Stress sharing as cognitive glue for collective intelligences: A computational model of stress as a coordinator for morphogenesis

We conclude that stress sharing increases the cognitive light cone of an embryo compared to an embryo without stress sharing (Fig. 5B.I). As development proceeds, the radius of the cognitive light cone decreases, lasting longer for an embryo with stress sharing (Fig. 5B.II), but terminating prematurely in case of an embryo without sharing (Fig. 5B.III).

Sequential morphogenesis causes stress to fluctuate over the course of development.

Next, to observe the spatio-temporal time course of stress during development, we manually broke down the target pattern (smiling face) into a set of sequential targets and observed how stress varied as each target pattern was introduced. Specifically, we broke down the target pattern of the smiling face into a set of discrete components: left eye only > right eye only > eyes only > eyes and smile > complete face. We set each of these components as the target pattern starting from the “left-eye only” target and moving towards the “complete face” target. We introduced a new target only when development had optimized the source pattern to the current target pattern. We identified this point by observing the stress value: as long as it decreased, optimization was treated as in-progress.

We took a single embryo of each kind (stress-sharing & without stress-sharing), scrambled their elements randomly from the final target pattern (complete face), and then let them develop towards each sequential partial target pattern, and plotted the average stress within the embryo throughout development (Fig. 6).Fig. 6Stress fluctuates for a population w/sharing, oscillating up and down over the course of development, eventually dropping to zero. (A): Normalized stress (over all cells in an embryo) over the course of developmental for a competent population with stress sharing. Initially stress is high owing to the random structure of the embryo's cellular structure. At the same time, a target (left eye pattern) was set as the target to the developmental process. Once the left eye pattern was achieved at generation 5, a new target (one with both, left and right eye) was introduced. Once such a pattern was achieved, a new target (a smile, along with the eyes) was set, and finally, once this pattern was achieved, the entire face was set as target. Throughout such part-by-part morphogenesis, stress continued to drop and rise corresponding to settling at a target pattern, versus moving towards a new pattern. (B): Normalized stress (over all cells in an embryo) for a population without Stress sharing. Stress continues to oscillate as patterns are incrementally introduced at various local minima, but optimization towards these patterns fail because cells are restricted in their movement due to the absence of stress sharing. Stress eventually settles at a non-zero value giving rise to a scrambled pattern. In the absence of stress sharing, such competency relies heavily on mutations to nudge patterns towards a target. Since no mutations were given here, competency did not help.Fig. 6

We observed that in both kind of grids, stress fluctuated. On introducing a target pattern, stress momentarily increased and then continued to decrease until the current target pattern was attained to the best possible extent by the competency process of the grid. In a stress-sharing embryo, stress progressively decreased until the relevant target pattern was perfectly achieved (Fig. 6A), whereas in embryos without stress sharing, the target pattern was only partially formed due to the constrained cell-movement within its elements (Fig. 6B). Consequently, a stress-sharing embryo was capable of perfectly forming each sequential target pattern and stress was able to reach zero at step 40 (Fig. 6A). The without-sharing embryos however, was unable to form any of the sequential target patterns well. Tiny improvements of ∼1 % in fitness were noticed between each sequential pattern, but progress was limited to movement of less than 55 cells on average (compared to 4500 cells on average for the stress-sharing embryo) and development lasted for 10 steps only (Fig. 6B).

We conclude that sequentially introducing new features increases the average stress, but given enough competency and a communication mechanism (sharing), individual features can be formed perfectly with the corresponding feature's average stress reducing to zero. However, without a communication mechanism, no matter the competency value, cells are restricted in their movement and tend to get stuck in localized patches. Thus, a communication mechanism tied to their homeostatic loop (such as stress-sharing) is key if competency is to have an impact on reorganization capacity.

When studying minimal models of agency, it's important to ask what can be detected by external observers of the agent vs. what is known only to the system itself (a primitive version of the privacy property of minds). Specifically, since stress is a direct measure of the distance to a morphogenetic setpoint, it might be expected that by observing the stress maps, it would be possible to guess what pattern the cells were attempting to implement – to read the goal state of the system. Could an external observer predict the target pattern being developed by observing fluctuations in stress? We addressed this question by reducing an embryo's reorganization dynamics during development into a series of stress maps. The stress map of an embryo at any time step was a gradient of stress in its two-dimensional grid space. It was obtained by first identifying stressed cells (including those with shared stress) and drawing its space-gradient. By observing the dynamics of such a stress map over the course of developmental time, we sought to determine whether it would reveal the target being formed, as is attempted in the efforts of neural decoding [[60], [61], [62], [63]] (Fig. 7).Fig. 7Stress is not predictive of the target pattern being developed. (A): Stress map of an embryo with competent stress sharing ability over several stages of development. Development towards two independent target patterns, a thumb-up and a smiling face, is shown in sequence A.I and sequence A.II respectively. Stress maps shown here are at developmental stages of 0 %, 25 %, 50 %, 75 %, and 98 % to completion. The stress map at any stage is an indication of the directional derivative of stressed-cells with respect to developmental time. Arrows indicate the gradient vector of a corresponding stressed-cell at any stage during development.

