Model inputs, parameter derivation, and parameter estimation

The model was run individually for each cat on each study day to predict the steady state of ¹³C under different dietary treatments. Thus, all the constant variables were calculated individually for each cat within each experiment. The following parameters were constants in the model and must be provided by the user: iGa (= 0), iPl (equation 1), iB (equation 2), iCO, PGOG (equation 4), PCOC (= VCO₂), iGa*(= 0), iPl* (equation 12), iBt* (equation 13), iCO* (equation 14), Hot_Prime (equation 17), Hot_Constant (equation 18), k_pb, k_bp, k_pc, and k_co. Gastric emptying delay was set at either 0, 25 or 50 min; depending on the time of appearance of ¹³CO₂ in breath for each cat in each period. The iCO was assumed to be 20,000 µmol, based on the bicarbonate level of 20 mEq/L which is within the reference range for healthy adult cats. The VCO₂ during fasting was collected automatically using Qubit calorimetry software (Customized Gas Exchange System and Software for Animal Respirometry; Qubit Systems Inc., Kingston, ON) for each cat in each study. Preliminary values for each rate constant (e.g., k_pb) were derived algebraically from steady state equations 6, 7, 9, and 11, and were then adjusted within each cat-period to achieve the lowest residual sum of squares between observed and predicted APE_CO2. To predict F¹³CO₂, the fitted model was run to isotopic steady state and background enrichment was subtracted from the predicted ¹³C enrichment (CO*/CO) at steady state and used as APE_CO2 in equation 1.