Introduction

The social interactions of myxobacteria (Myxococcales) are particularly noteworthy for the membrane fusion and the transfer of toxins. Diverse species of myxobacteria can transiently fuse their outer membranes with those of other cells, a process referred to as outer membrane exchange (OME)1. By topological alteration of membranes that leads to fusion, the multiple types of membrane lipids, lipoproteins, lipopolysaccharides, and proteins diffusible in the outer membrane are bidirectionally exchanged1,2 (Fig. 1a–c). Certain impairments in phenotypes are transiently recovered by OME with normal cells. For example, non-motile bacteria temporarily become motile by gaining motility protein after OME with the motile donor3,4. Moreover, OME homogenizes the outer membrane of different cells within a short period of time5.

Fig. 1: The traits of the myxobacterial outer membrane exchange and visual description of the handshake-dependent rock-paper-scissors-like model.
figure 1

a Two myxobacteria with compatible TraA receptors can merge their outer membrane (OME). Cao and Wall5 referred to OME as the molecular handshake. b The horizontal half-section of the myxobacteria performing OME. Outer and inner membranes are illustrated with green and purple membranes, respectively. c TraA receptors regulate the specificity of OME. The cohort protein TraB is necessary for OME, but it is not involved in the specificity. In this model, all myxobacteria were assumed to have functional TraA/B proteins. During OME, proteins embedded in the outer membrane and the constituent lipids are bidirectionally exchanged including SitA toxins. d The evolutionary dynamics of green-beard interaction of the sitAI alleles is similar to a rock-paper-scissors (RPS) game. As sitAI interactions require OME, I propose that OME is an epistatic green-beard effect while toxin transfer is hypostatic to OME. Such hierarchical social interaction can be labeled as a handshake-dependent RPS-like model. However, the actual hypostatic green-beard interactions are different from classical RPS games because there could be multiple types of the scissors and competition between scissors could result in mutual damage rather than a tie.

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OME is mediated by homotypic interactions between identical or compatible TraA receptors1. Upon contact with compatible TraA receptors, they aggregate to form fusion junctions (‘molecular handshake’ sensu Cao and Wall), reminiscent of eukaryotic gap junctions5. While TraB facilitates OME, the experimental results show that it is the TraA that determines the specificity4. The sequence of the TraA variable domain determines the compatibility for OME, wherein an A/P205 residue plays the pivotal role4. By detecting whether OME occurs between different alleles of TraA receptors, the map of the recognition groups can be formulated3,4. It is predicted that there are more than a few dozen recognition groups within which OME occurs3. As material transfer mediated by OME is advantageous to defective or undernourished recipients and OME is established among cells with identical green-beard alleles, traA is a facultative helping green-beard gene6. However, such recognition groups are not strictly partitioned as a weak level of OME is observed between myxobacteria from different recognition groups3,4. The altruistic interaction between cells with different green-beard alleles can be interpreted as a recognition error7.

For a colony composed of clonal bacteria, the benefit of OME is straightforward under the framework of inclusive fitness8. The complication arises when a distantly related strain possesses the compatible traA allele. In this case, materials necessary for survival are shared with non-kins, which conflicts with the general principles of kin selection2. Furthermore, OME with foreign strains entails a life-threatening risk as toxins that are specifically detrimental to recipients may flow in2. This would be the reason that all species of Myxococcales that have functional traA genes also have sitA genes which produce toxins that are transferred via OME9. Conversely, sitA genes are absent in Myxococcales that lack traA homologs9. The rigid interdependence of traA and sitA strongly indicates the role of sitA in social interactions mediated by OME. As its etymology (swarm inhibition toxin) implies, SitA toxins work as nucleic-acid-degrading enzymes that result in fatal damage to the cells that lack the corresponding immunity protein SitI (Ref. 2). sitA and sitI are closely located in the genome, and the lethal effect of sitA is nullified if there is a cognate sitI (Ref. 9). Genomic analysis revealed that there are 6 families of SitA each of which is composed of diversified toxins9,10. The multiplicity of sitAI loci (13–83 loci) in the genome and distinctive combination of them (repertoire) establishes the ‘self-identity barcodes’ (sensu Vassallo and Wall)9. Likewise, the presence of multiple toxins can be referred to as ‘multicolored green beards’ (sensu Biernaskie et al.)11. Under the microbial toxin–antidote system composed of a single toxin type, the toxin-producing strain outcompetes the vulnerable strain lacking corresponding immunity; the immune strain that does not produce toxins outcompetes the toxin-producing strain; the vulnerable strain outcompetes the immune strain11,12. It is expected that such cyclic dominance referred to as rock-paper-scissors (RPS) competition where no strategy is strictly dominant promotes strain diversity11,12.

Moreover, the exchange of different repertoires of toxins resulting in growth inhibition or antagonism would have facilitated the diversification of the social groups9,10. Acquisition of a novel type of sitAI, presumably by horizontal gene transfer (HGT) or recombination, is predicted to confer a selective advantage to that strain9,10. However, the social interaction of the sitAI cannot operate unless two cells establish OME via compatible TraA receptors9,10.

Here, I propose to label traA as an epistatic green-beard gene in that the harming effect of green-beard sitAI is not functional unless two cells carry the (partially or fully) compatible traA alleles2,13,14. In this sense, sitAI is a green-beard gene hypostatic to traA (Ref. 14). No study up to date has analyzed the evolutionary dynamics of hierarchical green-beard genes that are reliant on other green-beard genes. Given that OME is comparable to the handshake5 and RPS dynamics of the toxin–antidote system11 are dependent on OME, I propose a handshake-dependent rock-paper-scissors-like (RPSL) model where a handshake is a prerequisite to playing an RPSL game (Fig. 1d). Due to the plurality of the sitAI allele pairs, the actual cyclic dynamics of myxobacteria are more complicated and divergent than the classical RPS model (Fig. 2, Supplementary Figs. 2, 3). By introducing a novel category of the green-beard effect combined with permissiveness in recognition, this model can clarify the elevated diversity of myxobacterial social alleles. Furthermore, this conceptualization could be used to develop a hypothetical technique to disrupt cancer cooperation by implementing fusogenic defectors. A detailed explanation of novel concepts is provided in the following sections.

