Modeling and data analysis of biochemical oscillators using Chemical Master Equation and AI: applications to the NF-kB activity in patient derived xenografts

There are two stages from DNA sequence of a gene to protein: transcription, i.e. the process of making a strand of RNA molecule, and translation, that is the process by which a protein is synthesized from the information contained in a molecule of RNA. In the process of transcription, proteins called “transcription factors” play a central role because they bind to a DNA sequence and help the transcription initiation complex. In this work of thesis, we are particularly interested in modeling the nuclear factor-kappa B (NF-kB) activity which is ubiquitous within cells and its dysfunction leads to chronic diseases, cancers, neurodegenerative diseases and much other. However, we do not start immediately modeling its behavior. In this stochastic context, firstly we aim to deepen into algorithms to solve the Chemical Master Equation (CME) giving an our alternative algorithm called “hybrid” because it combines the Gillespie’s Stochastic Simulation Algorithm (SSA) with the tauleaping algorithm with the aim to improve the algorithm’s speed; secondly we analyse the stochastic simulation results of three basics genetic circuits (the simplest model of gene expression, the autorepressor and the toggle switch); third, we faced the problem of parameters estimation of these simple models using artificial neural networks; finally, aware of what we have learned after all such steps, we provide a very little NF-kB model using the CME. The relevant results are the following: the hybrid algorithm applied to the first genetic model is faster than the SSA in configurations where the number of molecules produced tends to be high; periodicity arises from what we defined as unpredictable (being stochastic processes); neural networks learn to predict the model parameters given the autocorrelation as input but the choice of chemical specie makes the difference; finally, our little NF-kB model shows an oscillating behavior that is similar to the one found by experiments.