As development proceeds, stressed cells grow fewer in number, and is reflected by the reduced number of gradient vectors. Note that at 100 % completion, the stress map is an empty field.(B.I): Similarity between the stress map of an embryo w/sharing and the thumbs-up target pattern over the course of development. Similarity increases from 0.53 to 0.61 over 100 developmental stages. In contrast, a randomized stress pattern (which was set up as a control) shows no such trend (black trace), helping differentiate competent sharing based cellular reorganization and random cell movements.(B.II): Similarity between the stress map of an embryo w/sharing and the smiling-face target pattern during development. Similarity decreases from 0.47 to 0.25 over 80 stages of development. A randomized stress pattern was set up as control at each developmental-stage and helped in discerning the effect of competency from the effects of random cell movements (black trace).Fig. 7

We qualitatively assessed predictability of the target by observing the in-time variation of the stress map (Fig. 7A) and observing how visual cues in the stress map allowed predictability, and quantitatively by plotting a similarity metric (see Supplement S3 for details) between the stress map and the target pattern (Fig. 7B) to see if a trend emerges over the course of development.

In this experiment, we employed two different stress-sharing embryos, each of which developed towards two different target patterns (a thumbs up pattern, and a smiling face pattern). We observed that in both cases, during the initial stages of development, the stress map provided partial cues as to the target being formed, but these visual cues disappeared later (at 50 % to completion in both the thumbs-up pattern and the smiling face pattern), providing no definite hint as to the target pattern being formed. (Fig. 7.I and Fig. 7.II). Note that at 100 % completion the stress map would be a blank grid with no stressed cells and therefore no gradients (see Suppl emental Videos 5 and 6 for continuous time evolution of their respective stress maps). Further, it could be that we are observing these “visual cues” precisely because we are primed to see it. To provide a more quantitative assessment we resorted to a similarity metric between the stress map and the target. The similarity metric was chosen to be the inverse l2-distance between the stress map and the target pattern, existing within [0.0, 1.0] with 0.0 indicating no similarity and 1.0 indicating an exact match.

Observing the similarity plot provided a more confusing picture. While for the thumbs-up pattern, the stress maps’ similarity with the target grew from ∼0.53 to ∼0.63, for the smiling face pattern it decreased from ∼0.48 to ∼0.25. Additionally, in each of these plots, we compared the similarity of a random stress map to the target (black trace in Fig. 7B) as control. While the random stress map had a similarity hovering around 0.5, the similarity for the stress sharing embryo varied based on the target being formed.

We conclude that in the absence of prior knowledge about the target pattern being formed, it is unlikely that an external observer can predict the structure being developed by visually inspecting the stress pattern alone. While the similarity metric can indicate the presence of a non-random target being formed, no other predictive information is apparent from either the stress map or its similarity trend with the target during development. Thus, while local stress directly reflects the distance of a cell from its optimal position, the ability to share stress prevents a straightforward inference of the system goal from data available to external observers.

The ability to make desired changes at the system level (repair of complex birth defects, induction of regeneration of appendages, self-assembly of novel biobots, etc.) is hampered by the difficulty of the inverse problem. In most cases, it is not possible to infer changes in the genes determining protein sequence must be made in order to reach a complex anatomical outcome. However, the increasing realization that biological tissues offer high-level interfaces for control, in the same way that learning and communication offers behavioral control without micromanaging individual neurons, suggests novel strategies for their manipulation which are already beginning to be applied in biomedicine [24,25].

The flexible, adaptive aspect of morphogenesis has been modeled as a set of navigation policies within anatomical morphospace [14]. By recasting changes in growth and form as the behavior of cell groups in transcriptional, physiological, and anatomical problems spaces, all of the tools of behavioral science and autonomous system engineering (control theory, cybernetics) can be brought to bear [11,12,64]. Specifically, we have argued that advances in bioengineering and regenerative medicine will require a better understanding the policies with respect to how cellular collectives navigate the landscapes of these problem spaces under different perturbation [11,12,65]. However, the development of such strategies relies on a better understanding of how groups of cells cooperate toward specific outcomes.

