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

Adaptive success in the biosphere requires the dynamic ability to adjust physiological, transcriptional, and behavioral responses to environmental conditions. From chemical networks to organisms to whole communities, biological entities at all levels of organization seek to optimize their predictive power. Here, we argue that this fundamental drive provides a novel perspective on the origin of multicellularity. One way for unicellular organisms to minimize surprise with respect to external inputs is to be surrounded by reproductively-disabled, i.e. somatic copies of themselves – highly predictable agents which in effect reduce uncertainty in their microenvironments. We show that the transition to multicellularity can be modeled as a phase transition driven by environmental threats. We present modeling results showing how multicellular bodies can arise if non-reproductive somatic cells protect their reproductive parents from environmental lethality. We discuss how a somatic body can be interpreted as a Markov blanket around one or more reproductive cells, and how the transition to somatic multicellularity can be represented as a transition from exposure of reproductive cells to a high-uncertainty environment to their protection from environmental uncertainty by this Markov blanket. This is, effectively, a transition by the Markov blanket from transparency to opacity for the variational free energy of the environment. We suggest that the ability to arrest the cell cycle of daughter cells and redirect their resource utilization from division to environmental threat amelioration is the key innovation of obligate multicellular eukaryotes, that the nervous system evolved to exercise this control over long distances, and that cancer is an escape by somatic cells from the control of reproductive cells.

Our quantitative model illustrates the evolutionary dynamics of this system, provides a novel hypothesis for the origin of multicellular animal bodies, and suggests a fundamental link between the architectures of complex organisms and information processing in proto-cognitive cellular agents.

The unicellular lifestyle dates back to the origin of life on Earth some 3,900 million years ago (Mya) [1] and remains successful today, with the vast majority of genetic as well as niche diversity found in the unicellular microbial world [2]. Unicellular prokaryotes and later, eukaryotes also developed facultatively multicellular lifestyles, e.g. in microbial mat communities, involving mutual dependence and division of labor (reviewed by [3–5]). Eukaryotes developed, in addition, the obligate multicellular lifestyle; indeed the eukaryotic cell is itself sometimes regarded as the initial obligate multicellular organism [6]. Unlike facultative multicellularity, obligate multicellularity compromises or altogether eliminates the independent reproductive fitness of at least some of the cells involved. What would induce cells to give up independent reproductive fitness in favor of a completely-dependent lifestyle as part of an obligate multicellular organism? This question is often answered by the analogy of a “contract” in which cells cooperatively surrender independent reproductive fitness for the benefits of group selection [7,8]; however, the mechanisms driving such arrangements have remained unclear. Here we suggest that obligate multicellularity provides a solution, typically satisficing not optimizing, to the problem of minimizing errors in the prediction of the behavior of the environment. The selection pressure for obligate multicellularity is, if this is correct, essentially thermodynamic [9,10].

While facultative multicellularity is commonplace among both prokaryotes and eukaryotes, obligate morphologically-complex multicellularity is rare, occurring in only five eukaryotic clades (reviewed by [1,11,12]). Somatic multicellularity, in which cell division is restricted wholly or significantly to specialized stem and/or germ cells, is characteristic of the Metazoa. Following Haeckel [13], it has long been theorized that ancestral metazoa were clonal colonies of morphologically-identical cells. Recent ultrastructural and phylogenomic studies have established choanoflagellates as the closest extant unicellular relatives of metazoa [14] and provided significant new evidence to support James-Clark’s [15] hypothesis that choanoflagellates are homologous to sponge choanocytes, and hence that facultative rosette colonies of choanoflagellates are plausible models of ancestral multicellularity [16]. Such studies also suggest that multicellularity may be a Holozoan character predating the choanoflagellate – metazoan split [1,12]. Funayama [17,18] has suggested that choanocytes are ancestral to the ameboid archeocyte stem cells of demosponges, consistent with the observation of alternating flagellate and ameboid forms elsewhere in the unicellular holozoa [12].

