Fig 1.
Model description A. The inherent tradeoff between planktonic cells and biofilms.B. Fraction of live bacteria cells per aggregate size on bean leaf (adapted from [19]). In essence, cells within smaller aggregates do not survive prolonged and recurring dry periods while cells in larger aggregates do. C. Schematic depiction of the model. The top layer is the bulk fluid, hosting the planktonic sub-population. The bottom layer is the surface, hosting the sessile sub-population. D. The model includes planktonic and sessile cells. At each time step, the cells may grow and divide, die due to stress, and change their state. E. Stress is modeled as the hourly probability of cell death, and is a function of both local cell density and the hydration state. The probability to die due to desiccation is high in aggregates below the protection threshold QL. In addition, to account for overcrowding, the probability of death increases above density QH. F. Preferential attachment is modeled as a step-like function of local cell density.
Table 1.
Model parameters.
Table 2.
Equations and functions.
Fig 2.
PA can confer fitness advantage and there is an optimal attachment threshold.
A. Typical simulation dynamics of population size and nutrient concentration over five diel cycles. In general, the population size increases during the wet periods and decreases during the dry periods. Fluctuations in population size are dictated by nutrient availability, periodic stress and spatial arrangement of the cells. Dynamics presented from a simulation with RA where cells attach and detach at the same constant probability (ARA = D = 0.01 [h−1]) B. Population sizes at the end of a five diel cycle simulations with different PA thresholds (QPA). Each data point is mean±SE of 10 simulations. Pie diagrams represent relative abundance of planktonic and sessile cells. The dashed line represents the population size of the optimal RA simulation, i.e. RA with the highest yield among all tested ARA values. C. Snapshot from the optimal PA strategy (QPA = 12). D. Snapshot from the optimal RA strategy. Snapshots C and D were taken at the end of day 5. Sessile cells are shown in red, planktonic in green.
Fig 3.
Optimal preferential attachment threshold depends on protected density threshold.
A. Comparison of different preferential attachment thresholds (QPA), corresponding to different strategies, at various conditions differing in desiccation stress density thresholds QL. Each data-point is the mean of 10 simulations. Color indicates the fraction of planktonic cells from the entire population. Black circle marks the optimal strategy. B. Interpolated optimal attachment threshold QPA as a function of the desiccation stress density threshold QL.
Fig 4.
Aggregate-distribution dynamics help explain how the optimal PA strategy works.
A-F. Aggregate-size distribution dynamics. Bar height indicates number of aggregates within size range at specific time point. Bar color indicates the average number of different linages per aggregate. The curve on top shows total population size and ratio of planktonic to sessile cell count A. PA with QPA = 4. B. PA with QPA = 12, C. PA with QPA = 20, D. RA with ARA = 0.001, E. RA with ARA = 0.01, F. RA with ARA = 0.9.
Fig 5.
Attachments with the optimal PA (QPA = 12) enrich yet-to-be protected aggregates or maintain already-protected aggregates.
Quantification of attachments of planktonic cells in various PA strategies, as a function of the local density at the attachment site. Histograms represent attachment events during the five day simulation (mean over 10 simulations). Standard errors are negligible in this scale.
Fig 6.
PA confers fitness advantage over RA in most of the analyzed phase plane and even extends the Hutchinsonian niche under periodic (but not constant) stress.
A. Relative advantage of high-ARA RA over low-ARA RA under periodic stress, as a function of source nutrient concentration (Nc) and death rate of unprotected cells (SL). Color bars represent the ratio between the population sizes at the end of a five day simulations. At low SL values, the faster growth of the planktonic population compensated for the lower protection, and thus lower ARA prevails (green zone). At higher SL values, the formation of protected aggregates compensates for the lower growth rate, and higher ARA rates result with a higher population size (red zone). B. Relative advantage of PA over RA under periodic stress. Zone a: The optimal PA strategy results with survival while all RA strategies lead to extinction in >80% of repeated simulations. Formation of protected aggregates occur only with PA. Zone b: PA is superior when growth rate is high enough to support the formation protected aggregates. Zone c: At Low Nc and low SL, PA and RA yield populations that are similar in size. C. Same as in (B) but under constant stress. The Y axis SL values in (C) were modified so that the overall survival chances of unprotected cells during 24h of stress equal the survival chances during the 12h dry conditions of the periodic stress.
Fig 7.
Comparison of different wet-dry diel cycle splits (duration of wet and dry periods), and their effects on the optimal strategy.
The most successful strategy in each set of conditions is marked by a square, and the color of other strategies show their yield relative to the optimal one. Data is based on the mean value of 10 simulations.
Fig 8.
The underlying mechanism of the PA strategy.
The beneficial effect of preferential attachment is strongly dependent on the attachment density threshold. PA accelerates the growth of larger aggregates by recruitment of planktonic bacteria. The effect of the PA mechanism depends on the attachment density threshold, A. Low attachment density threshold: Most enriched aggregates do not surpass the protected zone, since the total rate of preferential attachments is divided among a large number of aggregates. B. Optimal attachment density threshold: Preferential attachment to a small group of aggregates which surpass the critical size. C. High attachment density threshold: (few or) no aggregates are large enough to draw the planktonic population.