The scaling of goals from cellular to anatomical homeostasis: an evolutionary simulation, experiment and analysis

The dynamics of the gap junctions were similar in this anxiolytic experiment to what they were when stress was used (figure 2). However, we observed that at 90 steps, the tissue reached only 82.8% of the target morphology. And at 99 steps, the collective of cells corresponding to the location of the red stripe of the French flag dies. The collective achieved 67.3±2.8% of the target morphology over 20 runs.

These experiments reveal that, in the absence of stress, anatomical homeostasis is not reached nor maintained during the lifetime of the cells. By contrast, when stress is available to the cells, the tissue reaches 95.1% of the French flag target morphology at 90 steps and it maintains the morphology after this step.

Thus, we conclude that cells exploit the ability to use the stress mechanism to implement morphogenesis and survival of development.

Having seen the importance of stress mechanisms among cells, we next wanted to know if the stress system featured a window of optimality: is too much stress bad for this process, as it is for real biological systems? Thus, we artificially induced a very high stress (compared to what is needed and used during the French flag resolution) at the locations of the white stripe at 110 steps of the simulation (figure 6). With this excess stress, we simulated an environmental stressor that is not adaptively informative about the current situation of the tissue since it had already reached a version of the French flag compatible with survival (e.g. the cells receive enough energy). Stress decreased immediately without changing the states of the cells. At step 140, a line of blue cells appeared in the white stripe. It seems that stress was only instructive at specific concentrations inside the cells, and then blue cells appeared in the white stripe. Stress transformed the cells close to the borders of the stripes into reservoirs of morphogen molecules, and by accumulating them, they became blue. It seems the cells evolved by making stress instructive only at specific levels as it had no effect during those last 30 steps and it kept decreasing.

We conclude that evolution used stress as a communication system using a particular encoding, in which stress level is instructive and has effects on cell behaviour only at specific concentrations.

Evolution finds more than one way to solve a problem. Here, we analysed the counterexamples—the individuals that can solve the problem without the use of stress. In 10 evolutions that achieved a fitness score superior to 90% on average (over 20 runs) for reaching the French flag, simulations acheived 93±2.6% of target morphology with stress and 91.5±8% when anxiolytics are added. However, 70% of the evolved tissues use the stress system but it is not systematically functional. This high standard deviation for the anxiolytics experiment is explained by the fact that for the majority of the evolved individuals, stress is not fundamental to reach the target morphology. For one evolved tissue, the absence of stress results in embryonic death during development, while for others it has no negative impact. Quantitatively, 1/10 of the evolved tissues used stress as an instructive signal and died when anxiolytics were added. This is true for the evolved tissue in the different experiments above. This ratio is low but, in terms of biological evolution, it would be sufficient to spread into the entire population over time if it increases the overall fitness of the organism during evolution. The other virtual embryos are still able to develop the French flag without stress even if they used it as a result of artificial evolution. Three in 10 of the virtual embryos had better scores on average on the French flag in the presence of anxiolytics, meaning that stress is a noisy signal for them.

Why does biological evolution use stress—does the use of the stress system in our simulation increase the adaptive responses of the organisms in more complex scenarios? In order to answer this question, we used the same 10 virtual evolved tissues that achieved a fitness score superior to 90% on average over 20 runs for reaching the French flag and ran an experiment where the target morphology changes during the development phase (at 60 steps; see figure 7) and cells that die are immediately regenerated by white cells. With these conditions, the 10 virtual embryos obtained a mean score of 74±17.4% on the new target morphology. For the one embryo using the stress system as functional, we obtained a mean score of 89.2±4.5% and for the nine others that do not use stress as instructive, the mean was 73±18.6%. We applied a one sample t-test to compare these two means and found the difference statistically significant (with p-value = 0.0312). Thus, it is possible that stress enables adaptive responses in potentially harmful environments.

