Re-Membering the Body: applications of computational neuroscience to the top-down control of regeneration of limbs and other complex organs

Abstract

A major goal of regenerative medicine and bioengineering is the regeneration of complex organs, such as limbs, and the capability to create artificial constructs (so-called biobots) with defined morphologies and robust self-repair capabilities. Developmental biology presents remarkable examples of systems that self-assemble and regenerate complex structures toward their correct shape despite significant perturbations. A fundamental challenge is to translate progress in molecular genetics into control of large-scale organismal anatomy, and the field is still searching for an appropriate theoretical paradigm for facilitating control of pattern homeostasis. However, computational neuroscience provides many examples in which cell networks (brains) store memories of geometrical states and coordinate their activity towards proximal and distant goals. In this Perspective, we propose that programming large-scale morphogenesis requires exploiting the information processing by which cellular structures work toward specific shapes. In non-neural cells, as in the brain, bioelectric signaling implements information processing, decision-making, and memory in regulating pattern and its remodeling. Thus, approaches used in computational neuroscience to understand goal-seeking neural systems offer a toolbox of techniques to model and control regenerative pattern formation. Here, we review recent data on developmental bioelectricity as a regulator of patterning, and propose that target morphology could be encoded within tissues as a kind of memory, using the same molecular mechanisms and algorithms so successfully exploited by the brain. We highlight the next steps of an unconventional research program, which may allow top-down control of growth and form for numerous applications in regenerative medicine and synthetic bioengineering.

1. Introduction

1.1. The challenge of next-generation regenerative bioengineering

A key goal in regenerative medicine is to replace damaged or aging organs, for example the repair of entire amputated limbs ¹. Taking the control of biological growth and form to its ultimate conclusion, bioengineering hopes to eventually be able to make self-repairing living structures in any desired configuration – the so-called “biobots” (bioengineered hybrid constructs with specific morphology and function) ². However, even when it becomes possible to make any cell type from stem cells, how would we restore a complete hand or eye? Micromanaging the construction process at the lowest level is likely not feasible for such complex structures. A teratoma tumor may possess hair, teeth, and muscle, but lacks appropriate 3D organization, demonstrating that well-differentiated cell types are necessary but not sufficient for forming a functional complex structure. Moreover, what is required is not merely correct initial morphogenesis, but understanding and implementing reparative robustness in the face of subsequent challenges. Fortunately, the field of developmental and regenerative biology provides extensive proof-of-principle of control circuits that enable efficient self-repair and dynamic control of multicellular, large-scale shape ^1a.

Eggs reliably self-assemble into adults with many distinct tissues in precise geometric configuration. Crucially, the embryos of many species are not pre-determined mosaics, but display astonishing capabilities of self-repair, dynamic rescaling, dynamic reconfiguration, and functional plasticity (Figure 1). For example, embryos that are split or combined early in development revise their developmental program to the number of available cells and give rise to multiple complete organisms. Dynamic re-scaling of organs allows even adults to incorporate foreign tissue and re-pattern it appropriately; transplanted cockroach legs with the wrong number of segments will undergo intercalation to restore leg segmentation more appropriate to the leg’s new location ³, while planarian flatworms continually reconfigure their body tissues to maintain correct relative proportions despite changing cell number during starvation ⁴.

Figure 1. Examples of dynamic pattern regulation.

Large-scale patterning during regeneration and embryogenesis often exhibits flexible growth programs that work to achieve a specific target morphology. (A) Embryos of many species can be split in half but result in two perfectly normal individuals – monozygotic twins (photo by Oudeschool via Wikimedia Commons). (B) Similarly, mouse embryos can be joined together and yet re-pattern to give rise to a normal animal. (C) Salamander limbs can regenerate perfectly following amputation, and the process stops when a correct limb is rebuilt. (D) A tail grafted onto a flank of an amphibian slowly remodels into a limb – a structure more appropriate to its new anatomical position; this includes re-specification of the distal-most tip into fingers, showing that the process is non-local (because the immediate environment of the tail tip is its expected “tail” context, and it should have no reason to change unless it received long-range signals). (E) In some species of deer, damage at a particular spot on the invariant branched structure will result in an ectopic tine appearing in that same location next year after the antlers are shed and re-grow (used with permission ¹⁷²). (F) A tadpole modified during development such that its craniofacial organs are in the wrong positions nevertheless develops into a normal frog, showing the ability of morphogenesis to flexibly correct unexpected initial states towards the same anatomical outcome (frog image courtesy of Erin Switzer; tadpole image used with permission ⁶). These examples illustrate the ability of biological systems to robustly pursue or maintain a goal state specified at the level of topological arrangement of organs – a capability we must learn to exploit, for transformative applications in synthetic bioengineering. We do not discuss plants, because though they often possess impressive powers of regeneration ¹⁷³, they generally have no fixed target morphology at the level of the entire organism. Images in panel F are courtesy of Douglas Blackiston and Erin Switzer.

Adult salamanders regenerate amputated limbs, tails, eyes, jaws, hearts, and portions of the brain; remarkably, the rapid growth that produces these new structures stops once the correct pattern has been completed. Moreover, tails ectopically grafted to the flank of an amphibian host slowly remodel into limbs ⁵, revealing the body’s ability to coordinate cell behavior towards a specific anatomical plan. The same remarkable capability is revealed in the process of metamorphosis, as tadpoles will correct experimental rearrangements of their craniofacial structures to reach a normal frog facial anatomy ⁶. In all of these cases, the correct shape outcome can be seen as a homeostatic target range; interestingly, in some species (such as deer antlers, crabs, and planaria), this target anatomy can be re-set permanently ⁷, revealing that the encoding of the ideal homeostatic anatomical state is somewhat labile and not genetically fixed.

The fact that the process of limb regeneration ⁸ and embryogenesis ⁹ can reprogram (normalize) tumor cells into normal structures highlights the causal potency of not only single-cell states but of large-scale anatomical configurations. Development, cancer, and regeneration are distinct processes, which may involve diverse underlying molecular mechanisms in addition to conserved ones. However, what all of these examples have in common is a kind of “shape homeostasis” – the ability of systems to flexibly regulate cell-level events in order to achieve higher-level (organ-, tissue-, or whole-organism) patterning states despite deviations from those states. While recent advances in bio-printing, materials engineering, and scaffolding ¹⁰ seek to address creation of complex structures, these technologies do not address the functionality of adaptive (on-demand) remodelling, nor reveal the endogenous biology that allows cellular structures to implement specific morphology changes aimed toward a correct configuration. Here, we define “Target Morphology” as that anatomical state towards which remodelling occurs, and which, when reached, causes a cessation to proliferation and morphogenetic rearrangements.

The major knowledge gap is the understanding of how remodeling of complex shape is driven by the physical activity and information processing of smaller subunits (not necessarily cells). Next-generation bioengineering must move beyond direct assembly of cell types, toward the control of the built-in error correcting morphogenetic networks and the programming of shape by specifying organs and their topological relationships ¹¹. A key issue for the future of biology and medicine is to find the appropriate theoretical paradigm with which to understand complex pattern regulation besides feed-forward emergence, and derive quantitative models with predictive power that will enable rational modification of shape for engineering and biomedical applications. Here we discuss a complementary, top-down approach, which can encompass the known molecular elements that implement pattern formation: chemical gradients ¹², physical forces ¹³, and bioelectrical signaling ¹⁴. We propose that the field of computational neuroscience has developed theoretical and computational tools that can help understand and exploit pattern regulation as a closed-loop cybernetic system that incorporates feedback mechanisms and operates on high-level (anatomical) metrics (Supplemental Figure 1).

1.2. A new approach: top-down programming of pattern formation

Today’s dominant approach to pattern regulation is bottom-up – the hope that complex outcomes can be understood via “emergence” once we have all of the relevant details on cellular, subcellular, and protein interactions. However, it is widely recognized that there remains a gulf between ever finer-resolution analyses of molecular pathways and global understanding of the control of large-scale measurable such as topological arrangement of organs. Indeed, direct management of emergent patterning cascades ^{2, 11b, 15} is likely to be limited by the inverse problem that plagues complex emergent systems ⁷. We hypothesize that efficient programming at the level of anatomical outcome can be achieved if we harness the kind of top-down control algorithms that have been so successfully exploited by nervous systems in the control of animal behavior, and which are studied in the field of computational neuroscience.

