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.
We show that the relaxation dynamics of unfolded in vacuo lysozyme is not random. Analyses of molecular dynamics trajectories in a convenient space of molecular shape descriptors reveal a "favored" pattern of transitions leading to stable conformations. The relaxation paths exhibit a balanced change in shape features: globular spheroids are formed slowly enough to allow the proper entanglement of secondary-structural elements. The present study shows that a protein in vacuo can actually (re)fold into native and quasinative structures. The driving force for these transformations is intrinsic to the polypeptide chain.
ABSTRACT:We revisit the notion of structural similarity along a reaction path within the context of a generalized electronic diabatic (GED) molecular model. In this approach, a reaction involving two closed-shell stable species is described as the evolution of a quantum state that superimposes at least three diabatic electronic species (reactant, product, and an open-shell transition state) coupled by an external electromagnetic field. Reactant and product amplitudes in this general state are also modulated by changing the geometry of a system of classical positive charges interacting with the electrons. By mapping these amplitudes over nuclear configurational space, we can follow the total quantum state along a reaction coordinate and establish its similarity to each of the diabatic species. As a result, chemical processes, and useful notions such as those of energy barriers and the Hammond postulate, emerge as consequence of Franck-Condon-like transitions between quantum states.
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