Fig. 2: Cyclic dominance in myxobacterial sitAI and concept of the domain shift in RPS-like dynamics.
figure 2

a As there are multiple sitAI loci in a single myxobacterium, multiple RPS games can take place. Thus, sitAI repertoire can be interpreted as multicolored beards (chromatic font colors represent ‘beard colors’). As revealed in the previous study, colored beards, false beards, and non-beards establish cyclic dominance. The direction of the double-lined arrow represents the side of dominance, and the gray color of the arrow implies that OME is not required for dominance. b sitAI repertoire of each cell determines the relationship of the aggressor, susceptible, or freeloader. For myxobacteria, transfer of the toxins requires OME, dependent on epistatic green-beard gene traA. The mutation of traA alleles in susceptibles can protect them from the invasion of aggressors (blue dashed arrow). I propose to label the minority with (partially) incompatible traA as the masked beard. The solid black arrow illustrates the HGT in sitAI that introduces additional pairs of functional sitAI alleles. The dashed black arrow represents loss-of-function mutation (LOF Mut.) in sitA, and the dashed gray arrow represents loss-of-function mutation in sitI. The dominance of susceptibles over freeloaders does not require OME as the toxin transfer is not involved. c Masked beards generated from (specificity-changing) mutations in traA alleles in the susceptibles (red and blue dashed arrows) establish another domain of cyclic dominance. Therefore, such a transition can be referred to as the domain shift in hypostatic green-beard RPSL competition. d Handshake was used to illustrate OME. The colors of the hands correspond to the compatibility of the TraA receptors. e Depending on sitAI repertoire after HGT, various types of aggressors can appear as illustrated with different hand gestures representing scissors in (b). In such cases, both strains of myxobacteria labeled revengers may sustain the damage due to the toxin transfer (spite). f Depending on the types of HGT, diversified competition dynamics may occur. For simplicity, suppose that there are 6 sitAI loci and the susceptible cell (labeled SC-0, paper) has colored-beard and false-beard genotypes in locus 4 and locus 5, respectively. HGT-a and HGT-b confer colored-beard sitAI genotypes in locus 1 and locus 2, respectively. HGT-a and HGT-b transform the original susceptible cells into aggressor cells (labeled AG-a and AG-b), while the OME between these two aggressor cells imposes a mutual cost to each cell. If the damaging effects of toxins produced by sitA in loci 1 and 2 are the same, the spite is symmetric. If HGT-b,c results in colored-beard genotypes in loci 2 and 3, then the AG-a will receive more damage after OME with AG-b,c (given that each sitA imposes the same damage). In this case, AG-a with mutated traA can evade such damage (domain shift). The additional HGT-a transforms AG-b,c to AG-a,b,c. As AG-a,b,c imposes one-sided damage to other aggressor cells, they are relatively susceptibles when interacting with AG-a,b,c. The generalized evolutionary dynamics are illustrated in Supplementary Fig. 3. g AG-a produces a toxin (by sitA of locus 1) that is harmful to AG-b. AG-b produces a toxin (by sitA of locus 2) that is harmful to AG-a. Hence, AG-a and AG-b are revengers of each other. While AG-b,c is an aggressor to SC-0, it is a susceptible to AG-a,b,c, implying that the aggressor–susceptible relation is relative. Colored numbers illustrate sitA loci for the toxin production. Set-theoretical definitions of relations are provided in Supplementary Definitions 1–3.

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In addition, the compatibility of OME and the diversified toxin repertoire were pointed out as the mechanisms of kin discrimination1. Though it is intuitive that higher relatedness is positively correlated with the compatibility of traA and sitAI alleles, there has been no mathematical investigation of how the hierarchical green-beard effect is linked to the estimation of the relatedness. Using the Bayesian principle, I derived expected relatedness based on cues from OME and bidirectional toxin transfer, which can be used to elucidate principles of the social evolution that interconnect the kin selection and the green-beard effect.

Definitions of epistatic, hypostatic green beards, and domain shift

Suppose that there is a green-beard gene that facilitates aggregation or fusion among the cells. In this case, this green-beard gene is facultative helping as cooperation (adhesion, transfer, fusion) is primarily performed among the sharers of the same alleles13. Once the association is established, there could be another green-beard gene whose social effect is essentially dependent on the association. Specifically, SitA produced by one cell cannot harm the other cells unless OME is established. In brief, if there is a green-beard gene whose full functionality requires the matching of another green-beard gene, then the former should be defined as the hypostatic green-beard gene and the latter as the epistatic green-beard gene. I coined the terms after epistasis and hypostasis in genetics15 in that the presence of the epistatic gene is the prerequisite for the phenotypic expression of the hypostatic gene (Supplementary Fig. 2).

The plurality of the toxin types transferred during OME can be described as multicolored beards11, and the presence or absence of each beard color can be digitized into barcodes9. As previously investigated, toxin–antidote systems follow RPS dynamics given that there is a single type of a toxin11. When multiple sitAI alleles are present, each pair of sitA and cognate sitI corresponds to the ‘specific beard color’11 (Fig. 2a). For each hypostatic green-beard sitAI pair, the colored beard produces the specific toxin with cognate immunity. In this paper, I will use the term colored beards, rather than green beards, to indicate the possession of the toxin and the cognate immunity because each sitAI allelic pair (sitA and cognate sitI alleles) corresponds to different beard colors. Green-beard effects, on the other hand, will be used to denote the general kind selection principles in social evolution16, such as epistatic green-beard effects. The hypostatic false-beard sitAI allelic pair is equipped with immunity while not producing the toxin11. Non-beard sitAI allelic pair produces neither toxin nor immunity protein of that beard color11. The sitAI allelic pair that produces a toxin without cognate immunity is implausible as such a pair would be lethal to the host cell.