The rest of the article is organized as follows. We first discuss one set of control pathways that has recently been implicated in just such a large-scale control of pattern: developmental bioelectricity. Slow changes of resting potential in non-excitable cells regulate the coordination among cells required for morphogenesis, and appear to confer on all tissues capabilities that are usually thought of only in association with neuronal networks. Developmental bioelectricity is of high relevance for regenerative biology because it demonstrates practical applications for exploiting neural-like information processing within somatic structures during morphogenesis. Here, we highlight some features of non-neural cell signaling that can be mapped to information processing in the brain, and elaborate the implications for designing top-down intervention strategies. We next discuss both algorithmic and molecular homologies between information processing in the central nervous system (CNS) and pattern regulation during regeneration development. We propose that shape regulation may be efficiently understood and manipulated as a kind of learning and (constructive) memory/recall process - in analogy to a scheme in which generative models learn and memorize patterns and error-correction mechanisms trigger actions that involve body changes (e.g., growth and differentiation) that restore them as necessary. In this discussion, we hold to an objective, unambiguous, empirical success criterion for any approach to pattern formation, not an a priori commitment to a philosophical position. The best model is the one that optimally facilitates predictable changes in large-scale shape, regardless of whether the model is formulated in terms of genes, information, topological concepts, or anything else (top-down, bottom-up, or mixed). We conjecture that developmental bioelectricity is an emerging field ideally placed to facilitate the practical transfer of insights from computational neuroscience into control of dynamic morphogenesis in biomedicine and bioengineering.

Our goals in this Perspective are to: 1) Refocus the community on the design challenge of programming dynamic, adaptive remodeling capabilities, beyond stem cell differentiation; 2) Review data in developmental bioelectricity, showing how the function of endogenous ionic gradients can be harnessed to implement neural-like information processing in regenerative and bioengineering applications relevant to all cell types; 3) Introduce concepts from computational and cognitive neuroscience, widening the toolbox of bioengineers with new ideas that can be exploited to design mechanistic strategies for top-down control of growth and form (processes with a goal state, not only bottom-up emergence); and 4) Offer a specific example of a mathematical methodology that can be used to model - and possibly control - pattern formation from a top-down perspective. We synthesize these ideas into a hypothesis about the algorithmic and molecular homologies between information processing in the central nervous system (CNS) and pattern regulation during regeneration development.

2. Harnessing non-neural bioelectricity to implement organ-level programming

2.1. The basics of molecular bioelectricity: definitions and tools

Developmental bioelectricity refers to signaling among non-excitable cells mediated by endogenous electric fields and differences in resting potential ^{14d, 16}. These bioelectrical states are created by ion channel and pump proteins that maintain voltage gradients across the cell membrane, and are transduced into a variety of transcriptional and epigenetic cell responses by known mechanisms (including neurotransmitter movement) ^{14e, 17}. Pattern regulation by specific spatial distributions of transmembrane potential (V_mem) within tissues has recently been implicated as an instructive factor in numerous patterning events during development, regeneration, and cancer suppression ¹⁸, revealing how many cell types exploit the physics of ion flows to communicate much like neurons in the brain, and how this dynamics helps shape complex large-scale morphogenesis. Crucially, as in the CNS, the spatio-temporal patterns of somatic bioelectrical signaling are regulated by flexible electrical synapses known as gap junctions, which establish iso-potential cell regions and maintain dynamic boundaries between compartments with distinct voltage gradients and thus different anatomical fates ¹⁹. It is not surprising that these versatile regulatory building blocks are also implicated in memory, learning, and establishment of circuits in the CNS ²⁰. McCulloch’s answer to why the mind is in the head: “Because there, and only there, are hosts of possible connections to be performed as time and circumstance demand it” ²¹, in fact applies also to somatic tissues. Highly dynamic changes in selective gap junctional communication and tunneling nanotubes allow any cell field to form complex activity-dependent networks that communicate via electric and neurotransmitter-mediated signaling during pattern formation ^{19, 22}. Many cell types, including cancer cells ²³ and skin ²⁴ cells, are known to propagate gap junction-dependent electrical waves, and GJs regulate global decision-making during the patterning of the somatic left-right axis ²⁵, tumorigenesis ²⁶, head-tail polarity ²⁷, and tail regeneration ²⁸.

Recent advances have resulted in new tools for studying developmental bioelectricity at the molecular level, and for mechanistically linking biophysical events with downstream genetic targets via dissection of transduction machinery ²⁹. Voltage-responsive fluorescent dyes ³⁰ (Figure 2A,B) and genetically-encoded voltage reporters ³¹ allow the monitoring of bioelectric state of complex tissues in vivo. Novel reporters (nano-scale materials that can report physiological parameters via MRI imaging) will even further facilitate the bioelectric profiling of thick and complex tissue, although even today’s technology is sufficient to characterize important structures in metazoan patterning models in vivo ^{30, 32}. Most importantly, a panel of constructs encoding well-characterized gap junctions, ion channels, and pumps enable the targeted modulation of V_mem and network topology in any cell group (Figure 3), for functional studies ³³. Mis-expressed or endogenous ion translocator proteins can be regulated pharmacologically, and the technique of optogenetics, which is revolutionizing neuroscience ³⁴, has now been applied to the control of regeneration-specific bioelectric signals ^{32d, 35}.

Figure 2. Non-neural cells use bioelectrical signaling for pattern formation.

(A) Voltage-reporting fluorescent dyes reveal a rich pattern of bioelectrical communication among early frog embryo cells. (B) During later development in the frog embryo, a prepattern of hyperpolarization is seen (lighter cells) which establishes the prospective boundaries of craniofacial gene expression and the location of anatomical organs: in this way, bioelectric state information directly and functionally encodes the anatomy and structure of the face (used with permission ⁵⁷). If this bioelectric pattern is artificially perturbed, predictable changes in face morphology result. (C) Targeted changes of bioelectric state, by misexpression of ion channel mRNA in frog embryos in vivo, reprogram body regions at the level of organs: without having to specify the details, a portion of the gut can be re-specified to form a complete eye (red arrowhead; used with permission from ³³). (D) The process involves not only the cells whose voltage properties were changed (marked with blue lineage dye) but also recruits some of the host’s unaltered cells toward making a complete circular lens, revealing a non-local property of bioelectric organ induction.

Figure 3. Tools for perturbing bioelectrical networks.

Much as in the nervous system, there are 2 basic options for experimentally modulating the activity of bioelectric networks in developmental contexts. Analogous to synaptic plasticity, the connectivity of the network can be modified, by blocking endogenous gap junctions (electrical synapses), either pharmacologically or via misexpression of a dominant negative connexin subunit, or introducing novel gap junctional connections by driving expression of wild-type connexins or connexin mutants with desired gating/permeability properties. Analogous to intrinsic plasticity, one can instead modify directly the bioelectrical state of specific cells. Pharmacological, genetically-encoded, or optogenetic strategies can be used to modify which channels are expressed in cells, or which are open/closed. Guided by the Goldman equation, these interventions can be designed to result in desired changes of resting potential in the targeted cells. Images in this figure were created by Jeremy Guay of Peregrine Creative.

Suppression screen analysis, in combination with targeted depolarization or hyperpolarization, has shown that slow bioelectrical signals in vivo are transduced into downstream changes of transcription and chromatin modification by regulation of calcium and serotonin signaling ^{32c, 33, 36}, just as in neurons. Additional transduction machinery also exists, making use of voltage-gated movement of butyrate ³⁷, voltage-sensitive phosphatases ³⁸, and receptor clustering ³⁹ to convert specific ranges of resting potential (and changes therein) into downstream transcriptional responses and second-messenger signaling events.

2.2. Bioelectric state controls single cell function

The V_mem state of cells and their neighbors determines cell behaviors, in concert with other signaling modalities. In general, terminally differentiated, quiescent cells tend to be strongly polarized (bearing a more-negative resting potential), while embryonic, stem, and tumor cells tend to be depolarized (closer to zero) ⁴⁰. The picture is complicated by the fact that many cells in fact do not have a single V_mem, but like neurons bear a set of distinct voltage domains over their surface ⁴¹ – analogous to the way an action potential travelling down an axon establishes local domains of depolarization that can underlie computation ⁴². While the functional significance of voltage microdomain patterns within single cells (e.g., a combinatorial code of voltage domains on the membrane) has not yet been tested, regulation of overall cell V_mem is beginning to be used in bioengineering contexts to regulate cell connectivity ⁴³, wound healing ⁴⁴, and differentiation ⁴⁵.