Obligate, morphologically-complex multicellularity is a canonical major transition in evolution, establishing the multicellular organism as a Darwinian individual characterized by genetic interests and reproductive fitness [6,19]. As Szathmáry [6] emphasizes, the division of labor possible with multicellularity enables fitness-increasing synergistic interactions between distinct cell types, and hence specific selection for such interactions. Models of the evolution of complex multicellularity have, accordingly, focused on fitness and selection at the whole-organism level [7,8,20–22]. Motivated by Solana’s [23] primordial stem cell hypothesis, experimental and modeling results suggesting that stem cells (neoblasts) in asexual freshwater planaria remain Darwinian individuals [24] and by a conception of cancer as an escape from organism-scale control [25–28], here we consider the selection pressures that could drive a transition to multicellularity from the perspective of a single reproductive cell. We suggest that the largely-somatic multicellular bodies of metazoa can, in general, be considered protective environmental niches constructed by stem and/or germ cells to assure their own future reproductive fitness. We formulate this suggestion in terms of the Free Energy Principle (FEP) defined by Friston [9,10] as the claim that reproductive (proto-)stem cells construct multicellular bodies in order to reduce the variational free energy of information exchange with the immediate environment and hence to minimize prediction error as regards their own survival. From this FEP perspective, somatic multicellularity is a natural outcome of environmental challenges faced by free-living cells, with the primary genetic driver of multicellularity being the development of intercellular signals for cell-cycle arrest.

In this “imperial” model of multicellularity [24], reproductively-competent stem and/or germ cells produce reproductively-incompetent somatic cells in order to advance their own genetic interests by establishing an environment-facing cellular layer that reduces uncertainty and improves predictive power (and thus physiological adaptation) for the internal cells.

We begin by considering the effects of increasing environmental lethality, due to predators, pathogens, toxins or other threats, on populations of dividing cells in environments with different resource levels. Using a simple parametric model, we show that the combination of high resource levels with high lethality favors a phase transition from a rapidly-dividing population to one in which significant resources are devoted to reducing environmental threats. We then generalize from environmental lethality to any source of high variational free energy [9,10]. We suggest that a protective environment composed of reproductively-disabled progeny provides a satisficing, though not necessarily optimal, solution to the problem of minimizing variational free energy and hence prediction error. Using a quantitative model of stem and somatic cells in an external environment characterized by varying levels of lethality, we investigate the parameter dependence of the transition to multicellularity. We show that a protective multicellular body can be modeled as a Markov blanket that undergoes a phase transition to informational opacity as the environmental free-energy buffering capacity of somatic progeny is increased. Finally, we review evidence that the ancestral genetic toolkit of holozoans is sufficient to support the transition to multicellularity. We discuss these results from two perspectives: that of individual cells as information processing units that can be assembled into a computational interface with the environment, and that of cancer as an escape by somatic cells from “imperial” oversight and control.

The model simulation employs a 30 by 60 grid of possible cell locations (1800 total) with lethality varying from 0% per stem cell division cycle to 100% per stem cell division cycle along the long axis in 60 equal increments. Stem cells are seeded in random positions at 5% density. The probability that a stem cell will die before reproducing is determined by the lethality b of the cell it occupies, multiplied by the protection β it receives from neighboring somatic, i.e. non-reproductive cells, if any.

The level a of reproductive resources for stem cells in the environment is fixed by a parameter setting. The local resource level αa, where the parameter α represents the availability of reproductive resources to a stem cell at a given location, determines the probability of stem-cell division at that location on each cycle. The value of α for a stem cell is reduced by 20% for each neighboring stem cell by default; this reduction parameter is adjustable. If the production of somatic progeny is enabled, the resource availability α for a stem cell is increased by 20% for each neighboring somatic cell by default; this parameter is also adjustable.

Stem cells are only allowed to divide if they have a neighboring open cell; this restriction models the relative rigidity of the somatic body.

Somatic cells protect neighboring cells, stem or somatic, by an adjustable factor β. Somatic cells resist lethality by an adjustable factor, with a default of 20%.

