Stochastic modeling of fluctuations in the NF-kB activity of neoplastic cells

In the last decade there has been a thriving development of quantitative methods in the field of biomedical physics, both in the modeling of biological complex systems and in the statistical analysis of experimental results. In this thesis we examine the effect of a variety of stimuli on the NF-kB activity's oscillation in metastatic colorectal cancer cells using probabilistic models such as the Chemical Master Equation and the Bayesian statistics. After a brief introduction we explain the theoretical foundations of the Master Equation approach and of the Bayesian inference, together with a brief dip in the subject of Hamiltonian Monte Carlo methods. In the continuation we create a solvable model using the Master Equation approach and we gain insights concerning its eigenvalues distribution in the complex plane. We therefore build a Bayesian regression model and we use it to analyze the oscillating autocorrelation function of the previous stochastic model in order to test the capabilities of the statistical model. Finally we analyze the biological data using the previously created and tested statistical model, exploring and commenting the results and outlining further research directions.