Abstract

This work is motivated by protein aggregation phenomena   in neurodegenerative  diseases. A key observation of \textit{in-vitro}   polymerization experiments of prion protein is the large variability   of the so-called 'nucleation time',  which is experimentally defined   as the lag time before the polymerization of proteins trully starts.     In this context, we study a stochastic version of a well-known   nucleation model in physics, namely the Becker-D\”oring model.   In this model, aggregates may increase or decrease their size   one-by-one, by capturing or shedding a single particle. I will   present numerical and analytical investigation of the   nucleation time as a first passage time problem.   I also will present limit theorem techniques to study the link   from the discrete size Becker-D\”oring model to a continuous size version (the Lifshitz-Slyozov model) and (numerically observed) large deviations from the mean-field limit.   Finally, I will present state-of-the art studies of more   general stochastic coagulation-fragmentation models.