Improved parameter estimation and design optimization for In Vitro ligand binding experiments
C. Steven Ernest II(1,2), Andrew Hooker(1) and Mats O. Karlsson(1)
(1) Department of Pharmaceutical Biosciences, Uppsala University, Sweden; (2) Eli Lilly and Company, Indianapolis, IN
Objectives: Previous analyses have demonstrated that simultaneous non-linear regression (SNLR) versus sequential non-linear regression (NLR) provided better approximation to the true values of ligand binding parameter estimates with focus on resolution of two binding sites, relative binding densities, receptor occupancy and number of data points[1]. The aim of this study was to extend this previous work and compare SNLR and NLR with commonly encountered experimental error, specifically residual variability (RUV) of binding measurements, experiment to experiment variability (BEV) and non-specific binding (NSB). Additionally, optimal design of these ligand binding experiments was examined.
Methods: Monte Carlo simulation and estimation were used to evaluate the performance of various NLR and SNLR methods for estimating ligand binding parameters. Data simulation and estimation were performed using FOCE(I) in NONMEM VI. Simulation followed by parameter estimation of ligand binding data was performed for equilibrium, dissociation, association and non-specific binding experiments. Subsequently, these four experimental types were implemented in the optimal design software PopED 2.08 [2] to optimize ligand concentrations and sampling times for SNLR analysis.
Results: Parameter estimation was significantly improved using SNLR compared to NLR when RUV and BEV were varied up to 25%. Evaluation of NSB demonstrated that subtraction of non-specific from total ligand binding data led to highly biased and variable parameter estimates using both NLR and SNLR. However, simultaneous analysis of total binding and NSB data resulted in <5% bias of parameter estimation. In contrast, NLR analysis of NSB and total binding data still lead to highly biased parameter estimates. Optimization of these highly standardized experiments show that the ligand binding experiments can be substantially improved by the use of an optimized design compared to the standard design when using SNLR. These designs resulted in low predicted uncertainty of parameter estimates in most tested cases with a dramatically decreased sampling schedule.
Conclusion: Overall, SNLR provided superior resolution of parameter estimation in both precision and accuracy compared to NLR. In addition, substantial improvement can be made to the design of these experiments enabling a large reduction (>50%) in the samples/ligand concentrations needed to estimate parameters with high certainty.
References: [1] Karlsson M.O. and Neil A. (1988) Estimation of Ligand Binding Parameters by Simultaneous Fitting of Association and Dissociation Data: A Monte Carlo Simulation Study. Mol Pharmacol 35:59-66. [2] PopED, version 2.08 (2008) http://poped.sf.net/.
