Effects of environmental fluctuations on co-culture composition and intermixing
We first tested the effects of fluctuations between anoxic (inducing a mutualistic interaction) and oxic (inducing a competitive interaction) conditions on co-culture composition (quantified as the ratio of consumer-to-producer at the expansion edge) and interspecific mixing (quantified as the number of interspecific boundaries divided by the colony circumference). We expected that, over a series of anoxic/oxic transitions, the ratio of consumer-to-producer at the expansion edge and the degree of intermixing would both decrease (Fig. 1d). To test this, we performed range expansions where we transitioned the environment between anoxic and oxic conditions. While we performed the experiments with defined anoxic and oxic incubation times, our main prediction (i.e., that repeated transitions between anoxic and oxic conditions can induce irreversible pattern transitions that alter co-culture composition and functioning) is independent of the time spent under either of those conditions as far as cells can adjust their metabolism to the new environment (Fig. 1d).
As expected, the ratio of consumer-to-producer and the intermixing index both decreased over the series of anoxic/oxic transitions (Fig. 2a, b). The changes in these quantities appear to have two distinct dynamic phases; a first phase with a relatively steep decay and a second phase with a shallower decay. We therefore modeled their dynamics using a two-phase linear regression model [53,54,55]. During the first phase, the ratio of consumer-to-producer decreased significantly more rapidly at pH 7.5 (r2 = 0.90, p = 2 × 10−9, coeff = −0.0374, 95% CI = [−0.038, −0.0368]) than at 6.5 (r2 = 0.94, p = 1 × 10−7, coeff = −0.0103, 95% CI = [−0.0108, −0.0097]) (Fig. 2a). We observed consistent results for the intermixing index, where it also decreased significantly more rapidly at pH 7.5 (r2 = 0.90, p = 2 × 10−9, coeff = −0.0289, 95% CI = [−0.0295, −0.0284]) than at 6.5 (r2 = 0.93, p = 9 × 10−8, coeff = −0.01, 95% CI = [−0.0109, −0.0098]) (Fig. 2b). During the second phase, the change in the ratio of consumer-to-producer did not significantly differ between pH 7.5 (r2 = 0.90, p = 2 × 10−9, coeff = 0.0008, 95% CI = [0.0002, 0.0014]) and 6.5 (r2 = 0.94, p = 1 × 10−7, coeff = 0.0003, 95% CI = [−0.0002, 0.0008]) (Fig. 2a). However, we observed that the decrease in the intermixing index was significantly different between pH 7.5 (r2 = 0.94, p = 2 × 10−9, coeff = 0.0018, 95% CI = [0.0013, 0.0024]) and 6.5 (r2 = 0.94, p = 8 × 10−8, coeff = −0.0019, 95% CI = [−0.0025, −0.0013]). Overall, the final ratio of consumer-to-producer is lower at pH 7.5 (mean = 0.0163, SD = 0.01) than at 6.5 (mean = 0.052, SD = 0.02) (two-sample two-sided t-test; p = 0.03, n = 4) (Fig. 2). Consistently, the final intermixing index is also lower at pH 7.5 (mean = 0.0039, SD = 0.0032) than at 6.5 (mean = 0.0107, SD = 0.0049) (two-sample two-sided t-test; p = 0.05, n = 4) (Fig. 2b).
a Co-culture composition measured as the ratio of consumer-to-producer. b Intermixing between the consumer and producer measured as the intermixing index, where N is the number of interspecific boundaries between the two strains. Experiments were performed at pH 6.5 (strong mutualistic interaction) (magenta data points) or pH 7.5 (weak mutualistic interaction) (cyan data points). Each data point is for an independent replicate (n = 4). The solid black lines are the two-phase linear regression models for pH 6.5, while the dashed black lines are the two-phase linear regression models for pH 7.5. Images of the final expansions after 350 h of incubation at c pH 6.5 and d pH 7.5. The scale bars are 1000 μm.
The results described above yielded two important outcomes. First, the modeled two-phase linear regression of the ratio of consumer-to-producer and the intermixing index both depended on the strength of the mutualistic interaction, where the initial rate of decay was faster at pH 7.5 than at 6.5 (Fig. 2a, b). Thus, as the strength of the interdependency increases, the decay in the ratio and the intermixing index slows. Second, at pH 6.5 we never observed the complete loss of the consumer from the expansion edge (i.e., neither the ratio of consumer-to-producer nor the intermixing index reached zero) (Fig. 2a, b), which is counter to our initial expectation (Fig. 1d).
We further performed controls under continuous oxic and continuous anoxic conditions (Supplementary Fig. S5). The ratio of consumer-to-producer and the intermixing indices both significantly differed between continuous oxic and continuous anoxic conditions regardless of the pH (two-sample two-sided t-tests; p < 0.05, n = 5) (Supplementary Fig. S5). Thus, these two quantities of spatial self-organization depend on the environmental conditions. The ratio of consumer-to-producer and the intermixing indices also significantly differ between continuous oxic and fluctuating conditions, again regardless of the pH (two-sample two-sided t-tests; p < 0.05, n1 = 4; n2 = 5) (Supplementary Fig. S5). This provides evidence that these two quantities are significantly modulated by periods of anoxic conditions. However, the ratio of consumer-to-producer and the intermixing indices were not consistently significantly different between continuous anoxic and fluctuating conditions (Supplementary Fig. S5). Thus, periods of anoxic conditions appear to have larger effects on these two quantities than do periods of oxic conditions, which would be expected as anoxic conditions create an interdependency between the strains.
