Implementing knot-theoretical characterization methods to analyze the backbone structure of proteins: application to CTF L7/L12 and carboxypeptidase A inhibitor proteins

Overcrossing spectra of protein backbones: characterization of three-dimensional molecular shape and global structural homologies

A procedure is developed and applied to characterize the global shape and folding features of the backbone of a chain molecule. The methodology is based on the following concept: the probability of observing a rigid placement of a backbone in 3-space as a projected curve with N overcrossings. The numerical computation of these probabilities allows one to construct the overcrossing spectrum of a macromolecule at a given configuration. Although the spectrum is built from the knowledge of the nuclear geometry of the main-chain atoms, the shape descriptor overlooks local geometrical features (such as distances and contacts) and provides a characterization of essential (topological) features of the overall fold, such as its compactness and degree of entanglement. In contrast with other shape descriptors, the present approach gives an absolute characterization of the configuration considered, and not one that is relative to an arbitrarily chosen reference structure. Moreover, it is possible to discriminate between folding features that otherwise may not be distinguished when using other geometrical or topological global descriptors. The overcrossing spectrum is proposed as a tool that complements current structural analyses of macromolecules, especially when monitoring structural homologies within a group of related or unrelated polymers. In this work, we apply the methodology to the analysis of proteins having the globin fold. The results are compared with those of other proteins exhibiting similar size and number of residues. Some basic properties of the spectra as a function of the chain length are also discussed.

Global characterization of protein secondary structures. Analysis of computer-modeled protein unfolding

Analyses of structural and molecular shape changes undergone by a protein during an unfolding process are presented. The procedure, based on a spherical shape map method, provides a topological description of a three-dimensional macromolecular structure. Local properties of the backbone are used to derive a global characterization of its fold. A spherical shape map of backbone crossings is associated with a given macromolecular conformation. The map is built by classifying each point on the sphere according to the crossing pattern obtained when the backbone is observed along a direction defined by the center of the sphere and the chosen point. The surface of the sphere can be divided in equivalence classes. All the points within a given class correspond to directions from which the backbone has the same overcrossing pattern. Automatic computation and display of these equivalence classes is discussed, as is the implementation of the technique on a computer graphics workstation. The graphical manipulation simplifies the analysis of these maps when following a change in the conformation of the backbone. The procedure is illustrated with the results of a molecular dynamics computer simulation of the unfolding of the bacteriophage T4 glutaredoxin protein (in the form of its polyglycine model). The method gives a novel description of the differential structural stability for the characteristic secondary structural elements (alpha-helices and beta-sheets) present in the protein. Recognition of the persistence of structural elements over the simulation time is performed in an unbiased manner.