Latent forces for partial differential equations applied to mrna concentration inference in drosophila melanogaster early development

Modelling transcriptional regulation provides amazing challenges that encourage the convergence between mathematics, physics, chemistry, biology, medical care, electronics instrumentation and computer science. One of the most challenging features that modelling transcriptional regulation provides is to establish how protein expression levels and messenger ribonucleic acids (mRNA) expression levels interact to provide a robust process that ensures function within a living cell. In the work presented in this dissertation, the Bicoid protein expression level and the Bicoid mRNA expression level are described using a reaction-di usion PDE (Partial Di erential Equation) based mechanistic model integrated with protein expression data available from FlyEx database using Gaussian processes. The problem reported in this document consists in inferring the mRNA expression level using available data from protein expression pro les (Temporal Pro les), speci cally from Bicoid protein. This work presents a methodology based on Gaussian processes regression models e ectively combined with mechanistic models based on partial di erential equations. Assuming that the mRNA expression levels and the protein expression levels are jointly gaussian and that both are related through a partial di erential equation, given data from the protein expression pro les, inference can be made upon the mRNA expression level by estimating the parameters of the posterior Gaussian process distribution. In addition to this, in available literature, the problem reported in this document was approached using ordinary di erential equations and discretized partial di erential equations. The novel methodology proposed, deals with the problem using the complete solution for a partial di erential equation based on Green and Heaviside boundary functions, hence considering the propagation of the excitation in the spatio-temporal domain

Dissecting the sharp response of a canonical developmental enhancer reveals multiple sources of cooperativity.

Developmental enhancers integrate graded concentrations of transcription factors (TFs) to create sharp gene expression boundaries. Here we examine the hunchback P2 (HbP2) enhancer which drives a sharp expression pattern in the Drosophila blastoderm embryo in response to the transcriptional activator Bicoid (Bcd). We systematically interrogate cis and trans factors that influence the shape and position of expression driven by HbP2, and find that the prevailing model, based on pairwise cooperative binding of Bcd to HbP2 is not adequate. We demonstrate that other proteins, such as pioneer factors, Mediator and histone modifiers influence the shape and position of the HbP2 expression pattern. Comparing our results to theory reveals how higher-order cooperativity and energy expenditure impact boundary location and sharpness. Our results emphasize that the bacterial view of transcription regulation, where pairwise interactions between regulatory proteins dominate, must be reexamined in animals, where multiple molecular mechanisms collaborate to shape the gene regulatory function

The Formation of the Bicoid Morphogen Gradient Requires Protein Movement from Anteriorly Localized mRNA

New quantitative data show that the Bicoid morphogen gradient is generated from a dynamic localized source and that protein gradient formation requires protein movement along the anterior-posterior axis

Dynamic multifactor hubs interact transiently with sites of active transcription in Drosophila embryos.

The regulation of transcription requires the coordination of numerous activities on DNA, yet how transcription factors mediate these activities remains poorly understood. Here, we use lattice light-sheet microscopy to integrate single-molecule and high-speed 4D imaging in developing Drosophila embryos to study the nuclear organization and interactions of the key transcription factors Zelda and Bicoid. In contrast to previous studies suggesting stable, cooperative binding, we show that both factors interact with DNA with surprisingly high off-rates. We find that both factors form dynamic subnuclear hubs, and that Bicoid binding is enriched within Zelda hubs. Remarkably, these hubs are both short lived and interact only transiently with sites of active Bicoid-dependent transcription. Based on our observations, we hypothesize that, beyond simply forming bridges between DNA and the transcription machinery, transcription factors can organize other proteins into hubs that transiently drive multiple activities at their gene targets.Editorial noteThis article has been through an editorial process in which the authors decide how to respond to the issues raised during peer review. The Reviewing Editor's assessment is that all the issues have been addressed (see decision letter)

Physically-inspired Gaussian process models for post-transcriptional regulation in Drosophila

The regulatory process of Drosophila is thoroughly studied for understanding a great variety of biological principles. While pattern-forming gene networks are analysed in the transcription step, post-transcriptional events (e.g. translation, protein processing) play an important role in establishing protein expression patterns and levels. Since the post-transcriptional regulation of Drosophila depends on spatiotemporal interactions between mRNAs and gap proteins, proper physically-inspired stochastic models are required to study the link between both quantities. Previous research attempts have shown that using Gaussian processes (GPs) and differential equations lead to promising predictions when analysing regulatory networks. Here we aim at further investigating two types of physically-inspired GP models based on a reaction-diffusion equation where the main difference lies in where the prior is placed. While one of them has been studied previously using protein data only, the other is novel and yields a simple approach requiring only the differentiation of kernel functions. In contrast to other stochastic frameworks, discretising the spatial space is not required here. Both GP models are tested under different conditions depending on the availability of gap gene mRNA expression data. Finally, their performances are assessed on a high-resolution dataset describing the blastoderm stage of the early embryo of Drosophila melanogaster