In summary, we found that the stress system is not always needed to resolve the French flag problem during development. For this problem, anatomical homeostasis without stress is possible but exploiting spatial propagation of stress information seems to increase adaptive fitness by improving performance in scenarios where the normal process of morphogenesis is impacted by external perturbations. As has been suggested [7], stress is an ideal parameter for evolution to exploit as a representation of the error in homeostatic contexts, and the drive to reduce stress could then implement ‘grow and remodel until complete’ in regenerative settings [7].

To truly understand how cellular collective behaviour solves morphogenetic problems, and to derive efficient interventions for biomedical contexts, it is essential to understand what the cells are communicating to each other: what information is available to groups of cells? How does its propagation through the tissue enable the cohesion of multiple competent agents into an emergent individual at a higher level of organization that can achieve a morphogenetic goal? Thus, we next applied information-theoretic measures to analyse the dynamics of the tissue during anatomical homeostasis. We computed the local active information and local transfer entropy for the original simulation without any perturbation (figure 2). We also computed the transfer entropy from one stripe to another to understand if one sub-collective could drive the information dynamics and ultimately the anatomical homeostasis (figure 8).

The transfer entropy from stress of one agent to its neighbour started to increase in the tissue at time step 55. Then we wave an important increase at time step 59 in the locations of the white and red stripes. This correlates with the increase of stress in the same spatial locations. The overall transfer entropy was almost 300 bits at this time step (figure 8c). Then, the transfer entropy decreased and reached a steady state around 0. The black squares represent negative local transfer entropy, meaning that the cells receive information from the stress that is misleading for predicting their next state. We also compared the transfer entropy from stress of one cell to its own state and found it to be much less important than the transfer entropy from the stress of one cell to the states of its neighbours (figure 8c). This suggests the key signalling mode for the stress is paracrine, not autocrine.

The dynamics of the local AIS on the cell states followed different dynamics. When transfer entropy was increasing, we observed several spatially located negative local AIS among the spatial locations of the white and red stripes (see figure 8a). At 55, 59 and 60 time steps, the AIS was mainly negative for the white stripe, after which it increased gradually until it reached steady state (figure 8a,b). For the red stripe, AIS also decreased globally until around step 70 and then we observed an important increase, indicating cells could predict better their future state from the past memory. Concurrently, the stress is decreasing. The local AIS of the blue stripe was 0 throughout as the cells in this region never changed their states. Thus, stress increases concurrently with a decrease in local AIS in the tissue (as seen in figure 8b) or, in other words, when the cellular memory does not effectively predict the future. This is compatible with the definition of stressors as unpredictable and/or uncontrollable stimuli [76,77].

We also computed the average local transfer entropy from one stripe to another, from the cells corresponding to the spatial locations of the red stripe to the white and conversely (figure 8d). This averaged transfer entropy was 0 at each time step for the blue to red and white stripes and from each of those to the blue. Using a time window of k = 4, before 60 steps, we observed a peak of 250 bits of transfer entropy from the red stripe to the white, suggesting the tissue changes were driven by the red stripe. Just after 60 steps, this reversed: transfer entropy from the red stripe to the white stripe decreased and transfer entropy from the white stripe to the red became much higher, with a peak around 450 bits of information suggesting that the white stripe was now driving the change in the states. The ‘organizer’ region (here defined as a region or group of cells in a tissue that can induce and instructively pattern other cells) seemed to change over time, suggesting embryonic regions take turns driving the large-scale process.

Finally, to evaluate the direction of information flow, we looked at local transfer entropy from energy to the state of each individual cell, taking an average across all cells in the whole tissue, as well as the converse—transfer entropy from the cell state to energy (figure 9a). The first peak we observed, at around 55 steps, corresponded to the transfer entropy from energy to states, indicating information flow came from the anatomical homeostatic loop. After 60 steps, the two transfer entropies overlapped. At the same time, the average energy of all stripes was either increasing or started to stop decreasing (figure 9b). Thus, in our scheme, the information was first driven by the anatomical loop, and the energy needed for single-cell survival was controlled by this loop.

