Search bioRxiv⌕ Search

bioRxiv · 10.1101/2021.06.09.447824

Monod model is insufficient to explain biomass growth in nitrogen-limited yeast fermentation

Abstract

The yeast Saccharomyces cerevisiae is an essential microorganism in food biotechnology; particularly, in wine and beer making. During wine fermentation, yeasts transform sugars present in the grape juice into ethanol and carbon dioxide. The process occurs in batch conditions and is, for the most part, an anaerobic process. Previous studies linked limited-nitrogen conditions with problematic fermentations, with negative consequences for the performance of the process and the quality of the final product. It is, therefore, of the highest interest to anticipate such problems through mathematical models. Here we propose a model to explain fermentations under nitrogen-limited anaerobic conditions. We separated the biomass formation into two phases: growth and carbohydrate accumulation. Growth was modelled using the well-known Monod equation while carbohydrate accumulation was modelled by an empirical function, analogous to a proportional controller activated by the limitation of available nitrogen. We also proposed to formulate the fermentation rate as a function of the total protein content when relevant data are available. The final model was used to successfully explain experiments taken from the literature, performed under normal and nitrogen-limited conditions. Our results revealed that Monod model is insufficient to explain biomass formation kinetics in nitrogen-limited fermentations of S. cerevisiae. The goodness-of-fit of the herewith proposed model is superior to that of previously published models, offering the means to predict, and thus control fermentations. ImportanceProblematic fermentations still occur in the winemaking industrial practise. Problems include sluggish rates of fermentation, which have been linked to insufficient levels of assimilable nitrogen. Data and relevant models can help anticipate poor fermentation performance. In this work, we proposed a model to predict biomass growth and fermentation rate under nitrogen-limited conditions and tested its performance with previously published experimental data. Our results show that the well-known Monod equation does not suffice to explain biomass formation.

Source connections

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Henriques, D., Balsa-Canto, E.. 2021-06-10. Monod model is insufficient to explain biomass growth in nitrogen-limited yeast fermentation. https://doi.org/10.1101/2021.06.09.447824

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related preprints

Low-fidelity simulator selection for multi-fidelity inference of epithelial vertex models

Vertex models link cell division, neighbour exchange, and intercellular forces to epithelial tissue form through parameters such as junctional line tension and perimeter contractility. Bayesian inference of these parameters from data quantifies their uncertainty, but for stochastic models of proliferating tissues it requires many costly simulations. Multi-fidelity simulation-based inference reduces this cost by training on many runs of a cheaper, less accurate ('low-fidelity') simulator before refining with a few full ('high-fidelity') runs. Low-fidelity versions can be constructed in several ways, for example by stopping simulations early, coarsening the timestep, or averaging fewer replicates, but it is unclear which to choose before committing to costly training. To address this, we introduce PRISM (Paired Ranking Index for Simulator Matching), a screen that compares each candidate with the full simulator on paired runs, scoring agreement in cell-packing statistics against cost. For a vertex model of a proliferating tissue, PRISM flags stopping early as unreliable before training; once trained, this choice can produce confidently wrong parameter estimates. By contrast, a coarser timestep, within the range tested, is cheap and accurate; while fewer replicates are accurate but too costly. Using a screened low-fidelity simulator, multi-fidelity inference outperforms approximate Bayesian computation and neural-network inference trained on full simulations alone, at matched cost and with well-calibrated uncertainty. The same pattern recurs for a second vertex model fitted to published Drosophila pupal-wing imaging data, although there stopping halfway proves safe. Together, our findings suggest that which approximations are safe depends on the model, and that screening them before training makes multi-fidelity inference of tissue mechanics practical.

systems biology↗

Calibrating developmental dynamics from single-cell atlases: lineage paths outrun least-action routes

Single-cell atlases infer developmental dynamics from destructive snapshots, yet how far realized lineage paths depart from such inferred dynamics has never been measured with controls. We introduce LADD (Least-Action Developmental Dynamics), a measurement framework that learns a stochastic developmental vector field from time-series single-cell RNA-seq and computes minimum-action and minimum-time paths, together with a three-layer calibration protocol that separates genuine path deviation from the generic cost of centroid measurement, and we compare its forecasting component with optimal-transport and flow-matching methods. In the lineage-resolved Caenorhabditis elegans atlas, the raw action ratio of observed lineage-centroid trajectories to optimal paths is 3.79, yet forward-simulated ensembles of the learned model itself score 2.07, leaving a genuine excess of about two-fold. In zebrafish (Danio rerio), the observed ratio sits entirely at the model's floor. Three mechanisms that could explain the residual deviation (detours, flow-opposition, and fate-map complexity) are each excluded; what remains is speed, with lineages moving 30-43% faster along the learned flow. We report validity boundaries for temporal resolution, cross-species comparison, and energetic interpretation, delimiting where action-based trajectory comparisons are meaningful.

systems biology↗

Choice of annotation data significantly impacts automated reconstruction of genome-scale metabolic networks

Genome-scale metabolic models are valuable tools for studying metabolism in many applications, such as metabolic engineering or understanding human disease. However, curated models are available for only a limited number of organisms, and generating high-quality models for additional organisms remains a challenge. To help address this challenge, several software tools have been developed that can produce draft models in an automated fashion, but the quality of these draft models lags behind manually curated ones. Thus, there is still a need to improve these tools. Previous work has focused primarily on developing better methods for each step in the reconstruction process, such as gene annotation and gap-filling. Here, we focus on the data that underlies these methods, such as known connections between protein sequence and function. We find that changing the source of reconstruction data has a substantial impact on the contents and predictions of generated models. In fact, the source of data can have a bigger impact than the choice of reconstruction method. Additionally, we show that the reconstruction process is sensitive to the accuracy of gene annotations in the reconstruction data. Finally, we demonstrate the importance of having functional annotation data from an organism that is closely related to the one for which a model is being built. These observations highlight the importance of reconstruction data and identify principles that should be considered when selecting data for reconstruction tools.

systems biology↗