Abstract
Mathematical models that combine predictive accuracy with explanatory power are central to the progress of systems and synthetic biology, but the heterogeneity and incompleteness of biological data impede our ability to construct such models. Furthermore, the robustness displayed by many biological systems means that they have the flexibility to operate under a range of physiological conditions and this is difficult for many modeling formalisms to handle. Flexible nets (FNs) address these challenges and represent a paradigm shift in model-based analysis of biological systems. FNs can: (i) handle uncertainties, ranges and missing information in concentrations, stoichiometry, network topology, and transition rates without having to resort to statistical approaches; (ii) accommodate different types of data in a unified model that integrates various cellular mechanisms; and (iii) be employed for system optimization and model predictive control. We present FNs and illustrate their capabilities by modeling a well-established system, the dynamics of glucose consumption by a microbial population. We further demonstrate the ability of FNs to take control actions in response to genetic or metabolic perturbations. Having bench-marked the system, we then construct the first quantitative model for Wilson disease—a rare genetic disorder that impairs copper utilization in the liver. We used this model to investigate the feasibility of using vitamin E supplementation therapy for symptomatic improvement. Our results indicate that hepatocytic inflammation caused by copper accumulation was not aggravated by limitations on endogenous antioxidant supplies, which means that treating patients with antioxidants is unlikely to be effective.
Highlights
In silico mathematical models are valuable tools in biological research since they can deepen our understanding of biological systems, especially when data availability is a limiting factor, and reduce the time and costs associated with experiments through predicting their outcomes
We have developed and implemented Flexible nets (FNs), as a formal framework for the modeling, analysis, and control of complex dynamic systems
FNs were inspired by Petri nets and are useful for intuitively modeling the relationships between the state of the system and the processes altering it
Summary
In silico mathematical models are valuable tools in biological research since they can deepen our understanding of biological systems, especially when data availability is a limiting factor, and reduce the time and costs associated with experiments through predicting their outcomes. In order for the model to correctly the extent of accumulation of copper in represent yeast physiology, we expect the glucose-equivalent the liver is generally accepted as a clinical diagnostic measure, maintenance requirement, which is independent of the specific follow-up liver biopsies to monitor whether treatment results in growth rate, and of the availability of nutrient and reduced copper levels are not commonly performed. We observed that proportional activities (compared to wild type) above 0.7 did not cause any accumulation of copper in the liver with the given constraints and the adopted objective This was in line with earlier reports on the genotype–phenotype relationships in Wilson disease investigating the loss of ATP7b activity in mutants having both a pathogenic or a neutral phenotype where any mutant with a loss in enzyme activity less than 30% maintained normal copper transport capability[33] and was considered neutral in its phenotypic effect. This suggests dietary supplementation with antioxidants is unlikely to provide any additional benefits to the established two-phase therapy
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