The conformational and protonation properties of linear polyelectrolytes are studied by means of accurate Statistical Mechanics models and Molecular Dynamics and Monte Carlo Simulations. Statistical Mechanics (SM) is a very useful tool in polymer science, since it allows to connect the polymer chemical structure with physical properties such as gyration radius, end-to-end distance, optical and elastic properties, etc. An intriguing case is weak polyelectrolytes, polymers able to change the charge of its monomers by binding of small ligands (such as protons or metals). In these systems, charge becomes a dynamical property able to adapt to its chemical environment as a function of factors such as pH, ionic concentration or interaction with other charged species, phenomena known as Charge Regulation (CR). Classical SM techniques used in the study of conformational properties of polyelectrolytes do not consider CR. To overcome this limitation, recently a new technique has been developed using Semi-Grand Canonical Monte Carlo (SGCMC) simulation program developed by our research team to study different kind of polyelectrolytes in solution. To familiarize with these systems, the student will use these programs and similar ones, as the ESPResSo package to compare them for cases without intermolecular interactions between polyelectrolytes. Furthermore, the student will generalize the program to include the interaction with other polyelectrolytes and charged nanoparticles. This will allow to study the effect of the charge regulation, pH and ionic strength, in the dynamics and conformational and ionization properties of the polyelectrolytes, IDPs and nanoparticles.