Permissive aggregative group formation favors coexistence between cooperators and defectors in yeast

Abstract

In Saccharomyces cerevisiae, the FLO1 gene encodes flocculins that lead to formation of multicellular flocs, that offer protection to the constituent cells. Flo1p was found to preferentially bind to fellow cooperators compared to defectors lacking FLO1 expression, enriching cooperators within the flocs. Given this dual function in cooperation and kin recognition, FLO1 has been termed a "green beard gene". Because of the heterophilic nature of the Flo1p bond however, we hypothesize that kin recognition is permissive and depends on the relative stability of the FLO1⁺/flo1^- versus FLO1⁺/FLO1⁺ detachment force F. We combine single-cell measurements of adhesion, individual cell-based simulations of cluster formation, and in vitro flocculation to study the impact of relative bond stability on the evolutionary stability of cooperation. We identify a trade-off between both aspects of the green beard mechanism, with reduced relative bond stability leading to increased kin recognition at the expense of cooperative benefits. We show that the fitness of FLO1 cooperators decreases as their frequency in the population increases, arising from the observed permissive character (F_+- = 0.5 F₊₊) of the Flo1p bond. Considering the costs associated with FLO1 expression, this asymmetric selection often results in a stable coexistence between cooperators and defectors.

Fig. 1. Mechanical measurement of Flo1p bond properties and mixing predictions.

Probability density functions of the measured maximum detachment force F_d for A FLO1⁺/FLO1⁺ (n = 1567, 6 cell interaction pairs), B FLO1⁺/flo1⁻ (n = 1311, 6 cell interaction pairs) and C flo1⁻/flo1⁻ interactions (n = 905, 6 cell interaction pairs). The dotted lines indicate the mean detachment forces. D–F Probability density function of the rupture length d_r of cell-cell interaction, measured by maximum distance with significant adhesive forces. The dotted lines indicate the mean rupture lengths. G Based on the bond energies, E = F_dd_r/2, the colony structure was predicted by the differential adhesion hypothesis (DAH). Single cell-force spectroscopy data of Flo11p was obtained from [12]. Dots indicate the median energy, bars indicate the 25th and 75th quantile. H DAH predicts segregation, spreading, and intermixing based on the ratio of bond energies.

Fig. 2. Effect of shear on heterotypic Flo1p-dependent flocculation.

A Temporal progression of flocculation starting from a homogeneously mixed population of FLO1⁺ (red) and flo1⁻ (blue) at increasing time points $\stackrel{°}{\gamma }$t, shown for a cooperator frequency x_i = 0.5, high density, ρ_high = 1.66 × 10⁷ cells/ml and shear rate $\stackrel{°}{\gamma }$ = 1 s⁻¹. B–E Endpoint of flocculation at various shear rates, shown for cooperator frequency x_i = 0.5. F Time evolution of the mean cluster size C for high (ρ_high  = 1.66 × 10⁷ cells/ml) and low density (ρ_low = 0.83 × 10⁷ cells/ml) for varying shear rate (color legend identical to G). The black lines indicate exponential fit C(t) = C_∞[1 − exp(−t/τ)] and a stretched exponential C(t) =  C_∞[1 − exp(−(t/τ)^β)] fit for the high and the low density respectively. At high (“super-critical”) density, the projected area, integrated across a circular flow line is larger than one, and the system reaches a dynamic steady-state. At low (“sub-critical”) density, this projected area is lower than one, and collisions become exceedingly rare after closed flow lines have been depleted of cells, see also Supplementary Figs. S1, S2. G Mean steady-state cluster size C_∞ in function of cooperator frequency x_i for varying shear rate, see also Supplementary Fig. S3. H Cluster composition for clusters of size > 2 cells for varying shear rate. The dotted black line indicates cooperator frequency x_i = 0.5. Bars indicate standard deviation. I Cluster relatedness in function of shear rate $\stackrel{°}{\gamma }$ and cooperator frequency x_i, see also Supplementary Figs S4, S5. The mean of four independent simulation repeats is shown (n = 4).

Fig. 3. Population dynamics in FLO1 cooperation.

A Three sequential ecological processes are considered; flocculation, selection by sedimentation and growth. B Cluster size selection probability P(survive) in function of steady-state cluster size C_t,final. Cooperator enrichment ∆x after selection at varying selection strength α is shown for $\stackrel{°}{\gamma }$ = 14 s⁻¹. C selected FLO1⁺ cells experience a growth deficit relative to flo1⁻ of 3% as reported by Smukalla et al. [13]. Cooperator enrichment curves at moderate selection strength (α = 0.4, $\stackrel{°}{\gamma }$ = 14 s⁻¹) and increasing growth time expressed as generations which are the number of population doublings of flo1⁻ cells in between successive flocculation events. The mean and standard deviation of four independent simulation repeats is shown (n = 4). (D) Classification of cooperator enrichment curves in evolutionarily stable strategies (ESS) cooperation, coexistence, defection. ESS in function of α and growth time between successive flocculation events for high and low density, see also Supplementary Fig. 2. (E) Experimental characterization of cooperator enrichment for various rotor amplitudes in the presence and absence of Ca²⁺. The mean and standard deviation of three independent experimental repeats are shown (n = 3).

Fig. 4. Effect of Flo1p bond properties on evolutionary stability.

A Cooperator enrichment ∆x after flocculation and selection for permissive and direct kin recognition. B Evolutionarily stable strategy (ESS) for permissive and direct kin recognition. For direct kin recognition, bistability emerges when ∆x is increasing at the zero point [50]. C Relatedness r in function of initial cooperator frequency x_i for permissive and direct kin selection. D Cooperative benefits relative to the fully cooperative system x_i = 1 for both permissive and direct kin recognition. E Empirical FLO1⁺/FLO1⁺ detachment force variability F_d. Effect of bond strength on the ESS at strong selection (α = 1). F Final cluster size C_tfinal in function of initial cooperator frequency x_i for varying homotypic detachment forces F₊₊, conserving F₊₊ ≈ 2 F₊₋. (G) Relatedness r in function of F₊₊, conserving F₊₊ ≈ 2 F₊₋ shown for x_i = 0.5. Results are shown for low density (ρ_low = 0.83 × 10⁷ cells/ml) and shear rate γ = 14 s⁻¹. The mean and standard deviation of three independent simulation repeats are shown (n=3).