Prions are unusual protein assemblies that propagate their conformationally-encoded information in absence of nucleic acids. The first prion identified, the scrapie isoform (PrPSc) of the cellular prion protein (PrPC), caused epidemic and epizootic episodes [1]. Most aggregates of other misfolding-prone proteins are amyloids, often arranged in a Parallel-In-Register-β-Sheet (PIRIBS) [2] or β-solenoid conformations [3]. Similar folding models have also been proposed for PrPSc, although none of these have been confirmed experimentally. Recent cryo-electron microscopy (cryo-EM) and X-ray fiber-diffraction studies provided evidence that PrPSc is structured as a 4-rung β-solenoid (4RβS) [4, 5]. Here, we combined different experimental data and computational techniques to build the first physically-plausible, atomic resolution model of mouse PrPSc, based on the 4RβS architecture. The stability of this new PrPSc model, as assessed by Molecular Dynamics (MD) simulations, was found to be comparable to that of the prion forming domain of Het-s, a naturally-occurring β-solenoid. Importantly, the 4RβS arrangement allowed the first simulation of the sequence of events underlying PrPC conversion into PrPSc. This study provides the most updated, experimentally-driven and physically-coherent model of PrPSc, together with an unprecedented reconstruction of the mechanism underlying the self-catalytic propagation of prions.