As each cell contains multiple types of sitAI pairs, the actual myxobacterial cell-to-cell competition dynamics are more sophisticated than RPS dynamics stemming from a single toxin and a cognate immunity. Depending on sitAI repertoire (collection of colored beards, false beards, non-beards) of two strains, three categories of unidirectional dominance can be formulated (Fig. 2b, Supplementary Definitions 1, 2). Aggressors impose unidirectional toxin damage to susceptibles as aggressors have colored-beard sitAI alleles that susceptibles do not have. Freeloaders, equipped with false-beard sitAI alleles, are resistant to toxins from others that freeloaders do not produce (Supplementary Fig. 1b). By toxin transfer via OME, freeloaders can be protected from foreign intruders owing to the toxins produced by the aggressors. However, freeloaders do not need to spend the metabolic cost required to produce the toxin. Even in the absence of foreign intruders, freeloaders will outcompete the aggressors by saving the metabolic cost of toxin production. In this case, OME is not necessary for the freeloaders to gain a selective advantage. Suppression of sitA or insertion of sitI is experimentally feasible2, and certain bacterial species are immune to bacteriocins they do not produce11,17. For instance, Escherichia coli can be resistant to colicin that it does not produce12,18. However, there is no conclusive evidence, to my knowledge, that hypostatic false beards (carrying sitI without cognate sitA) are present in the natural myxobacteria population. As a single loss-of-function mutation in sitA allele can impose a false-beard trait, I assumed in this study that false-beard myxobacterial alleles and the associated freeloaders exist. Further genomic analysis will elucidate the existence of hypostatic false-beard alleles in myxobacteria. Meanwhile, susceptibles can grow faster than freeloaders by saving the metabolic cost for SitI production, given that there is no aggressor invasion. Similar to allelic-level cyclic dominance of false beards, colored beards, and non-beards, it is expected that strains of freeloaders, aggressors, and susceptibles exhibit cyclic dominance (Fig. 2b).

In addition to the strict dominance between strains, two strains may sustain mutual damage due to the exchanged toxins that are ineffective to one strain but detrimental to another (Supplementary Figs. 1c, 3d, Supplementary Definition 3). Spite between such revengers could be either symmetric or asymmetric (Fig. 2e, f). Worth mentioning is that the pairwise relationships of aggressors, susceptibles, freeloaders, and revengers are relative. With respect to sitAI repertoire, a strain that is an aggressor to one strain could be susceptible to another strain and vice versa (Supplementary Figs. 1d, e). Considering the cyclic dominance, I propose to designate aggressors, freeloaders, and susceptibles to scissors, rock, and paper, respectively (Fig. 2b). Unlike classical RPS games, there could be multiple types of aggressors depending on sitAI repertoire, illustrated with different scissor-like hand gestures (Fig. 2b–g).

When susceptibles compete with aggressors, susceptibles can avoid sustaining toxic damage by converting their TraA receptor phenotype (Fig. 2b). Hence, when confronting aggressors of compatible traA alleles, mutations in traA alleles (or alleles associated with relevant pathways)19,20 will be selected for among susceptibles, as it can prevent OME with the aggressors. To avoid complications, let traA mutation in this study indicate a mutation in TraA specificity without losing the membrane-fusing functionality of TraA. In addition, traA mutations of this model do not refer to synonymous or silent mutations.

Domain in this study refers to the compatibility of OME so that cyclic or mutual competition of hypostatic green-beard sitAI alleles can take place. traA mutation that partially or completely prevents OME with its parental population establishes another domain of sitAI competition, which I labeled domain shift (Fig. 2b, c). Note that domains are not strictly exclusive, as TraA receptors can interact with other types of TraA receptors (permissiveness)3,4.

The mutated traA allele is reminiscent of a loner in social interactions in that it prevents interaction with others21,22. In previous studies, cyclic dominance was investigated among loners, cooperators, and defectors21,22. Rather than one of the strategies in RPS dynamics, it should be noted that the traA mutation and domain shift do not affect the RPS strategies determined by sitAI alleles. In other words, the traA genotype lies in a different hierarchy from sitAI alleles, distinguishing this from cyclic dominance composed of loners that compete with cooperators and defectors.

Results

Demarcation, serial transfer, and motility rescue

The simulation model developed in this study (Supplementary Figs. 4–7, Supplementary Movie 1, Supplementary Tables 1–3) can recapitulate notable features of myxobacterial social interactions. Angles of demarcation bands obtained from the control condition are nearly homogeneously distributed from 0° to 180° (Supplementary Fig. 8b, e). This implies that there is no specific trend of antagonistic growth interactions between the two strains. Angles of demarcation bands when two subpopulations have (partially or fully) compatible TraA receptors while their SitA/I phenotypes are mutually detrimental (revengers) exhibited the unimodal distribution with a peak around 90° (Supplementary Fig. 8f, g, Supplementary Movies 2, 3). Demarcation strength and fidelity of partially and fully compatible groups were significantly higher than those indices of the control (Supplementary Fig. 8c, d), resembling empirical results of colony merger assays2. In other words, bacterial cells in the simulation cannot grow properly at the interface between two strains, and such an interface acts as the demarcation zone. The effects of the motility rescue and serial transfer are identified in the simulation as well (Supplementary Figs. 9, 10, Supplementary Movies 4, 5).

Selection for the traA-minor groups

A specificity-altering mutation in a traA allele may occur in a colony composed of genetically homogeneous myxobacteria. A myxobacterium with a mutated traA allele will establish a small aggregation of the conspecific cells (traA minority in Fig. 3a, Supplementary Movie 6). In this colony composed of traA majority and traA minority, randomly selected myxobacteria may gain additional sitAI alleles via HGT, transforming them into aggressors (Fig. 3b–d, Supplementary Movie 7). While different types of HGT can generate diverse types of aggressors that result in complex dynamics (Supplementary Fig. 3), a single type of HGT was postulated in each simulation to reduce complexity. In the absence of HGT, there is no significant change in the proportions of traA minority during the simulation (Fig. 3e). When transformation into aggressors comes into account, traA mutation confers a significant fitness advantage with respect to the changes in the proportions (Fig. 3f). traA mutation that imposes incompatibility in OME with the parental population is significantly more favorable than a mutation conferring partial compatibility.

