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Proteins are one of the two fundamental classes of biomolecules (together with nucleic acids), covering basically all the functional roles in living sys- tems. In the last fifty years, a big effort was devoted to the computer sim- ulation of the dynamics of these systems, in order to get a better insight in their structure and behavior, and to complement the experimental studies. However, the size of the system, time scale reachable in simulations and ac- curacy of the representation are limited by the computer power. Although the Moore law has ensured - up to now - the exponential increase in time of the latter, currently, simulations with atomic accuracy can address a virus size only on very brief time scales, or very limited portion of the cell, while only single proteins can be represented on the macroscopic time scales.
Therefore, in order to study dynamical biological systems, coarse grained models are considered a natural solution to overcome the limits of the atom- istic models. These models represent the system at a lower resolution, re- ducing the number of explicit degrees of freedom of the system and freedom providing a lighter and accelerated dynamics of system. Depending on the level of coarse graining, macroscopic time scales for systems of biologically interesting size can currently be afforded.
The hierarchical organization of the protein structure naturally suggest a possible level of coarse graining, namely that of one interacting center (also called ”bead”) per amino-acid, being the latter the basic chemical unit of a protein. Among ”one-bead-models” the subclass of those with the bead placed over Cα emerges as that better representing the conformation of the backbone and the secondary structures. The class of Cα one bead models, also called ”minimalist”, is the focus of this Thesis work.
In the last decade a number of minimalist models was developed, all rep- resenting the interactions by means of empirical force fields (FF) consisting of a sum of analytical or numerical terms. Different models differ by the num- ber and composition of the FF terms (more or less phisics-chemistry based), and by the parameterization strategy, which can be based over higher level theories (typically atomistic simulations) or on experimental data (i.e. data set of experimental structures, inclusion of other kind of macroscopic and thermodynamic informations). As a consequence, the model can be more or less general and transferable. Usually, accuracy and transferability are in conflict: the more bias towards a given structure is included, the more that structure will be accurately represented, but the less transferable and predictive is the model. In order to overcome this problem, most of the cur- rently available minimalist models include some a priori knowledge of the secondary or tertiary structures within the parameterization, which can be called a ”partial bias”. Clearly, the general goal is to build a model both accurate and predictive, and therefore, unbiased.
This Thesis goal is to make some steps along this route. The chosen strat- egy is to follow a physics based approach, related to the fundamental nature of forces acting within the proteins. Basically, the primary structure of a pro- tein (i.e. sequence and polypeptide chain) is stabilized by covalent chemical bonds, while the secondary structure (e.g. helical or sheet-like structures) is stabilized by specific hydrogen bonds. Higher level structures (tertiary and quaternary) are stabilized by other specific interactions, such as disulphide and salt bridges.
The specific aim of this work is to build a general minimalist model to be used for unstructured proteins. Therefore, no hydrogen bonding or other specific interactions are included in the FF, and the model is parameterized based on a data-set of unstructured proteins. This strategy has resulted in a quite general ad unbiased model able to reproduce the structure and dynam- ics of class proteins, namely the “intrinsically disordered proteins” (IDP), which is very interesting per se. In addition it can be considered as a zero- point approximation over which hydrogen bonding and other interactions can be added in order to build models for structured proteins, in rational and physically-based fashion.
Besides the primary result (i.e. the model for IDPs, description of the dy- namics of some specific cases, etc) this work has returned interesting insight into the whole class of IDPs. First, due to the absence of stable conforma- tion, the structural data on these proteins are very elusive. Therefore already building the dataset was a particularly hard task, which can be considered a side-result of this work and lead to a deep reconsideration of the definition of secondary structure. Second, these proteins elude one of the paradigms of the biomolecular chemistry, namely the relation between structure and function: they do not have a very well defined structure, but they do have a function. Therefore, a reliable model for this class can help re-defining this paradigm, including into it dynamical information. Finally, for the same reason, this model can shed light on the behavior and function of the unstructured inter- mediates of the folding process for structured proteins.