Mathematical models of cystic fibrosis as a systemic disease.

Cystic fibrosis (CF) is widely known as a disease of the lung, even though it is in truth a systemic disease, whose symptoms typically manifest in gastrointestinal dysfunction first. CF ultimately impairs not only the pancreas and intestine but also the lungs, gonads, liver, kidneys, bones, and the cardiovascular system. It is caused by one of several mutations in the gene of the epithelial ion channel protein CFTR. Intense research and improved antimicrobial treatments during the past eight decades have steadily increased the predicted life expectancy of a person with CF (pwCF) from a few weeks to over 50 years. Moreover, several drugs ameliorating the sequelae of the disease have become available in recent years, and notable treatments of the root cause of the disease have recently generated substantial improvements in health for some but not all pwCF. Yet, numerous fundamental questions remain unanswered. Complicating CF, for instance in the lung, is the fact that the associated insufficient chloride secretion typically perturbs the electrochemical balance across epithelia and, in the airways, leads to the accumulation of thick, viscous mucus and mucus plaques that cannot be cleared effectively and provide a rich breeding ground for a spectrum of bacterial and fungal communities. The subsequent infections often become chronic and respond poorly to antibiotic treatments, with outcomes sometimes only weakly correlated with the drug susceptibility of the target pathogen. Furthermore, in contrast to rapidly resolved acute infections with a single target pathogen, chronic infections commonly involve multi-species bacterial communities, called "infection microbiomes," that develop their own ecological and evolutionary dynamics. It is presently impossible to devise mathematical models of CF in its entirety, but it is feasible to design models for many of the distinct drivers of the disease. Building upon these growing yet isolated modeling efforts, we discuss in the following the feasibility of a multi-scale modeling framework, known as template-and-anchor modeling, that allows the gradual integration of refined sub-models with different granularity. The article first reviews the most important biomedical aspects of CF and subsequently describes mathematical modeling approaches that already exist or have the potential to deepen our understanding of the multitude aspects of the disease and their interrelationships. The conceptual ideas behind the approaches proposed here do not only pertain to CF but are translatable to other systemic diseases. This article is categorized under: Congenital Diseases > Computational Models.

Mapping the evidence of the effects of environmental factors on the prevalence of antibiotic resistance in the non-built environment: Protocol for a systematic evidence map.

BACKGROUND: Human, animal, and environmental health are increasingly threatened by the emergence and spread of antibiotic resistance. Inappropriate use of antibiotic treatments commonly contributes to this threat, but it is also becoming apparent that multiple, interconnected environmental factors can play a significant role. Thus, a One Health approach is required for a comprehensive understanding of the environmental dimensions of antibiotic resistance and inform science-based decisions and actions. The broad and multidisciplinary nature of the problem poses several open questions drawing upon a wide heterogeneous range of studies. OBJECTIVE: This study seeks to collect and catalogue the evidence of the potential effects of environmental factors on the abundance or detection of antibiotic resistance determinants in the outdoor environment, i.e., antibiotic resistant bacteria and mobile genetic elements carrying antibiotic resistance genes, and the effect on those caused by local environmental conditions of either natural or anthropogenic origin. METHODS: Here, we describe the protocol for a systematic evidence map to address this, which will be performed in adherence to best practice guidelines. We will search the literature from 1990 to present, using the following electronic databases: MEDLINE, Embase, and the Web of Science Core Collection as well as the grey literature. We shall include full-text, scientific articles published in English. Reviewers will work in pairs to screen title, abstract and keywords first and then full-text documents. Data extraction will adhere to a code book purposely designed. Risk of bias assessment will not be conducted as part of this SEM. We will combine tables, graphs, and other suitable visualisation techniques to compile a database i) of studies investigating the factors associated with the prevalence of antibiotic resistance in the environment and ii) map the distribution, network, cross-disciplinarity, impact and trends in the literature.

Discrete Biochemical Systems Theory.

