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  • In this study we explore different mathematical models for


    In this study, we explore different mathematical models for describing the IVIVC of a preclinical dataset of 12 different dual GPR109A/GPR81 agonists. The objective is to establish a predictive model of in vivo lipolysis suppression in the rat based on in vitro potency data. First, a nonlinear mixed effects pharmacokinetic and pharmacodynamic (PKPD) model was applied to a longitudinal data set of rat in vivo lipolysis (Fig. 2, path 1). From that model, in vivo EC50 values of NEFA inhibition were derived. These estimates subsequently served as the targets for a number of different in vitro-in vivo prediction models. Either primary adipocyte lipolysis potency data (Fig. 2, path 2), or in vitro cell assay potency data for GPR81 (Fig. 2, path 3) or GPR109A (Fig. 2, path 4) were used to fit simple linear regression models of in vivo EC50. The in vitro potency data were acquired from overexpressing cell systems, i.e., ace inhibitor that artificially express high levels of either GPR81 or GPR109A. The assay works by measuring decreases in cAMP, which occurs when GPR81 or GPR109A become activated and inhibits the production of cAMP via their effect on adenylyl cyclase (see Fig. 1). We also compared three simple methods of combining the in vitro cell assay data. Current biological understanding suggests that GPR81 and GPR109A function as metabolic sensors activated by different endogenous mediators, and that activation of either GPR81 or GPR109A is likely sufficient to deactivate the cAMP pathway (Cai et al., 2008, Ahmed, 2011). Based on this, a logical-circuit OR-model was our primary candidate (Fig. 2, path 5a). To challenge this model we also considered a logical-circuit AND-model (Fig. 2, path 5b), and a multivariate linear regression model (Fig. 2, path 5c). We demonstrate that combining the in vitro data from the two cell assays improves prediction of in vivo effects for all three models, to the same level or better than using primary adipocyte data. Among these models the OR-model is most suitable for future in vitro screening due to its mechanistically inspired structure. Not only does this model provide adequate predictions of in vivo EC50 but it also predicts the potential for a compound to selectively target GPR81. Finally, as an illustration of how to apply the OR-model in practice, we used it to predict in vivo potencies for 1651 other compounds whose potencies so far only have been determined in the two in vitro cell assays.
    Conclusion The in vivo pEC50 for NEFA release in the rat was derived for 12 GPR81/GPR109A agonists, including the historically well-known nicotinic acid. By integrating in vitro cell assay potency data for both receptors, these in vivo pEC50 values could be reasonably well predicted by a simple mathematical model. The prediction precision was higher compared to an alternative set of predictions based on data from rat primary adipocytes, which are comparatively more demanding to generate. Moreover, the model also enabled predictions of the in ace inhibitor vivo selectivity between the receptors. These findings suggest that compound screening should be supported by predictive in vitro-in vivo models and that this approach is expected to reduce animal use and experimental cost, and therefore allows faster and leaner drug discovery. The following are the supplementary data related to this article.
    Introduction During bone development and bone remodeling process, osteoblast differentiation is tightly regulated for its specific metabolic needs [1]. Recently, it has been shown that mature calvarial osteoblastic cells relied more on aerobic glycolysis than oxidative phosphorylation during differentiation process [2,3]. In hypoxic bone marrow environment, the direct activation of glycolysis via the expression of oxygen-stable form of hypoxia inducible factor 1α (Hif-1α) or by deleting von Hippel-Lindau (VHL) stimulates bone formation [4,5]. Multiple bone inducing factors, as WNT proteins and PTH, stimulate aerobic glycolysis to control osteoblast differentiation [2,6]. WNT3A promotes osteoblast differentiation and bone formation through activating glycolysis via a LRP5 dependent but β-Catenin independent signaling [6]. PTH stimulates aerobic glycolysis via Igf-mTORC2 signaling in cultures of osteoblast-lineage cells that contributes to bone anabolism effect of PTH [2].