Somatic multicellularity as a satisficing solution to the prediction-error minimization problem

From an FEP perspective, one would expect cells to respond to increasing environmental lethality in one of the two ways given by the theory of active inference: either by changing their prior probability distributions and hence their regulatory models or by acting so as to change their environments and hence their posterior, i.e. input, probability distributions.2 Modifying the genome is the most available way of altering the prior probability distribution, i.e. the generative model of the environment, for prokaryotes; the enormous genetic diversity of prokayrotes [2,41] suggests that genome modification is the primary prokaryotic strategy for dealing with environmental change. Rapid genome modification by lateral gene transfer is ubiquitous among prokaryotes, with environmental-response genes particularly frequently transferred [42–44]. Motility is the most available way of altering the posterior probability distribution; the eukaryotic development of the cytoskeleton enabled multiple motility solutions for unicellular eukaryotes, with environment-dependent morphological changes supporting different motility solutions, e.g. flagellar propulsion and ameboid crawling, available in many lineages [12]. Motility is, however, only useful if the lethality of the environment varies significantly over short distances and hence permits escape. Somatic multicellularity can, we suggest, be understood as a more radical solution to the problem of altering the posterior probability distribution in an environment in which lethality varies only over longer ranges (Figure 3). The reproductive cells within an obligate multicellular organism alter their environment by constructing and then inhabiting a new environment that they largely control, i.e. one with consistently low VFE.

The components employed for this construction project are their own progeny, the most predictable living components available.10.1080/19420889.2019.1643666-F0003Figure 3.a) The theory of active inference postulates that systems challenged by high environmental free energy respond either by updating their prior probability distributions or world models, or by altering their posterior probability distributions by acting on the world so as to change its effects on them. b) Reproductive cells challenged by environmental lethality can be expected either to update their prior probability distributions by altering their genomes, or to execute some behavior that changes their environment’s lethality. Genome modification by rapid evolution or lateral gene transfer is primarily a prokaryotic strategy. Motility is a successful, primarily eukaryotic strategy when environmental lethality varies over short ranges. Building a multicellular structure, a body, that protects reproductive cells from the environment provides a solution when escape is not possible.

The most important criterion for a synthetic, protective environment is that it not be or become a competitor. From a fitness perspective, the simplest way to assure non-competition is by constructing the environment out of cells or other materials, e.g. extracellular matrix components, that have no independent genetic interests or reproductive fitness. Such materials cannot respond to environmental variation by varying their allocation of resources to reproduction; hence they are intrinsically more predictable than reproductively-competent cells. Hence a system – a reproductive cell – driven to minimize VFE can be expected to build a somatic body comprising non-reproductive cells as a protective environment in preference to either a clonal (i.e. fraternal) or aggregative (i.e. egalitarian) body composed of other reproductively-competent cells. The demosponges, with a single class of proliferative, totipotent stem cells (the archeocytes), exemplify this body-building strategy [17], suggesting that it may be ancestral in the Metazoa. That a single class of proliferative, totipotent stem cells (the neoblasts) are also found in planaria [24] indicates that an all-or-nothing strategy for regulating cellular reproduction was maintained at least into early-branching bilaterals.

To extend our earlier model to this situation, suppose that C can reproduce a copy C’ of itself with time-varying state c’(t) = a’(t) × p’(t) as above, and interpose this C’ as a protective buffer between itself and E as shown in Figure 4. Protection by C’ replaces the exposure β of C with some βprot < β; if protection is complete, βprot = 0. Assume as above that the reactions R and R’ are negligible, and consider the simplest case, reproduction of an exact copy C’ with prediction mapping P’ = P and environmental exposure β’ = β. In this case, the probability of C’ dying and requiring replacement to prevent re-exposure of C to E in any reproductive cycle is β’ Δlethal; if β’ Δlethal ≥ 0.5αa, all available resources must be dedicated to reproduction for protection, and C remains exposed to E during part of each cell cycle. Hence the ability of C to maintain C’ is critically dependent on the availability of reproductive resources and their efficient use by C. As before, population survival is only possible if β’Δlethal ≤ αa/(1 + αa). Reproducing an exact, reproductively-competent copy as protection against a lethal environment is, therefore, no better as a strategy than aggregation.10.1080/19420889.2019.1643666-F0004Figure 4.Adding a buffer between C and E by reproducing a copy C’ of C. Competition for reproduction-enabling resources is eliminated C’ if reproductively disabled.

