Efficient parameter estimation for spatio-temporal models of pattern formation: case study ofDrosophila melanogaster

Abstract

We show that parameter estimation for pattern formation models can be efficiently performed using an evolution strategy (ES). As a case study we use a quantitative spatio-temporal model of the regulatory network for early development in Drosophila melanogaster. In order to estimate the parameters, the simulated results are compared to a time series of gene products involved in the network obtained with immunohistochemistry. We demonstrate that a (mu,lambda)-ES can be used to find good quality solutions in the parameter estimation. We also show that an ES with multiple populations is 5-140 times as fast as parallel simulated annealing for this case study, and that combining ES with a local search results in an efficient parameter estimation method.

Spatial gradients of protein-level time delays set the pace of the traveling segmentation clock waves

“…In the posterior PSM simulations, we employed a global parameter estimation algorithm called stochastic ranking evolutionary strategy (SRES) to identify the parameter sets that give the best model fitness to experimental data in wild type and her1 −/− , her7 −/− , hes6 −/− , her7 −/− ;hes6 −/− and notch1a −/− mutants (supplementary methods). The SRES method creates superior results in large-scale biological systems (Fakhouri et al, 2010;Fomekong-Nanfack et al, 2007;Moles et al, 2003).…”

A Hierarchical Gene Regulatory Network for Adaptive Multirobot Pattern Formation

“…To understand biological development, a large number of GRN models have been suggested [10] either for reconstructing developmental subnetworks based on biological data [18], [29], [57], or for simulating biological development in computational environments [26], [60] for solving engineering problems, such as structural design [15], [61], electronic circuits design [70], control [55], [63] and self-configuration of modular robots [49], [50]. Furthermore, computational GRN models have been used for analyzing fundamental properties of GRNs such as robustness and evolvabilily [8], [33], and for synthesizing typical regulatory dynamics [19], [31].…”

“…Since we are considering pattern generation for entrapping multiple targets, the formulated pattern, to which the robots will converge, should neither be too far away from (may not be able to trap the targets), nor too close to the targets (the targets may pose danger to the robots if they are too close to the targets). Therefore, the fitness function is defined as follows: (18) where d 0 is set to 1, sig() is a sigmoid function as defined in Eqn. (6).…”

Stages of Gene Regulatory Network Inference: the Evolutionary Algorithm Role

“…However, this method was only applied to synthetic data for a very small network (2 genes). Another more recent application of a classic evolutionary algorithm is that of Fomekong-Nanfack et al (2007). This employs an evolutionary strategy to optimise model parameters for a 6-gene developmental network for Drosophila Melanogaster, based on partial differential equations, (reaction-diffusion model, Section 2.2.1).…”

“…Evolutionary algorithms have the advantage of being intrinsically parallel, facilitating efficient multi-threading of the optimisation process. Several examples of parallel implementations exist in evolutionary methods for GRN modelling, (Daisuke & Horton, 2006;Fomekong-Nanfack et al, 2007;Imade et al, 2004;2003;Spieth, Streichert, Speer & Zell, 2005a). These correspond to both grid and cluster systems, while parallel frameworks for analysis have been implemented and are publicly available (Spieth et al, 2006;Swain et al, 2005).…”