SOME PHYSICAL APPROACHES TO PROTEIN FOLDING

To understand how a protein folds is a problem which has important biological implications. In this article, we would like to present a physics-oriented point of view, which is twofold. First of all, we introduce simple statistical mechanics models which display, in the thermodynamic limit, folding and related transitions. These models can be divided into (i) crude spin glass-like models (with their Mattis analogs), where one may look for possible correlations between the chain self-interactions and the folded structure, (ii) glass-like models, where one emphasizes the geometrical competition between one- or two-dimensional local order (mimicking alpha helix or beta sheet structures), and the requirement of global compactness. Both models are too simple to predict the spatial organization of a realistic protein, but are useful for the physicist and should have some feedback in other glassy systems (glasses, collapsed polymers,...). These remarks lead us to the second physical approach, namely a new Monte-Carlo method, where one grows the protein atom-by-atom (or residue-by-residue), using a standard form (CHARMM,...) for the total energy. A detailed comparison with other Monte-Carlo schemes, or Molecular Dynamics calculations, is then possible; we will sketch such a comparison for poly-alanines. Our twofold approach illustrates some of the difficulties one encounters in the protein folding problem, in particular those associated with the existence of a large number of metastable states.