In their natural environment plants are part of a rich ecosystem including numerous and diverse microorganisms in the soil. It has been long recognized that some of these microbes, such as mycorrhizal fungi or nitrogen fixing symbiotic bacteria, play important roles in plant performance by improving mineral nutrition. However, the full range of microbes associated with plants and their potential to replace synthetic agricultural inputs has only recently started to be uncovered. In the last few years a great progress has been made in the knowledge on composition of rhizospheric microbiomes and their dynamics. There is clear evidence that plants shape microbiome structures, most probably by root exudates, and also that bacteria have developed various adaptations to thrive in the rhizospheric niche. The mechanisms of these interactions and the processes driving the alterations in microbiomes are however largely unknown. In this review we focus on the interaction of plants and root associated bacteria enhancing plant mineral nutrition, summarizing the current knowledge in several research fields that can converge to improve our understanding of the molecular mechanisms underpinning this phenomenon.

Escherichia coli diauxie is a fundamental example of metabolic adaptation, a phenomenon that is not yet completely understood. Further insight into this process can be achieved by integrating experimental and computational modeling methods. We present a dynamic metabolic modeling approach that captures diauxie as an emergent property of subpopulation dynamics in E. coli monocultures. Without fine-tuning the parameters of the E. coli core metabolic model, we achieved good agreement with published data. Our results suggest that single-organism metabolic models can only approximate the average metabolic state of a population, therefore offering a new perspective on the use of such modeling approaches. The open source modeling framework that we provide can be applied to model general subpopulation systems in more-complex environments and can be extended to include single-cell-level stochasticity.

Understanding microbial ecosystems means unlocking the path toward a deeper knowledge of the fundamental mechanisms of life. Engineered microbial communities are also extremely relevant to tackling some of today's grand societal challenges. Advanced meta-omics experimental techniques provide crucial insights into microbial communities, but have been so far mostly used for descriptive, exploratory approaches to answer the initial ‘who is there?’ question. An ecosystem is a complex network of dynamic spatio-temporal interactions among organisms as well as between organisms and the environment. Mathematical models with their abstraction capability are essential to capture the underlying phenomena and connect the different scales at which these systems act. Differential equation models and constraint-based stoichiometric models are deterministic approaches that can successfully provide a macroscopic description of the outcome from microscopic behaviors. In this mini-review, we present classical and recent applications of these modeling methods and illustrate the potential of their integration. Indeed, approaches that can capture multiple scales are needed in order to understand emergent patterns in ecosystems and their dynamics regulated by different spatio-temporal phenomena. We finally discuss promising examples of methods proposing the integration of differential equations with constraint-based stoichiometric models and argue that more work is needed in this direction.

The last few years have seen the advancement of high-throughput experimental techniques that have produced an extraordinary amount of data. Bioinformatics and statistical analyses have become instrumental to interpreting the information coming from, e.g., sequencing data and often motivate further targeted experiments. The broad discipline of “computational biology” extends far beyond the well-established field of bioinformatics, but it is our impression that more theoretical methods such as the use of mathematical models are not yet as well integrated into the research studying microbial interactions. The empirical complexity of microbial communities presents challenges that are difficult to address within vivo/in vitroapproaches alone, and with microbiology developing from a qualitative to a quantitative science, we see stronger opportunities arising for interdisciplinary projects integrating theoretical approaches with experiments. Indeed, the addition ofin silicoexperiments, i.e., computational simulations, has a discovery potential that is, unfortunately, still largely underutilized and unrecognized by the scientific community. This minireview provides an overview of mathematical models of natural ecosystems and emphasizes that one critical point in the development of a theoretical description of a microbial community is the choice of problem scale. Since this choice is mostly dictated by the biological question to be addressed, in order to employ theoretical models fully and successfully it is vital to implement an interdisciplinary view at the conceptual stages of the experimental design.

The ability of phototrophs to colonise different environments relies on robust protection against oxidative stress, a critical requirement for the successful evolutionary transition from water to land. Photosynthetic organisms have developed numerous strategies to adapt their photosynthetic apparatus to changing light conditions in order to optimise their photosynthetic yield, which is crucial for life on Earth to exist. Photosynthetic acclimation is an excellent example of the complexity of biological systems, where highly diverse processes, ranging from electron excitation over protein protonation to enzymatic processes coupling ion gradients with biosynthetic activity, interact on drastically different timescales from picoseconds to hours. Efficient functioning of the photosynthetic apparatus and its protection is paramount for efficient downstream processes, including metabolism and growth. Modern experimental techniques can be successfully integrated with theoretical and mathematical models to promote our understanding of underlying mechanisms and principles. This review aims to provide a retrospective analysis of multidisciplinary photosynthetic acclimation research carried out by members of the Marie Curie Initial Training Project, AccliPhot, placing the results in a wider context. The review also highlights the applicability of photosynthetic organisms for industry, particularly with regards to the cultivation of microalgae. It intends to demonstrate how theoretical concepts can successfully complement experimental studies broadening our knowledge of common principles in acclimation processes in photosynthetic organisms, as well as in the field of applied microalgal biotechnology.

Summary: To obtain insights into the dynamics of nutrient exchange in arbuscular mycorrhizal (AM) symbiosis, we modelled mathematically the two‐membrane system at the plant–fungus interface and simulated its dynamics. In computational cell biology experiments, the full range of nutrient transport pathways was tested for their ability to exchange phosphorus (P)/carbon (C)/nitrogen (N) sources. As a result, we obtained a thermodynamically justified, independent and comprehensive model of the dynamics of the nutrient exchange at the plant–fungus contact zone. The predicted optimal transporter network coincides with the transporter set independently confirmed in wet‐laboratory experiments previously, indicating that all essential transporter types have been discovered. The thermodynamic analyses suggest that phosphate is released from the fungus via proton‐coupled phosphate transporters rather than anion channels. Optimal transport pathways, such as cation channels or proton‐coupled symporters, shuttle nutrients together with a positive charge across the membranes. Only in exceptional cases does electroneutral transport via diffusion facilitators appear to be plausible. The thermodynamic models presented here can be generalized and adapted to other forms of mycorrhiza and open the door for future studies combining wet‐laboratory experiments with computational simulations to obtain a deeper understanding of the investigated phenomena.