Fig. 3: The schematics and results of the simulations estimating the effect of the traA diversity.
figure 3

a Two myxobacterial strains depicted with different surface colors have different traA genotypes while their sitAI barcodes are the same. Major strain outnumbers minor strain in the initial population size. traA alleles of the major group could be either compatible, partially compatible, or incompatible with the minor group. b Horizontal gene transfer may transform randomly selected myxobacteria into aggressors which gained additional sitAI alleles. OME with the original cells (susceptibles) and aggressors results in damage of susceptibles. c The surface color represents the traA genotype and dark stripes are used to denote the aggressors. d The sitAI genotypes of susceptibles and aggressors. In this simulation, all functional sitAI alleles present in susceptibles are present in aggressors. Aggressors have sitAI alleles that are absent in susceptibles (Families 2 and 4). e In the absence of the transformation into aggressors, mutations in the traA alleles generating the traA-minor group have no significant effect with respect to the proportional fitness. Black, blue, and red markers represent the mean proportional fitness when traA-minor groups possess traA alleles that are compatible (control), partially compatible, and incompatible with those of traA-major groups, respectively. Error bars represent the sample standard deviation. Two nutrient environments were applied: stable nutrient conditions (solid error bars) and fluctuating nutrient conditions (dashed error bars, Supplementary Movie 6). Fluctuating nutrient conditions resulted in a reduction in overall fitness and inflation of variance. f Proportional fitness of traA minority when randomly selected myxobacteria in the population, regardless of the group types, transformed into the aggressors. As traA-minor groups are less likely to possess aggressors, OME insulation from the traA-major groups conferred a fitness advantage in traA-minor groups. Lines connecting the datasets represent statistical significance (alpha level = 0.001). g Same as (e) with fitness incorporating fruiting body formation. On the assumption that the number (rather than the proportion) of the traA-allele-sharing cells primarily affects the formation of the fruiting body, the traA minority with partially compatible or incompatible traA alleles exhibits significantly lower fitness than the traA majority. h Same as (g) with aggressor invasion. i Explanations of the diagrams used in this figure.

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On the other hand, the population size (cell number) of the myxobacteria with compatible traA alleles could be the critical factor for fruiting body formation23. The fitness can be derived by incorporating the possibility of establishing the fruiting body (aggregational fitness, Supplementary Fig. 7). In the absence of aggressor-generating HGT (aggressor invasion), the economies of scale are identified in that members of the larger traA-compatible group gain higher aggregational fitness (Fig. 3g). Under these circumstances, traA mutation is significantly disadvantageous whose trend is diluted when HGT is considered (Fig. 3h). While fluctuating nutrient availability broadly reduced average fitness and increased its variance, it had no specific or substantial effects on traA minority. The mathematical explanations on the proportional fitness and effect of the fruiting body formation are provided in Supplementary Equations 15–24.

Cyclic dominance in sitAI alleles and effect of traA mutation

Two strains from aggressors, freeloaders, and susceptibles with the same initial subpopulation sizes competed in the simulation (Fig. 4a–d). Diverse structures of traA compatibility were explored (Fig. 4e–k). Two homogeneous strains with compatible or partially compatible traA alleles follow RPS dynamics (Fig. 4l–q) as previously clarified11. Suppose that each strain is composed of a traA-major group and a traA-minor group (Supplementary Movie 8). The traA allele of the traA minority is partially compatible or incompatible with the cognate traA majority (Fig. 4g–j). traA mutation has no significant effect on traA minority fitness in the competition between freeloaders and susceptibles, and the competition between freeloaders and aggressors (Supplementary Fig. 11). The traA minority in the competition between susceptibles and aggressors exhibited context-dependent dynamics (Fig. 4r–u). Except for one case (MCmP, Fig. 4r), the order of the fitness is conserved: susceptible traA minority, aggressor traA majority, aggressor traA minority, susceptible traA majority, from the highest to the lowest (Fig. 4s–u). However, this ranking is based on the condition that the initial proportion of traA minority, which is spatially clustered, is 0.1. Changes in proportion may affect the order or significance of the fitness comparisons as the interaction frequency among different types will vary. All comparisons are supported by statistical significance (Bonferroni-corrected alpha level = 0.001).

Fig. 4: Visual description of the RPSL simulation framework and simulation results.
figure 4