Effective protection from a lethal environment requires the production of progeny or materials that have decreased environmental sensitivity relative to C, i.e. that have β’ < β. Non-reproductive cells can be expected to have β’ < β, due both to their lower metabolic requirements [45,46] (see also below) and their ability to re-tool metabolism toward the production of either inert protective materials or active defenses. The production of long-lived non-reproductive progeny increases fitness if it allows the subsequent production of protected reproductively-competent progeny, e.g. daughter stem cells. If k protective cells must be produced every m cell cycles, with k < m, the population of reproductive cells is able to grow as r(n/m)(m – k) over an elapsed time nτ; for k ≪ m, this approaches the best-case rate rn.

To investigate this model of non-reproductive, i.e. somatic progeny as highly-predictable protectors of reproductive cells, assumed here to be totipotent stem cells as in demosponges or planaria, from the external environment, we have developed a quantitative simulation that embeds stem cells in an environment of varying lethality and allows parameters governing their ability to reproduce either stem or somatic progeny to be manipulated (see Methods). Consistent with the model, unprotected stem cells cannot successfully invade an environment with greater than 50% lethality (b = 0.5) on each division cycle even if reproductive resources are optimal (Figure 5(a)).10.1080/19420889.2019.1643666-F0005Figure 5.Typical model simulation runs under different conditions. The simulation depicts an environment varying in lethality from 0% (b = 0, black, left margin) to 100% (b = 1.0, red, right margin). Stem cells (green) are randomly seeded in this environment at a density of 5% and allowed to reproduce for 120 division cycles. Neighboring stem cells compete for reproductive resources. Somatic progeny (blue) protect their nearest-neighboring cells, whether these are stem or other somatic cells. a) Stem cells alone cannot invade the higher-lethality half of the environment, even with optimal reproductive resources (a = 1.0). Here neighboring stem cells suffer a 20% resource reduction (α = 0.8) due to competition; removing this reduction does not allow them to cross the 50% lethality boundary. b) Moderately (50%, i.e. β’ = 0.5) protective but relatively long-lived (50% resistance to lethality) somatic cells allow mainly small colonies in the moderately-lethal (50% – 75%) sector of the environment (a = 0.8, probability of somatic-cell progeny 50%).

c) Fully (100%, β’ = 0) protective but shorter-lived (only 20% resistance to lethality) somatic cells allow larger colonies to populate even the high-lethality (75% – 100%) sector of the environment (a = 0.8, probability of somatic-cell progeny 50%). d) Fully-protective and relatively long-lived (50% resistance to lethality) somatic cells allow invasion of the lethal sector of the environment (a = 1.0, probability of somatic-cell progeny 25%).

When the production of somatic progeny is enabled, different combinations of protective ability and resistance to lethality lead to different abilities for stem cells protected by somatic-cell “bodies” to colonize the higher-lethality (> 50%) sector of the environment. In general, long-lived but only moderately-protective (β = 0.5) somatic cells enable small colonies at moderate lethality (Figure 5(b)), while shorter-lived but fully-protective (β = 0) somatic cells enable larger colonies even at high lethality (Figure 5(c)). Combining these somatic-cell advantages enables invasions of the entire environment (Figure 5(d)). The increasing occupation of the high-lethality (b > 0.5) part of the environment as the protection of stem cells by somatic cells increases is shown in Figure 6.10.1080/19420889.2019.1643666-F0006Figure 6.Increasing occupation of the high-lethality (b > 0.5) half of the environment as the somatic cell protection factor 1 – β is increased from 0.0 to 1.0, with all other parameters as in Figure 5c. Filled circles show averages over 10 runs with random starting populations; bars show full range of results obtained.

In these simulations, stem cells that are fully enclosed by a somatic “body” cannot escape to generate new progeny. They can and do, however, explore the external environment whenever one of the surrounding somatic cells dies; most such pioneering stem cells die before reproducing if the environmental lethality is greater than 50%. “Budding” of a stem cell with its surrounding somatic cells from a large connected mass to form an independent colony has been observed in some simulation runs.