The model simulation is implemented in javascript using the HTML 5 Canvas function for display. All probabilities are calculated by comparing random numbers generated by the javascript Math.random function to parameterized limit values. The simulation is available for use and its source code can be examined at https://chrisfieldsresearch.com/somatic-protection-model.htm.

A multicellular body composed primarily of reproductively-disabled somatic cells is a eukaryotic innovation widely recognized as a major evolutionary transition [6,19]. Why, however, would an ancestral eukaryotic cell devote reproductive resources to the generation of non-reproductive progeny? Doing so manifestly decreases reproductive fitness. What selective environment would tolerate and even reward this fitness-decreasing strategy long enough to enable the cellular differentiation and synergistic interactions characteristic of complex multicellularity to arise?

Here we suggest that a high-resource environment that is also high in potential lethality, e.g. due to the presence of predators, pathogens, toxins, changing conditions, or other threats, rewards the investment of reproductive resources to produce a multicellular somatic body, provided the body is capable of protecting its reproductive cells from the environment. Such a high-lethality environment imposes a conflict between the demands of short-term reproductive fitness and short-term survival; a protective body resolves this conflict in favor of survival at the expense of fitness. In this picture, the primary evolutionary innovation enabling the multicellular lifestyle is not increased cooperation between reproductively-competent cells as suggested by either “fraternal” or “egalitarian” aggregation-based models [7,8] (see also [29] for a review of aggregation-based models), but rather the ability of a reproductively-competent cell to actively suppress the reproductive potential of its somatic progeny. This innovation is most fully expressed in obligately-sexual organisms in which a single, gamete-producing stem cell lineage, i.e. a specific germ lineage, is the sole carrier of reproductive fitness.

To describe this situation quantitatively, consider a uniform population of free-living, reproductive cells in a resource-rich environment, and let τ be the minimal cell-cycle time for these cells. If every cell divides in each period of length τ, then the population size N(t) after n cycles, i.e. at t = nτ is: Nt=N0⋅2n

where N0 is the initial population size. If only r of the cells divide on each cycle, we can write: Nt=N0⋅rn

where 0 ≤ a,b ≤ 1 are parameters describing the environment and 0 ≤ α,β ≤ 1 are parameters describing the cells. These parameters are interpreted as follows: a measures the availability of resources for reproduction in the environment, with a = 0 being starvation conditions allowing population maintenance only and a = 1 being sufficient resources for (in practice) unlimited growth.b measures the lethality of the environment, with b = 0 being completely benign and b = 1 being complete lethality for the population in question.α measures the efficiency with which available resources are employed for reproduction by a given cell, with α = 0 being minimal and α = 1 maximal efficiency.β measures the degree to which dividing cells are exposed to the environment, with β = 0 complete protection from the environment and β = 1 complete exposure.

Maximum population growth is clearly achieved when a = α = 1 and either b = 0 or β = 0.

For independent, free-living cells, we can set α = β = 1, i.e. the cells employ all available resources for reproduction and are fully exposed to the environment. In this case, increasing the environmental lethality b causes population collapse as shown in Figure 1, with populations in resource-poor environments (i.e. a < 1) collapsing sooner but no populations able to maintain growth above b = 0.5.10.1080/19420889.2019.1643666-F0001Figure 1.Plots of population growth rn for n = 10 from a single initial cell as functions of environmental lethality b under different assumptions. Pink, blue and purple curves show the effect of decreasing resource levels on the rate of population collapse as lethality increases. Light and dark green curves show relative stability of fully (β = 0) or partially (β = 0.4) protected populations at different levels of resource-use efficiency.

What happens, however, when cells are able to divert some fraction of the available resources from reproduction to protection, i.e. to shielding themselves from the environment? At high resource levels and low lethality, this is a low-fitness strategy: the resulting protected populations are lower than unprotected free-living populations, even when losses due to environment lethality are taken into account. As lethality increases, however, this ceases to be the case, as shown in Figure 1. Population survival past b = 0.5, in particular, requires protection from the environment regardless of resource level or resource-usage efficiency. A fitness-optimizing population would, therefore, be expected to undergo a phase transition from unprotected to protected at a critical point in b, the lethality level at which the declining free-living population reached the protected population sustainable at the achievable values of α and β. Population survival (i.e. r ≥ 1) requires βb ≤ αa/(1 + αa). We show below that this phase transition can be represented as crossing a percolation threshold, here given by the above inequality.