These strategies work because V_mem is not a read-out or a house-keeping parameter but is a functional determinant of cell state, such as proliferative capacity, migration, and plasticity ⁴⁶. Differentiation and proliferation are controlled by changes in V_mem, as has been shown in human mesenchymal stem cells ^{45a, 47}, cardiomyocytes ⁴⁸, iPSCs ⁴⁹, vascular muscle ⁵⁰, embryonic stem cells ⁵¹, myoblasts ⁵², the specification of neurotransmitter types ⁵³, and the precise control of precursor differentiation ⁵⁴ in the developing nervous system and heart. Given the known roles of V_mem in regulating normal migration, differentiation, and proliferation, it is not surprising that control of bioelectric states is also increasingly implicated in the developmental dysregulation known as cancer ^{23, 55}, and is a suspected causal agent in several kinds of birth defects ⁵⁶.

2.3. Bioelectric regulation of large-scale pattern formation

Most importantly, bioelectric signals also mediate long-range coordinating influences. Spatio-temporal gradients of V_mem among cells in vivo are now known to regulate organ identity, positional information, size control, and polarity of anatomical axes ^{14e, 18}. One mode of V_mem signaling is as a prepattern. Much like Hox genes, whose combinatorial patterns of gene expression encode specific body regions during development, bioelectric prepatterns in the developing face of the frog and planarian models regulate the gene expression, size, and shape of craniofacial components ⁵⁷. In the frog for example (Figure 2B), patterns of hyperpolarization in the nascent face reveal the prospective locations of the eyes and other structures; experimental perturbation of these distributions alters the boundaries of expression of face patterning genes such as Frizzled, with the expected effects on craniofacial anatomy. Spatial differences of resting potential can serve as a direct scaffold for subsequent morphogenesis.

Bioelectric gradients also specify orientation of the LR axis in frog and chick embryos ^{36d, 58} and set the size of regenerating structures in segmented worms, the brain in frog embryos, and regenerating zebrafish tails ^{32c, 59}. The gradients created by ion transporters, such as the V-ATPase, are required for consistently-oriented left-right patterning of the heart and viscera ^36d, fin regeneration ⁶⁰, and eye development ⁶¹. The instructive information is mediated by bioelectric gradients per se, and not other functions of ion channel proteins or chemical signaling by specific ions: pattern can be predictably altered by specific modulation of those spatial gradients using any convenient channel or ion to achieve the desired change in V_mem state ^{33, 36c}. This offers the opportunity for bioengineers to use structured light (for optogenetic activation) ⁶² or substrates with embedded channel drugs ⁶³, to impose patterned bioelectrical states on in vitro constructs or regenerating tissues for augmented control of morphogenesis.

In addition to directly specifying the pattern of subsequent anatomy, some bioelectric signals trigger whole developmental modules. In the case of tail regeneration in Xenopus, forcing a regeneration-specific bioelectric state in non-regenerative animals for just one hour overcame physiological, chemical, and age-dependent blockade of regenerative capacity to induce complete regrowth of this complex neuromuscular appendage over 8 days ⁶⁴. Importantly, a very simple (low information content) and brief stimulus, such as “pump protons”, is sufficient to initiate a complete and self-limiting cascade of events that rebuilt the entire appendage ^16a, in essence providing a “build whatever normally goes here” signal. Likewise, imposition of a bioelectric state via misexpression of specific ion channels can rescue normal brain formation despite the presence of a mutated form of the Notch protein, which otherwise significantly impairs neural development ^32c. These examples reveal that bioelectric state can function as a master regulator, exploiting the innate modularity of developmental cascades; this is consistent with a regenerative medicine strategy which seeks to avoid the need to micromanage morphogenesis of complex structures but rather rely on calling up patterning subroutines already present in the host.

Moreover, bioelectric signals can reprogram the identity of whole somatic regions toward different organs. The morphogenesis of new regeneration blastemas in planaria can be redirected to form heads or tails by imposition of appropriate bioelectric state ^{36a, 59a}. In vertebrates, whole eye formation can be induced ectopically, far outside the head, even within mesoderm or endoderm tissue (Figure 2C) by misexpression of specific ion channels in vivo ³³. This process is mediated by a feedback loop between hyperpolarization and eye genes such as Rx1, but importantly, “master eye inducer” genes such as Pax6 cannot recapitulate this effect (do not induce eyes outside the head in vertebrates), illustrating the benefits of including bioelectric signaling to enhance control over pattern formation. These data reveal that simple stimuli can trigger much more complex, coherent responses (a property that is very familiar to researchers working on memory and hierarchical representation of cognitive content in the brain).

Bioelectric signaling is often not cell-autonomous: cells with unique voltage characteristics serve as organizers, recruiting un-manipulated host tissues to participate in the ectopic morphogenesis (Figure 2D). Bioelectric signaling in normal development, and also in cancer induction ^36c and suppression ^37c, is inherently non-local – another property it shares with the way information is distributed within neural networks. For example, during formation of the vertebrate brain, the size of the resulting structure is regulated by bioelectrical information collected from distant regions of the embryo ^{32c, 59c}, implementing a kind of distributed processing also observed during brain function. Much as in the nervous system, electrical circuits in non-spiking somatic cells can coordinate long-range physiological decision-making during pattern regulation.

These examples illustrate the fact that bioelectric signaling provides instructive information to patterning processes by integrating state information across considerable distances, and reveals that morphogenesis can be programmed at the level of complex multi-cellular shape (organs), not only by specifying individual cell types. We suggest that the transformative advances in this field will come not only from ever more-detailed studies of bioelectric signal transduction cascade within individual cells, but will require understanding the bioelectric code: the mapping between dynamics of spatially-distributed (tissue-scale) bioelectric states and the resulting anatomical outcomes. This parallels neuroscientists’ efforts to understand the way that memories and cognitive content are physically represented by the electrical states of brain tissue ⁶⁵. The output of somatic bioelectric networks is cellular patterning activity (proliferation, differentiation, migration, and gene expression), much as the output of neural bioelectric networks is muscle contraction and glandular activity.

2.4. Bioelectricity and non-genetic storage of morphogenetic signals

The information-bearing signal (the necessary and sufficient trigger) for events such as eye induction, head determination, brain formation, or tail regeneration via V_mem change is a spatially-distributed physiological state, not a gene product ¹⁶. In many contexts, the exact channel or pump used to trigger such morphological changes is often irrelevant – many sodium, potassium, chloride, or proton conductances can be used to achieve the same morphogenetic outcome as long as the appropriate V_mem distribution is enforced ^{33, 36c, 57}. This means that the actual cause of the given morphological change can be a bioelectrical property not necessarily in 1:1 correspondence with any mRNA or protein. Because channels and pumps can open and close post-translationally, two cells expressing precisely the same mRNA and protein can be in very different bioelectrical states. The cautionary message of these data are that tracking gene expression, and even protein levels, is insufficient – efficient control in regenerative and bioengineering outcomes will necessarily require incorporating sensors and modulators of in vivo physiological state. Rich patterns of bioelectrical gradients can exist in a transcriptionally homogenous tissue and be completely invisible to protein and mRNA profiling, precisely in the way that the specific memories of a neural network are not directly visible from a simple survey of which proteins and genes are present. This makes a clear link to the general concept of memory in the information sciences, since engineering models of memory, like electric flip-flop circuits or classic magnetic coil core memory systems, store data in stable energy flow patterns. Indeed, non-neural cells are now known to express ion channel types that implement stable memory elements for discrete voltage states ⁶⁶, and synthetic bioengineering may exploit as an entirely new kind of memory medium.

One recent set of findings provides an illustration of how bioelectric circuits during regeneration can stably store pattern memory. Planarian flatworms have the remarkable ability to regenerate completely from partial body fragments ⁶⁷, and the construction of a head or a tail at the correct location in each cut fragment by stem cells is guided in part by an endogenous bioelectric circuit ^36a. Our neural analogy suggests that this information may be stored in the stable modes of the real-time dynamics of a bioelectric circuit implemented by the somatic tissues; if so, then it should be configurable at this same level – our model predicts that it should be possible to stably (permanently) reprogram the basic architecture of the planarian without altering its normal genomic sequence, much as new memories can be added to a brain without requiring genomic changes specific to each mental state. Indeed, we showed that interfering with the “short term memory”, by directly modifying the pattern of resting potentials in the tissue, does indeed allow us to change the tail end of a fragment into a normal head during one round of regeneration ^{36a, 59a}.

