Proteins are flexible molecules involved in all biological functions. Understanding these functions actually requires delving into protein structure, thermodynamics, and kinetics. This talk will be devoted to two problems in this area. The first one is the (uniform) generation of conformations of a protein backbone in the so-called rigid geometry model. We will present a method based on algebraic solutions of the so-called tripeptide loop closure. The second one deals with the calculation of the volume of high dimensional polytope, a questions closely related to the computation of density of states in statistical physics.[-]