Almost every biomedical systems analysis requires early decisions regarding the choice of the most suitable representations to be used. De facto the most prevalent choice is a system of ordinary differential equations (ODEs). This framework is very popular because it is flexible and fairly easy to use. It is also supported by an enormous array of stand-alone programs for analysis, including many distinct numerical solvers that are implemented in the main programming languages. Having selected ODEs, the modeler must then choose a mathematical format for the equations. This selection is not trivial as nearly unlimited options exist and there is seldom objective guidance. The typical choices include ad hoc representations, default models like mass-action or Lotka-Volterra equations, and generic approximations. Within the realm of approximations, linear models are typically successful for analyses of engineered systems, but they are not as appropriate for biomedical phenomena, which often display nonlinear features such as saturation, threshold effects or limit cycle oscillations, and possibly even chaos. Power-law approximations are simple but overcome these limitations. They are the key ingredient of Biochemical Systems Theory (BST), which uses ODEs exclusively containing power-law representations for all processes within a model. BST models cover a vast repertoire of nonlinear responses and, at the same time, have structural properties that are advantageous for a wide range of analyses. Nonetheless, as all ODE models, the BST approach has limitations. In particular, it is not always straightforward to account for genuine discreteness, time delays, and stochastic processes. As a new option, we therefore propose here an alternative to BST in the form of discrete Biochemical Systems Theory (dBST). dBST models have the same generality and practicality as their BST-ODE counterparts, but they are readily implemented even in situations where ODEs struggle. As a case study, we illustrate dBST applied to the dynamics of the aryl hydrocarbon receptor (AhR), a signal transduction system that simultaneously involves time delays and stochasticity.

Inference of dynamic interaction networks: A comparison between Lotka-Volterra and multivariate autoregressive models.

Networks are ubiquitous throughout biology, spanning the entire range from molecules to food webs and global environmental systems. Yet, despite substantial efforts by the scientific community, the inference of these networks from data still presents a problem that is unsolved in general. One frequent strategy of addressing the structure of networks is the assumption that the interactions among molecular or organismal populations are static and correlative. While often successful, these static methods are no panacea. They usually ignore the asymmetry of relationships between two species and inferences become more challenging if the network nodes represent dynamically changing quantities. Overcoming these challenges, two very different network inference approaches have been proposed in the literature: Lotka-Volterra (LV) models and Multivariate Autoregressive (MAR) models. These models are computational frameworks with different mathematical structures which, nevertheless, have both been proposed for the same purpose of inferring the interactions within coexisting population networks from observed time-series data. Here, we assess these dynamic network inference methods for the first time in a side-by-side comparison, using both synthetically generated and ecological datasets. Multivariate Autoregressive and Lotka-Volterra models are mathematically equivalent at the steady state, but the results of our comparison suggest that Lotka-Volterra models are generally superior in capturing the dynamics of networks with non-linear dynamics, whereas Multivariate Autoregressive models are better suited for analyses of networks of populations with process noise and close-to linear behavior. To the best of our knowledge, this is the first study comparing LV and MAR approaches. Both frameworks are valuable tools that address slightly different aspects of dynamic networks.

ENaC regulation by phospholipids and DGK explained through mathematical modeling.

Cystic fibrosis is a condition caused by mutations in the cystic fibrosis transmembrane conductance regulator (CFTR). It is also thought to increase the activity of epithelial sodium channels (ENaC). The altered function of these ion channels is one of the causes of the thick dehydrated mucus that characterizes the disease and is partially responsible for recurrent pulmonary infections and inflammation events that ultimately destroy the lungs of affected subjects. Phosphoinositides are signaling lipids that regulate numerous cellular processes and membrane proteins, including ENaC. Inhibition of diacylglycerol kinase (DGK), an enzyme of the phosphoinositide pathway, reduces ENaC function. We propose a computational analysis that is based on the combination of two existing mathematical models: one representing the dynamics of phosphoinositides and the other explaining how phosphatidylinositol 4,5-bisphosphate (PI(4,5)P2) influences ENaC activity and, consequently, airway surface liquid. This integrated model permits, for the first time, a detailed assessment of the intricate interactions between DGK and ENaC and is consistent with available literature data. In particular, the computational approach allows comparisons of two competing hypotheses regarding the regulation of ENaC. The results strongly suggest that the regulation of ENaC is primarily exerted through the control of PI(4,5)P2 production by type-I phosphatidylinositol-4-phosphate 5-kinase (PIP5KI), which in turn is controlled by phosphatidic acid (PA), the product of the DGK reaction.

Thickness of the airway surface liquid layer in the lung is affected in cystic fibrosis by compromised synergistic regulation of the ENaC ion channel.

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)P2). 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)P2 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)P2 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)P2 abundance, particularly in CF conditions, which suggests that manipulation of phosphoinositide metabolism may promote therapeutic benefits for CF patients.

A Mathematical Model of the Phosphoinositide Pathway.

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.