Stochastic modelling of dynamical systems in biology

In this thesis two relevant biological problems will be addressed from a statistical modelling perspective. The first regards the study of hematopoiesis, a still not well understood biological process rarely observable in humans due to technical and ethical reasons. Hematopoiesis is responsible for the to production and replenishment of all blood cellular components and occurs throughout the whole life. Improving our knowledge about the dynamics of this process can help scientists and clinicians to understand better the mechanisms behind blood disorders and cancers, refine transplantation protocol, define novel strategies for diseases with unmet clinical need. Exploiting follow-up data collected from three patients recruited in a gene therapy clinical trial for Wiskott-Aldrich syndrome, a rare blood disorder, we are able to track the in vivo evolution and differentiation of several corrected hematopoietic stem cells, for a follow-up period of three years. The second biological investigation lies in the context of neuroscience. We focused our attention on neuron communication at the level of its most elementary operating systems, spontaneous neurotransmitter release occurring at single synapses. Despite the investigative nature of this research, it may be potentially clinically relevant in the future for a better understanding of many neurodegenerative diseases.