Regular articleHigh biomass density promotes density-dependent microbial growth rate
Introduction
The study of predator-prey interactions has been the object of intense researches for several years. As in many subfields of ecology, the science behind predator-prey investigations has been driven by theory, including important advances in mathematical models as tools for understanding and predicting the functioning of ecosystems (cf. [1]. Predator-prey models have been studied mathematically since the publication of the Lotka [2] and Volterra [3] Lotka-Volterra equations in 1920 and 1926 based on the hypothesis of resource (prey)-dependence where the functional response of the predator (i.e. number of prey captured per predator per unit of time) is a function of the absolute prey density noted g(N). This hypothesis was questioned by Arditi and Ginzburg in the 1990s [4] (see their recent book on density-dependence [4]), who proposed a specific case of density-dependence, named ratio-dependence, where the prey capture rate is a function of the ratio of the prey density over predator density noted g(N/P).
In microbiology, researchers have often faced similar problems in describing the growth-rate of microorganisms growing on substrates or in the study of competition through resource depletion. The modelling of the functional response, also named the microbial specific growth rate or the reaction kinetics was lifted at the same time in theoretical ecology and in microbial ecology. It is particularly interesting to notice that several models, developed in these two disciplines independently, and thus bearing different names, propose in fact the same growth rate expressions [5]. In other words, the same mathematical functions are used to describe micro as well as macro-organisms growth. The latter being more difficult to handle than microbes, the microbiology has appeared since a few years as a field, particularly suited to study questions of general ecology [6]. If we exclude complex mechanisms such as inhibition, functions describing the growth rate of microorganisms can be classified into two main classes, depending whether they involve only the resource (substrate or nutrient) concentration in the medium containing the culture, as in the case of the Monod model [7] or both substrate and biomass (or predator) densities as in the case of the Contois model [8]. In fact, what is of relative importance with respect to a pure culture (both models have very similar predictions for pure cultures) becomes very important for complex ecosystems in the sense Monod-like models predict extinction of all species in competition on a single substrate, but one (this well-known property is called the competitive exclusion principle and has been studied in ecology from the 1950s, cf. for instance Hardin [9] while Contois-like models allow coexistence of several species (cf. for instance Lobry and Harmand [10].
If we consider Monod functions, for a constant feed rate, the chemostat theory predicts that the equilibrium should only depend on the dilution rate D and be independent of the input substrate concentration Sin (on the condition that this latter one is large enough to supply enough resource for the micro-organisms to grow). This prediction was tested by varying dilution rates and influent substrate concentration and letting the chemostat reaching its steady state while measuring the effluent substrate concentration s* [5]. However, it was only verified for pure cultures. When working with mixed cultures (such as in wastewater treatment or fermentation processes) or using a multicomponent substrate, it is well known that the effluent concentration do not depend only on the dilution rate, but also on the concentration of substrate Sin in the influent [11], [12], [13], [14]. The independence of the growth rate at steady state with respect to Sin in the chemostat has been questioned, following experimental observations since 1959 by Contois, Yoshinori [15] by including the ratio s/x in the expression of the growth rate instead of the absolute value of available substrate and thus emerging an effect of density-dependence. On the latter, the question of the mechanisms at the origin of this phenomenon can be questioned.
In the present work, we investigate whether a high density of biomass can generate density-dependent growth rate as proposed in Harmand and Godon [16], and formalized in Lobry and Harmand [10]. We therefore propose experiments in a chemostat or CSTR (Continuous Stirred Tank Reactor) followed by a macroscopic modelling approach and a study of the proposed models to determine what type of growth rate is the most appropriate to explain the experimental data. The novelty with respect to the literature lies in the fact we have followed not only substrate and biomass densities but also monitored microbiology of the complex ecosystem used together with the structure of the biomass. Our results show that density-dependent kinetics may emerge not only from a high density, but also from the structuration of the biomass in flocs.
The paper is organized as follows. We first describe the experiments we performed in chemostat with the different parameters we monitored, we recall the qualitative predictions that can be done from the assumptions on the microbial growth rate at the scale of the whole biomass and we describe the method of the models identification. Then, we show and analyse the results at the light of the monitored parameters and of the modelling approach before some conclusions and perspectives are drawn.
Section snippets
Experimental setup and experiment
The experimental work is divided into two consecutive series of experiments applied in a chemostat device: a first series, named SE1, with increasing substrate step-loads and a second series SE2 where these loads were applied decreasingly. A hydraulic retention time of 24 h was maintained constant throughout the experiments.
All experiments were carried out in the same continuous biological reactor (Fig. 1). The reactor consisted of a glass vessel (noted [1] on Fig. 1) inoculated with constant
Raw data analysis and yield determination
The data sets SE1 and SE2 are plotted in Fig. 2, Fig. 3 and the equilibrium values for each set of experiment and for each Sin are presented in Table 3.
We observe from Table 3 that equilibrium values for the substrate are different for all experiments. In addition, all s*/x* ratios at equilibrium are also different. In other words, following the theoretical qualitative results recalled in the Material & Methods section, neither a pure Monod-type nor a pure Contois-type kinetics can explain the
Conclusion and perspectives
In this paper, we analysed the results of experiments realized in a chemostat to study the growth rate properties of a complex microbial ecosystem. To do so, we relied on experimental data of two series of experiments named SE1 and SE2. The main characteristics of the chemostat were monitored over the experiments, including variables such as the biomass and substrate density, microscopic observations, the structure of the bacterial community and the granulometry of flocs. In addition, a
Aknowledgements
Authors thank Roger Arditi for fruitful comments in designing the experiments and the discussions we had about the results during the Bernoulli Seminar Series workshop Microbial ecology and mathematical modelling (15–19 December 2014), part of the Role of mathematics and computer science in the ecological theory Program, July–December 2014, CIB/EPFL, Lausanne, Switzerland.
The first author recognises the help of the Ministry of Higher Education of Tunisia for the half-scholarship awarded to her
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