mRNA diffusion explains protein gradients in \textit{Drosophila} early development

TL;DR

This paper introduces a mathematical model where extit{bicoid} mRNA diffusion explains the formation of the protein gradient in extit{Drosophila} early development, aligning well with experimental data and supporting recent findings.

Contribution

The study presents a new diffusion-based model for extit{bicoid} mRNA and protein gradient formation, validated with experimental data and consistent with recent observations.

Findings

Model accurately reproduces protein gradient with 5-8% error

Inferred mRNA diffusion coefficient matches theoretical and experimental values

Supports the hypothesis that mRNA diffusion explains protein gradient formation

Abstract

We propose a new model describing the production and the establishment of the stable gradient of the Bicoid protein along the antero-posterior axis of the embryo of \textit{Drosophila}. In this model, we consider that \textit{bicoid} mRNA diffuses along the antero-posterior axis of the embryo and the protein is produced in the ribosomes localized near the syncytial nuclei. Bicoid protein stays localized near the syncytial nuclei as observed in experiments. We calibrate the parameters of the mathematical model with experimental data taken during the cleavage stages 11 to 14 of the developing embryo of \textit{Drosophila}. We obtain good agreement between the experimental and the model gradients, with relative errors in the range 5-8%. The inferred diffusion coefficient of \textit{bicoid} mRNA is in the range 4.6\times 10^{-12}-1.5\times 10^{-11}m^2s^{-1}, in agreement with the theoretical predictions and experimental measurements for the diffusion of macromolecules in the cytoplasm. We show that the model based on the mRNA diffusion hypothesis is consistent with the known observational data, supporting the recent experimental findings of the gradient of \textit{bicoid} mRNA in \textit{Drosophila} [Spirov et al. (2009) Development 136:605-614].