturally detects injury when the cell cluster is damaged as vector transport redistributes morphogens with respect to the new boundaries introduced by the specific injury. After injury, the morphogens achieve a new, similar steady-state to that preceding injury, which instructs the regeneration of missing features. Therefore, the model assists in providing a deeper understanding of mechanisms required to specify single cell activities such as gene expression changes and differentiation which lead to homeostasis and coordination over multiple levels of scale.

Conclusions
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Planaria are an important model for a very fundamental phenomenon: pattern homeostasis, which allows regulative regeneration to restore complex anatomical structures. It is widely acknowledged that the discovery of molecular signaling relationships has far outpaced our understanding of the origin of order and the ability of complex systems to remodel to correct anatomical patterns from diverse starting conditions. Fully quantitative models are an essential step for the field of developmental biology, and are an important emerging tool for rational discovery of interventions in regenerative medicine. The framework presented here is a powerful environment for general use, within which future findings in planarian regeneration and other systems can be predicted and interpreted. The model and simulation environment facilitate the addition of new data in this field to explore self-organizing dynamics that cannot be inferred from arrow diagrams alone, and make novel predictions about the large-scale behavior of molecular pathways. Our model contains a regulatory network which recapitulates a majority of published genetic and pharmacological manipulations, and makes new predictions for regenerative outcomes for a wide variety of experimental manipulations, both genetic, chemical and physical, which we successfully validated here. Furthermore, the modeling of neuronally-mediated vector transport of morphogens was validated in new experiments indicating the importance of dynein-based transport in morphogen localization as well as showing the reorientation of head-tail polarity in fragments, according to their nerve polarity, without any treatment.

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Even more importantly, our model and its analysis are proposed as a proof-of-principle effort, applicable potentially to a wide range of patterning contexts, as a first step towards an integrated modeling system within which complex, emergent dynamics can be explored.