Novel computational methods, when coupled with physiologically mechanistic understanding of biological systems, drive the development of improved in silico models that assist scientists and clinicians with disease research and treatment design. One potential area for improved patient care is in treating cystic fibrosis (CF), a genetic disorder characterized by a malfunctioning cystic fibrosis transmembrane conductance regulator (CFTR). The disease causes dehydration of the lung epithelial surface. Primary patient morbidity occurs from this dehydration in the airways, leading to thickened, static mucus, infection, and respiratory failure. Currently, one of the most common treatments for CF is the inhalation of hypertonic saline in order to rehydrate the apical surface liquid (ASL) layer and improve mucociliary clearance (MCC). Accurately characterizing fluid transport and ASL volume regulation will allow insight into the relationship between the introduced treatment and its effects. A deterministic model structure coupled with a sufficient optimization algorithm should provide patient-specific parameters that accurately predict treatment outcomes.
A cell-scale model of an epithelial cell was constructed using the Matlab software suite (© 2015, The MathWorks, Natick, MA). Sixteen ordinary differential equations described the transport dynamics of chloride, sodium, potassium, water, and diethylene triamine pentaacetic acid (DTPA) in the ASL layer, cell interior, and basolateral bath. DTPA is a small, hydrophilic molecule that is radiolabeled and used to measure changes in airway liquid adsorption during functional imaging studies, and in the model it serves as a paracellular marker. A binary switch on CFTR terms differentiated CF (off) and non-CF (on) cells in the model. An affine parallel-tempering Markov-chain Monte Carlo (APT-MCMC) algorithm then fit model parameters to experimental 24-hour DTPA transport and ASL volume data using a least-sum of squares objective function.
Estimated parameter sets characterize cell homeostasis, paracellular DTPA transport, and apical volume regulation under experimental conditions, lending validity to the model structure. CF cells exhibit higher Epithelial Sodium Channel (ENaC) and Calcium-activated Potassium Channel (CaKC) permeabilities but lower transcellular and paracellular hydraulic permeability than non-CF cells. Increased ENaC permeability in CF agrees with existing literature, and it occurs to preserve cell electroneutrality in response to increased chloride retention. However, lower transcellular permeability in CF relative to non-CF contradicts experimental literature. The discrepancy between CF-and non-CF paracellular hydraulic permeability raises the possibility of particular parameters not being identifiable from the existing data in the optimization procedure – a potential structural limitation of the model. The parameter space should therefore be further examined, and properties such as profile likelihood should be assessed to better identify possible model limitations.
Model simulations predict apical volume regulation and DTPA transport in both the CF and non-CF cases after 10 μL apical challenge and apical infusion of approximately 12,000 counts of DTPA. In comparison to experimental data, the sum squared errors (SSE) for CF and non-CF outputs are 1.37 and 7.36, respectively, on the basis of microliters (ASL) and thousands of counts (DTPA). For the non-CF case the model captures the dynamics well, despite experimental uncertainty in ASL volume measurements at some intermediate time points. CF volume and DTPA dynamics were captured well for all timepoints. Additionally, a simulated spike in cell volume in non-CF cells followed by a sharp decrease and leveling occurs due to feedback regulation terms present in the basolateral rectifying channels, as would be expected in an experimental setting.
Overall, DTPA dynamics and ASL volume are well captured by the model. Parameter estimation techniques will be further refined to ensure the reasonableness of ion channel permeabilities. Moreover, additional analysis must be performed to confirm the physiological validity of in vitro data, as well as to correctly characterize potassium transport channels and their effects on overall osmolite balances.
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