Thermodynamic Limits and Optimality of Microbial Growth

Abstract

Understanding microbial growth with the use of mathematical models has a long history that dates back to the pioneering work of Jacques Monod in the 1940s. Monod’s famous growth law expressed microbial growth rate as a simple function of the limiting nutrient concentration. However, to explain growth laws from underlying principles is extremely challenging. In the second half of the 20th century, numerous experimental approaches aimed at precisely measuring heat production during microbial growth to determine the entropy balance in a growing cell and to quantify the exported entropy. This has led to the development of thermodynamic theories of microbial growth, which have generated fundamental understanding and identified the principal limitations of the growth process. Although these approaches ignored metabolic details and instead considered microbial metabolism as a black box, modern theories heavily rely on genomic resources to describe and model metabolism in great detail to explain microbial growth. Interestingly, however, thermodynamic constraints are often included in modern modeling approaches only in a rather superficial fashion, and it appears that recent modeling approaches and classical theories are rather disconnected fields. To stimulate a closer interaction between these fields, we here review various theoretical approaches that aim at describing microbial growth based on thermodynamics and outline the resulting thermodynamic limits and optimality principles. We start with classical black box models of cellular growth, and continue with recent metabolic modeling approaches that include thermodynamics, before we place these models in the context of fundamental considerations based on non-equilibrium statistical mechanics. We conclude by identifying conceptual overlaps between the fields and suggest how the various types of theories and models can be integrated. We outline how concepts from one approach may help to inform or constrain another, and we demonstrate how genome-scale models can be used to infer key black box parameters, such as the energy of formation or the degree of reduction of biomass. Such integration will allow understanding to what extent microbes can be viewed as thermodynamic machines, and how close they operate to theoretical optima.

A hierarchical thermodynamic imperative drives the evolution of self-replicative life systems towards increased complexity

“…In fact, it could be argued that from a quantum mechanics probabilistic point of view (Schrödinger, 1967) a bona fide SR system must be able to grow under a suitable set on conditions and this constraint ( for P SR ≥ P SRdecay under favourable conditions) should be considered an inherent property of SR biological system. Furthermore, this constraint is consistent with our empirical observation of SR systems in nature at all levels, where system growth is observed when a suitable set of conditions is present, from isolated bacterial growth (such as in a bio-incubator) to a mature complex ecosystem being perpetuated over time (Desmond-Le Quemener & Bouchez, 2014; Jorgensen, 2007; Kleerebezem & Van Loosdrecht, 2010; Kleidon, 2009; Saadat et al, 2020).…”

“…2 and figure 1b and 2 bottom left panel). This constrained equation is consistent with our observation of SR systems in nature at all levels, where system growth is observed whenever suitable conditions are present, from isolated bacterial growth (such as in a bio-incubator) (England, 2013; Saadat et al, 2020) to a mature complex ecosystem being perpetuated over time (Desmond-Le Quemener & Bouchez, 2014; Jorgensen, 2007; Kleerebezem & Van Loosdrecht, 2010; Kleidon, 2009).…”

“…Furthermore, as previously justified (England, 2013), when applying this equation to the process of self-replication (SRn), we can intuitively assume that the probability of the forward reaction ( P 1→2 or P SR ) is much higher than the reverse reaction probability ( P 2→1 or ), where the SRn process “undoes” itself following a time reversal trajectory. In fact, it has been suggested that the process of SRn is irreversible from a practical point of view (England, 2013; Saadat et al, 2020). Thus, the RHS term of equation 1.1, , can be assumed to always have a positive value for an established SR system undergoing SRn/growth (figure 1).…”

Thermodynamic limitations of metabolic strategies for PHB production from formate and fructose in Cupriavidus necator

“…Biomass formation and the final step of PHB synthesis were assumed to be sufficiently thermodynamically forward driven under all conditions and were excluded from the MDF analysis. The driving force of biomass formation is challenging to determine and can differ vastly, even in more detailed metabolic models (Saadat et al, 2020).…”

Unlocking Elementary Conversion Modes: ecmtool Unveils All Capabilities of Metabolic Networks

“…Cellular metabolism was seen as a black box: without having knowledge of the metabolic details, so-called macrochemical equations were calculated which specify the stoichiometry of the conversion of nutrients into biomass (cells) and by-products. 1 , 2 , 3 , 4 , 5 , 6 Precise measurements of heat exchange, nutrient uptake, and product formation were used to develop thermodynamic theories of cellular growth, 7 which led to the improvement of biotechnological processes. 5 , 8 These methods could not always be applied: they were not exhaustive, and required experimental data and basal knowledge of metabolic pathways.…”