Reply to Balsa-Canto et al.: Growth models are applicable to growth data, not to stationary-phase data

We are glad to see interest in our computational approach for predicting microbial growth in a mixed culture from growth curve data (1). Balsa-Canto et al. (2) provide experimental and numerical results to conclude that growth curve data are insufficient to predict the dynamics in mixed cultures. We believe that this conclusion results from a mismatch between the experimental design of Balsa-Canto et al. (2) and the models used in our approach. Still, their observations suggest directions for further analysis of both our general approach and specific growth and competition models used within this approach.

Balsa-Canto et al. (2) demonstrate that the yeast Saccharomyces cerevisiae wins competitions against Saccharomyces kudriavzevii (see also ref. 3), despite the competition model predicting that S. kudriavzevii would win. They report similar results from numerical simulations. We suggest these differences are due to several factors. First, the growth and competition models used in our approach (equations 1 through 3 in ref. 1) focus on growth experiments that end when the culture reaches the stationary phase (e.g., a single day, as in figure 3 in ref. 1). Consequently, these models assume growth- and resource-based competition. However, these assumptions fail during the stationary phase after the limiting resource has been consumed. Indeed, the yeast competitions in ref. 2 ran for over a week, with cells entering the stationary phase after ∼24 h, and the majority of data points both in the experiments and in the simulations are from the stationary phase; in some cases the simulations seem to exclude a growth phase altogether (figure 2c.3 in ref. 2). Thus, different models must be used when focusing on competition during the growth vs. stationary phase. Second, our approach assumes frequent sampling of the growth dynamics. However, only about 4 samples were collected from the yeast cultures between inoculation and the stationary phase, and a similar protocol was used in the simulations. This is hardly enough data for fitting the 6-parameter Baranyi–Roberts model (4) or the 4-parameter Richards model (5) used in our approach to model growth. Third, the above growth models do not consider biphasic growth curves that can emerge when Saccharomyces species shift between carbon sources (6). Fourth, the success of S. cerevisiae in a week-long competition experiment may be due to emergence of mutants or altered phenotypic states. These may affect growth dynamics in an unpredictable manner that cannot be accounted for by our approach.

In conclusion, our approach was designed to predict growth in a mixed culture, with resource-based competition during a single growth phase, sampled at a high frequency. We suggest applying it to experiments that use an automatic microplate reader to measure optical density every 15 to 30 min over a 12- to 48-h period that includes a lag phase, an exponential growth phase, a deceleration phase, and entrance to the stationary phase (1). Application to significantly different experiments may require changing the growth and/or competition models used.