Dynamical models for diabetes: insights into insulin resistance and type 1 diabetes

This thesis summarizes my work in systems biology as a PhD student at The Microsoft Research - University of Trento Centre for Computational and Systems Biology (COSBI) and at the University of Trento, department of Mathematics. Systems biology is an interdisciplinary field that aims at integrating biology with computational and mathematical methods to gain a better understanding of biological phenomena [5, 6]. Among these methods, mathematical and dy- namical modeling have driven the discovery of mechanistic insights from the static representations of phenomena, that is, data. As a result, mathematical and dynamical models have now become standard tools to support new discoveries in biology and in public health issues. For example, models assist governments in determining the policies to contain the spreading of the diseases and in decisions such as vaccine purchases [7]. Similarly, complex and accurate models of the cardio-vascular systems guide surgeons during many procedures on pa- tients [8]. Furthermore, dynamical models of signaling cascades help researchers in identifying new potential drug targets and therapies for many diseases [9]. We used these modeling techniques to address biological questions related to diabetes and insulin resistance. Within this framework, this thesis contains two articles I contributed to, that focus on diabetes. These works are published in the journal of Nature Scientific Reports and are included in Chapters 3 and 4. A significant contribution to the development of these models, and models in general, is given by optimization. Optimization is often used in modeling to determine certain unknown values or factors in a way that allow the model to optimally reproduce the experimental data. Moreover, the parameters of a model that correctly describe the undergoing dynamics may be used as diagnostic tools [10–13]. To this end, this thesis contains a methodological appendix that includes a review of optimization algorithms that has been submitted to the journal of Frontiers in Applied Mathematics and Statistics, special topic Optimization. The content of this article is reported in Appendix A.