Article: Non-linear optimisation with constraints for four-parameter logistic model used in cell-based in-vitro assay Journal: International Journal of Data Mining and Bioinformatics (IJDMB) 2021 Vol.25 No.3/4 pp.129 - 144 Abstract: Cell-based in-vitro assays are commonly used to perform chemical toxicity assessments. These assays usually employ a technical replicate to increase the reliability of the experimental data. Realising consistent assessment using the replicates is a key challenge in cell-based in-vitro assays. In this study, a novel constrained non-linear optimisation that estimates the Four-Parameter Logistic (4PL) model is proposed to overcome variability in the replicate measurements. First, the tested substance's toxicity intensities are calculated by comparing its Time-dependent Cellular Response Curves (TCRCs) with the TCRC of the negative control, which evaluates the cell inhibition/death at a particular time point. Next, the variability of each toxicity intensity is set as a discount factor, and a constrained non-linear optimisation is constructed. The Levenberg-Marquardt algorithm is used to obtain the optimal parameters of the 4PL model. Furthermore, a linearised 4PL model is presented to set initialised values for non-linear optimisation. Two case studies are conducted to validate the proposed method. The analysed results confirm that the proposed method achieves consistent results. Inderscience Publishers - linking academia, business and industry through research

Title: Non-linear optimisation with constraints for four-parameter logistic model used in cell-based in-vitro assay

Authors: Shan Chen; Tianhong Pan; Haoran Li

Addresses: School of Electrical and Information Engineering, Jiangsu University, Zhenjiang, Jiangsu 212013, China ' School of Electrical Engineering and Automation, Anhui University, Hefei, Anhui 230601, China ' School of Electrical and Information Engineering, Jiangsu University, Zhenjiang, Jiangsu 212013, China

Abstract: Cell-based in-vitro assays are commonly used to perform chemical toxicity assessments. These assays usually employ a technical replicate to increase the reliability of the experimental data. Realising consistent assessment using the replicates is a key challenge in cell-based in-vitro assays. In this study, a novel constrained non-linear optimisation that estimates the Four-Parameter Logistic (4PL) model is proposed to overcome variability in the replicate measurements. First, the tested substance's toxicity intensities are calculated by comparing its Time-dependent Cellular Response Curves (TCRCs) with the TCRC of the negative control, which evaluates the cell inhibition/death at a particular time point. Next, the variability of each toxicity intensity is set as a discount factor, and a constrained non-linear optimisation is constructed. The Levenberg-Marquardt algorithm is used to obtain the optimal parameters of the 4PL model. Furthermore, a linearised 4PL model is presented to set initialised values for non-linear optimisation. Two case studies are conducted to validate the proposed method. The analysed results confirm that the proposed method achieves consistent results.

Keywords: four-parameter logistic model; cytotoxicity; RTCA; real-time cell analyser; non-linear optimisation.

DOI: 10.1504/IJDMB.2021.122848

International Journal of Data Mining and Bioinformatics, 2021 Vol.25 No.3/4, pp.129 - 144

Accepted: 01 Nov 2021
Published online: 13 May 2022 *

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Title: Non-linear optimisation with constraints for four-parameter logistic model used in cell-based in-vitro assay

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