Phosphoinositides are signalling lipids that constitute a complex network regulating many cellular processes. We propose a computational model that accounts for all species of phosphoinositides in the plasma membrane of mammalian cells. The model replicates the steady-state of the pathway and most known dynamic phenomena. Sensitivity analysis demonstrates model robustness to alterations in the parameters. Model analysis suggest that the greatest contributor to phosphatidylinositol 4,5-biphosphate (PI(4,5)P2) production is a flux representing the direct transformation of PI into PI(4,5)P2, also responsible for the maintenance of this pool when phosphatidylinositol 4-phosphate (PI(4)P) is decreased. PI(5)P is also shown to be a significant source for PI(4,5)P2 production. The model was validated with siRNA screens that knocked down the expression of enzymes in the pathway. The screen monitored the activity of the epithelium sodium channel (ENaC), which is activated by PI(4,5)P2. While the model may deepen our understanding of other physiological processes involving phosphoinositides, we highlight therapeutic effects of ENaC modulation in Cystic Fibrosis (CF). The model suggests control strategies where the activities of the enzyme phosphoinositide 4-phosphate 5-kinase I (PIP5KI) or the PI4K + PIP5KI + DVL protein complex are decreased and cause an efficacious reduction in PI(4,5)P2 levels while avoiding undesirable alterations in other phosphoinositide pools.

The lung epithelium is lined with a layer of airway surface liquid (ASL) that is crucial for healthy lung function. ASL thickness is controlled by two ion channels: epithelium sodium channel (ENaC) and cystic fibrosis (CF) transmembrane conductance regulator (CFTR). Here, we present a minimal mathematical model of ENaC, CFTR and ASL regulation that sheds light on the control of ENaC by the short palate lung and nasal epithelial clone 1 (SPLUNC1) protein and by phosphatidylinositol 4,5-biphosphate (PI(4,5)P 2 ). The model, despite its simplicity, yields a good fit to experimental observations and is an effective tool for exploring the interplay between ENaC, CFTR and ASL. Steady-state data and dynamic information constrain the model's parameters without ambiguities. Testing the hypothesis that PI(4,5)P 2 protects ENaC from ubiquitination suggests that this protection does not improve the model results and that the control of the ENaC opening probability by PI(4,5)P 2 is sufficient to explain all available data. The model analysis further demonstrates that ASL at the steady state is sensitive to small changes in PI(4,5)P 2 abundance, particularly in CF conditions, which suggests that manipulation of phosphoinositide metabolism may promote therapeutic benefits for CF patients.

For close to a century, Lotka-Volterra (LV) models have been used to investigate interactions among populations of different species. For a few species, these investigations are straightforward. However, with the arrival of large and complex microbiomes, unprecedently rich data have become available and await analysis. In particular, these data require us to ask which microbial populations of a mixed community affect other populations, whether these influences are activating or inhibiting and how the interactions change over time. Here we present two new inference strategies for interaction parameters that are based on a new algebraic LV inference (ALVI) method. One strategy uses different survivor profiles of communities grown under similar conditions, while the other pertains to time series data. In addition, we address the question of whether observation data are compliant with the LV structure or require a richer modeling format.

The Lotka-Volterra (LV) model was introduced in the early 20th Century to describe predator-prey systems. Since then, the model has been expanded to capture the dynamics of numerous types of interacting populations and to include the effects of external factors from the environment. Despite many simplifying assumptions, the LV approach has proven to be a very valuable tool for gaining insights into the dynamics of diverse biological interaction systems. In particular, recognizing the critical importance of microbiomes for human and environmental heath, LV systems have become effective tools of analysis and, indeed, the default for quantitatively assessing interactions within these large microbial communities. Here we present an overview of parameter inference methods for LV systems, specifically addressing individuals entering the field of biomathematical modeling, who have a modest background in linear algebra and calculus. The methods include traditional local and global strategies, as well as a recently developed inference method based strictly on linear algebra. We compare the different strategies using both lab-acquired and synthetic time series data. We also address a recent debate within the scientific community of whether it is legitimate to compose large models from information inferred for the dynamics of subpopulations. In addition to parameter estimation methods, the overview includes preparatory aspects of the inference process, including data cleaning, smoothing, and the choice of an adequate loss function. Our comparisons demonstrate that traditional fitting strategies, such as gradient descent optimization and differential evolution, tend to yield low residuals but sometimes overfit noisy data and incur high computation costs. The linear-algebra-based method produces a satisfactory solution much faster, generally without overfitting, but requires the user to estimate slopes from the time series, which can introduce undue error. The results also suggest that composing large models from information regarding sub-models can be problematic. Overall, there is no clear “always-best method” for inferring parameters from data, and prudent combinations may be the best strategy.