a Two strains with identical (compatible) traA alleles are spatially mixed. b Striped cells are aggressors containing sitA alleles that are detrimental to susceptibles (plain cells). c Susceptible myxobacteria (blue cells) may have different traA alleles that could be compatible or partially compatible with traA alleles of the aggressors. d Among the susceptible myxobacteria, a small group of cells can gain mutations in traA alleles, converting them into traA minority (light blue cells). The other susceptible cells accordingly become the traA majority. traA majority and traA minority may have partially compatible or incompatible TraA receptors. Likewise, the aggressor strain can be divided into the traA majority and minority (striped yellow cells). e Two strains (Str1, Str2) with compatible traA alleles with different sitAI repertoire. In each homogeneous group, the control group (C1, C2) was postulated which has the identical spatial distribution as the traA-minor groups in the subsequent simulations. The population size of the control group was traced to derive the proportional fitness which is used to investigate whether a mutation in the traA allele confers fitness advantage (r–u). HC: homogeneous compatible. f Same as (e) for two homogeneous strains with partially compatible traA alleles. HP: homogeneous partial. g Two major groups (M1, M2) have compatible traA alleles, while the minor groups (m1, m2) have partially compatible traA alleles with their cognate major groups. Two minor groups are incompatible for OME. MCmP: major compatible, minor partial. h While major groups have compatible traA alleles, minor groups cannot form OME with other groups. MCmI: major compatible, minor incompatible. i Same as (g) except that two traA-major groups have partially compatible traA alleles. MPmP: major partial, minor partial. j Same as (h) except that two traA-major groups have partially compatible traA alleles. MPmI: major partial, minor incompatible. k Triple bars between groups imply that both groups have compatible traA alleles. A thick dashed line represents partial compatibility between traA alleles of the two groups, while traA alleles within each group are homogeneous. l A freeloader strain (rock) and a susceptible strain (paper) with compatible traA alleles competed in the simulation arena. The comparison of proportional fitness indicates that susceptibles outcompete freeloaders given that there is no traA-minor group. The upper right asterisk indicates that the two datasets are significantly different (Wilcoxon signed-rank test). m Same as (l) for partially compatible strains. n, o Same as (l, m) for susceptibles and aggressors. p, q Same as (l, m) for freeloaders and aggressors. r traA-minor group of susceptibles (blue circles) exhibits significantly higher proportional fitness compared with the parental traA group (control, blue squares) that has identical traA alleles with the traA majority of the aggressors (MCmP). The fitness of the susceptible traA minority is significantly higher if traA mutation results in incompatibility with the parental population (blue dashed arrow). Conversely, the opposite trend is identified for traA minority of aggressors (red dashed arrow). The integer of each marker represents the rank within the dataset based on statistical significance. In this panel, the parental traA group of susceptibles has significantly lower fitness than other groups and is thus assigned rank 4. However, altering the initial proportion of the traA minority (0.1 in this simulation) may influence the relative fitness dominance between the groups. s–u Same as (r) for MCmI, MPmP, and MPmI, respectively. The asterisks imply that all groups within each panel are significantly different. v Explanations of the diagrams used in this figure.

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Becoming traA minority in susceptibles conferred fitness advantage compared with maintaining the traA genotype in all competitions between susceptibles and aggressors. The size of the advantage is significantly greater if traA mutation provides insulation from OME with other groups (blue dashed arrows in Fig. 4r–u). Conversely, the traA minority in aggressors with incompatible traA alleles has significantly lower fitness compared with that with the partially compatible traA alleles (red dashed arrows in Fig. 4r–u).

Therefore, when susceptibles and aggressors with partially or fully compatible traA alleles interact, there is a selection pressure for traA mutation in susceptibles, resulting in the domain shift in RPSL dynamics. In contrast, traA mutations in aggressors under this condition will be selected against.

Expected relatedness derived from hierarchical green-beard compatibility

Let binary random variables Π and Γ denote OME and (unidirectional or mutual) deterioration induced by the toxin transfer, respectively (Fig. 5a–e). Φ represents the coefficient of consanguinity24 (0 ≤ Φ ≤ 1) which is the measure of the relatedness in this study (Fig. 5f). For instance, Φ = ϕ implies that traA alleles of two myxobacteria are identical by descent25 (IBD) with the probability of ϕ. μk denotes the k-th raw moment of Φ such that μk = E[Φk]. Therefore, μ1 demonstrates the average relatedness of the population, and μ2 is the average squared relatedness.

Fig. 5: Bayesian analysis of the expected relatedness based on epistatic/hypostatic green-beard compatibility and conceptual illustration of fusogenic autologous cell defection.
figure 5

a The absence of OME between myxobacteria was represented by Π = 0 or (for brevity) Π−. b If two myxobacteria perform OME, then it was represented by Π = 1 or Π+. c In the mathematical model, it was assumed that two myxobacteria have compatible hypostatic green-beard alleles if toxin transfer via OME gives no damage to both cells. Γ = 1 or Γ+ represents such compatibility. The spiky rod-like elements illustrate the toxins, and C-shaped elements are immunity proteins. Immunity proteins can bind to their cognate toxins (same surface colors) to eliminate the toxicity. d If two cells have compatible epistatic green-beard alleles but incompatible hypostatic green-beard alleles (which are mutually damaging), then two cells sustain damage due to the interchange of different toxins (gray and red elements), represented by Γ = 0 or Γ− after Π+. e The graphical description of SitA and SitI proteins. Note that the actual structures of SitA and SitI are different from the diagrams in this figure. The diagrams depict the specificity of the toxin–immunity interactions. f The coefficient of consanguinity was used as the measure of bacterial relatedness. Two circular elements of identical orientation represent bacterial haploid genomes (i.e., circular DNA strands from two bacteria). If the red regions that comprise 70% of the genome are from the common ancestor (IBD: identical by descent), then the coefficient of consanguinity is 0.7. Other regions with diverse colors represent the non-IBD genome resulting from mutations or horizontal gene transfers. g It was proven in this study that the compatibility of epistatic and hypostatic green-beard alleles ensures a high degree of expected relatedness (Supplementary Proposition 2). However, the expected relatedness from incompatible toxin transfer following OME (E[Φ | Γ−, Π+]) might be higher than the plain expectation (E[Φ]). These arguments are supported by the computational investigation (Supplementary Tables 4, 5). h The theoretical analysis of the hierarchical green-beard effect could be the conceptual foundation for a hypothetical method for disrupting cancer cooperation because cell fusion with the tumor cell mediated by the surface receptors may reduce the oncogenicity of the hybrid. i Suppose that there are two types of fusogenic surface receptors on tumor cells (type A: light green, type B: dark red), comparable to the fusogenic epistatic green-beard effect. j Insertion of the fusogenic hypertumor into the tumor cluster may reduce the oncogenicity due to the consecutive cell fusions with tumors sharing identical fusogenic receptors.

