Modeling of free fatty acid dynamics: insulin and nicotinic acid resistance under acute and chronic treatments

Abstract

Nicotinic acid (NiAc) is a potent inhibitor of adipose tissue lipolysis. Acute administration results in a rapid reduction of plasma free fatty acid (FFA) concentrations. Sustained NiAc exposure is associated with tolerance development (drug resistance) and complete adaptation (FFA returning to pretreatment levels). We conducted a meta-analysis on a rich pre-clinical data set of the NiAc-FFA interaction to establish the acute and chronic exposure-response relations from a macro perspective. The data were analyzed using a nonlinear mixed-effects framework. We also developed a new turnover model that describes the adaptation seen in plasma FFA concentrations in lean Sprague-Dawley and obese Zucker rats following acute and chronic NiAc exposure. The adaptive mechanisms within the system were described using integral control systems and dynamic efficacies in the traditional [Formula: see text] model. Insulin was incorporated in parallel with NiAc as the main endogenous co-variate of FFA dynamics. The model captured profound insulin resistance and complete drug resistance in obese rats. The efficacy of NiAc as an inhibitor of FFA release went from 1 to approximately 0 during sustained exposure in obese rats. The potency of NiAc as an inhibitor of insulin and of FFA release was estimated to be 0.338 and 0.436 [Formula: see text], respectively, in obese rats. A range of dosing regimens was analyzed and predictions made for optimizing NiAc delivery to minimize FFA exposure. Given the exposure levels of the experiments, the importance of washout periods in-between NiAc infusions was illustrated. The washout periods should be [Formula: see text]2 h longer than the infusions in order to optimize 24 h lowering of FFA in rats. However, the predicted concentration-response relationships suggests that higher AUC reductions might be attained at lower NiAc exposures.

Keywords: Disease modeling; Dosing regimen; Meta-analysis; Nonlinear mixed-effects (NLME); Tolerance; Turnover models.

Fig. 1

Schematic illustration of how the dependency between NiAc and FFA has been modeled in previous studies (a) and how the dependencies between NiAc, insulin, and FFA were modeled in this study (b). Solid lines represent fluxes while dashed lines represent control. NiAc inhibits the turnover of insulin (1). Insulin, in turn, has feedback mechanisms that inhibits its turnover (2) and stimulates its fractional turnover (3). Both NiAc (4) and insulin (5) inhibit the turnover of FFA. In this study, FFA has a single feedback mechanism which inhibits its turnover (6), while in previous studies, FFA was modeled using an additional feedback mechanism which stimulates its fractional turnover (7)

Fig. 2

NiAc disposition models for lean Sprague-Dawley (a) and obese Zucker rats (b). NiAc is either infused directly into the central compartment (intravenous administration) or absorbed via a subcutaneous compartment (subcutaneous administration via an implanted mini-pump)

Fig. 3

Exploration of insulin-time course data for acute NiAc dosing (a) and (c), and chronic NiAc dosing (continuous infusion) (b) and (d) for lean and obese rats, respectively. The data is presented as the mean response ± the standard error of the mean. The blue lines represent the NiAc treated animals, the red lines vehicle control group, and the thick black line represent the NiAc infusion period (Color figure online)

Fig. 4

Mechanisms of insulin dynamics. The parameters $k_{\text{inI}}$ and $k_{\text{outI}}$ represent the turnover rate and fractional turnover rate, respectively. The turnover of insulin is inhibited by the NiAc action function $H_{\text{NI}}(C_{\text{p}})$. Tolerance and rebound is captured by the moderator compartments $M_{\text{1I}}$ and $M_{\text{2I}}$, which act on the turnover rate and fractional turnover rate of insulin, respectively. The regulator $R_{\text{I}}$, representing an integral feedback controller, acts on the turnover rate of insulin, in that it strives to maintain insulin baseline, $I_0$, despite persistent external effects on the turnover

Fig. 5

Mechanisms of FFA dynamics. The parameters $k_{\text{inF}}$ and $k_{\text{outF}}$ represent the turnover rate and fractional turnover, respectively. The turnover of FFA is inhibited by the NiAc action function $H_{\text{NF}}(C_{\text{p}})$. Tolerance and rebound are captured by the moderator compartment $M_{\text{F}}$, which acts on the turnover rate of FFA. The regulator compartment R acts on the turnover rate of FFA and the fractional turnover rate of R is affected by insulin

Fig. 6

Exploration of FFA-time course data for acute NiAc dosing (a) and (c), and chronic NiAc dosing (continuous infusion) (b) and (d) for lean and obese rats, respectively. The data is presented as the mean response ± the standard error of the mean. The blue lines represent the NiAc treated animals, the red lines vehicle control group, and the thick black line represent the NiAc infusion period (Color figure online)

Fig. 7

Visual predictive checks for lean Sprague-Dawley rats. The first column shows the PK fit, the second column the insulin, and the third column the FFA. The rows represent the different protocols of NiAc (as described in the Experimental protocols section). The dots represent the data, with colors indicating separate individuals, the black line the estimated median individual, and the grey area the 90% population prediction interval

Fig. 8

Visual predictive checks for obese Zucker rats. The first column shows the PK fit, the second column the insulin, and the third column the FFA. The rows represent the different protocols of NiAc (as described in the Experimental protocols section). The dots represent the data, with colors indicating separate individuals, the black line the estimated median individual, and the grey area the 90% population prediction interval. No exposure data were available from the Cont. protocol (g).

Fig. 9

Model simulations of acute and chronic action of NiAc exposure $H_{\text{NF}}$ (a), insulin-driven integral control (b), and moderator feedback (c) on the FFA turnover. Acute and chronic FFA response (d). Red lines show lean rats and black lines obese rats. The dashed lines show the baseline FFA response (Color figure online)

Fig. 10

Model predicted reduction in FFA exposure in a median obese rat at steady-state (i.e., after multiple dosing). (a) illustrates the predicted average reduction in 24 h FFA area under the curve and (b) illustrates the proportional reduction, in comparison to the baseline level. The predictions are made for a range of infusion protocols with 0.25–12 h of NiAc exposure followed by 0–12 h washout period. The x-axis represents the infusion time and the y-axis represents the washout time. The model predicts an optimal infusion regimen of $\sim$2-h longer washout period than the infusion. The maximal AUC reduction is 5.60 mM h

Fig. 11

Predicted steady-state concentration-response (left-hand y-axis) and concentration-action (right-hand y-axis) relationships for obese rats. The black line represents the FFA response, the blue line the inhibitory action of NiAc on FFA turnover, the red line the insulin action on FFA turnover, and the purple line the moderator action on the FFA turnover. The $I{C}_{\text{50F}}$ and the $N_{\text{50F}}$ concentrations are given by the black vertical lines (Color figure online)