Remarkably however, interfering with “long term memory”, by altering network connectivity in the planarian fragment (targeting electrical synapses known as gap junctions ^{20a, 68}), results in fragments developing heads at both ends and this state is permanent across future rounds of cutting ²⁷. Weeks after the initial gap junction-modifying treatment, (Figure 4A–E), when these 2-headed animals have their heads and tails amputated again (in just water, with no further perturbation), the same 2-headed phenotype results, and this is repeated upon subsequent amputations. Thus, a transient perturbation of physiological cell:cell connectivity stably changes the pattern to which the animal regenerates upon damage, despite normal genomic sequence! This phenotype is stable across the animal’s usual reproductive mode (fission) – genome sequencing of 2- and 1-headed planaria would reveal no differences, illustrating how patterning information can be stored at the level of a bioelectric circuit. While epigenetic processes may be involved, note that chromatin modification mechanisms alone are not a sufficient explanation since the ectopic heads (tissue which might be suggested to have been epigenetically reprogrammed into a head state from its original tail identity) are thrown away at each generation of cutting. What remains is a gut fragment, which somehow knows that it is to form 2 heads, not 1, upon further cutting; what has been changed in such worms is not only the anatomy of one region of the animal, but the encoded pattern that any fragment must rebuild if removed from the body. Such permanent reprogramming of the planarian bodyplan has not been demonstrated using any other method.

Figure 4. Pattern memory encoded in bioelectric circuits.

Planaria (A) can regenerate any body region, and their head-tail polarity is regulated in part by an endogenous voltage gradient. When the head and tail are removed and the middle fragment is treated with reagents that alter the topology of the bioelectric network (gene-specific RNAi targeting innexin proteins, or gap junction-targeting drugs that wash out in 24 hours, B), a 2-headed planarian results (C). Remarkably, weeks later, when these animals are cut and re-cut in plain water, 2-head worms continue to result (D,E) despite the animal’s normal genome and the fact that “epigenetically reprogrammed” tissues are removed at each round of cutting. This illustrates the distributed encoding of target morphology among all body regions, the storage of pattern information in bioelectrical properties distinct from genomic information, and the ability to alter the shape to which this animal repairs upon damage by changing network connectivity among cells long-term memory (all ideally mirrored by the known properties of long-term memory). Bioelectric circuits that could stably store such state information consist, much like neurons, of voltage potentials driven by ion channels (F, transcriptional changes in the expression of which are analogous to intrinsic plasticity in neuroscience) and of connectivity via highly tunable electric synapses – gap junctions (G, changes in which are analogous to synaptic plasticity). (H) Positive feedback loops between voltage states (an aggregate, systems property) and voltage-sensitive ion channel states allow stable attractors of distinct bioelectrical states. Together with known mechanisms of synaptic plasticity implemented by gap junctions, calcium, and neurotransmitters (I), these components should allow the creation of mechanistic models of pattern memory and the construction of synthetic bioengineered devices with memory and self-repair capabilities. Panels A-E used with permission ¹⁸. Images in panels F and G were created by Jeremy Guay of Peregrine Creative. Images in panel H used with permission ^75b.

The current challenge in this field is to integrate molecular-genetic ⁶⁹ and anatomical ⁷⁰ datasets with emerging biophysical models of memory encoded in the bioelectric states of cells ⁷¹. While much remains to be investigated (including tracing the specific patterns of GJ connectivity in living fragments to understand network topology), the planarian example illustrates several important points. First, information functionally determining the large-scale anatomical state of the post-regeneration organism is encoded in the bioelectric signaling among somatic cells. Second, alterations of the bioelectric pattern result in long term, stable changes in the shape memory (similar to synaptic plasticity), while maintaining the organism’s same genomic sequence. Third, the information about basic anatomical polarity and body organization must be stored in a distributed form throughout the animal since the altered tissue is discarded at each round of cutting.

These important features of developmental bioelectricity suggest intriguing parallels with information processing in the brain ⁷² (Table 1). We hypothesize that the basic components of bioelectric signaling enable neural-like networks in non-neural tissues (Figure 4F–I, Supplemental Fig. 2–3). For example, the distributed storage of information in bodies could parallel the way information is distributed within neural networks ⁷³. From an evolutionary point of view, this is unsurprising, as neurons evolved by specializing for speed those bioelectrical processes that were already present in far more ancient cell types and being used for morphogenesis ⁷⁴. We propose the hypothesis that not only key molecular components of ionic signaling are conserved between neurons and non-excitable cells, but also the algorithms by which they process information. We conjecture that the tricks that brains exploit to guide adaptive behavior evolved from similar computational memory processes that were first evolved to control body patterning, both using some of the same biochemical, electrical, and physiological mechanisms ⁷⁵.

Table 1.

conceptual mapping between cognition and pattern formation

Cognitive concept	Patterning concept
Action potential movement within an axon	Differential patterns of Vmem across single cells’ surface
Local field potential (EEG)	Vmem distribution of cell group
Intrinsic plasticity	Change of ion channel expression based on Vmem levels
Synaptic plasticity	Change of cell:cell connectivity via Vmem’s regulation of gap junctional connectivity
Activity-dependent transcriptional changes	Bioelectric signals’ regulating gene expression during patterning
Neuromodulation	Developmental (pre-nervous) signaling via neurotransmitters such as serotonin moving under control of bioelectrical gradients
Direct transmission	Cell:cell sharing of voltage via nanotubes or gap junctions
Volume transmission	Cell:cell communication via ion levels outside the membrane or voltage-dependent neurotransmitter release
Synaptic Vesicles	Exosomes
Sensitization	Cells become sensitized to BMP antagonists to stabilize neurogenesis
Functional lateralization	Left-right asymmetry of body organs
Taste and olfactory perception	Morphogenetic signaling by diffusible biochemical ligands
Activity-dependent modification of CNS	Control of anatomy by bioelectric signaling within those same cells
Critical plasticity periods	Competency windows for developmental induction events
Autonomic reflexes	Wound healing
Voluntary movement	Remodeling, regeneration, metamorphosis
Memory	Shorter term: Regeneration of specific body organs. Longer term: Morphological homeostasis over decades as individual cells senesce; altering basic body anatomy in planaria by direct manipulation of bioelectric circuit
Pattern completion ability of neural networks (e.g., attractor nets)	Regeneration of missing parts in partial fragments (e.g., planaria)
Forgetting	Cancer, loss of regenerative ability
Addiction	Limb becomes unable to regenerate without nerve once exposed to nerve
Encoding	Representation of patterning goal states by bioelectric properties of tissue
Visual system feature detection	Organ-level decision making during morphogenesis
Holographic (distributed) storage	Any small piece of a planarian remembers the correct pattern (even if it has been re-written)
Instinct	Hardwired patterning programs (mosaic development)
Behavioral plasticity	Regulative developmental programs and regenerative capacity
Self-modeling	Surveillance of anatomical state by brain
Goal-seeking	Embryogenesis and regeneration work towards a specific target configuration despite perturbations
Sub-goaling in problem solving tasks	Developmental modularity
Adaptivity and Intelligence	Morphological rearrangements carry out novel, not hardwired, movements to reach the same anatomical configuration despite unpredictable initial starting state
Tabula rasa	Cells could be a (semi) universal constructor, able to build any shape that can be specified via the pattern memory code
Age-dependent cognitive decline	Age-dependent loss of regenerative ability
Optogenetic insertion of false memories	Optogenetic induction of regeneration or ectopic organs
Reading of semantic content from brain scans	Detecting differences in target morphology from fluorescent voltage dye data

Legend: possible mapping of concepts in cognitive neuroscience to examples in pattern formation (listed in rough order of level of organization, from low to high descending).