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Though two traA alleles do not share the same ancestral origin, they could be compatible for OME because a single type of a traA allele could be prevalent in a population. In addition, different traA alleles may establish OME due to the permissiveness3,4. The effect of the non-IBD allelic frequency and permissiveness was implemented in a coefficient ε (0 ≤ ε ≤ 1). Given that OME has occurred (Π+), Bayesian analysis shows that the expected relatedness is

$$E\left[\Phi \, |\,{\Pi }^{+}\right]=\frac{\left(1-\varepsilon \right){\mu }_{2}+\varepsilon {\mu }_{1}}{\left(1-\varepsilon \right){\mu }_{1}+\varepsilon }\ge {\mu }_{1}.$$
(1)

Therefore, OME is a reliable cue for higher relatedness compared with the population mean relatedness (Supplementary Equation 34). However, a higher prevalence of the traA alleles and permissiveness is associated with a lower estimated value of relatedness (Supplementary Proposition 1). As an extreme case, OME does not provide any additional information on relatedness if all myxobacteria can perform OME regardless of the genotypes (ε = 1, Supplementary Corollary 1).

Furthermore, the following relations can be derived (Supplementary Proposition 2).

$$E\left[\Phi \, | \,{\Pi }^{-}\right]\le E\left[\Phi \right]\le E\left[\Phi \,|\,{\Pi }^{+}\right]\le E\left[\Phi \,|\,{\Pi }^{+},{\Gamma }^{+}\right].$$
(2)

Once two myxobacteria perform OME and the toxin transfer is not damaging, this implies that the two myxobacteria are highly related. Computational results of Supplementary Examples 1 and 2 corroborate this argument (Supplementary Tables 4, 5, Supplementary Fig. 12). Intriguingly, expected relatedness derived from unmatched sitAI alleles after OME (E[Φ | Π+, Γ−]) could be lower or higher than the population mean relatedness (Fig. 5g). Supplementary Examples 1 and 2 illustrate the cases of the former and the latter. The detailed mathematical proofs are provided in the Supplementary Materials.

Discussion

SitA is a toxin of myxobacteria that is transferred during outer membrane exchange (OME) mediated by TraA receptors1,2. As toxin-generating sitA is accompanied by sitI conferring immunity to the cognate toxin, OME of a cell carrying sitA with other cells depriving cognate sitI is detrimental to the recipients2. While fusion and toxin–antidote systems are well-known mechanisms of the microbial green-beard effects6,8, no study up to date comprehensively investigated the case where multiple toxin–antidote green-beard alleles are reliant on the fusogenic green-beard effect. As such, in addition to the previous classifications of the single-layered green-beard effects6,13, I defined a novel category of the epistatic and hypostatic green-beard genes. Furthermore, as RPS-like toxin transfer requires handshake-like OME between cells, I propose a handshake-dependent RPSL model (Fig. 1d) to illustrate the evolutionary dynamics of myxobacteria. Unlike conventional RPS competition, however, the repertoire of multiple sitAI alleles combined with TraA compatibility induces cyclic dynamics with diverse pathways (Supplementary Fig. 3a). Using simulations that capture the movement and social interactions of myxobacteria, I investigated the effects of the traA diversification across various conditions.

First, suppose that there is a myxobacterial strain that has identical traA and sitAI alleles. A small number of the myxobacteria can gain additional sitAI alleles via HGT, transforming them into aggressors. Consequently, the larger population size is correlated with the risk of spontaneously emerging aggressors, and the existence of a single aggressor in the vicinity can threaten the fitness of the strain sharing the compatible traA allele with the aggressor. A traA-minor group with distinct traA alleles is more likely to evade such encroachment by aggressors. However, subpopulation size sharing identical traA alleles might be the essential factor for collective aggregation, such as the fruiting body formation23,26. Under the adverse environment in which fruiting body formation is required to endure the hostile period, the traA-minor group whose subpopulation size is insufficient to establish the fruiting body may perish. However, the exact effect of the traA compatibility on fruiting body formation remains to be clarified.

Second, spontaneously generated aggressors equipped with hypostatic colored-beard alleles (additional sitAI allelic pairs) can establish a colony of a considerable size. In a well-mixed spatial condition, freeloaders that have an identical repertoire of sitI alleles with the aggressors, while not carrying all sitA alleles that aggressors have, will be selected for (Fig. 2b). Freeloaders can obtain toxins from aggressors that will protect them from foreign strains. Although foreign intruders are absent, freeloaders have the selective advantage as they do not need to spend metabolic costs for toxin production. Once aggressors become extinct and freeloaders prevail, susceptibles that lack sitI alleles that the freeloaders carry will outcompete the freeloaders because susceptibles do not spend energy associated with sitI. However, this dominance requires the lack of the risk that foreign strain transfers the toxin that is ineffective to freeloaders but detrimental to susceptibles. When a susceptible strain is confronted with an aggressor strain, traA mutations in susceptibles that prevent OME with the aggressors confer a fitness advantage in competition (Fig. 2b). As the damaging effect of the hypostatic green-beard genotype becomes ineffective due to the mutated traA alleles, I labeled the mutation in traA alleles as the ‘masked beard.’ Unless TraA or TraB receptors become disabled, masked beards establish another domain for hypostatic green-beard competition determined by sitAI repertoire, referred to as domain shift in RPSL dynamics (Fig. 2c). Masked beards are distinguished from loners of cyclic dominance composed of cooperators, defectors, and loners21,22 in that hypostatic green-beard RPSL strategies are dependent on the epistatic green-beard genotype. In other words, traA mutation does not affect the beard color of the hypostatic green-beard genes, but brings about a domain shift of them. While traA mutations in other pairs of competitions are neutral with respect to the proportional fitness (Supplementary Fig. 11), susceptibles that performed the domain shift are more likely to survive when they have contact with aggressors (Fig. 4r–u). In contrast, traA mutations in aggressors adjacent to the susceptibles are disadvantageous.

With respect to Croizer’s paradox27, evolutionary pressure for the diversifying traA alleles and cyclic dominance in the hypostatic green-beard effect (Fig. 2) can explain the higher degree of polymorphism and rapid diversification of TraA recognition groups1,3,10. However, the pros and cons of polymorphism are subject to conditions such as the genotypes of the competitive strains and nutrient availability. Under adverse environments where fruiting body formation is strictly necessary for long-term survival, a larger subpopulation size sharing OME compatibility could be favored23. On the other hand, a larger subpopulation is more prone to the spontaneous rise of the aggressors by gaining additional sitAI alleles through HGT.