A key aspect is that in biology, problem-solving capacity of systems often derives from the competencies of their parts. Stress in this case is a motivating driver of homeostatic adjustments for the cells. It should be noted that some excellent work has been done in the area of understanding how networks (such as gene-regulatory networks) can be guided by stress dynamics to find their way in high-dimensional spaces [[66], [67], [68], [69], [70], [71], [72]].

We constructed a model in which anatomical homeostasis, driven by a set of competent sub-agents, can be examined with respect to a possible role for stress sharing. This model of cellular morphogenesis allowed us to test the hypothesis that sharing of stress, as an indicator of error (distance from the target morphology), would facilitate morphogenesis, be favored by evolutionary processes, and enlarge the effective cognitive light cone of individual cells (increase the scale of goal-directed activity, as befits a mechanism for facilitating collective intelligence dynamics).

We observed that allowing cells to leak stress to their neighbors is beneficial for morphogenesis, allowing the cell collective to reach their target morphology faster and reliably when compared to controls (Fig. 3). This effect persisted across a range of grid sizes, and was due to cells being able to move over longer distances. This movement builds in more freedom and redundancy, which is especially helpful during later stages of morphogenesis when fine-grained improvements are required to finish the pattern (Fig. 5). In effect, the propagation of stress implements a kind of implicit altruism: without having to provide a mechanism for cells to coordinate or care directly about their neighbors’ state, a simple leak mechanism ensures that the stress in one region motivates other cells to work to relieve it. By envisioning leaked stress molecules as features of the microenvironment around stressed cells, our results are also consistent with prior proposals that stigmergy (ability of subunits, such as ants or cells, to leave each other messages in an external medium of the environment) is a universal coordination mechanism [73,74]. We think that this is precisely the kind of simple mechanism biological evolution would seize upon, to increase the collectivity of subunits in a body.

One prediction made by our approach is that cells should leak molecules used as stress markers; indeed, apparently this has been observed for one such molecule – HSP90, a heat-shock protein which also occurs extracellularly [75]. We are currently testing these predictions at the bench, establishing reporter assays for stress and studying how it may spread and with what consequences.

We have previously studied a different but related effect, in which competition for informational and metabolic resources by cells within a single body actually contributes to morphogenetic coordination, such as for example ensuring identical growth of left and right limbs. When cells do not compete (acquiring resources from an infinite reservoir), no cell knows what any other cell did or did not take from that reservoir. However, finite reservoirs allow cells to coordinate their activity because the current state of the reservoir provides information about how much other cells have taken from it. In effect, limiting pools of resources become a kind of global, stigmergic scratchpad, bearing the evidence of activity of cells across distance and enabling them to communicate through this kind of global variable [76,77]. These kind of mechanisms, along with others based on memory propagation between cells [55], contribute to the “cognitive glue” that binds individual cells to common purpose.

One way to think about unconventional agents such as groups of cells is to model the size of their cognitive light cone: the spatio-temporal distance that represents the size of the largest goal states which their homeostatic mechanisms can pursue. Multicellular development scales these cognitive light cones from the single cell-scale metabolic and transcriptional goals of individual cells to the grandiose, large-scale setpoints of anatomical structures in morphospace. Disorders of this process, such as cancer [78,79], result from a pathological restriction of this radius of concern, when cells treat the rest of the body as external environment. Put another way, cognitive light cone model [55] formalizes the notion of functional care or concern as being defined by the distance at which things that happen can stress an agent to the point of initiating actions to effect change. To explore the hypothesis that stress sharing potentiates collectivity and helps scale morphogenetic goals, we quantified the cognitive light cone of cells with and without stress sharing.

In our analysis, we saw that enabling the sharing of stress initially increases the cognitive light cone of cells, as measured by the farthest distance a given cell can use as the setpoint for its subsequent activity. This is consistent with a role for stress sharing in enlarging “pro-social” behaviors in the tissue. However, during its lifetime, each virtual embryo transitions from large-scale rearrangements to small-scale fine-tuning (similarly to how real development progresses from the major refactoring of gastrulation to local refinement in late stages). While cells can take on long-range goals when sharing stress, their effective radius of concern shrinks over time, as it becomes less relevant to take distant events into account (Fig. 5B).

These dynamics make an interesting prediction for the biology of aging [80]. While embryonic development involves progressive reduction of error from a prepattern that keeps changing to pull the embryo from stage to stage, eventually the prepattern stops changing and major rearrangements cease – maturity. However, a mature organism is not a static structure because cells inevitably senesce, die, and must be replaced. An adult organism is in equilibrium but its new cells must continuously be placed correctly, not only in anatomical space but also in physiological and metabolic spaces, when they appear. Thus, the homeostatic process continues, but with a very small cognitive light cone that involves only the local microenvironment for resisting tissue degradation. Our model suggests that modulators of stress response may be candidate targets to modulate tissue replacement and aging in vivo.

