Model-driven analysis of gene expression control

During this PhD, I worked on three different aspects in the broad field of experimental and theoretical analysis of gene regulation.
The first part, "Quantifying the strength of miRNA-target interactions", addresses the problem of predicting mRNA targets of miRNAs. I show that biochemical measurements of miRNA-mRNA interactions can be used to optimise the parameter inference of a pre-existing model of miRNA target prediction. This model named MIRZA, predicts miRNA-mRNA binding using 25 energy parameters that describe the miRNA-mRNA hybrid structure, with 2 base pairing parameters for the AU and GC pairs, 3 configuration parameters for the symmetric and asymmetric loops, and 21 positional parameters for the 21 nucleotides of the miRNA sequence. MIRZA was built to infer these parameters from Argonaute protein CLIP data, which captures potential targets of miRNAs. Upon the publication of precise measurements of chemical kinetic constants of miRNA-mRNA binding interactions between a mRNA target and a set of systematically mutated miRNA sequences, we reasoned that such data could be used to improve the parameters inference of the MIRZA model. After showing that the prediction of the existing model on the set of measured miRNA-mRNA pairs shows high correlation with the binding energy calculated from the measurements, I used simulations as a proof of principle of the inference procedure and to design measurements that would be needed to infer the parameters of the MIRZA model.
Staying in the field of miRNA, in "Single cell mRNA profiling reveals the hierarchical response of miRNA targets to miRNA induction", I developed an approach to infer miRNA targets based on scRNA-seq data from cells that express the miRNA at different levels. A miRNA can target several hundreds of different mRNAs and is present in the cell in limited quantities, implying that the interaction of a target mRNA with a specific miRNA depends on its concentration and on the interactions of the miRNA with its other targets. In other words, since miRNA binding is exclusive, mRNA targets compete for the same miRNA pool. Therefore, the concentrations of the thereby coupled mRNAs depend not only on the miRNA concentration but also on the concentration of every competing mRNA that is targeted by the same miRNA. To study this, HEK 293 cell lines were constructed to inducibly express a miRNA (hsa-miR-199a) as well as the mRNA encoding a green fluorescent protein. Express from the same promoter as the miRNA, this mRNA allows the monitoring of the miRNA concentration. The study aimed not only to determine the parameters of individual mRNA-mRNA interactions, but also to assess the degree to which mRNAs act in a competitive manner to influence each other's expression. scRNA-seq was chosen to bring the resolution needed to reach these goals. The effect of the miRNA on a bound target is to increase its decay rate, hence the expression levels of the targets depends on the miRNA concentration and their binding energy. To gain insight into the target binding energy, we constructed a model considering mRNA transcription rate, the miRNA-mRNA binding/unbinding rate, the mRNA decay rates in the bound and unbound state, and the free/bound concentration of miRNA. We showed that the model can be factored in terms of the miRNA concentrations in individual cells and the miRNA-mRNA target interaction parameters and we solved the model to obtain estimates of miRNA-mRNA interaction parameters, which we showed explain the mRNA levels in cells more accurately than the sequence-based computationally predicted interaction energies.
Finally, in "Bayesian inference of the gene expression states from single-cell RNA-seq data" I carried out fundamental technical work on the normalisation of count data obtained in scRNA-seq experiments. As introduced above, multiple strategies have been developed with the aim of reducing the high level of noise present on such data, and estimating a 'true' biological state of expression for each gene in each cell. While the project aimed to reconstruct the Waddington landscape of regulator activity based on the single cell gene expression measurements, at the start of the project we realised that there is no satisfactory solution to gene expression normalisation in single cells in the literature. Thus, we tackled this problem with a Bayesian model, considering each gene independently and inferring a posterior probability of gene expression in each cell. Our model assumes a log-normal distribution of gene expression across cells and additional Poisson noise caused by the stochastic process of gene expression and the sampling process introduced by the mRNA capture in experimental protocols. These normalised gene expression values are the basis of a motif-activity response based approach for inferring the activity of TFs and miRNAs in individual cells, and for reconstructing the underlying landscape.
The application of this normalisation algorithm to reconstruct a landscape is presented in the last part, "Realizing Waddington’s metaphor: Inferring regulatory landscapes from single-cell gene expression data". There I present the mathematical principles needed to formally define a landscape following the idea of Waddington from 1957, and I propose two applications of the landscape. First I show that it defines cell types as local minima, and secondly, in the case of cells undergoing differentiation, I show how the landscape can be used to find developmental path and the transcription factors associated with the differentiation process.