The phase transition shown in Figure 1 is, we suggest, the phase transition to complex multicellularity implemented by the free-living holozoan ancestors of the metazoa. It is highly plausible that the period between the rise of heterotrophic eukayotes, i.e. predators roughly 800 Mya [1] and the appearance of multicellular Ediacaran fauna roughly 575 Mya saw not only rapid eukaryotic diversification but multiple instances of population-scale exposure to high-lethality environmental change. Such changes can be expected to have imposed severe selective pressure inducing multiple population bottlenecks. In the sections that follow, we employ Friston’s [9,10] FEP to develop a scenario in which a reproductively-disabled somatic body is a solution to the challenge of protecting oneself from a challenging environment.

The FEP characterizes organisms as systems that behave so as to minimize the variational free energy (VFE) of their environments [9,10]. The VFE of the environment measures the unpredictability – the “variational freedom” – of the environment and hence the mismatch between the environment’s behavior and the organism’s expectations about its behavior. Zero VFE corresponds to perfect predictability of its environment by an organism or, equivalently, of an organism by its environment. Minimizing net information flow minimizes net energy transfer; hence minimization of VFE is a least-action principle analogous to the energetic least-action principles of physics [30]. In a Bayesian setting, zero VFE corresponds to equality between posterior and prior probabilities, where both provide completely accurate accounts of outcomes. While the FEP has primarily been applied in a cognitive-neuroscience context, it is a general principle applicable to organism-environment dynamics at evolutionary, developmental, or learning time scales [10,31].

Living beings face numerous challenges due to the ever-changing chemical, physical, and biological events in their immediate environment. Successful organisms, tissues (e.g. populations of neurons [32]), and even societies (e.g. swarm intelligence [33]) must act in order to adaptively respond to these challenges [34,35]. Gene-regulatory networks, organelle machinery, cell behaviors, system-level physiological changes, and behavior are among the mechanistic options available to biosystems at multiple scales in the face of stresses. As Friston [10] has emphasized, maintenance of homeostasis is the fundamental predictive problem faced by any organism, and the probability of continuing homeostasis is the fundamental prior probability for any organism. To incorporate reproductive fitness, we can extend the meaning of “homeostasis” to include maintaining the cell cycle at the rate allowed by the environment. Prediction failures, i.e. differences between posterior and prior probabilities of continuing homeostasis, including continuing reproduction, can be addressed either by revising priors (i.e. learning) or acting in a way that alters the posteriors (“active inference”). An important special case of the former is revision of Bayesian precision assignments to either environmental inputs or expectations, implemented in humans by changes in salience and attention [36].

A threatening environment challenges the maintenance of homeostasis and therefore has high VFE; a lethal environment takes this challenge to the extreme. We can, from this perspective, see the phase transition from growth to protection shown in Figure 1 as an instance of active inference, i.e. behavior change that preserves the prior probability for continuing homeostasis. What is this behavior change? Merely curtailing cell division is not by itself protective. In facultative multicellular eukaryotes such as Dictyostelium, mitotic arrest followed by aggregation, collective motility, differentiation and spore formation increases the probability of population-level survival. The Dictyostelium spore, like spores in general, is a differentiated form that isolates the cellular components needed for later reproduction from the environment. Spore-generating cells actively induce the cell-cycle arrest and differentiation of the supporting stalk cells, which do not contribute DNA to the subsequent population, by secreting small-molecule morphogens [37,38]. Here we suggest that obligate multicellular organisms adopt a very similar strategy, in which reproductive cells actively induce cell-cycle arrest and differentiation by cells dedicated to protection against the environment. The key difference between obligate and facultative multicellular strategies is that in obligate multicellular organisms, reproductive cells induce differentiation and disable reproduction in their own progeny.

