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.

Plants are constantly exposed to changing environments, sometimes leading to extreme conditions and stress. For example, sudden exposure to high light leads to excess absorbed light energy, causing reactive oxygen species (ROS) formation. ROS damage the photosynthetic machinery, particularly the D1 protein in photosystem II (PSII), which therefore needs to be continuously repaired and replaced. The effect of the damage inflicted by high light is a prolonged decrease in photosynthetic efficiency. Hence, it is not surprising that photoinhibition has been subject to numerous experimental studies investigating its effects in the context of crop productivity. However, it has become apparent that classical measures of photoinhibition, i.e., changes in the chlorophyll fluorescence parameter F_v/F_m, are not only determined by the loss of PSII core function but also by processes such as energy transfer and quenching. Mathematical models can help dissect the influences on such fluorescence signals and quantify the contributions of various interacting mechanisms. We present a mathematical model with a dynamic description of the photosynthetic electron transport chain (PETC), non- photochemical quenching, and photoinhibition. With our model, we investigate the interconnection between quenching, photoprotection, and fluorescence using simulations and experimental data. We found that different energy-dissipating properties of intact and damaged PSIIs, as well as energy transfer between PSIIs, are critical components that need to be included in the model to ensure a satisfactory fit to the experimental data. We envisage that our model provides a framework for future investigations of photoinhibition dynamics and its importance for plant growth and yield.

The biotechnological exploitation of microorganisms enables the use of metabolism for the production of economically valuable substances, such as drugs or food. It is, thus, unsurprising that the investigation of microbial metabolism and its regulation has been an active research field for many decades. As a result, several theories and techniques were developed that allow for the prediction of metabolic fluxes and yields as biotechnologically relevant output parameters. One important approach is to derive macrochemical equations that describe the overall metabolic conversion of an organism and basically treat microbial metabolism as a black box. The opposite approach is to include all known metabolic reactions of an organism to assemble a genome-scale metabolic model. Interestingly, both approaches are rather successful at characterizing and predicting the expected product yield. Over the years, macrochemical equations especially have been extensively characterized in terms of their thermodynamic properties. However, a common challenge when characterizing microbial metabolism by a single equation is to split this equation into two, describing the two modes of metabolism, anabolism and catabolism. Here, we present strategies to systematically identify separate equations for anabolism and catabolism. Based on metabolic models, we systematically identify all theoretically possible catabolic routes and determine their thermodynamic efficiency. We then show how anabolic routes can be derived, and we use these to approximate biomass yield. Finally, we challenge the view of metabolism as a linear energy converter, in which the free energy gradient of catabolism drives the anabolic reactions.

Photosynthetic organisms use photosynthesis to harvest sunlight and convert the solar energy into chemical energy, which is then used to reduce atmospheric carbon dioxide into organic molecules. This process forms the basis of all life on Earth, and stands at the beginning of the food chain which feeds the world population. Not surprisingly, many research efforts are currently ongoing aiming at improving growth and product yield of photosynthetic organisms, and several of these activities directly target the photosynthetic pathways. Metabolic Control Analysis (MCA) shows that, in general, the control over a metabolic flux, such as carbon fixation, is distributed among several steps and highly dependent on the external conditions. Therefore, the concept of a single 'rate-limiting' step is hardly ever applicable, and as a consequence, any strategy relying on improving a single molecular process in a complex metabolic system is bound to fail to yield the expected results. In photosynthesis, reports on which processes exert the highest control over carbon fixation are contradictory. This refers to both the photosynthetic 'light' reactions harvesting photons and the 'dark' reactions of the Calvin-Benson-Bassham Cycle (CBB cycle). Here, we employ a recently developed mathematical model, which describes photosynthesis as an interacting supply-demand system, to systematically study how external conditions affect the control over carbon fixation fluxes.

The modelbase package is a free expandable Python package for building and analysing dynamic mathematical models of biological systems. Originally it was designed for the simulation of metabolic systems, but it can be used for virtually any deterministic chemical processes. modelbase provides easy construction methods to define reactions and their rates. Based on the rates and stoichiometries, the system of differential equations is assembled automatically. modelbase minimises the constraints imposed on the user, allowing for easy and dynamic access to all variables, including derived ones, in a convenient manner. A simple incorporation of algebraic equations is, for example, convenient to study systems with rapid equilibrium or quasi steady-state approximations. Moreover, modelbase provides construction methods that automatically build all isotope-specific versions of a particular reaction, making it a convenient tool to analyse non-steady state isotope-labelling experiments.

Plants are constantly exposed to changing environments, sometimes leading to extreme conditions and stress. For example, sudden exposure to high light leads to excess absorbed light energy, causing reactive oxygen species (ROS) formation. ROS damage the photosynthetic machinery, particularly the D1 protein in photosystem II (PSII), which therefore needs to be continuously repaired and replaced. The effect of the damage inflicted by high light is a prolonged decrease in photosynthetic efficiency. Hence, it is not surprising that photoinhibition has been subject to numerous experimental studies investigating its effects in the context of crop productivity. However, it has become apparent that classical measures of photoinhibition, i.e., changes in the chlorophyll fluorescence parameter F _v /F _m , are not only determined by the loss of PSII core function but also by processes such as energy transfer and quenching. Mathematical models can help dissect the influences on such fluorescence signals and quantify the contributions of various interacting mechanisms. We present a mathematical model with a dynamic description of the photosynthetic electron transport chain (PETC), non-photochemical quenching, and photoinhibition. With our model, we investigate the interconnection between quenching, photoprotection, and fluorescence using simulations and experimental data. We found that different energy-dissipating properties of intact and damaged PSIIs, as well as energy transfer between PSIIs, are critical components that need to be included in the model to ensure a satisfactory fit to the experimental data. We envisage that our model provides a framework for future investigations of photoinhibition dynamics and its importance for plant growth and yield.