Machine learning approaches to modelling bicoid morphogen in Drosophila melanogaster

Abstract

Bicoid morphogen is among the earliest triggers of differential spatial pattern of gene expression and subsequent cell fate determination in the embryonic development of Drosophila melanogaster. This maternally deposited morphogen, diffusing along the anterior-posterior axis of the embryo, establishes a concentration gradient which is sensed by target genes. In most computational model based analyses of this process, the translation of the bicoid mRNA is thought to take place at a fixed rate in the anterior pole of the embryo. Is this process of morphogen generation a passive one as assumed in the modelling literature so far, or would available data support an alternate hypothesis that the stability of the mRNA is regulated by active processes?

This thesis demonstrates a Bicoid spatio-temporal model in which the stability of the maternal mRNA is regulated by being held constant for a length of time, followed by rapid exponential degradation. With the mRNA regulation, three computational models of spatial morphogen propagation along the anterior-posterior axis are analysed:

(a) passive diffusion with a deterministic differential equation, (b) diffusion enhanced by a cytoplasmic flow term and (c) stochastic diffusion modelled by Gillespie simulation.

Comparison of the parameter estimation in these models by matching to the publicly available data, FlyEx, suggests strong support for mRNA regulated stability. With a non-parametric Bayesian setting, we have applied Gaussian process regression to infer the mRNA regulation function as a posterior density. With synthetic data obtained from a linear spatio-temporal dynamical system and the experimental measurements (FlyEx), this approach is capable of inferring the driving input. Apart from confirming the validity of a regulated mRNA source, this work also demonstrates the applicability of a powerful non-parametric model of Gaussian processes in a spatio-temporal inference problem. In line with recent experimental works, we have also analysed this model with a spatial gradient of maternal mRNA, rather than being fixed at the anterior pole. Our final work is to analyse the dynamical topology of the gap gene network, which is the major developmental activity, taking place after the establishment and interpretation.

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Identifiers

ORCID for Mahesan Niranjan: orcid.org/0000-0001-7021-140X

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