While competition in each sitAI pair of myxobacteria follows cyclic dominance, the actual social dynamics of myxobacteria composed of aggressors, susceptibles, freeloaders, and revengers is distinct from RPS cyclic dominance. For instance, two strains can exchange detrimental toxins resulting in mutual damage, as in the sitAI repertoires of demarcation simulation (revengers, Fig. 2e, Supplementary Fig. 8a). The damage of one strain could be greater than that of the other strain depending on the asymmetric sitAI repertoires, implying the asymmetry in spite28. As there could be multiple types of aggressors and revengers, the path of cyclic dominance can be diversified (Supplementary Fig. 3). Moreover, myxobacteria employ other means of toxin delivery including type VI secretion system10,29, a feature not directly addressed in this study. The incorporation of diverse types of HGT and mutations combined with domain shift will elucidate the evolutionary stability of spite and genetic diversity, which should be the topic of subsequent studies.

For microorganisms lacking the cognitive capability to distinguish the genealogical kin, spatial proximity stemming from partitioning of the clones is an efficient method for narrow-sense kin discrimination8. Compatibility of the epistatic and hypostatic green-beard alleles indeed is a decent cue for the relatedness, similar to phenotype matching in kin selection8. As previously reported30, Supplementary Proposition 1 shows that polymorphic traA marker is associated with higher estimated relatedness after OME. The notable finding of the Bayesian analysis is that estimated relatedness derived from unmatched sitAI repertoire following OME via compatible traA genotypes could be higher or lower than the population average relatedness (Supplementary Examples 1, 2). This implies that spite may occur between two myxobacteria whose relatedness is above the population average. Although the relatedness in this study refers to the coefficient of consanguinity24, these findings could be used to investigate the evolution of spite through the lens of kin selection28,31.

The conceptualization of the hierarchical green-beard effect can be applied to the social interactions of cancer cells32. Combined with mutations in signaling pathways, cancer cells emit diverse diffusible cancer growth factors (CGFs) that stimulate the growth of the producer (autocrine effect) and the adjacent cancer cells (paracrine effect)32. As the production of such materials is costly while exposure to them brings benefits, cheating cancer cells that are responsive to cancer growth factors without producing them will outcompete the neighboring CGF-producing cancer cells32. The introduction of cheaters labeled as hypertumors33,34 into the cancer cluster may induce regression of the tumor cluster, a hypothetical method of autologous cell defection35,36. From the perspective of social evolution, CGF production in cancer cells corresponds to gift–password system8, and it was recently proposed that the green-beard effect may play a critical role in cancer cooperation37.

Myxobacterial OME is comparable to the cancer cell fusion by which cancer cells fuse with other cancer cells or normal cells, including macrophages and fibroblasts, which is implicated in cancer stemness, tumor heterogeneity, and metastasis38,39,40,41. Fusogenic proteins such as syncytin-1 could be the mediators of cancer cell fusion42, and accordingly, they might be analogous to TraA receptors of epistatic green-beard fusion. The consequences of cancer cell fusion are multifaceted, as it may promote or demote the oncogenicity39,41,43. Certain genes of the cell before the fusion may act to manipulate the hybrid cell to elevate their fitness after fusion. For instance, mutated oncogenes in a cancer cell can facilitate their proliferation after the cell fusion with the macrophages38. On the other hand, the fusion between cancer cells and mesenchymal stem cells can lead to growth suppression43. Contrasting effects on the oncogenicity after cell fusion are reminiscent of the diverse consequences of hypostatic green-beard effects after myxobacterial OME. Implementation of the fusion-prone cell line that leads to tumor suppression (similar to aggressors in Fig. 3b, c) can be envisaged as another form of autologous cell defection35,36 (Fig. 5h–j). As an example, a cancer cell could be engineered to obtain essential organelles such as mitochondria by fusion with other cancer cells. As this engineered defector can save energy to produce organelles, it will proliferate faster than the original cancer cells. Saturation of a tumor cluster by such fusogenic looters will lead to autologous regression as few cells in the cluster can produce essential organelles. Despite the differences between myxobacterial OME and cancer cell fusion, including the fusion persistency and the possibility of nuclear fusion, the investigation of two-level hierarchical social interaction will elucidate the evolutionary dynamics of cancer cell fusion and possible approaches to disrupt cancer cooperation.

Methods

Cell movement

All myxobacteria cells were assumed to be rod-shaped. Each cell can absorb the nutrients around the cell. A previous in vitro study revealed that microbial growth is positively associated with the size of the Voronoi area44. However, as it is implausible that the nutrient that is excessively remote from the cell influences the growth, I defined a range around each cell within which the nutrient can be absorbed. Therefore, in this simulation, the nutrient absorption is in proportion to the overlapping area of the Voronoi patch and a disk that represents the absorption radius (Supplementary Fig. 5, Supplementary Movie 1). Once the nutrient is absorbed, the proportional amount of the nutrient is removed from the nutrient map.

Considering the chemotaxis of the myxobacteria, each myxobacteria follows the gradient of the nutrient density while a mild level of randomness is involved. When two cells become closer to a certain degree, repulsion comes into effect to avoid the infinite accumulation of cells at a spot with the highest nutrient density. Not to make cells escape the simulation testbed, another type of repulsion is applied when a cell becomes close to the testbed boundary. In addition, each bacterium attempts to maintain its previous moving direction (inertial effect). The distance that a cell can move during a time step is determined by the motility protein that the cell possesses.

Precise explanations of simulations are provided in the Supplementary Materials.