These parallels with neural information processing are of more than theoretical interest, because in computational neuroscience and cybernetics, practical methods have been developed for pursuing a top-down approach to the control of complex hierarchical systems. These data are not only germane to philosophical discussions of levels of control in biology ⁷⁶, but suggest an empirical, tractable research program for programming shape at a level of organization beyond individual cells. Certainly bioelectric cues do not determine morphogenesis on their own: they represent just one layer of a complex morphogenetic field, which guides patterning through interplay with biochemical gradients, transcriptional networks, and materials properties. While a number of these modalities offer cross-scale emergence and long-range control ⁷⁷, we believe that the available state-of-the-art tools (both technical and conceptual) for understanding electrical networks offer the most tractable approach toward understanding and control of large-scale pattern regulation in vivo. Below we discuss in detail a possible top-down approach to pattern formation, using tools from computational neuroscience that are more fully described in the Appendix.

3. A top-down perspective on pattern control

3.1 Target morphology, error-correction mechanisms, and bioelectrical signals

Could cell behavior be guided by an algorithm that minimizes - in the cybernetic sense of error-correction - the deviation from a specific Target Morphology? We hypothesize that developmental bioelectricity implements true pattern memory. A target morphology could be encoded within tissues using the same kind of mechanisms and algorithms that (learn and) store cognitive memories of shapes and patterns within the brain’s bioelectrical network, and underlie directed behavior that seeks to recapitulate encoded goal states.

We propose that models should be explored in which the goal state of anatomical repair is encoded as a true memory of shape, and in which the processes of regeneration make use of recall and decision-making algorithms that parallel those known to occur in neuronal networks. Taking the shape memory analogy seriously immediately leads to two important and testable consequences. First, it suggests that the many tools available to modify memories (from training and behavior shaping to optogenetic inception of memories directly into brains ⁷⁸) or to induce plastic changes in somatosensory representations (e.g., extensions of the "body schema" due to training and tool use ⁷⁹) could be adapted to developmental bioelectricity to program morphogenesis by re-writing the target states (as in the planarian example above). Second, it suggests that the existing body of knowledge about goal-seeking behavior (from addiction to goal-directed choice circuits) can be mined to create mechanistic but high-level models of how bodies adjust their shape to the same final outcome despite external perturbation. It should be noted that in modeling pattern formation as a primitive cognitive agent, we posit no conscious awareness – merely the same kinds of mechanistic, non-controversial processes that for example allow genetically-specified instincts to guide the spatially-patterned activities of insect behavior.

3.2 What might a top-down model of target morphology look like?

We provide an example of a top-down approach to target morphology and morphogenetic fields ⁸⁰ by using a specific framework developed in computational neuroscience, the Free Energy principle (which is fully described in the Appendix). Note that "free energy" as used here is a mathematical quantity, not to be confused with, say, an animal’s metabolic resources or physical properties of its body. Here, minimizing free energy corresponds for an organism to restricting itself to a limited number of "states" that it can occupy, and which are valuable - hence, minimizing free energy roughly corresponds to maximize value. The notions of "state" and "value" are abstract; for example, although an animal might occupy many states (including e.g., being in proximity of a predator) it can enhance its fitness if it restricts itself to valuable states (e.g., being in proximity of food) and roughly correspond to its ecological niche. The free energy principle is thus an attempt to formalize how biological entities maintain their order, and it is now widely adopted in neuroscience, see the Appendix and ⁸¹”.

In a Free Energy perspective we cast the growth (or regeneration) of a body part as an action - in the sense that it changes the state of the system and can in principle change (lower) its free energy ⁸²: in other words, an organism can tend to minimize free energy by growing and/or by regenerating body parts. The meat of such a project would be to specify hypotheses for how the system knows the consequences of actions (i.e., acquiring internal generative models), what counts as a state having low free energy (i.e., be a close match of the target morphology), and how are these states coded and memorized (e.g. as priors). Here, models and target morphology could be in part genetically determined but also can be acquired during development through self-modeling ⁸³ or somatic surveillance.

To tentatively analyze embryonic development according to the Free Energy rules, suppose that genes predefine some initial priors, which describe "good" states of the system (like ‘being close to food’ in animals); here, equivalently, the "good" states would correspond to some aspects of the target morphology (possibly, without the need to fully specify it), much like the center-boundary structure of the aforementioned primordial soup is not prespecified. The system needs also to specify some initial actions that are available (e.g., chemical messages) to be potentially exploited to achieve "better" states (i.e. with lower free energy). In this context, growing or regenerating a specific body part is considered as an action (or a subroutine); such developmental modules are well-known from early experiments with homeotic transformations (HOX genes) and more recent bioelectrical inductions of whole organs ^{11a, 16a, 84}. Let’s assume that initially the free energy of the system is non-zero. Thus according to the usual rule of Active Inference the organism can act to diminish it: growing. Although this process is bootstrapped in a genetically pre-specified way, then it is regulated by the usual rules of free energy minimization.

As the body grows, it also implicitly learns the equivalent of generative models (i.e., the effects of specific actions and how they change the free energy) or in other terms it models its own growth process (and acquire models that can be potentially reused later on). These models take the form of electrochemical states and they include new priors that encode for example the good "target morphologies" (that is, those having low free energy) that are discovered during growth. In other words, while the initial (genetically encoded) priors include some constraints and pre-specify good (adaptive) morphological states for the organism, specific target morphologies are learned or discovered, through self-modeling, during growth. The growth of a healthy body represents a stable solution to the problem of minimizing free energy - in the sense that, when the body is fully grown, it is in a state of low free energy. Any change (damage or aging) actually increases free energy; thus the system tries to counteract this by ‘coming back’ to its (learned) target morphology.

This speculative model is a framework, one example that entails an answer to the problem of how target morphologies are acquired and then reused as targets (e.g. for regeneration). During embryonic development, free energy minimization guides morphogenesis without a fully specified "stored template" because the template itself has to be created (in the form of priors and generative models). Learning a template might correspond to acquiring new "prior" knowledge on which are "good states" for a system to minimize free energy, and which function as set points within the hierarchical generative models supporting active inference. However, once a "template" or target morphology has been created that represents a stable solution to the problem of free energy minimization, it can be used to guide remodeling, morphostasis, and regeneration in a top-down manner¹.

In this perspective, the problem of shape regulation is understood as a kind of memory/recall process, where generative models (learn to) encode a pattern or target morphology and error-correction mechanisms trigger actions that restore the pattern. Both the acquisition and the restoration of the target morphology are active processes - where specific actions that involve body changes (e.g., growth) obey to the imperative of free energy minimization.

A detailed implementation of this idea is described in Figure 5 and ⁸⁵. Here, cell groups self-organize to produce - and successively re-build - a target morphology (a simple form with head, body and tail) under a free energy minimization scheme. In this simplified example, the target morphology itself is not learned - although it could be with some extensions of the model - but assumed to be pre-specified (e.g., genetically). However, there is one aspect of the target morphology that is not genetically encoded but emerges during growth: the cells are initially identical and do not a priori belong to (say) head, both or tail (they all have an identical generative model) see Figure 5A. This means that cells are not "pre-destined" to a unique place but they must undergo a complex epigenetic process and "find their own place" in the morphology - thus, essentially, migrate and differentiate until the whole cell group achieves the target morphology, see Figure 5B. This situation is similar to the dramatic remodeling occurring during planarian regeneration ^{4, 59a} or the repair of craniofacial defects during frog metamorphosis ⁶.

Figure 5. Pattern formation and regeneration using the free energy principle (FEP).

(A) A sample computational model ⁸⁵, in which undifferentiated cells self-organize to reach a target morphology, corresponding to a (simple) multicellular animal with head, body, and tail (e.g., a planarian). The target morphology is specified in such a way that, when it is achieved, all cells essentially sense the “right” electrochemical signals – a state in which no further remodeling (cellular activity) is necessary. However, the problem for the cells is ”finding their place” in this target morphology; because cells are initially undifferentiated, each can (in principle) become part of the head, body, or tail. This morphogenetic process is formulated as an inferential, FEP problem (B), where essentially the whole system undergoes a series of changes (e.g., in cellular position) until the target morphology is achieved. While changing their place, cells emit signals (chemical and/or physiological) that in turn guide the other cells, until a collective solution is found that corresponds to the state where the free energy of the whole system is minimized. Once the system has reached a stable solution, it can be perturbed, e.g., cut into two parts, (C) and this can lead to a new morphogenetic process with the regeneration of two organisms. Perturbing the system in more severe ways can lead to various forms of dysmorphogenesis (not shown, see ⁸⁵). Note that this self-organizing process is guided by an objective function (free energy minimization) and lends itself to top-down analysis, while able to accommodate known details of cellular signaling. Images reused according to the Creative Commons license from references ^{85, 160}.