We conclude that stress was very informative in the state changes of direct neighbours of one cell. Stress increased concurrently with a decrease in local AIS in the tissue (as seen in figure 8b). This is similar to biological systems where stressors are defined as unpredictable stimuli. In our scheme, evolution used the stress system as a communication system that was activated when memory of past events was not effective for predicting the future. There was a wave of information flow from red to white stripes, and it seems that the larger anatomical homeostasis loop came first in terms of information flow from energy to differentiation state. Taken together, these analyses reveal the dynamics of the information flow in the tissue. We observed an emergent behaviour when the ‘organizer’ region changes over time, stress is used as a communication system with the neighbours, and the higher level of homeostasis (anatomical homeostasis) came first in the dynamics suggesting that top-down information is key to manipulate the dynamics of the tissue.

The sudden remodelling of cell fates after a long period of apparently quiescent, stable pattern in our model (figure 4) predicts that something similar may occur in biological systems. Might some phenotypes that seem complete in fact need to be followed for much longer to observe the true dynamic? We indeed found this to be the case [78], for planarian flatworms [79] regenerating after exposure to U0126, a blocker of ERK/MAP kinase signalling which plays an important role in many model systems of regeneration [74,80–82]. Several studies have shown that ERK inhibition immediately following amputation leads to the formation of headless animals [74,80,81]. These headless animals that regenerate after ERK inhibition had previously been assumed to have reached a terminal, stable morphology [74]. However, when we monitored them for 18 weeks following ERK inhibition, we observed a remarkable phenotype in which some of the headless animals suddenly began to repattern, with some regaining a wild-type single-headed morphology.

To quantify this phenomenon, we defined repatterning as any morphology change occurring after four weeks post-cutting. In headless animals observed from when they were cut until their death (n = 181), 22% showed some form of sudden repatterning even though regeneration had completed and morphogenesis had ceased weeks prior (figure 10b). Importantly, this repatterning occurred without any intervention. The remaining 78% of headless animals did not show any change in morphology except for shrinking in size, as headless animals are unable to feed and therefore allometrically scale down over time [83]. We observed repatterning from four weeks onwards and the majority of repatterning occurred between 4 and 10 weeks (figure 10c). After 10 weeks only sporadic new repatterning was observed, although some worms began forming new heads as late as 18 weeks after cutting. This spontaneous repatterning that allows the re-establishment of a normal morphology many weeks after regeneration is completed suggests the existence of tissue processes that operate on a time scale much longer than previously known. Anatomically, the observed repatterning fell into four different categories. In the most common repatterning type (61% of all repatterning worms), normal single-headed wild-type morphology was regained (figure 10b,d(i)). The second most common phenotype (18%) was a polarity reversal, in which, following fissioning of a headless animal, the posterior blastema formed into a head (figure 10b,d(ii)). The remaining two categories represent the rare animals that exhibited growths which did not lead to the formation of a head, in the form of either dorsal outgrowths (D/V repatterning, 10%, figure 10d(iii)) or lateral outgrowths (11%, figure 10d(iv)).

When headless animals repatterned to form a new head, the pigmentation of the round anterior end began to lighten and the tissue flattened out, forming a structure resembling a blastema (figure 10e). Once the blastema formed, first one eyespot appeared (figure 10e(ii)) and then the second one formed with a few days' delay (figure 10e(iii)), along with the head reshaping to regain the typical morphology (figure 10e(iv)(v)). In addition, animals were stained using synapsin antibodies to visualize regrowth of the underlying brain tissue at intervals during the repatterning process. This showed that early brain repatterning occurred via the formation of a cluster of neural tissue at the anterior rounding of the ventral nerve cord (figure 10f(i)). Brain structures formed progressively from there, first in an apparently unorganized manner (figure 10f(ii)), before expanding and reforming into a well-organized brain resembling that of a normal animal (figure 10f(iii–v)). While the repatterning process resembles normal head regeneration in its progression, the timeframe was distinctly slower than normal head regeneration [84], taking up to 25 days from the first observation of changes at the anterior to a fully formed head.