To characterize the phase transition to multicellularity more precisely, consider the environment E as a source and the cell C as a receiver of VFE, i.e. prediction-violating information. We can represent protective cells and/or their internal processes collectively as a channel that probabilistically decreases the transmitted VFE, i.e. has an effective β < 1. Any such channel can, alternatively, be decomposed into a network of smaller channels, each of which transmits VFE with a well-defined probability, with interconnections between these channels representing cross-modulation or other probabilistic dependency. Such a network constitutes a “Markov blanket” as defined by Pearl [47] around the cell C (technically, the internal states of cells directly interacting with both E and C form the Markov blanket; “expanding” each cell into a network of internal processes creates a multi-layer Markov blanket). Markov blankets provide a general model of the interactions between biological systems and their environments [3,10]. We assume here that the conditional dependencies that define the Markov blanket around the cell C are in a state of flux and can be affected by regulatory changes within C (in the language of active inference, actions by C) that alter either its sensitivity to environmental VFE or the behavior and hence protective capabilities of its neighboring cells. Decreasing exposure to environmental VFE is then a matter of C finding the right set of conditional dependencies, i.e. the right Markov blanket, to interpose between itself and E.

If we only consider transmission of VFE from E to C, ignoring the corresponding flow from C to E (i.e. the reaction map R) as above, we can represent the Markov blanket as a weighted directed graph with nodes {k} and connection weights given by a real matrix M with elements Mij representing the probability of transmitting VFE from node i to node j. The Mij represent, in this case, the coupling or conditional dependency between the states i and j. Some subset {kin} of the nodes represent states of E, while another, disjoint subset {kout} of nodes represent states of C as shown in Figure 7; intermediate nodes represent states of intermediate cells, e.g. non-reproductive somatic cells surrounding C. In the simplest case, transmission of VFE through the blanket can be considered effective only for values of the conditional dependencies Mij above some threshold; hence these can be considered binary without loss of generality. The effective transmission from E to C is, in this case, given by counting paths between them. A binary blanket in which every pair of nodes is connected has the maximal number of paths; one in which no nodes are connected has no paths. If {kin} ∪ {kout} = {k} (i.e. the graph representing the Markov blanket is bipartite), only if Mij = 0 for all i, j are there no paths from E to C; otherwise this is not the case.10.1080/19420889.2019.1643666-F0007Figure 7.a) Simplified representation of a Markov blanket. Input nodes represent environmental states that transmit environmental VFE to a network of intermediate nodes, with conditional dependencies specified by a connectivity matrix Mij. Output nodes represent protected cell states that receive the “blanketed” VFE. It is natural to interpret distinct input nodes as transmitting the VFE of different dimensions of the environment, e.g. pathogenicity or toxicity.

b) A network very near its percolation threshold: removing either link A or B results in opacity. On the other hand, adding any downward-going link between black nodes, or between black and green nodes, increases the cell’s exposure to its environment.

Markov blankets in which every input node is connected by a path to some output node and vice-versa fully expose C to E, i.e. correspond to β = 1. Such blankets are in a natural sense “transparent” to VFE. States in which no path exists from any input node to any output node fully protect C from E, correspond to β = 0, and are in a natural sense “opaque.” The transition from only local communication between nodes (i.e. opacity) to global communication between essentially all nodes (i.e. transparency) as connections are randomly added to an information-transmission network has been extensively studied using percolation theory, e.g. in models of epidemics [48,49], predator-prey interactions [50], intracellular coordination of mitochondrial function [51], and long-range signaling in microbial communities [52]. Such transitions are characterized by a critical point, the percolation threshold, at which opacity switches exponentially to transparency or, as in the problem of interest here, transparency switches exponentially to opacity. The number of connections that must be added to reach the percolation threshold from below, or removed to reach it from above, depends strongly on the size, local connectivity, and density of long-range connections in the starting graph [48]. In particular, the percolation threshold rapidly decreases as the number of long-range connections in the starting graph is increased.

