Formation and Interpretation of morphogen gradients: Insights from mathematical modeling

Abstract

Patterning of developing tissues by non-uniform distributions of transcription factors is a common strategy used by a large number of multi-cellular organisms. Different levels of a transcription factor activate transcription of different genes and thus lead to expression of distinct combination of genes within sub-domains of the tissue. Depending on the specific genes transcribed, the tissue develops to form different body-parts of the adult organism. The early <italic>Drosophila</italic> embryo is one of the best studied systems for patterning by non-uniform distribution of transcription factors. In this dissertation, different classes of mathematical models have been employed to study the distribution properties and transcriptional activity of the transcription factor - Dorsal (Dl) that patterns the DV axis of the embryonic tissue.

Specifically, we developed a differential-equation based model for nucleo-cytoplasmic shuttling and protein-protein interactions between Dl and its binding partners (Chapter 2). Model parameters were estimated using a global optimization technique (Genetic Algorithm) based on quantitative measurements of Dl protein distribution along the DV axis. The ensemble of estimated parameters was statistically analyzed and experimentally tested to generate predictions for the dynamics of the gradient of Dl. The model predicts that the gradient of Dl maintains a constant shape and increases in amplitude during the last five nuclear division cycles of the syncytial embryo. These dynamics are expected to have a significant influence on the patterning of the embryo.

Further, we developed statistical and thermodynamic models for the interpretation of the Dl gradient. One of the first questions that arises in the study of patterning by transcription factor gradients is the `range' of the input signal; i.e. the part of the tissue where gene expression is regulated by the signal. We developed a computational statistical framework to estimate the range and associated confidence interval for any transcription factor gradient (Chapter 3). The framework was demonstrated on the gradient of Dl and the estimates were validated using multiple measurements of the input signal and its target genes. Finally, we developed a thermodynamic model to gain insights into the mechanism of gene transcription by Dl and its co-factor Zelda. The model describes the different microstates for activation of gene transcription and predicts the spatial profile of gene activation in response to the input factor profiles. Model predictions were tested using measurements for transcription of <italic>short gastrulation</italic>(<italic>sog</italic>) in wild-type and mutant backgrounds. The model also explains the dynamics of the <italic>sog</italic> activation profile during embryogenesis. These statistical and thermodynamic models can be directly applied for other transcription factors in <italic>Drosophila</italic> and can also be readily extended to study patterning in other developing systems.