The number of spatial jackpot events depend on pH
We next tested whether the number of spatial jackpot events that emerge during range expansion depend on the pH, and thus on the strength of the mutualistic interaction. Here, we define a spatial jackpot event as a continuous region of the consumer that persists to the expansion edge. We found that the number of spatial jackpot events was higher at pH 6.5 than at 7.5 (Figs. 3 and 4). We observed mean numbers of spatial jackpot events of 3.5 (SD = 1.3, n = 4) at pH 6.5 and 0.75 (SD = 0.5, n = 4) at pH 7.5, and these mean numbers are significantly different from each other (two-sample two-sided t-test; p = 0.007, n = 4) (Figs. 3 and 4c). Thus, the number of spatial jackpot events is larger at pH 6.5 and slows the observed decay in the ratio of consumer-to-producer and the intermixing index over repeated transitions between anoxic/oxic conditions (Fig. 2).
Images are after 350 h of range expansion. a Using reflected light, the surface morphology of the entire expansion area is visible. Transitions between anoxic (mutualistic interaction) and oxic (competitive interaction) conditions are imprinted in the expansion biomass as concentric rings (black arrow). b The transitions between anoxic and oxic conditions (black arrow) are more visible using the bright field. c Detail of the spatial jackpot events that developed during different incubation conditions. White stars indicate spatial jackpot events that did not advance to the expansion edge while the white arrows indicate transitions between anoxic and oxic conditions. d Transitions between anoxic and oxic conditions caused a change in the spatial self-organization of spatial jackpot events. The white arrows indicate a decrease followed by an increase in width. All scale bars are 1000 μm.
At both a pH 6.5 (strong mutualistic interaction) and b pH 7.5 (weak mutualistic interaction), the producer-first expansion pattern dominates the expansion area. However, both pH conditions foster the emergence of spatial jackpot events. c The cyan data points are the numbers of spatial jackpot events that persisted to the expansion edge at pH 7.5. The magenta data points are the numbers of spatial jackpot events that persisted to the expansion edge at pH 6.5. Means are indicated by the gray lines. Congruent to experimental observations, the predicted number of spatial jackpot events in the numerical simulations is higher at pH 6.5 than at 7.5.
Agent-based model elucidates putative mechanisms for the persistence of spatial jackpot events
To provide further support that the number of spatial jackpot events that emerge during range expansion depends on the pH, and thus on the strength of the mutualistic interaction, we simulated range expansions under fluctuating environmental conditions using an agent-based mathematical model (Fig. 4a, b). While the experiments performed in this study reveal the spatial distributions of strains at the population level, the mathematical model captures the growth dynamics throughout the range expansion at the single-cell level and relates observed processes (such as the nucleation of spatial jackpot events and persistence during range expansion) to the underlying growth dynamics and associated substrate landscape.
We found that during anoxic conditions, nitrate (NO3−) is consumed by the producer, resulting in the formation of a nitrate gradient with low concentrations at the expansion origin and higher concentrations at the expansion edge (Fig. 5a). During oxic conditions, the producer does not consume nitrate and nitrate diffuses deep into the expansion area, which diminishes or even eliminates the previously established radial nitrate gradient (Fig. 5a, b). This reduces the effect of nitrate limitation and equilibrates the growth rates of the two strains (i.e., there is a less pronounced relative growth rate advantage of the consumer) (Fig. 5a, b). At pH 6.5, nitrite (NO2−) toxicity slows the growth of the producer and prevents nitrite from accumulating significantly (Fig. 5c). In comparison, at pH 7.5 nitrite accumulates to larger concentrations and there is a smaller relative difference in growth rates between the producer and consumer at the expansion edge (Fig. 5d).
Spatially resolved relative growth rates (realized growth rate divided by maximum growth rate) for a strong and b weak mutualistic interactions. Under oxic conditions (competitive interaction), growth rates declined radially from the periphery to the center due to carbon limitation. Under anoxic conditions (mutualistic interaction), growth rates also declined radially for the producer due to nitrate (NO3−) limitation, whereas the consumer benefitted from the ubiquitous availability of nitrite (NO2−). Total nutrient content in the simulated domain for c strong and d weak mutualistic interactions. In comparison to static anoxic conditions, nitrate limitation was less prominent due to diffusion of nitrate into the expansion area during oxic conditions. c For a strong mutualistic interaction, nitrite concentrations were low due to the overall higher relative abundance of the consumer. d For a weak mutualistic interaction, nitrite accumulated within the domain due to a lack of strong nitrite toxicity. e When comparing growth rates between weak and strong mutualistic interactions, the producer has a larger difference in growth rate between the two conditions whereas the consumer has a smaller difference.