Green-beard interactions

Considering the actual diversity of the traA and sitAI alleles4,10, it was postulated in the simulation that there are 6 groups of traA alleles enumerated from traA Group 1 to 6 (Supplementary Fig. 4a). The circular distance between two groups determines whether OME can occur. TraA receptors from the same group can establish OME. With the lower probability, TraA receptors from groups with a circular distance of 1 can also form OME. For example, TraA receptors from Group 1 and Group 6 (circular distance = 1) can perform OME, while those from Group 2 and Group 5 (circular distance = 3) cannot. Each traA group is composed of 10 subtypes (Supplementary Fig. 4b). The circular distance between two subtypes of the TraA receptors also influences OME probability. The specific equations for OME probability and the rate of material exchange are provided in Supplementary Materials (Supplementary Equations 9, 10, 12, 13, Supplementary Table 3).

Once OME is established, two connected myxobacteria exchange their materials including SitA toxins, nutrients, and motility proteins. There are 5 sitA families and each family is composed of 7 subtypes (Supplementary Fig. 4c). The toxin generated by a specific sitA allele is neutralized by the cognate (the same family and subtype) SitI antidote. Although the cognate antidote is absent, the antidotes produced by the sitI alleles of the same family with the toxin alleviate the damage (Supplementary Fig. 6, Supplementary Equation 11).

Validation of the simulation model

I tested whether the proposed simulation model can illustrate the well-known characteristics of the myxobacteria experiments. First, two strains of myxobacteria that have mutually deteriorating sitAI genotypes (revengers) were placed in the vicinity (Supplementary Fig. 8). I measured the strength, reliability, and angle of the demarcation band. This simulation demonstrates the growth antagonism between the two strains2,10. If there is a strong mutual growth inhibition between the two strains, the angle of the apparent demarcation band should be around 90°.

Second, one strain that can produce motility protein interacted with another strain that cannot produce motility protein (Supplementary Fig. 9). The dispersion of the strains (Supplementary Equation 14) and intracellular levels of motility proteins were recorded. This simulation is a representation of stimulation assay based on motility rescue4.

Third, one myxobacteria strain in the simulation can produce certain materials (producer strain), while another recipient strain cannot (Supplementary Fig. 10). This material has no influence on the physiology of the myxobacteria, taking into account the fluorescent materials frequently used in the empirical myxobacterial experiments1. The transferred materials of the recipient strain were recorded. In other sets of simulations, an intermediate strain was postulated. This intermediate strain can form OME with the producer strain and another non-producer (recipient) strain, while such a non-producer strain cannot form OME with the producer strain.

Effect of traA diversity with identical sitAI genotypes and horizontal gene transfers

To investigate the consequences of the traA mutation that alters the OME specificity within a homogeneous myxobacteria population, 10 out of 100 myxobacteria were assumed to have mutated TraA receptors (Fig. 3). Those 10 myxobacteria sharing identical mutated TraA receptors are clustered with the same average spatial density as other myxobacteria. This cluster is randomly located within the original population (Supplementary Movie 6). As a control simulation, all myxobacteria were set to have identical traA and sitAI genotypes. Ten clustered myxobacteria were selected within the homogeneous population (control type, Fig. 3i), and their fitness was measured. In other words, the fitness of the control type is that of the homogeneous (unmutated) population, considering the effect of the initial subpopulation size.

As experimental sets of simulations, the traA of the minority group was postulated to be partially compatible or incompatible with its parental group with respect to OME. The fitness of such minority groups was recorded and compared with the reference fitness (fitness of the control type) to verify whether possessing the mutated TraA receptors is advantageous.

As genetic information can be transferred via HGT9,10, the condition of the aggressor invasion was implemented. Under such a condition, 10 randomly selected myxobacteria regardless of their traA genotypes were assumed to gain additional sitAI alleles. Acquisition of sitAI alleles converts the myxobacteria to hypostatic green-beard aggressors with their traA genotypes unchanged (Supplementary Movie 7). OME of the original myxobacteria (susceptibles) and aggressors damage the former.

This study considers two types of fitness. Firstly, fitness was calculated from the proportion variation from the initial composition to the composition at time step 300. Secondly, to incorporate the situation when the formation of the fruiting body formation is advantageous for survival, the population size of strains rather than the composition (proportion) was considered. If there is a sufficient number of myxobacteria with identical traA alleles, one could speculate that they are more likely to form fruiting bodies, conferring additional fitness advantage to them23. Even if a myxobacteria has a partially compatible or incompatible traA genotype with the other myxobacteria, there is a small probability that the myxobacteria can be included in the fruiting body primarily composed of another traA type. This assumption can be attributed to the recognition error of the green-beard interaction as previously reported7,45. In addition, two types of environmental conditions were tested: constant nutrient density (Supplementary Movie 7) and fluctuating nutrient density (Supplementary Movie 6). When comparing the fitness estimates under the same condition, I used the Kruskal–Wallis test with the corresponding post hoc tests (MATLAB functions kruskalwallis and multcompare) with modified alpha level. Considering the inflated false positive rates from multiple comparisons, the alpha level in this study was set to 0.001 (Bonferroni correction).

Cyclic dominance and domain shift of hypostatic green-beard alleles

Two types of myxobacteria are spatially mixed where one strain and another strain represent a competition of susceptibles v. aggressors; aggressors v. freeloaders; or freeloaders v. susceptibles (Fig. 4). With the same initial population size of 100, two homogeneous strains competed for 300 time steps, and dominance was estimated by comparing proportional fitness with the Wilcoxon signed-rank test (MATLAB function signrank). While strict dominance could be absent as in the case of revengers, HGT in the simulations was assumed to generate identical transformations, preventing the emergence of revengers.

traA-minor groups with partially compatible or incompatible TraA receptors with their parental population may exist. The fitness of traA majority and minority of each strain was recorded. I used the Kruskal–Wallis test with the corresponding post hoc tests to compare the proportional fitness of such groups with modified alpha levels. When comparing the proportional fitness of two traA-minor groups from different conditions (dashed arrows in Fig. 4r–u), I used the Mann–Whitney U test (MATLAB function ranksum) with modified alpha levels.