• beta2-Microglobulin
• Molecular Dynamics
• Coarse grained
• well-tempered metadynamics
• cPCA analysis

β2-Microglobulin (β2m) is a globular protein that in specific environmental conditions (presence of copper ions or seeds, low pH value, mutations) self-associates into insoluble fibrillar amyloid structures, which tend to deposit in tissues and joints. The consequence is a serious diseases, the so-called dyalisis related amyloidosis (DRA), typical in patients with longstanding uremia and hemodialysis treatment. Besides its medical importance, β2m is also interesting as a model system. In fact, several degenerative diseases (e.g. Alzheimer’s) are associated with the conversion of native proteins into amyloidogenic forms, and in the last two decades, β2m has been considered prototypical for studies on these systems.
The systemic deposition of β2m fibrils has been ascribed to several factors, but the mechanism responsible for the formation of the amyloid fibrils is still unclear. The full elucidation of the aggregation process requires the identification of all the conformational states and oligomeric structures (molecular complex of few monomers) adopted by the protein. This is due to the nature of the process, which may be described as a dynamic equilibrium between diverse structural species.
Data on some of the different structural states of β2m are available from X-Ray crystallography and NMR spectroscopy. These have been complemented by a number of atomistic classical molecular dynamics (MD) study, aimed at elucidating the details of structure and internal dynamics, the determinants of the structural transitions and hints about the aggregation. However, both the structural transitions and aggregation processes are very slow compared to the time-scales that can be reached in atomistic simulations. This restricts the picture obtained with atomistic MD to a partial view of the whole process.
On the other hand, one could address the system with a low resolution (Coarse Grained, CG) model, allowing easily reaching the sufficient time scales. This achievement is payed with a generic loss in local accuracy, unless particular efforts are put in the parameterization of the model.
In order to be able to address the slow transition dynamics without loosing accuracy, this Thesis reports a multi-scale MD study, combining atomistic with CG simulations performed with a minimalist model (one bead per amino acid). Atomistic simulations are used to explore the local and fast dynamics and to obtain an accurate parameterization of the CG model, which is then used to perform the slow dynamics. The net result is that the large size-time scales can be reached in simulation without loss in accuracy and with very modest computational resources.
The atomistic simulations of this work were performed using a standard empirical force field, whose accuracy has been tested in the course of several decades. Conversely, the available minimalist models are far from a standard. Consequently an important part of this Thesis’s work consisted in optimizing the minimalist force field. This has been done combining data from atomistic simulations with experimental data from different sources. As already mentioned, the net result is a model combining good accuracy with high predictive power, but, yet, extremely simple, and consequently computationally cheap.
The model was then applied to the simulation of the transition pathway from a state close to the native configurations to a fibrillar or amyloidogenic one. This has additionally required including multi-stability in the model. This task was achieved building an interpolated force field using a set of interconnected one-dimensional double-well potentials resulting in a bistable minimalist CG model. Physico-chemical and energetic data are included into the parameterization, providing the model accuracy also in the description of free energy landscape. To the aim of accurately exploring of the free energy landscape, advanced sampling techniques have been applied, including principal component analysis in Cartesian coordinates and well-tempered metadynamics simulations.
The bistable force field, despite its simplicity, is able to describe the transition pathway, well reproducing the free energy difference in the underlying free energy surface. In addition, the simulations analysis reveals specific determinants which are preparatory to the aggregation process. This, indeed, is the most natural direction for future de- velopments of this work. Starting from the results of this Thesis, the simulation of the aggregation process only requires adding inter-monomer interactions, which is costless, because these were already optimized by others. It is to be remarked that, given the very low computational cost of this model, this simulation can be addressed without the recourse to extreme parallelization. Another interesting development is on the pharmacological level: any new insight into the determinants of oligomerization can suggest possible strategies to prevent it. These would require more focused studies, for instance, the identification of a site for a possible aggregation inhibitor drug and its design, which could be performed with standard drug design methodologies.