One of the key open questions in evolutionary developmental biology, as well as basal cognition [8,20], is how single-cell capacities (competency in physiological and metabolic spaces) scale up to enable systems to solve problems in morphogenetic space (anatomical homeostasis), such as axial polarity and body-wide positional information axes. Because intelligence can be defined as competency in navigating arbitrary problem spaces, and all agents are fundamentally composites of other parts, it is important to understand how evolutionary forces and generic dynamics [85–87] work together to scale up collectives and pivot their simple homeostatic properties into more complex capabilities. Here, we presented an evolutionary simulation of the scaling of goals from individual cell-level metabolism to embryo-wide axial positional information. This system is a model of multi-scale homeostasis that illustrates how cells can join into collectives that solve problems in new spaces. We found that evolution was able to use the shared stress system to coordinate across space and time, and developed error-minimization and homeostatic capacities (as demonstrated by robustness to perturbation). The resulting tissue was found to be robust to external perturbation, and use of the stress system was both instructive for initial morphogenesis and necessary for long-term survival.

While maintaining allostasis, the tissue also tried to get rid of the few aberrantly placed blue cells after development, taking the collective temporarily away from the French flag target morphology, to then allow homeostatic mechanisms to drive it back to normal, resulting in long-term maintenance and survival of the tissue. This corresponds in the TAME framework [7] to ‘delayed gratification’—the ability to not get trapped in local minima by temporarily stepping further from the goal in the problem space. This ability to move away from the goal in order to reach a better solution later (following not only minimum-distance paths) is an important capability of some cognitive systems. Degrees of this kind of ‘delayed gratification’ in cybernetic systems enable more sophisticated behaviour, along the continuum from simple ‘roll downhill’ mechanisms to complex problem-solving systems [7]. Interestingly, neither of these things were directly selected for during the evolutionary cycle, revealing how some capabilities of multi-scale homeostatic systems can emerge as a kind of ‘free lunch’, without direct selection pressure [2,88].

Our analysis reveals the emergent functional connections between the single-cell and anatomical homeostatic loops. Each cell has one goal, to survive, and it corresponds to being in the appropriate state to receive energy (with the other members of the collective), e.g. navigating in a one-dimensional metabolic continuous space but by discretizing it: the new emergent problem space solution has three instances (blue, red, white), corresponding to different cell fates along a positional information axis. On the other hand, the collective/tissue has a morphogenetic goal, the French flag, and it is simultaneously navigating a problem space of 3n instances (n, number of cells).

Our model made a surprising prediction—spontaneous and sudden re-initiation of morphogenetic activity long after patterning has completed. This phenomenon was recapitulated by the results of in vivo experiments in planaria. Of course, our model is provisional, and not claimed to definitively capture all of the complexity of the biology, but the fact that it reproduces surprising behaviour not predicted by other known models is reassuring. Such minimal models are an important contribution to the field of molecular biology and genetics, which are awash in enormous datasets of detail and in need of conceptual tools for extracting understandable meso-scale dynamics sufficient to explain the observed biological robustness.