The complexity of this epigenetic process emerges when one considers that each cell that tries to find its place influences every other cell by emitting gradients that those other cell sense - thus the population of cells has to find a "collective" solution to the problem ⁸⁶. In other words, while a cell "searches" its place in the morphology, it is guided by chemotactic signals continuously emitted by the other (surrounding) cells; but during the "search", it simultaneously emits chemotactic signals that guide the other cells, too. Importantly, the cell’s generative model encodes (genetic) beliefs about the chemotactic signals it will (should) express and sense if it occupied a particular place in the target morphology. But even with this information, the cell does not have the guarantee to receive (initially) the "right" signals, or the signals it expects. If all the (other) cells were initially in the right place, and thus emitted the right signals, a cell could find "its" place by simply moving over concentration gradients until it sensed the right signals emitted by the other cells. However, at the beginning of the morphogenesis all the cells are simultaneously trying to find a place. This introduces a sort of circular causality where the cells as a whole concurrently emit and sense signals that influence (and are influenced by) the movements of the other cells; the population has to collectively establish a "chemotactic reference frame" permitting each cell to find its place. A solution to this problem complex (in AI, one would say "multi-agent") problem if one casts the process as the minimization of the free energy of the cell population - because the free energy is minimized when, and only when, every cell occupies a unique target location (see the free energy dynamics in Figure 5B).

It is important to note that engaging in a continuous, dynamical exchange with the environment is essential for the system to maintain its structural and functional integrity and ultimately to guarantee its survival. In the pattern regulation example of Figure 5, "lesioning" the system - that is, preventing cell-cell signaling - leads to various forms of dysmorphogenesis (not shown), consistent with the known patterning changes induced by inhibition of cell communication and movement. Rather, "milder" simulated interventions such as cutting a well-formed animal into two parts induces a dynamic reorganization and regeneration of the target morphology, see Figure 5C.

These examples illustrate how a top-down strategy can tackle an important open problem in biology: how to develop and re-build a "target morphology" and how this produces testable hypotheses, given that all the components can be given a quantitative mathematical specification (see ⁸⁷ for another example of use of free energy principles to explain shape generation during limb regeneration). The example also illustrates that this top-down perspective is not at odds with useful concepts from (a useful more bottom-up) dynamical systems tradition, such as the notion of emergent self-organization; rather, here self-organization dynamics are contextualized within a general optimization scheme that also makes apparent and permits to predict - for example - under which conditions the perturbations lead to regeneration or dysmorphogenesis.

Some of the tools and modeling approaches for the top-down analysis of pattern formation are already available - often, in other research fields such as computational neuroscience. As a concrete step in the direction of making these tools useful for bioengineers, Figure 6 introduces a formal scheme for the formulation, mathematical analysis and simulation of pattern formation, using the free energy scheme elucidated so far. It emerges from this example that the formal and mathematical methods are in place but at the same time this research agenda requires developing novel quantitative tools; for example, to quantitatively assess the free energy of a biological system and how the states it can occupy change during growth and regeneration. It is important to note that this is now a very tractable task at the intersection of computational modeling and molecular biology – an area that is now ripe for research.

Figure 6. Formulating and solving a patterning problem via the free energy principle (FEP).

The figure schematizes a “methodological recipe” for formulating and solving a patterning problem using the free energy principle (FEP); see ⁸⁵ for one recent example where this approach has been successfully used. The methodology is composed of three steps. The first step (A) requires specifying mathematically the so-called generative model of the cells, or in other words their “internal states”, “active states”, “sensory states” and “external states”, along with their probabilistic dependencies and the prior knowledge (e.g., a previous, correct target morphology). The second step (B) requires specifying mathematically the exchanges (intercellular signalling) between the cells. Because the approach assumes that, for each cell, the behavior of (some or all) the other cells constitutes the “external state”, specifying the interactions between cells corresponds to specifying how the “active states” of one cell changes the “sensory states” or (some or all) the other cells. Intuitively, the active state of one cell might correspond to emitting chemical and/or physiological signals which can be sensed by other cells (the model requires specifying for example the gradients and concentrations that underlie this sort of intercellular signaling. The third and final step (C) corresponds to simulating the dynamics of the problem to find the solution that minimizes the free energy of the (collective) system. A MATLAB toolbox implementing a variational message passing scheme for free energy minimization is the SPM academic freeware (http://www.fil.ion.ucl.ac.uk/spm/); see also ⁸¹. Images reused according to the Creative Commons license from references ^{85, 160}.

The free energy principle is just one of the methods that can be used, and several others originating from cybernetics, artificial intelligence, computer science, and control engineering are potentially applicable (see the Appendix). Another example of mathematical approach and top-down methodology (which has not yet been applied to pattern formation, but could be extended to do so) is flux balance analysis ⁸⁸.

4. Broader implications: homologies between neural information processing and pattern regulation

The example we have discussed is consistent with the broader possibility that deep underlying parallels exist between the way information and cellular control are organized in the CNS and in morphogenesis; this motivates a cross fertilization of methods between these heretofore-disparate disciplines. Below we discuss cognitive-like processes in non-neural structures that underlie pattern regulation.

4.1 Information processing beyond the CNS

Concepts formally used to understand cognitive processes in neural tissue may be appropriate to understand regulation of pattern formation. The first requirement is that non-neural cells be able to support basic information processing as occurs in neural assemblies. Indeed, neural-like computation, decision-making, and memory have been reported in sperm ⁸⁹, amoebae ⁹⁰, yeast ⁹¹, and plants ⁹², using ubiquitous mechanisms that appear to be also involved in neural information processing, such as cytoskeleton ⁹³ and electrical networks ⁹⁴. It is clear that neural networks have no monopoly on such functions, and indeed fascinating examples of memory and neural-like dynamics have been found in bone ⁹⁵ and heart ⁹⁶.

4.2 Neural inputs to pattern formation

Non-neural tissues perform neural-like functions, while neurons compute using basic mechanisms appropriated from basic cell:cell signaling events. The role of electrical activity in shaping CNS structure is well-established ⁹⁷. Not surprisingly, neural outputs impinge on pattern formation in other tissues as well, as the two information-processing systems interface extensively. Examples include the control of proliferation and differentiation by the signaling dynamics of neural networks ⁹⁸, the induction of spinal cord regenerative rewiring by electrical activity ⁹⁹, the mispatterning of deer antler regeneration by neural inputs ¹⁰⁰, and the known dependence of regenerating salamander limbs on ¹⁰¹, and addiction to ¹⁰², nerves. Importantly, the role of neural inputs in regeneration pattern is not merely permissive, but rather carries instructive information, as revealed by the determination of head vs. tail morphogenesis by the directionality of a transplanted nerve cord ¹⁰³, the induction of distinct shapes in a regenerated tadpole tail from different locations of damage to the spinal cord very far away from the wound site ¹⁰⁴, or the control of seashell patterning by specific neural net output ¹⁰⁵.

4.3 Cognitive concepts in developmental biology

While a concerted effort to apply neuroscience paradigms in developmental biology has not yet been made, a number of authors have independently used such concepts to help explain pattern regulation. One of the earliest applications explored the extensive parallels between chemical gradients during development and signal processing in the visual system ¹⁰⁶, and indeed early quantitative models of patterning (explaining self-regulatory features like proportion regulation) were based on visual system function ¹⁰⁷. More recent efforts include the notion of memory for position during regeneration ¹⁰⁸ and development ¹⁰⁹, learning models of diabetic electrophysiology in pancreas ¹¹⁰, excitable cortex memory models of pseudopod dynamics ¹¹¹, and neural network models of chemical signaling ¹¹² (which showed formal isomorphisms between gene regulation networks and Hebbian learning in neural nets) ¹¹³. In addition to classical neuroscience concepts, more exotic group cognition models have been applied to patterning ¹¹⁴, while a few recent studies investigated the decision-making and formal computational capabilities of reaction-diffusion systems – a chemical signaling modality often used to model morphogenesis ¹¹⁵, which is now known to be Turing-complete ¹¹⁶ and to support semantic interpretations ¹¹⁷.

Crucially, cognitive neuroscience research has clearly shown that even high-level mental processes can affect cell growth and differentiation in the brain ¹¹⁸, providing a proof-of-principle roadmap for understanding more broadly how encoded information can have causal power in regulating the kinds of cell behaviors that make up morphogenesis.

