Multipolar representation of protein structure

BACKGROUND: That the structure determines the function of proteins is a central paradigm in biology. However, protein functions are more directly related to cooperative effects at the residue and multi-residue scales. As such, current representations based on atomic coordinates can be considered inadequate. Bridging the gap between atomic-level structure and overall protein-level functionality requires parameterizations of the protein structure (and other physicochemical properties) in a quasi-continuous range, from a simple collection of unrelated amino acids coordinates to the highly synergistic organization of the whole protein entity, from a microscopic view in which each atom is completely resolved to a "macroscopic" description such as the one encoded in the three-dimensional protein shape. RESULTS: Here we propose such a parameterization and study its relationship to the standard Euclidian description based on amino acid representative coordinates. The representation uses multipoles associated with residue Cα coordinates as shape descriptors. We demonstrate that the multipoles can be used for the quantitative description of the protein shape and for the comparison of protein structures at various levels of detail. Specifically, we construct a (dis)similarity measure in multipolar configuration space, and show how such a function can be used for the comparison of a pair of proteins. We then test the parameterization on a benchmark set of the protein kinase-like superfamily. We prove that, when the biologically relevant portions of the proteins are retained, it can robustly discriminate between the various families in the set in a way not possible through sequence or conventional structural representations alone. We then compare our representation with the Cartesian coordinate description and show that, as expected, the correlation with that representation increases as the level of detail, measured by the highest rank of multipoles used in the representation, approaches the dimensionality of the fold space. CONCLUSION: The results described here demonstrate how a granular description of the protein structure can be achieved using multipolar coefficients. The description has the additional advantage of being immediately generalizable for any residue-specific property therefore providing a unitary framework for the study and comparison of the spatial profile of various protein properties

Does Size Matter? The Multipolar International Landscape of Nanoscience

How do different countries tackle nanoscience research? Are all countries similar except for a trivial size effect, as science is often assumed to be universal? Or does size dictate large differences, as large countries are able to develop activities in all directions of research, while small countries have to specialize in some specific niches? Alternatively, is size irrelevant, as all countries have followed different historical paths, leading to different patterns of specialisation? Here, we develop an original method that uses a bottom-up definition of scientific subfields to map the international structure of any scientific field. Our analysis shows that nanoscience research does not show a universal pattern of specialisation, homothetic of that of a single global leader (e.g., the United States). Instead, we find a multipolar world, with four main ways of doing nanosciences.Fil: Levin, Luciano Guillermo. Universidad Nacional de La Pampa. Facultad de Ciencias Humanas. Instituto de Estudios Sociohistóricos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Jensen, Pablo. École normale supérieure de Lyon; FranciaFil: Kreimer, Pablo Rafael. Universidad Maimónides; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

On the conveyance of angular momentum in electronic energy transfer

When electronic excitation transfer occurs, it is of considerable interest to establish whether angular momentum can also be conveyed in the process. The question is prompted by a consideration that when the participating chromophores are atoms, ions, or molecular systems having high local symmetry, the electronic excited states that are involved are generally characterized not only by energy, but by angular momentum properties. Moreover, it is known that electron spin can be communicated between quantum dot exciton states. Resolving the general issue entails an electrodynamic representation exploiting irreducible tensor methods, the analysis being illustrated by application to energy transfer associated with a variety of multipolar transitions. The results exhibit novel connections between an angular momentum content of the electromagnetic coupling and a strongly varying distance dependence. It is concluded that the communication of angular momentum does not in general map unambiguously between a donor and energy acceptor

Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening

This work introduces a number of algebraic topology approaches, such as multicomponent persistent homology, multi-level persistent homology and electrostatic persistence for the representation, characterization, and description of small molecules and biomolecular complexes. Multicomponent persistent homology retains critical chemical and biological information during the topological simplification of biomolecular geometric complexity. Multi-level persistent homology enables a tailored topological description of inter- and/or intra-molecular interactions of interest. Electrostatic persistence incorporates partial charge information into topological invariants. These topological methods are paired with Wasserstein distance to characterize similarities between molecules and are further integrated with a variety of machine learning algorithms, including k-nearest neighbors, ensemble of trees, and deep convolutional neural networks, to manifest their descriptive and predictive powers for chemical and biological problems. Extensive numerical experiments involving more than 4,000 protein-ligand complexes from the PDBBind database and near 100,000 ligands and decoys in the DUD database are performed to test respectively the scoring power and the virtual screening power of the proposed topological approaches. It is demonstrated that the present approaches outperform the modern machine learning based methods in protein-ligand binding affinity predictions and ligand-decoy discrimination

How simple can a model of an empty viral capsid be? Charge distributions in viral capsids

We investigate and quantify salient features of the charge distributions on viral capsids. Our analysis combines the experimentally determined capsid geometry with simple models for ionization of amino acids, thus yielding the detailed description of spatial distribution for positive and negative charge across the capsid wall. The obtained data is processed in order to extract the mean radii of distributions, surface charge densities and dipole moment densities. The results are evaluated and examined in light of previously proposed models of capsid charge distributions, which are shown to have to some extent limited value when applied to real viruses.Comment: 10 pages, 10 figures; accepted for publication in Journal of Biological Physic