Auxin minimum triggers the developmental switch from cell division to cell differentiation in the root.

In multicellular organisms, a stringent control of the transition between cell division and differentiation is crucial for correct tissue and organ development. In the root, the boundary between dividing and differentiating cells is positioned by the antagonistic interaction of the hormones auxin and cytokinin. Cytokinin affects polar auxin transport, but how this impacts the positional information required to establish this tissue boundary, is still unknown.

Mathematical modeling and experimental validation of the spatial distribution of boron in the root of Arabidopsis thaliana identify high boron accumulation in the tip and predict a distinct root tip uptake function.

Boron, an essential micronutrient, is transported in roots of Arabidopsis thaliana mainly by two different types of transporters, BORs and NIPs (nodulin26-like intrinsic proteins). Both are plasma membrane localized, but have distinct transport properties and patterns of cell type-specific accumulation with different polar localizations, which are likely to affect boron distribution. Here, we used mathematical modeling and an experimental determination to address boron distributions in the root.

Modules identification in protein structures: the topological and geometrical solutions.

The identification of modules in protein structures has major relevance in structural biology, with consequences in protein stability and functional classification, adding new perspectives in drug design. In this work, we present the comparison between a topological (spectral clustering) and a geometrical (k-means) approach to module identification, in the frame of a multiscale analysis of the protein architecture principles. The global consistency of an adjacency matrix based technique (spectral clustering) and a method based on full rank geometrical information (k-means) give a proof-of-concept of the relevance of protein contact networks in structure determination.

Shedding light on protein-ligand binding by graph theory: the topological nature of allostery.

Allostery is a very important feature of proteins; we propose a mesoscopic approach to allosteric mechanisms elucidation, based on protein contact matrices. The application of graph theory methods to the characterization of the allosteric process and, more broadly, to obtain the conformational changes upon binding, reveals key features of the protein function. The proposed method highlights the leading role played by topological over geometrical changes in allosteric transitions.

Proteins as sponges: a statistical journey along protein structure organization principles.

The analysis of a large database of protein structures by means of topological and shape indexes inspired by complex network and fractal analysis shed light on some organizational principles of proteins. Proteins appear much more similar to "fractal" sponges than to closely packed spheres, casting doubts on the tenability of the hydrophobic core concept. Principal component analysis highlighted three main order parameters shaping the protein universe: (1) "size", with the consequent generation of progressively less dense and more empty structures at an increasing number of residues, (2) "microscopic structuring", linked to the existence of a spectrum going from the prevalence of heterologous (different hydrophobicity) to the prevalence of homologous (similar hydrophobicity) contacts, and (3) "fractal shape", an organizing protein data set along a continuum going from approximately linear to very intermingled structures.