A THERMOdynamic framework for modelling MICrobial growth and community dynamics – Thermomic

Microbial communities are key engines that drive earth’s biogeochemical cycles. However, existing ecosystem models have today exhibit only limited abilityies in to predicting microbial dynamics and require the calibration of multiple population specific empirical equations. In contrast, we build on a new kinetic «Microbial Transition State« (MTS) theory of growth derived from first physical principles. We show how the theory coupled to simple mass and energy balance calculations constitutes provides a framework that with intrinsically enclose important qualitative properties to model microbial community dynamics.

We first show how the theory can take into account simultaneously account for the influence of all the resources needed for growth (electron donor, acceptor and nutrients) while still producing consistent dynamics that fulfilling the Liebig rule of the a single limiting substrate. We also show the apparition of consistentconsistent patterns of energy dependent microbial successions in mixed culture settings without the need for calibration of population specific parameters calibration. WThen, we then illustrate show how this approach can be used to model a simplified activated sludge community. For To thatthis end, we compare MTS derived dynamics to with thoese of a widely used activated sludge model and show that similar growth yields and overall dynamics can be obtained using 2 two parameters instead of 12twelve. This new kinetic theory of growth grounded by a set of generic physical principles thus parsimoniously gives rise to consistent microbial population and community dynamics, which thereby pavinges the way for the development of a new class of more predictive microbial ecosystem models.

In 1875, Ludwig Boltzmann stated: «The general struggle for existence of animate beings is not a struggle for raw materials […] nor for energy […], but a struggle for entropy, which becomes available through the transition of energy from the hot sun to the cold earth«. In 1999, Urs von Stockar proposed his notion of «entropy driven growth« for microbial cultures (von Stockar & Liu, 1999). In 2001, Liu et al.; experimentally demonstrated the possibility of an «entropy driven« endothermic growth, using an acetate fed pure culture of Methanosarcina barkeri grown in a calorimeter. Some years later, Jeremy England made an important theoretical contribution (England, 2013). He proposed a statistical physics based analysis of self replicating phenomena by extending the Crooks fluctuation theorem (Crooks, 1999) to biological entities. He derived a lower bound for the amount of entropy that is produced during a process of self-replication and made the connection with the apparent rate of the phenomena. J. England even illustrated his results using the case study of Escherichia coli growing under non limiting substrate conditions. We propose to build further on this contribution. By doing so, it will be possible to derive a relation between the maximum growth rate and the entropy variation, which is a function of the temperature and the metabolic energy dissipation. This will result in a more generic growth equation, where the growth rate will depend only on energetic variables, temperature, one parameter and one constant. Furthermore, the contribution of entropy variation to growth rate will become explicit, giving substance to the initial intuition of Boltzmann about «the general struggle for entropy of animate beings«.

Hadrien Delattre, Elie Desmond Le Quéméner, Christian Duquennoi, Ahlem Filali, Théodore Bouchez. Consistent microbial dynamics and functional community patterns derived from first principles – 2019. The ISMEJ. (2019) 13:263–276
Hadrien Delattre, Elie Le Quéméner, Robbert Kleerebezem, Théodore Bouchez. Modeling the energy dependence of microbial growth. Minireview in revision for FEMS Microbiology Ecology.

Microbes are the most abundant living forms on earth and constitute "the microbial engines that drives earth biogeochemical cycles". To face current environmental challenges, it is becoming essential to better manage the natural recycling abilities of microbial communities to foster the emergence of appropriate ecosystems services. In this respect, residual organic waste streams can be considered as potential feedstocks that could be used for in microbial processes for the production of useful compounds (methane, hydrogen, organic molecules,…) through anaerobic digestion or future environmental biorefineries. To better design and optimize such processes, engineers need appropriate models stating explicitly the causal relationships between process design parameters, associated selective pressures, resulting microbial community structures and sustained functions.
Today however, the modelling of microbial dynamics only relies on many different phenomenological laws (Monod, Contois, Haldane,…). Being very useful in industrial biotechnological settings, where well defined cultures are operated in confined processes, their use for modelling mixed cultures in open systems is more challenging and usually requires intensive parameter fitting on a narrow experimental domain. The lack of knowledge about the basic principles underlying microbial growth is limiting our predictive capacity for biotechnological applications. There is today a need for stating a generic set of theoretical principles, which could be challenged by experiments, and that could give rise to models featuring an increased predictive power for better managing microbial communities. This is precisely the goal of the THERMOMIC project.
For that, environmental engineers have provided us with interesting insights by studying microbial growth yields and energy balance in great details. A generic method for deriving energy balances per unit of biomass formed has been established and validated using culture data from many different organisms, which allows the general calculation of growth stoichiometry (Kleerebezem & Van Loosdrecht, 2010). However, until recently, the link between thermodynamic balances and microbial growth dynamics was not understood.
We lately made a significant contribution in this direction. We proposed a thermodynamic theory of microbial growth by showing how systems constituted by microbes in contact with molecules could be likened to ensembles described by the laws of statistical physics. A growth equation was proposed, which links a flux (the growth of microbes) to a force (the energy density). Original prediction arose from the mathematical analyses of equations, that were found to be supported by experimental data, allowing the publication of this atypical theoretical work in a highly ranked journal (IF=9,302) (Desmond-Le Quemener & Bouchez, 2014). We today believe that this flux/force relationship between growth rate and energy could constitute the basis for a more generic framework for modelling microbial dynamics: this is the main working hypothesis of THERMOMIC project.
We therefore propose to combine skills in general and microbial ecology, statistical physics, applied mathematics and environmental engineering to (i) solidify the theoretical ground of thermodynamic growth models (WP1), (ii) to mathematically explore their characteristic features compared to current phenomenological approaches (WP2) and (iii) to assess their suitability for environmental engineering applications (WP3). The general THERMOMIC objective is to give rise to a comprehensive body of knowledge, relying on solid theoretical grounds, mathematically stated, supported by simulations and experiments, in order to renew our understanding of microbial dynamics and to propose new models featuring increased predictive abilities that could foster the emergence of sound engineering applications.