The observation that planarians are capable of recovering a wild-type bodyplan by spontaneously triggering a regeneration-like process, after maintaining a stable abnormal morphology for long periods of time, poses interesting questions about how abnormal morphologies are first maintained and how they are eventually detected to trigger correction. In other organisms, there is some evidence that remodelling of tissues to fit new morphologies can be part of regeneration, such as the remodelling of transplanted tail tissue into a limb in amphibia [89]. The repatterning reported here is distinct from previous studies where it was shown that general injury signals can induce regeneration in headless animals [74], as here we applied no triggering injury of any kind. The newly demonstrated ability to mount a regenerative response without any triggering injury is consistent with the idea that a MTR may not be necessary for regeneration to occur [90] and that subtle internal dynamics may be sufficient to initiate change long after the process appears to have reached a stable point. Our finding that the spontaneous repatterning is slower than normal regeneration is also consistent with other examples of regeneration in the absence of the MTR [90]. The timepoint at which repatterning starts appears to be stochastic within the population. The observation of sudden initiation of repatterning in a seemingly quiescent tissue raises a key question: what process in the tissue serves as a ‘clock’ that enables remodelling at a particular time frame? It must be distinct from the on-going and obvious morphogenetic processes because remodelling initiates suddenly, on a background of constant cell identity distributions.

Recently, Chou et al. found a dynamic in bacterial biofilms similar to the clock and wavefront model describing somitogenesis [91]. Interestingly, they observed that nitrogen stress response in the biofilm can form a complex pattern of concentric rings—revealing that spatial distribution of stress responses had occurred already at the time that social microbes emerged. Their results show that the development of bacterial biofilm collectives is driven by an oscillatory process that can locally amplify nitrogen stress responses, such that spores may develop in different areas of the biofilm even under a more abundant nutrient environment (not only in the starved interior of the biofilm). Interestingly, in our model, we observe a similar behaviour with a subtle oscillatory stress response of the cells in different areas of the tissue (figures 1b and 8a) allowing the formation of the French flag configuration. We found that the pattern generated by the stress response in our simulated tissue defines spatial regions where cells differentiate into the different stripes, a mechanism similar to that seen in the biofilm when various strains of bacteria differentiate into spores. This behaviour is similar to somitogenesis where a homogeneous tissue becomes segmented (transcriptionally and anatomically). In both our simulation and the biofilm, stress seems to play a key role and convey information leading to differentiation of the cells and bacteria similar to the clock and wavefront model. Our system is not similar in every aspect, but they resolve the same problem: how to create spatio-temporal order and to shift from cell-level metabolic goals to the much larger tissue-level morphogenetic goals. Thus, conserved dynamics could be relevant across bacterial, metazoan and in silico minimal models of the scaling of spatial patterning from single-cell metabolic and stress dynamics.

The communication system is fundamental for collective intelligence. In our scheme, communication is mediated via gap junctions, a well-known system for coordinating physiological and morphogenetic activity which has also been proposed to be an essential complement to enhancing collectivity [20,41,92]. In our simulation, three types of molecules can be exchanged: the morphogen, the stress molecule and its counterpart, the ‘anxiolytics’. In our simulation, stress plays a key role. Stress is an ambiguous and transdisciplinary concept we used from material science to physiology and ecology [62,93,94], encompassing different meanings: certain stimuli can be stressors; the emergency responses to the stressor is defined as the stress response; and chronic stress is the over-stimulation of the emergency responses [62]. In addition, the definitions of these three concepts are mutually dependent: a stimulus that initiates a stress response is a stressor, but the physiological or behavioural response is considered a stress response if it is initiated in response to a stressor. One solution has been to define stressors as stimuli that disrupt or threaten to disrupt homeostasis [95], but the concept of homeostasis has its own limitations [96]. A more general definition is that stressors are unpredictable and/or uncontrollable stimuli [76,77]. Interestingly, this last definition fits with the emergent use of the stress system in our simulation. Stress increased concurrently with a decrease in local AIS in the tissue as seen in figure 8b. Thus, in our scheme, evolution used the communication system as a stress system that was activated when the memory of past events was not effective for predicting the future.

This relates to the active inference framework and the free-energy principle, both of which have recently been developed to integrate homeostasis and allostasis [97], as applied to morphogenetic systems [98,99].