Bicoid gradient formation mechanism and dynamics revealed by protein lifetime analysis

Embryogenesis relies on instructions provided by spatially organized signaling molecules known as morphogens. Understanding the principles behind morphogen distribution and how cells interpret locally this information remains a major challenge in developmental biology. Here, we introduce morphogen‐age measurements as a novel approach to test models of morphogen gradient formation. Using a tandem fluorescent timer as a protein age sensor, we find a gradient of increasing age of Bicoid along the anterior–posterior axis in the early Drosophila embryo. Quantitative analysis of the protein age distribution across the embryo reveals that the synthesis–diffusion–degradation model is the most likely model underlying Bicoid gradient formation, and rules out other hypotheses for gradient formation. Moreover, we show that the timer can detect transitions in the dynamics associated with syncytial cellularization. Our results provide new insight into Bicoid gradient formation and demonstrate how morphogen‐age information can complement knowledge about movement, abundance, and distribution, which should be widely applicable to other systems

Efficient reverse-engineering of a developmental gene regulatory network

This is the final version of the article. Available from the publisher via the DOI in this record.Understanding the complex regulatory networks underlying development and evolution of multi-cellular organisms is a major problem in biology. Computational models can be used as tools to extract the regulatory structure and dynamics of such networks from gene expression data. This approach is called reverse engineering. It has been successfully applied to many gene networks in various biological systems. However, to reconstitute the structure and non-linear dynamics of a developmental gene network in its spatial context remains a considerable challenge. Here, we address this challenge using a case study: the gap gene network involved in segment determination during early development of Drosophila melanogaster. A major problem for reverse-engineering pattern-forming networks is the significant amount of time and effort required to acquire and quantify spatial gene expression data. We have developed a simplified data processing pipeline that considerably increases the throughput of the method, but results in data of reduced accuracy compared to those previously used for gap gene network inference. We demonstrate that we can infer the correct network structure using our reduced data set, and investigate minimal data requirements for successful reverse engineering. Our results show that timing and position of expression domain boundaries are the crucial features for determining regulatory network structure from data, while it is less important to precisely measure expression levels. Based on this, we define minimal data requirements for gap gene network inference. Our results demonstrate the feasibility of reverse-engineering with much reduced experimental effort. This enables more widespread use of the method in different developmental contexts and organisms. Such systematic application of data-driven models to real-world networks has enormous potential. Only the quantitative investigation of a large number of developmental gene regulatory networks will allow us to discover whether there are rules or regularities governing development and evolution of complex multi-cellular organisms.Funding: The laboratory of Johannes Jaeger and this study in particular was funded by the MEC-EMBL agreement for the EMBL/CRG Research Unit in Systems Biology, by Grant 153 (MOPDEV) of the ERANet: ComplexityNET program, by SGR Grant 406 from the Catalan funding agency AGAUR, by grant BFU2009-10184 from the Spanish Ministry of Science, and by European Commission grant FP7-KBBE-2011-5/289434 (BioPreDyn). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Inference of RNA Polymerase II Transcription Dynamics from Chromatin Immunoprecipitation Time Course Data

Gene transcription mediated by RNA polymerase II (pol-II) is a key step in gene expression. The dynamics of pol-II moving along the transcribed region influence the rate and timing of gene expression. In this work, we present a probabilistic model of transcription dynamics which is fitted to pol-II occupancy time course data measured using ChIP-Seq. The model can be used to estimate transcription speed and to infer the temporal pol-II activity profile at the gene promoter. Model parameters are estimated using either maximum likelihood estimation or via Bayesian inference using Markov chain Monte Carlo sampling. The Bayesian approach provides confidence intervals for parameter estimates and allows the use of priors that capture domain knowledge, e.g. the expected range of transcription speeds, based on previous experiments. The model describes the movement of pol-II down the gene body and can be used to identify the time of induction for transcriptionally engaged genes. By clustering the inferred promoter activity time profiles, we are able to determine which genes respond quickly to stimuli and group genes that share activity profiles and may therefore be co-regulated. We apply our methodology to biological data obtained using ChIP-seq to measure pol-II occupancy genome-wide when MCF-7 human breast cancer cells are treated with estradiol (E2). The transcription speeds we obtain agree with those obtained previously for smaller numbers of genes with the advantage that our approach can be applied genome-wide. We validate the biological significance of the pol-II promoter activity clusters by investigating cluster-specific transcription factor binding patterns and determining canonical pathway enrichment. We find that rapidly induced genes are enriched for both estrogen receptor alpha (ER) and FOXA1 binding in their proximal promoter regions.Peer reviewe