Our model studied stress propagation, and was constructed and analyzed from a purely functional metric of performance under various conditions as gauged by an external observer (error function). What about the valence of stress – what is it like to be an agent, made of silicon or proteins, at high or low error levels [[81], [82], [83], [84], [85]]? While we don't know what it’s like to be a cell or tissue under stress [36,86,87], stress as a readout of distance from homeostatic equilibrium is a familiar feature of large-scale biology and of our human experience. There have been studies of what it’s like to be simulated beings in simplified digital world [57], although we are not aware of studies that focus on the inner worlds of goal-directed artificial agents with stress dynamics.

Here we avoid discussion of the deeper questions of stress as felt prediction error [[88], [89], [90], [91]], metacognitive loops that allow agents to know what they are doing, and associated issues of first-person perspective that is so important to adaptive agents. However, our results do offer one bit of insight into the distinction between the information available to a system vs. what is perceivable by external observers of the system. We found that knowledge of the embryonic stress patterns do not enable one to deduce the morphogenetic goal state it is trying to reach. Such an agent's goals are largely inscrutable to externa observers (such as scientists, conspecifics, parasites, predators, etc.) The agent itself can perceive its homeostatic goal state, because it effectively reaches that target morphology precisely due to the stress distribution. This provides an interesting, yet primitive, example of “privacy” – a feature of brains that hampers efforts at neural decoding [[60], [61], [62], [63]], in which some features of 1st person cognition are inaccessible to 3rd person observers [92,93]. Apparently, even simple systems such as our virtual embryogeny [94,95], with stress sharing, exhibit emergent features of privacy in the context of homeostatic collectives.

Our model has a number of limitations that warrant possible extensions in future work. First, it is 2-dimensional – it is not known how such dynamics would play out in three, or higher-dimensional morphospaces. Moreover, our simulation tries to model the dynamics of each and every cell (albeit in a simpler discrete manner) rendering it too expensive to scale. Evolutionary simulations are especially intractable beyond an embryo size of 50x50 on a 256-core machine. A reductionist approach to stress sharing might reduce the simulation burden and enable further scaling. Regardless, massively parallel computing architectures will need to be considered to study a bio-realistic numbers of cells.

Our simulation takes place in a fixed, discrete grid, which cannot itself deform as cells move. As such, it does not capture some of the recurrent complexity of morphogenesis in which the action landscape of cells is modified by other cells’ actions. And, we only simulated two different cell states, reducing the possible complexity. Furthermore, we did not include multi-scale stress – future models will study the interplay of stress at different levels of organization in the same virtual embryo, from the molecular to the cell-, tissue-, and whole organism level, as new dynamics and problem-solving behaviors may emerge when homeostats are coupled [13,96].

Homeostasis, and mechanisms which expand the size of the goal states towards which it works, is a central concept for understanding agency [[97], [98], [99]], regenerative competency [11,12], and evolution [[50], [54],[100], [101], [102]]. Thus, future empirical work must identify mechanisms by which stress is sensed and distributed within and across groups of cells. Existing tools of molecular genetics and biophysics can then be deployed for loss- and gain-of-function studies of the role of stress in morphogenetic competency, to test the predictions of our model in vivo. More broadly, it may be that stress and geometric frustration [103] are a truly interdisciplinary concepts, reaching far beyond the conventional notions of psychological stress and highlighting a central symmetry across fields ranging from the computational mathematics and physics of Ising models and Hopfield networks [104,105] to the remarkable capabilities of regulative morphogenesis [5,54] and even the epigenetics of transgenerational inheritance [[106], [107], [108]]. Stress is a good candidate for a central invariant across active agents of highly diverse scale and composition. Feedback between computational models and wetlab biology, focused around the primary concept of the causal geometry of stress, offer the exciting potential to unify and advance aspects of the field of diverse intelligence in ways that benefit fundamental questions of cognitive science, robotics engineering, and biomedical disorders of homeostatic cellular collectives.

Lakshwin Shreesha: Writing – review & editing, Writing – original draft, Software, Methodology, Investigation, Formal analysis, Conceptualization. Michael Levin: Writing – review & editing, Writing – original draft, Supervision, Project administration, Methodology, Funding acquisition, Formal analysis, Conceptualization.

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:Michael Levin reports financial support was provided by 10.13039/501100011730Templeton World Charity Foundation Inc. for support of co-author Lakshwin Shreesha. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.