If we consider the input nodes of the Markov blanket around a cell to correspond to environmental states characterized by distinct dimensions of environmental lethality, e.g. pathogenicity or toxicity, long-range connections in the blanket correspond to multiple paths by which the cell can be exposed to each dimension of lethality. The relatively low percolation threshold of such a blanket means that many connections have to be severed to induce opacity and hence protection. A blanket in which each input node is linked to only one output node has fewer long-range connections, a higher percolation threshold, and hence a smaller number of links that must be severed to induce opacity (Figure 7(b)). One would, therefore, expect successful cells to produce protective progeny that are each specialized to deal with one kind of environmental threat, and to regulate the morphology and/or metabolism of each of these cell types to maximize its opacity, i.e. to minimize the exposure to environmental VFE of the protected cell by decreasing the VFE transmission of its Markov blanket. The tendency of regulatory [53], metabolic [54], and cell-cell communication [55] networks toward small-world [56] structure, in which long-range connections link distant clusters of nodes, renders this kind of specialization difficult to achieve.

Successful construction of a protective Markov blanket out of daughter cells requires two genetic capabilities: the ability to arrest the daughter’s cell cycle and the ability to modulate its gene expression and metabolism away from independent motility and continued cell division and toward adhesion, a specialized morphology, and the production of specialized products. Both comparative genomics and the cell and developmental biology of unicellular eukaryotes increasingly show that these capabilities were available in the genetic toolkit of ancestral holozoans.

As noted earlier, prespore cells in migratory Dictyostelium secrete morphogens (Differentiation-Inducing Factors or DIFs) that arrest the cell cycle and induce terminal differentiation in prestalk cells [37,38]. Native Dictyostelium DIFs have been shown to deactivate the Wnt pathway and suppress Cyclin D1 and hence cell division in mammalian cells by activating the GSK-3β kinase [57]. While the Wnt pathway appears to be unique to metazoans [58], GSK-3, a β-catenin homolog, and Frizzled homologs are present in Dictyostelium and are involved in cAMP-induced migration and cell adhesion [59] and epithelial polarity [60]. Additional signals involved in Dictyostelium spore differentiation, including the metazoan neurotransmitters GABA and glutamate, have also been identified and in part characterized [61]. Hence it is reasonable to assume that morphogens capable of both inducing cell-cycle arrest and regulating motility and adhesion are available to eukaryotes at least since the last common ancestor of Amoebozoa and Opisthokonts.

The availability of both whole-genome and sample sequences from choanoflagellates and earlier-branching holozoans confirms that not all, but many metazoan cell polarity, adhesion, signaling, and transcriptional control systems predate the choanoflagellate – metazoan split and may be ancestral to holozoans in general [1,62], with adhesion and motility regulators such as Src [63], the Rac/Rho second messengers [64], and cell-division regulators such as Myc [65] as prominent examples. The ancient roots of hormonal [66,67] and neurotransmitter [68,69] systems suggest that both were available to reproductive cells as a means of modulating or controlling the behavior of non-reproductive progeny in the earliest obligate multicellular organisms.

In all metazoans, distinct differentiated cell types perform distinct functions. From the perspective adopted here, these distinct functions can be seen as information-processing functions. Distinct non-reproductive cell types act in different ways to reduce environmental VFE, and to replace it, in their interactions with the reproductive cells with which they share inclusive fitness, with highly-predictable protective behavior. The modularization of protective and other supportive behaviors in distinct cell types is consistent with the vast expansion and diversification of transcription factors, relative to the unicellular eukaryotic toolkit, seen in multicellular eukaryotic lineages (reviewed by [70]). Such systematic reduction of VFE is precisely the role ascribed to functional networks of the nervous system by Bayesian approaches to cognition [9,71,72]. This view of somatic cells in general as essentially cognitive [73–75] suggests an integrative, scale-free approach to biological information processing that spans all of phylogeny, in which the sensory, regulatory and behavioral roles of the mammalian nervous system are seen as fundamentally analogous to the sensory, regulatory and behavioral roles of metabolic processes in unicellular organisms [76].

Within an “imperial” model of multicellularity that views reproductive, i.e. stem or germ, cells as both regulatory controllers of and receivers of information from surrounding somatic tissue [24], the VFE reduction performed by somatic cells is in service of the genetic interests of their parent stem/germ cells, interests which they share via inclusive fitness. Reproductive fitness remains, in this model, at the level of stem/germ cells; it is not necessary to define an independent “organismal” level of reproductive fitness as it is in aggregation followed by cooperation models [7,8]. Re-assertion of individual reproductive fitness by previously somatic cells (i.e. cancer) is not “cheating” on a cooperative “contract” that divides cellular labor [20] but rather escape from regulatory control. Somatic mutation is tolerated in this “imperial” setting provided it does not reprogram somatic cells toward division, i.e. cancer.