4.4 Similarities between morphogenesis and cognition

In this section, we highlight some of the deep similarities that erode the artificial boundary between brain and body. Importantly, numerous mechanisms are utilized by both – memory/learning and morphogenesis including connexins, ion channels, neurotransmitters, cAMP, CREB, HDAC, PKA, PKC, mTOR, and many more. Overall it should be noted that many cell types, not just neurons, utilize voltage potentials, calcium dynamics, neurotransmitters, and highly dynamic cell:cell connection patterns to process signals during pattern formation ^{75a, 119}. Significant recent advances exploiting this overlap include the investigation of neural-like dynamics to explain information processing in plants ¹²⁰, and the use of non-spiking, slowly changing voltage gradients to model memory ¹²¹ in animal systems. This latter effort becomes especially relevant given our proposal, developed below, that non-excitable cells support memory during pattern regulation. It is not often noted that many molecular components of memory, learning, and behavior are also critically involved in morphogenesis. However, nerve cells evolved by specializing much more primitive cell signaling functions first used for development ^{74a, 122}. Thus, it is likely a true homology - evolution predicts exactly this overlap of mechanisms, making more plausible the idea that undoubtedly-cognitive systems, brains, adapted (and improved) processes that were already being used for primitive cognitive functions during development.

Conservation of molecular mechanisms aside, how are we to understand the encoding of geometric shapes (target morphology for regeneration or development) within biophysical cell properties? This is a fundamental issue that requires integrating very different levels of organization and explanation. An example of this problem in developmental biology is revealed by the fact that depending on cell size, identical kidney tubules can be made of many cells via cell-cell communication or just one cell bending around itself (via intracellular cytoskeletal dynamics) ¹²³. The requirement of a “3D tube of a specific size” activates very distinct molecular mechanisms to achieve this goal depending on available material (cell size). Understanding such implementation independence requires that we understand how the goal of making a 3D tube of a given size and orientation, which cannot be defined as a single cell or molecular state, is represented as an initiating signal (and later recognized as a stop condition) in vivo. A key aspect of modern cognitive neuroscience is that it provides a roadmap for functionally linking high-level information (e.g., topological shape representations) to molecular level mechanisms occurring in cell networks. Salient examples (Figure 7C–E), with many lessons for bioengineering, include: the alterations of brain cell growth and differentiation by mental practices or spatial learning ¹²⁴, the insertion of specific (false) memories into the brain by optogenetic modulation of neural cells ^78a, and the read-out of mental imagery by processing of brain electrical states ¹²⁵. Developmental bioelectricity is a crucial nexus between cognitive science and regenerative biology, which provides an empirically-tractable set of pathways linking higher-order, top-down control and complex system representation and regulation of patterning by cell-level events.

Figure 7. Cognitive neuroscience paradigms and their application to models of pattern formation.

(A) The TOTE model of a cybernetic goal-directed process. Figure adapted from ¹⁷⁴. Words in Italics represent the main processes composing the principle. Thin arrows represent information flows. The double-headed arrow represents a process of comparison between the desired and the actual state value. The process starts from a Test. If the Test fails (i.e. a mismatch is detected between desired and actual state) an action is triggered (dashed arrow) that causes a cascade of effects such as a change in the actual state that are sensed and used in the next Tests. When the Test succeeds, the process ends. (B) The same model applied to a regenerative context, in which comparison of current anatomical state to a stored target morphology generates signals for cell growth, differentiation, and movement that progressively restore pattern. Cognitive neuroscience is also an example of a field in which high-level information has causal power and is mechanistically integrated with low-level (molecular) details of its encoding and manipulation. (C) Changes of mental state (learning specific patterns for example) alters cell behaviour in the brain (taken with permission from ^124b). (D) Manipulation of bioelectric states in the brain using optogenetic tools is able to insert specific cognitive content (false memories) ^78a. Credit: Collective Next. (E) Conversely, mental imagery can be read out by appropriate decoding of bioelectric state information from living brains (taken with permission from ^125a). In complement to today’s models (formulated entirely bottom-up, in terms of molecular pathways), we suggest that successful top-down models of regeneration (in which organ-level topological pattern is represented within somatic cells and guides cell behavior) could be formulated by borrowing insights from cognitive neuroscience.

5. Conclusions

5.1. Summary of new hypothesis: information processing in non-neural bioelectric networks

We propose that the apparent similarities between concepts in memory/decision-making and regenerative patterning are not merely anthropomorphic ways of speaking about the remarkable robustness of shape control, but underlie real homologies of molecular mechanisms and underlying control logic. Some possible mappings between major concepts in these fields are shown in Table 1. At a mechanistic level, cellular communication models using concepts from neuroscience (synaptic plasticity, long-term potentiation, Hebbian learning, etc.) may be applicable to understanding regenerative control. At a higher conceptual level, we propose that morphogenetic homeostasis may be best manipulated at the level of information processing. By improving cellular recall, and editing memories (specifically changing the stored encoding of a target morphology), as is already being addressed in neuroscience, we may be able to achieve far better control over regenerative processes than we have been able to achieve by micromanaging molecular pathways directly.

Currently, the ability to specify large-scale patterning outcomes is hampered by the difficulty of controlling emergent form by manipulating solely bottom-level molecular events. We propose a complementary strategy, to consider models in which cellular decisions are guided by a process that works to minimize the difference between the current configuration and a “target morphology”. Our specific hypothesis concerns one set of tractable molecular mechanisms for implementing top-down control of shape: the encoding of somatic pattern as the semantics of electrical activity outside the brain. Much as developmental modularity greatly enhances the efficiency of evolution ^{84, 126}, subgoaling is a key ingredient of effective real-time cognitive processes ¹²⁷; bioelectrical communication and encoding of “subroutine” modules by simpler representations (signals) underlies both, and is thus ripe to be exploited by bioengineering and synthetic morphology applications.

The parallels between neural information processing and regenerative patterning are strong, both at the level of molecular mechanism and of higher-order functions (Table 1). We propose to capitalize on the extensive experience of neuroscience in crossing the level between information (e.g., memories formed during learning or inborn as behavioral instincts) and its physical implementation (synaptic mechanisms and neural circuit dynamics) to address the single biggest question in the field of regeneration: how does an amputated blastema know what shape to make, and how does it know when to stop growing? Recent data implicate bioelectrical signaling in non-neural cells as a major regulator or large-scale anatomy, and show that the differences between neural and non-neural cells are not fundamental: all cells make networks with highly tunable electric synapses, and propagate signals via voltage dynamics and neurotransmitter signaling. It is likely that processing in the brain is a highly-accelerated version of basic cell mechanisms that existed long before a fast CNS was evolved for motile behavior; indeed, the computational abilities of astrocytes may be an intermediate case ¹²⁸; the role of non-spiking cells such as astrocytes and glia in memory and cognition ¹²⁹ reveal that the brain already knows how to process information in non-excitable cells. Developmental bioelectricity is thus the most likely physical mechanism for implementing top-down, goal-driven processes that might regulate pattern formation. More specifically, we propose that representation of anatomical goal states within bioelectric circuits of somatic tissue is a true kind of memory, both in terms of its conserved molecular mechanisms and in the algorithms through which it operates. Importantly, boelectricity is not the only signalling modality consistent with this approach; for example, Hox gene expression patterns “constitute a form of positional memory – an internal representation by a cell of where it is located within a multicellular organism” ¹³⁰.

In a sense, the current state of bioengineering is a kind of behaviorism, which ignores internal information representation and goal states and speaks only of cellular or molecular behaviors. Much as behaviorism was supplanted by a more powerful and empirically-successful theory of cognitive neuroscience (which exploits the reality of multi-level semantics, goal states, and information processing in the CNS), we argue that the next steps of biological control will involve taming the representation of patterning states within tissues. In this new strategy, bioengineers will seek to exert control by hijacking these bioelectrical pathways to rewrite the shape descriptor to which cells are working, and thus program pattern to an organ-level specification. Paralleling the development of cognitive science, we propose a kind of Intentional Stance towards models in this field, which focuses on extent of empirical control of shape, over a priori commitments to the form that such models must have (e.g., molecular pathways).