To make this suggestion precise, consider a cell C with time-varying state c(t) is embedded in an uncertain environment E with time-varying state e(t). Consider the cellular state c(t) to have two orthogonal components, c(t) = a(t) × p(t) defined by the the actions of functions: A:E→C,A:et→at+δtandP:C→C,P:ct→pt+δt,

for some suitably small time increment δt. We interpret A as the action of E on C to produce an “input state” a(t+ δt) and P as the prediction by the cell C of its future “internal state” p(t+ δt). The implementations of these state components may be, for example, the state of all membrane-bound receptors and channels at t for a(t) and the combined metabolome and transcriptome state at t for p(t). The prediction implemented by P is accurate (optimal) if the cell’s behavior given p(t) is an optimal response to the environmental conditions e(t) and hence to a(t); in this case, we can (abusing the notation somewhat) write p(t) = a(t). The prediction is satisficing if C is able to maintain homeostasis; clearly some satisficing solutions have higher fitness than others. The prediction function P implements, in this case, a “model” of the E – C interaction, in the sense defined by Conant and Ashby [39] in stating the good-regulator theorem; C can be viewed as regulating its interaction with E by using this model. Having an accurate model minimizes prediction error and maximizes fitness within the constraints dictated by the environment.

We can, similarly, consider the environmental state e(t) to have two orthogonal components, e(t) = r(t) × v(t) defined by the the actions of functions: R:C→E,R:ct→rt+δtandV:E→E,V:et→vt+δt,

where we interpret R is the reaction of C on E and V is the variation by E that generates its future state. From an informational perspective, the components C and E are symmetric; however, for simplicity we can assume E is “large” enough that R is negligible, so that e(t) ~ v(t). The interaction between C and E is summarized in Figure 2. The prediction problem faced by C is the problem of minimizing the difference Δ(t) = |a(t) – p(t)| between its input a(t) from E and its prediction p(t). An accurate or optimal solution to this minimization problem has Δ(t) = 0; a satisficing solution has 0 < Δ(t) ≤ Δlethal, where Δlethal is the prediction error sufficient to cause cell death.10.1080/19420889.2019.1643666-F0002Figure 2.Interaction between an environment E and an embedded cell C. The functions V and P specify environmental variation and cellular predictions, respectively.

As a simple example, suppose the states c(t) are vectors in R2 with norms |c(t)| ≤ 1 for all t, the states e(t) are real numbers in [0,1], the functions V, A, R, P [0,1]: → [0,1], the value V(e(t)) and hence e(t) is random as a function of t, and the function A(t) can be represented by a(t + 1) = β · e(t), with 0 ≤ β ≤ 1 as above representing the degree to which a(t) is “exposed” to e(t). Assume that P is the “homeostatic success” prediction that E and A are invariant, i.e. p(t + 1) = a(t). In this case, the prediction error Δ → 0 as β → 0. As β → 1, Δ(t) → random due to the randomness of e(t). The lethality b of the environment can, in this case, be identified with the level Δlethal of prediction error that is fatal; the fraction of cells that implement insufficiently accurate predictions and therefore die is βb = βΔlethal.

This model can clearly be extended to d real dimensions, variation in each of which is restricted to [0,1], representing distinct degrees of freedom of E that C needs to predict sufficiently accurately to maintain homeostasis and hence survive. If these dimensions are independent (i.e. orthogonal in R2d) and a prediction failure for any one dimension k is lethal (i.e. Δk > Δlethal(k)), then any one of 2d−1 distinct prediction failures will be lethal. In this case, survival is reasonably probable only if the environmental exposure β ~ 2−d. Free-living cells with d independently-lethal dimensions thus face an exponential prediction problem; solving this problem and hence surviving is clearly infeasible as d becomes large. Controlling the effective dimensionality of the environment is thus a key component of VFE reduction.1 Geometrically-symmetrical aggregates of identical cells in which all cells are equally exposed to the environment, e.g. Volvox colonies or choanoflagellate rosettes, provide protection against unicellular predators [40], but do not decrease β along other dimensions. Metazoan embryos that take this form are either protected within a specialized environment – an egg or womb – or suffer high mortality.