As noted earlier, re-allocation of resources away from reproduction is, on this model, one of the key enablers of multicellularity. Without such re-allocation, cells within an aggregate compete both for resources and genetically; the latter form of competition has been recently demonstrated in cytokinesis-inhibited Saccharomyces cerevisiae aggregates [77]. Somatic cells that reprogram to either normal reproductive cells or cancer cells must re-allocate resources to cell division, including high-turnover production of nucleotide bases, membrane components, and proteins [78–80]. Such reprogramming is inducible by multiple signals in vertebrates, the receptors or effectors for many of which (e.g. Src, Rho and Myc as noted earlier) are present in the ancestral toolkit.

By reprogramming metabolism for division, cancer cells are re-asserting an independent genetic interest and abandoning their previous role as somatic protectors of “normal” reproductive stem, non-stem progenitor or, in obligate sexual species, germ cells [20,81]. From their perspective, the host body is a protective environment which they can exploit to their own ends. One would expect, therefore, cancer cells to transmit regulatory signals to surrounding tissue, whether somatic or reproductive, to suppress cell division and otherwise minimize detectable VFE. Such suppression by tumor cells of cell division in surrounding non-tumor somatic tissue has been observed [82,83].

The nervous system is a multicellular eukaryotic innovation, evident as a network of cell-cell communication in Porifera [84], supported by specialized cells in Ctenophores, and fully developed in Cnidarians and Bilaterians [85,86]. Nervous systems are traditionally thought of as providing sensing and behavioral coordination functions at the level of the whole organism. The current model suggests an additional, deeply ancestral function of the nervous system: distributed control of cell proliferation. As bodies become more complex geometrically, local suppression of somatic-cell proliferation by individual stem cells becomes insufficient to maintain a regular shape; hence sponges, with interstitial stem cells but no long-distance neurons, are amorphous, but all other metazoans, with neurons, are not. The current model predicts that neural communication is directly involved in the regulation of somatic cell proliferation, and hence in the control of morphology. While innervation is known to be important for regeneration [87] and the nascent CNS has recently been found to be crucial for the patterning of distant somatic regions [88], the role of innervation in regulating proliferation, apoptosis, and neoplasia remains an active area for future research (reviewed by [89,90]).

Obligate sexuality with a differentiated germline places a second demand on proliferation control: germ cells must assure that non-germ stem cells do not proliferate indefinitely [23,24]. As germline cells are typically segregated early in development while stem cells remain relatively dispersed, regulation of stem cell proliferation requires a long-range mechanism. In organisms like C. elegans with invariant cell lineages [91], the solution is, in effect, for the germline cells to be the only adult stem cells. The current model predicts that in organisms with adult stem cells, stem cell proliferation will be under regulatory control by the germ line, with neural and/or hormonal systems as effectors.

The selection pressures that drove the transitions to obligate multicellularity with complex morphology in plant and animal lineages remain poorly understood. Here we have suggested that multicellularity solves a problem for proliferating cells: the problem of predicting the behavior of the environment. By surrounding themselves with reproductively-disabled copies of themselves, proliferating cells, which then become stem cells, provide for themselves a local environment that buffers the VFE of the larger environment outside. On this model, the transition to obligate multicellularity can be viewed as a phase transition in which the blanket of surrounding somatic cells becomes effective opaque to environmental variation. Maintaining this opacity is, as Clark [92] has pointed out, the key to maintaining autopoesis [93] for the blanketed system as a whole. As only a satisficing solution is required, the opacity of the blanket is not expected to be complete in any but the most challenging environments.

This model of the transition to multicellularity is consistent with an “imperial” view of the multicellular state as one in which stem cells effectively control the differentiation and behavior of somatic cells. It suggests that the fundamental role of neural signaling is the control of cell fate, and that cancer is an escape by somatic cells from the non-proliferating fate imposed on them by stem cells.