Validation of a morphogenesis Model of Drosophila Early Development by a Multi-objective evolutionary Optimization Algorithm

Abstract

We apply evolutionary computation to calibrate the parameters of a morphogenesis model of Drosophila early development. The model aims to describe the establishment of the steady gradients of Bicoid and Caudal proteins along the antero-posterior axis of the embryo of Drosophila. The model equations consist of a system of non-linear parabolic partial differential equations with initial and zero flux boundary conditions. We compare the results of single- and multi-objective variants of the CMA-ES algorithm for the model the calibration with the experimental data. Whereas the multiobjective algorithm computes a full approximation of the Pareto front, repeated runs of the single-objective algorithm give solutions that dominate (in the Pareto sense) the results of the multi-objective approach. We retain as best solutions those found by the latter technique. From the biological point of view, all such solutions are all equally acceptable, and for our test cases, the relative error between the experimental data and validated model solutions on the Pareto front are in the range 3% − 6%. This technique is general and can be used as a generic tool for parameter calibration problems.