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

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.