5.2. Next steps and transformative opportunities

There is little doubt that current approaches will continue to reveal molecular details of bioelectric signaling within cells. What will require out-of-the-box (interdisciplinary) thinking is the understanding of the bioelectric code: the mapping of distributed V_mem states to specific anatomical outcomes. How best to quantitatively model the circuit dynamics and resulting stable attractor states that orchestrate individual cell activity into maintenance of specific large-scale states? We have at least one example of a successful research program in which high-level semantics are being merged with molecular-level mechanisms: computational neuroscience; consideration of its deep insights could strongly enrich understanding of developmental biology.

Our hypothesis is testable, and suggests a rich research program. Specifically: (1) the development of improved methods for reading/writing bioelectrical state information into somatic tissues and sculpting non-neural bioelectric circuits (advances in optogenetics beyond excitable cells and in the synthetic biology of gap junction and neurotransmitter signaling) ^32d, (2) continued work on cracking the bioelectric code (understanding how bioelectric state information maps onto the topology of various patterning outcomes in tractable model systems such as planaria) ^16a, (3) formulation and testing of quantitative, molecular models of LTP, habituation, sensitization, and synaptic plasticity applied to slow bioelectric signaling in non-neural cell groups regulating regenerative growth ^96b, (4) use of reagents that impact cognition (hallucinogens, anesthetics ¹³¹, stimulants, nootropics/cognitive enhancers, etc.) in developmental and regenerative patterning assays to probe conservation of pathways between neuroscience and morphogenesis, (5) in silico study and synthetic implementation of biophysics models of circuits which can stably store bioelectric state information as attractor states of ion channel activity in arbitrary cell types ¹³², (6) creation of larger-scale computational models of regeneration and functional experiments in morphogenesis based on goal-seeking and error minimization algorithms with molecularly-specified metrics ¹³³, (7) exploration of molecular models of cognitive concepts (attention, autism spectrum, sleep, visual illusions/hallucinations, addiction) in specific patterning and mispatterning contexts, (8) experimental examination of learning and complex behavior ¹³⁴ in non-neural in vitro constructs to understand the cognitive powers of non-excitable cell networks ¹³⁵, (9) bioengineering platforms that reward and punish in vitro patterning systems for specific changes in growth and morphogenesis (seeking to demonstrate instrumental learning and top-down control of shape in developmental or regenerative contexts), and (10) a mechanistic investigation of the mechanism of persistence of memories through massive brain regeneration, which is likely to reveal the interface between somatic and neural memories ¹³⁶.

5.3. Broader outlook

We propose taking seriously the idea that patterning systems may be, in a mechanistic and algorithmic sense, primitive cognitive agents that remember specific shape configurations. One immediately tractable way to test these ideas is through mapping the bioelectric code; this way of tackling pattern regulation could provide empirically efficient control of biological shape for regenerative biologists and bioengineers. Top-down models may facilitate altering encoded goal states (e.g., target morphologies), bypassing the complexity explosion currently facing regenerative medicine’s attempts to control complex shape by tweaking molecules. It may be possible to efficiently “train” morphogenetic systems to desired outcomes, by providing rewards (or “objective functions”) for specific outcomes instead of micromanaging the underlying signaling. Likewise, a better understanding of the bioelectric code may allow optogenetic or similar methods to rewrite the target morphology in vivo, inducing cells to build desired patterns as a kind of universal constructor. Interestingly, this effort may also pay off in the reverse direction, shedding light on the semantics of bioelectric states in the brain. However, cybernetic strategies are applicable to top-down regulation via any mechanism, not only bioelectricity, and can readily be explored in the context of biomechanical forces, gene regulatory networks, etc. For example, an area to be investigated is the application of active inference models to gene-regulatory networks and protein interaction networks ¹³⁷, attempting to analyze their dynamics as an information-processing structure.

There is no doubt that for some systems, bottom-up emergence is a powerful framework ¹³⁸. We think it is also essential systematically explore the other side of the coin for those areas where complexity limits the efficiency of explanations at purely the molecular level ⁷. Computer engineering and neuroscience serve as proofs-of-principle that efficient control of complex systems can be pursued with top-down models of goal-directed activity. Concepts such as feedback control and goal-seeking algorithms must also be included in training courses that nowadays focus principally on differential equations for gradients and network analysis, omitting complementary perspectives from computer science and engineering despite the ubiquitous calls for a deeper integration across disciplines. Ultimately, it is an empirical question whether a given biological phenomenon is better addressed from a bottom-up, top-down, or combined perspective. Training young scientists in both approaches will permit them to exploit the remarkable opportunities revealed by the dynamic capabilities of pattern regulation, and reap the benefits of achieving complete control over growth and form.

Figure 8. Applying free energy models to understanding cognition, a “primordial soup”, and dynamic morphogenesis.

(A) A dynamical exchange between an agent and its environment as modeled in the active inference framework ⁸¹. Here, a discrepancy between the current sensory state and a goal state encoded in the internal state (reflecting some desired event or the homeostatic level of some variable) gives rise to interoceptive, proprioceptive, and exteroceptive prediction errors (red arrows). This produces a cascade of processes that ultimately enacts a sequence of actions (say, grasping and eating an apple). This process ceases when the interoceptive, proprioceptive, and/or exteroceptive feedback (e.g., the right gustatory sensations) matches the descending predictions (blue arrows) meaning that the organism has restored homeostasis through action. (B) A simulation of a “primordial soup” and the emergence of self-organization that is coherent with principles of active Bayesian inference; example from ¹⁶⁰. Left part: This “soup” comprises an ensemble of dynamical subsystems (the dots) that represent macromolecules. The macromolecules have a physical state (representing e.g. their position) and an electrochemical state (representing e.g. concentrations) that change according to simplified Newtonian dynamics and electrochemical dynamics (modeled in ¹⁶⁰ using a Lorenz attractor). Crucially, the states have short-range interactions: they are coupled within and between the subsystems comprising an ensemble. Center part: as the system evolves over time, a structure self-organizes that separates subsystems that are conditionally dependent (called internal states) and independent (called external states). Formally, this structure is called a Markov blanket: a kind of “statistical boundary” (more formally the set of node’s parents, children, and its children’s other parents in a Bayesian network). Note the clear separations - after evolution - in the location of subsystems (macromolecules) with internal states (blue), their Markov blanket (magenta and red), and external or hidden states (azure). States in the Markov blanket can be further subdivided into two sets: those that depend on internal states (red) and those that do not (magenta), called active states and sensory states, respectively. As noticed in ¹⁶⁰ in this spatial configuration “the active subsystems support the sensory subsystems that are exposed to hidden environmental states. This is reminiscent of a biological cell with a cytoskeleton that supports some sensory epithelia or receptors within its membrane.” Importantly, active states change external states (but are not affected by them) and so they maintain the structural and functional integrity of the Markov blanket. Indeed, “lesioning” internal, sensory or active states (by decoupling them from the rest of the system) quickly leads to the disruption of the Markov blanket - not shown here, but see ¹⁶⁰. Right part: These arguments suggest that a formal analogy can be established between active and sensory states and action and perception systems in living organisms, respectively. This speaks to an even more general interpretation of the self-organization process (shown in the Center part) in Bayesian terms, where the internal states are Bayesian models that infer/represent the hidden (azure) causes of sensory (magenta) states and cause these states through action (red). This can be verified if one considers that sensory states permit predicting external / hidden states - as shown in ¹⁶⁰. (C) The same scheme can be applied now to regeneration, where the “internal” (biochemical) states essentially encode a target morphology that can be acquired through a learning process that obeys to free energy minimization processes (e.g., as shown in B) or using unsupervised learning in generative architectures as explained in the main text. Once the target morphology is acquired, the same error-correction mechanism explained in (A) permit to trigger (regenerative) actions that restore it when it is disrupted. Images reused according to the Creative Commons license from references ^{85, 160}

Some animals regenerate limbs and remodel complex organs. Despite progress in molecular biology, we still lack understanding of the remarkable coordination of cell activity towards a large-scale anatomical outcome, stopping when target morphology is achieved. Cognitive neuroscience offers a paradigm for how cellular networks store memories of specific shapes and pursue goal states. We propose that these key insights map closely onto regenerative biology. Advances in developmental bioelectricity reveal that all cells could form networks using electrical communication to store and implement shape memories. We propose that bioelectricity is a nexus that shows how shape homeostasis can be implemented in somatic networks, and suggests tractable new approaches for increased control of growth and form in regenerative medicine and synthetic bioengineering.