Extended Data Fig. 8: Expansion dynamics with the attractant being the sole nutrient source.

This is one of the scenarios of chemotaxis investigated previously^18,76. Here, for comparison with the dynamics presented in the main text, we show the expansion dynamics of populations grown with glucose (a chemoattractant²¹) as the sole carbon source. a, For wild-type cells (HE206) spotted on 0.25% agar plate with glucose as the sole carbon source, photographs show the existence of an outer ring at the front of the expanding population for a range of glucose concentrations. Scale bars, 2 cm. The experiments were repeated once with similar results. b, Dependence of expansion speed on glucose concentration. Intuitively, reducing the glucose concentration would be expected to increase the expansion speed, as it would take less time for the population to consume the attractant. However, the circles show that reducing the glucose concentration reduced population expansion speed. Data show means of two biological replicates. c, Direct comparison of concentration dependence of expansion speeds in glucose only (open green squares), glycerol only (open black circles), glycerol or glucose with aspartate (red circles, purple squares); data for latter same as shown in Fig. 4d and Extended Data Fig. 7e, f. Expansion speed in glucose (~1–2 mm h⁻¹) is faster than in glycerol (not an attractant) but well below the cases for which (low) amounts of attractants are supplemented. Shown data points represent means of biological replicates (n = 2 or larger), with error bars (s.d.) shown for n ≥ 3; see Supplementary Tables 9, 10 for data and sample sizes. d, e, To understand the expansion behaviour, we used confocal scans to obtain the density profiles. The ring observed in the photograph is seen as a subtle density bulge at the front bounding a flat-density interior. Note the lack of an exponential trailing region, as observed when an attractant supplement is present (Fig. 2b, Extended Data Fig. 4i, photographs in Fig. 1a). The observed density profiles are comparable with those previously found with galactose as the attractant and the major nutrient source¹⁸. Experiments here were done with wild-type cells (HE206) (a–c) and fluorescence cells (HE274) (d, e). The confocal experiments were conducted once (expansion speeds are highly comparable to those measured manually). f, To capture the observed behaviours, we modified the GE model (Fig. 3a) using only one variable a to describe the attractant/nutrient. Consumption of the growth-enabling attractant is directly coupled to the increase in density via the yield Y. g, h, Fixing model parameters using available data for growth and chemotaxis on glucose (see Supplementary Text 2.4, 2.3 with parameters used listed in Supplementary Table 4), the model generated expansion speeds (green line in b) and density profiles that capture the experimental observations well; for comparison, a coarse-grained spatial resolution similar to the experiments was used to display the profiles obtained by the simulations. i, The model output can further be understood by a scaling analysis (Supplementary Text 2.6), resulting in the simple relation u² ∝ χ₀λ (equation (E8.e)). This relation is of the same form as the result of the Fisher–Kolmogorov dynamics, \({u}_{{\rm{FK}}}=2\sqrt{D\lambda }\) (see Extended Data Fig. 5), but with the chemotactic coefficient χ₀ replacing the diffusion coefficient D. j, k, The predicted dependence of u on λ and χ₀ (black lines) is validated by numerical simulations of the model (blue circles). The square-root dependence of the expansion speed on the chemotactic coefficient χ₀ stands in contrast to the linear dependence on χ₀ when an attractant supplement is provided (Extended Data Fig. 9d) and shows that the expansion dynamics with or without the attractant supplement are two distinct classes of mathematical problem. Note that the quantitative gain in expansion speed for the case with a supplemented attractant comes not only from the change in dependence on the chemotactic coefficient from \(\sqrt{{\chi }_{0}}\) to χ₀, but also from the freedom to use attractants that have large χ₀ but small λ, which can be compensated by nutrients that give largerλ. Both aspartate and serine are strong attractants but poor nutrients, and are thus most potent when used in combination with a good nutrient source. Thus, separating the role of substances as nutrients and as cues not only relaxes the underlying mathematical constraint but also relaxes the biological constraint so that good attractants need not be good nutrients. These results provide an important support for the central thesis of this work, that chemotactic cells gain fitness by expanding in nutrient-replete conditions as a ‘foresighted’ navigation strategy (see main text).

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