Novel approach to quantitative spatial gene expression uncovers genetic stochasticity in the developing Drosophila eye

Abstract

Robustness in development allows for the accumulation of genetically based variation in expression. However, this variation is usually examined in response to large perturbations, and examination of this variation has been limited to being spatial, or quantitative, but because of technical restrictions not both. Here we bridge these gaps by investigating replicated quantitative spatial gene expression using rigorous statistical models, in different genotypes, sexes, and species (Drosophila melanogaster and D. simulans). Using this type of quantitative approach with molecular developmental data allows for comparison among conditions, such as different genetic backgrounds. We apply this approach to the morphogenetic furrow, a wave of differentiation that patterns the developing eye disc. Within the morphogenetic furrow, we focus on four genes, hairy, atonal, hedgehog, and Delta. Hybridization chain reaction quantitatively measures spatial gene expression, co‐staining for all four genes simultaneously. We find considerable variation in the spatial expression pattern of these genes in the eye between species, genotypes, and sexes. We also find that there has been evolution of the regulatory relationship between these genes, and that their spatial interrelationships have evolved between species. This variation has no phenotypic effect, and could be buffered by network thresholds or compensation from other genes. Both of these mechanisms could potentially be contributing to long term developmental systems drift.

System drift and speciation

“…Is there evidence that this is actually occurring? System drift and network rewiring has been inferred across the tree of life [Wotton et al, 2015, Crombach et al, 2016, Dalal and Johnson, 2017, Johnson, 2017, Ali et al, 2019], and there is often significant regulatory variation segregating within populations. Transcription in hybrids between closely related species with conserved transcriptional patterns can also be divergent [Haerty and Singh, 2006, Maheshwari and Barbash, 2012, Coolon et al, 2014, Michalak and Noor, 2004, Mack and Nachman, 2016], and hybrid incompatibilities have been attributed to cryptic molecular divergence underlying conserved body plans [Gavin-Smyth and Matute, 2013].…”

Solution of Mixed-Integer Optimization Problems in Bioinformatics with Differential Evolution Method

“…R 2 adj = 0.32 RMS = 97.53 where R 2 adj is an adjusted coefficient of determination, HH, DL and ATO are expressions of genes hedgehog, Delta and atonal, respectively. The average accuracy of the obtained non-linear solutions ( R2 adj = 0.25) is slightly better than that of linear regressions ( R2 adj = 0.24) obtained in [111], but the deviation of accuracy is statistically significantly smaller (σ non−lin = 0.03 < 0.10 = σ lin ) according to the F-test (p-value= 8.4 × 10 −11 ). We compared the obtained results with a state-of-the-art method for grammatical evolution implemented in the gramEvol [40] package for R statistical software [107].…”

“…The DEEP method with proposed modifications was used to obtain a non-linear phenomenological model of the expression of atonal gene expression under the control of hedgehog and Delta genes in the developing Drosophila eye, using the grammatical evolution (GE) approach [112]. The quantitative data on gene expression obtained by processing of images of the eye discs were used for model construction [111]. The obtained solutions are highly non-linear, and the adjusted coefficient of determination showed almost the same average accuracy but significantly less deviation than the linear models obtained earlier.…”

“…The fruit fly Drosophila is an ideal model organism for different biological studies. In [111], the robustness in development was investigated using quantitative spatial gene expression in the morphogenetic furrow (MF), a wave of differentiation that patterns the developing eye disc. The MF passes from the posterior to the anterior of the disc over a period of two days (90 min per adjacent row of cells).…”

“…It is known that its expression is under the control of hedgehog and Delta genes. In [111], a regulation was modeled by linear regression function. A more general approach called grammatical evolution (GE) [112] allows the user to determine the analytic form of functional dependence by minimizing the deviation of model solution from data.…”