These underlying processes affect the numbers and persistence of spatial jackpot events during fluctuations between anoxic and oxic conditions. The high relative growth rate difference between the producer and consumer at pH 6.5 fosters persistence of the consumer at the expansion edge (Fig. 5a) leading to a higher number of spatial jackpot events that protrude to the expansion edge (Fig. 4c). At pH 7.5, the absence of nitrite (NO2−) toxicity results in a less prominent growth rate difference between the producer and consumer (Fig. 5b) and thus overall lower numbers of spatial jackpot events congruent with experimental observations (Fig. 4c).
Stability of co-culture composition and intermixing during environmental fluctuations
We next tested whether a steady-state co-culture composition and pattern of spatial self-organization emerges during repeated transitions between anoxic and oxic conditions. Here, we refer to stability as a lack of change in quantitative measures of co-culture composition and spatial self-organization over time. To test this, we quantified two spatial features; the ratio of consumer-to-producer (Fig. 6a) and the intermixing index (Fig. 6b). When tracking the two quantities over the 15 anoxic/oxic transitions, we observed that the two quantities evolve toward constant non-zero values with decreasing variance at both pH 6.5 and 7.5. The variance analysis reveals that the ratio of consumer-to-producer at pH 7.5 reaches a constant value more rapidly than at pH 6.5. The constant value emerges after seven transitions at pH 7.5 and after 12 transitions at pH 6.5. The variance in the intermixing index reaches zero after three transitions at pH 7.5 compared to the last transition at pH 6.5. This suggests that the producer is strongly dependent on the consumer when nitrite (NO2−) toxicity is high (pH 6.5), and there are likely stronger benefits for maintaining more balanced ratios of consumer-to-producer and increased intermixing (e.g., the producer advances slowly without the consumer in close spatial proximity to consume nitrite). In contrast, the variance in the ratio of consumer-to-producer and the intermixing index reaches zero earlier at pH 7.5 than at 6.5. This is intuitive, as the producer is less dependent on the consumer when nitrite toxicity is low, and there are therefore weaker benefits for maintaining balanced ratios of consumer-to-producer and intermixing (e.g., the producer can advance without the consumer).
a The difference in the ratio of consumer-to-producer between two subsequent transitions (anoxic/oxic) has a large variance at earlier times and reaches zero (i.e., stability) after seven transitions at pH 7.5 (weak mutualistic interaction). In contrast, the variance reaches zero after 12 transitions at pH 6.5 (strong mutualistic interaction). b The difference in the ratio of intermixing indices between two subsequent transitions (anoxic/oxic) reaches zero after three transitions at pH 7.5 and after 14 transitions at pH 6.5. The solid black lines are the means at pH 6.5 while the dashed black lines are the means at pH 7.5.
Effect of initial environmental conditions
Our experiments show that the strength of the mutualistic interaction is an important determinant of the numbers and persistence of spatial jackpot events. However, this outcome could be additionally influenced by the initial environmental conditions. We thus used mathematical modeling to test how the initial environmental conditions shape the final patterns of spatial self-organization by varying the initial redox conditions as well as the availability of growth-limiting nutrients (i.e., by providing nitrite [NO2−] in addition to nitrate [NO3−]) (Fig. 7). When nitrite is supplied together with nitrate, a higher number of spatial jackpot events persist to the expansion edge at both pH 6.5 and 7.5, with the similar trend that a higher number of spatial jackpot events emerge at pH 6.5 than at 7.5 (Fig. 7a, c). The interaction strength is amplified at pH 6.5, where local detoxification of nitrite amplifies the growth difference between the two strains and results in more optimal growth conditions in close proximity to spatial jackpot events (Fig. 7a, c).
a Standard experimental design with initially anoxic conditions and nitrate (NO3−) added exogenously as the growth-limiting substrate. b When expansion was initiated under oxic conditions, more spatial jackpot events emerged due to the initial growth of consumer cells at the expansion edge. c When expansion was initiated with an exogenous supply of both nitrate and nitrite (NO2−), the interdependence between the consumer and producer was alleviated and more spatial jackpot events proliferated to the expansion edge.
We further tested whether our results are robust to the initial redox conditions (Fig. 7a, b). When the fluctuations are initiated under oxic conditions, we observed higher numbers of spatial jackpot events persisting to the expansion edge at both pH 6.5 (mean = 7.75, SD = 1.25, n = 4) and 7.5 (mean = 3.5, SD = 1.29, n = 4). During the initial oxic phase, both the producer and consumer can proliferate, creating small pockets of kin cells. During the subsequent anoxic phase, the small pockets of kin cells have a higher chance of being shoved forward by the producer, and can thus form spatial jackpot events that protrude to the expansion edge. Therefore, regardless the initial redox condition, the strength of the interaction has a strong influence on the final spatial arrangement and number of spatial jackpot events.
Source: Ecology - nature.com
