Calibration and validation of a genetic regulatory network model describing the production of the gap gene protein Hunchback in \emph{Drosophila} early development

TL;DR

This paper presents a calibrated differential equations model of Drosophila gap gene protein Hunchback production, validated with experimental data, and highlights the use of multi-objective optimization for biological network analysis.

Contribution

It introduces a novel calibration and validation approach for a genetic regulatory network model using evolutionary optimization techniques.

Findings

Model accurately predicts Hunchback distribution when regulated by Huckebein.

Multi-objective optimization effectively calibrates biological models.

Validated the genetic regulatory network controlling Hunchback distribution.

Abstract

We fit the parameters of a differential equations model describing the production of gap gene proteins Hunchback and Knirps along the antero-posterior axis of the embryo of \emph{Drosophila}. As initial data for the differential equations model, we take the antero-posterior distribution of the proteins Bicoid, Hunchback and Tailless at the beginning of cleavage cycle 14. We calibrate and validate the model with experimental data using single- and multi-objective evolutionary optimization techniques. In the multi-objective optimization technique, we compute the associated Pareto fronts. We analyze the cross regulation mechanism between the gap-genes protein pair Hunchback-Knirps and we show that the posterior distribution of Hunchback follow the experimental data if Hunchback is negatively regulated by the Huckebein protein. This approach enables to predict the posterior localization on the embryo of the protein Huckebein, and we validate with the experimental data the genetic regulatory network responsible for the antero-posterior distribution of the gap gene protein Hunchback. We discuss the importance of Pareto multi-objective optimization techniques in the calibration and validation of biological models.