Model-Based Quantification of the Systemic Interplay between Glucose and Fatty Acids in the Postprandial State

Abstract

In metabolic diseases such as Type 2 Diabetes and Non-Alcoholic Fatty Liver Disease, the systemic regulation of postprandial metabolite concentrations is disturbed. To understand this dysregulation, a quantitative and temporal understanding of systemic postprandial metabolite handling is needed. Of particular interest is the intertwined regulation of glucose and non-esterified fatty acids (NEFA), due to the association between disturbed NEFA metabolism and insulin resistance. However, postprandial glucose metabolism is characterized by a dynamic interplay of simultaneously responding regulatory mechanisms, which have proven difficult to measure directly. Therefore, we propose a mathematical modelling approach to untangle the systemic interplay between glucose and NEFA in the postprandial period. The developed model integrates data of both the perturbation of glucose metabolism by NEFA as measured under clamp conditions, and postprandial time-series of glucose, insulin, and NEFA. The model can describe independent data not used for fitting, and perturbations of NEFA metabolism result in an increased insulin, but not glucose, response, demonstrating that glucose homeostasis is maintained. Finally, the model is used to show that NEFA may mediate up to 30-45% of the postprandial increase in insulin-dependent glucose uptake at two hours after a glucose meal. In conclusion, the presented model can quantify the systemic interactions of glucose and NEFA in the postprandial state, and may therefore provide a new method to evaluate the disturbance of this interplay in metabolic disease.

Fig 1. Overview.

Overview of the workflow: model (Fig 2), model calibration with clamp simulations (Figs 3 and 4) and oral challenge simulations (Fig 5), comparison of the calibrated model with independent data (Fig 6), analysis of model response to NEFA perturbations (Fig 7), and quantification of NEFA regulation in the meal response (Fig 8).

Fig 2. Mathematical model.

The mathematical model of systemic glucose (left), insulin (middle) and NEFA (right) metabolism consists of a total of 18 differential equations. Glucose concentrations are determined by glucose rate of appearance (Ra), endogenous glucose production (EGP), insulin dependent (U _id) and independent (U _ii) glucose uptake and–if applicable–renal excretion (E). Plasma NEFA dynamics are described in Eqs 3–7. In the model, glucose enters the system via simulated ingestion in Q _sto1, and lipid appearance is simulated by using the measured plasma TG concentration to calculate fatty acid spillover. For full model equations, we refer to S2 File. Matlab implementation and simulation files are provided as S3 File.

Fig 3. Clamp datasets: experimental data and simulation results.

Measurements from D_CLAMP1 (hyperinsulinemic, euglycemic clamp) [32] (A,B, red errorbars) and D_CLAMP2 [33] (C,D, red errorbars) with superimposed model outputs. The simulation represents the parameter set in S_sel that corresponds to a minimal value for V_EGP. A. Mean EGP as measured over the final half of a 360 minute clamp with low, medium and high NEFA concentration. B. Total glucose uptake (conditions and measurement time as in A). C. EGP measured during the final 60 minutes of the 120 minute clamp in experiments of group C that underwent an eu-insulinemic, hyperglycemic clamp with a saline infusion (C-) and with a combined intralipid and heparin infusion (C+). D. Total glucose uptake as in C, for experiments with a hyperinsulinemic euglycemic clamp (group A-, A+), hyperinsulinemic, hyperglycemic clamp (group B-, B+), and an eu-insulinemic, hyperglycemic clamp (group C- and C+). A short summary of the implementation in the model is provided in the Materials and Methods; full details of implementation can be found in S1 File.

Fig 4. Model calibration on clamp data.

To investigate propagation of parameter uncertainty in predictions and analyses a collection of parameter sets was selected. Measurements from D_CLAMP1 (hyperinsulinemic, euglycemic clamp) [32] (A,B, red errorbars) and D_CLAMP2 [33] (C,D, red errorbars) with superimposed model outputs as in Fig 3. Here, simulations representing the complete collection of selected parameter sets (S_sel) are shown, depictured as dots shaded from dark green for poor fits of EGP (high values of V_EGP) to light green for low V_EGP. We note in C, that not all parameter sets from S_sel describe the data, and that a bad correspondence of the simulations in A and C is shown with dark green color.

Fig 5. Model calibration on meal responses.

Data from D_MEAL [48] (red errorbars) and model simulations (S_ext, grey curves; and S_sel, green shading as in Fig 4) in response to an OGTT (A) and an OFTT (B).

Fig 6. Model prediction–NEFA kinetics during a multi-step insulin infusion.

To verify general NEFA kinetics, a multi-step insulin infusion (Campbell et al. [53]) was modelled by fixing glucose (A) and insulin (B) to clamped concentrations. As TG was not measured, it was fixed at 1000 μM. The initial NEFA concentration was fixed at the measured value. (C) Simulated NEFA concentration, S_sel (shades of green, as in Fig 4) and measurements of the independent clamp dataset [53] (red errorbars).

Fig 7. Model analysis–glucose homeostasis.

Perturbations of NEFA metabolism affect the AUC of the glucose, insulin and NEFA responses to the OGTT. A-D. Overview of perturbation strategy. A. Original OGTT response model. B. Perturbed model. C. Perturbation by increasing the initial NEFA concentration (P_bas in the illustration). D. Perturbation by reducing the insulin dependent inhibition of lipolysis (P_lip in the illustration). E-G-I. Relative change in AUC of NEFA (E), glucose (G) and insulin (I) in response to an increase in the initial concentration of NEFA. F-H-J. Relative change in AUC of NEFA (F), glucose (H) and insulin (J) in response to reduced insulin-dependent inhibition of lipolysis. Red markers represent individual simulation results per parameter set; the shaded area (dark red) gives the full range.

Fig 8. Model analysis—contribution of NEFA regulation in the postprandial glucose response.

A. Relative contribution of regulation by the NEFA-regulation term N_d1(t), on U_id during an OGTT, plotted at the time point where the absolute value of the NEFA regulation of U_id is maximal. B. Relative dependence of EGP suppression on the regulation by NEFA, plotted at the time point when the absolute NEFA-induced suppression is maximal. Colors indicate V_EGP (green shading as in Fig 4). The individual results represent the parameter sets in S_sel.