Abstract: The substantial conformational homogeneity of DNA double helix has recently allowed a good progress in the knowledge of the molecular mechanisms which control the functional organization of the genome as well as in the prediction of some biologically relevant structural properties. We developed an analytical method to study the effects of the sequence on modeling the three-dimensional superstructure of DNA based on the theoretically evaluated slight conformational perturbations of the different dinucleotide steps along the sequence. Such a model is capable of predicting in striking agreement with the experimental data: the atomic force microscopy visualization of relevant DNA tracts and in particular the dynamics of a pBR322 plasmide after the mechanical cut of the cycle; the gel electrophoresis anomalies of a very large pull of DNA tracts; the thermodynamic constants of the sequence dependent circularization reactions of many DNAs ranging from 100 to 100000 bp and the sequence dependent writhing transitions from relaxed to supercoiled circular forms also in the presence of DNA binding proteins; and finally, the nucleosome positions and the corresponding thermodynamic stability of more than 50 DNA tracts whose the nucleosome competitive reconstitution experimental data are available. The thermodynamic properties were obtained using an original statistical mechanic approach based on the first order elasticity which allows an analytical solution in Fourier space.

Abstract: The problem of the three-dimensional structure prediction in terms of the amino acid sequence is still an open question in spite of the progress of the conformational analysis and the molecular dynamics as well as of the more accurate knowledge of the force field. Some years ago we proposed a model which addresses the problem of the general trend of protein folding. Such transconformational process involves entangled movements of the polypeptide chain which are however progressively hampered by the growing importance of long range interactions whence only concerted transconformations can take place. We investigated the topological aspects of such constrained transformations and found that they are characterized by the invariance of the linking number of the polypeptide chain fitting ribbon in order to avoid the overcoming of high conformational energy barriers which would severely repress the kinetics of the process; under such a topological constraint the transconformations become highly cooperative. In order to select the topologically invariant pathways we have identified some significant parameters which characterize all the proteins independently of their tertiary structures. One of these is a topological parameter which quantifies the complexity of folding as the number of chain crossing averaged over all the possible projections of the structure. It is easily calculated and shows interesting and useful fractal properties. Using a folding representation as a complex function of the sequence we are at present trying extending to proteins the model we successfully developed to predict the superstructures of DNA.

Abstract: A theoretical method is proposed to identify structural domains in proteins of known structures. It is based on the distribution of the local axes of the polypeptide chain. In particular, a statistical analysis is applied to the contributions of the local axes to the absolute writhing number, a topological property of a space curve resulting from the number of self- crossings in the curve projections onto a unit sphere. This finding supports the hypothesis that topological requirements should be satisfied in the process of protein folding and in the final organization of the tertiary structures.