Network structure is key to collective intelligence [67,100,101]. It has been shown that flat, fully connected, network structures provide the most efficiency for collectives to resolve a task since that type of structure maximizes the aggregation of information received from members of the collective [100]. However, this kind of network is very costly as it necessitates n(n − 1) connections and is probably not biologically realistic. Indeed, in most cell networks, cells are only connected to their near neighbours. The stress system can be seen as another communication system and could play a role in changing the network structure to a flat (fully connected) structure, at least for some part of the network, thus facilitating information aggregation (see [102] for a review of non-local cell communication modalities).

One purpose of these kinds of simulations is to develop protocols that could enable robotics and artificial intelligence approaches to benefit from the kind of robustness and problem-solving ability observed in biology. In artificial intelligence, the fact that all intelligences are collective intelligences has not been emphasized [7], but there are recent attempts for swarm robotics and deep learning to develop new methods based on collective intelligence [48,103]. Deep learning has started to integrate the approach with adversarial networks with two networks working together [104]. Artificial collective intelligence is usually studied from the point of view of swarm intelligence or human society [105–107] but morphogenetic systems present several characteristics that swarms lack: a (growing) grid network architecture, the informational wiping property (cells do not know the origin of a given signal), and a different communication system closer to the information processing of a cellular automaton that can only communicate with its direct neighbours. In addition, in this work, we were interested in a reward that has to be explicitly global. In our simulation, individual cells have a high uncertainty on the reward, as it depends on how well the collective is performing. We developed a global mechanism which rewards for complex, non-local dynamics, solving a problem that is also known as ‘credit assignment’ in machine learning. We wanted to address the question of how this long-range reward can drive scale-up of single-cell competencies toward tissue-level goals without having to pre-specify each cell’s correct final state.

This is a way of mechanistically linking top-down rewards for system-level performance with the low-level component behaviours, addressing the problem of credit assignment, and is thus a step toward integrating the scaling of cognition findings into artificial intelligence by demonstrating dynamics that can lead to desired emergent properties across scales.

Lastly, it is interesting to consider the relevance of this system for basal cognition [108,109]. It has been argued that body patterning and behavioural control seem to share a common origin, not only via the mechanisms of ion channels and neurotransmitters, but also via the evolutionary pivot by which biology uses similar processes to solve problems from physiological to morphogenetic and ultimately three-dimensional behavioural spaces [8,9]. Indeed, several somatic tissues exhibit evidence of learning and basal cognition, including cardiac [110], bone [111] and pancreatic tissues [112], in addition to the large literature on learning and decision-making in microbes and other unicellular organisms [113–118]. These capacities are very old [119,120] and the molecular apparatus of higher cognition (ion channels, neurotransmitters and synaptic mechanisms) was already present in our unicellular ancestors [13]. Brains and neurons have been speed-optimized by evolution from other cell types [121]. But somatic cells did not lose their cognitive repertoire and computational capabilities during their transitions to multicellularity or in becoming part of metazoan swarms (bodies): they scaled them to pursue larger anatomical goals [4]. The symmetry between development/regeneration and traditional cognition is not simply an emergent result of hardwired processes, but the emergent result of a very plastic, context-dependent system that achieves invariant patterning outcomes under uncertainty. Biological systems have remarkable capacities to achieve the same morphogenetic outcomes despite a range of perturbations, such as different starting conditions, different numbers and sizes of cells, and various interventions (reviewed in [1,122]).

In this work, we simulated the transitions from single-cell homeostasis to anatomical homeostasis using stress, and tested the hypothesis that a minimal evolutionary framework is sufficient to scale small, low-level setpoints of metabolic homeostasis in cells to the larger morphogenetic setpoints of collectives (tissues) (figure 11). These transitions take place in a continuum from body patterning to cognition. We propose that evolution pivoted the collective intelligence of cells during morphogenesis of the body into traditional behavioural intelligence by scaling up the goals at the centre of homeostatic processes. This work is a first step towards a quantitative understanding of the scaling of cognition.