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During cell migration, cells become polarized, change their shape, and move in response to various internal and external cues. Cell polarization is defined through the spatio-temporal organization of molecules such as PI3K or small GTPases,…
The structures of proteins exhibit secondary elements composed of helices and loops. Comparison of several water-only hydrophobicity scales with the functionalities of two repeat proteins shows that these secondary elements possess…
Neural computation in biological and artificial networks relies on the nonlinear summation of many inputs. The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function, but…
Spatial organisation is a hallmark of all living cells, and recreating it in model systems is a necessary step in the creation of synthetic cells. It is therefore of both fundamental and practical interest to better understand the basic…
In this document, we study the interaction between different geometric structures that can be defined as morphisms of sections of the generalized tangent bundle $\mathbb TM:= TM\oplus T^*M\to M$. In particular, we show the behaviour of…
Predicting interactions between proteins is one of the most important yet challenging problems in structural bioinformatics. Intrinsically, potential function sites in protein surfaces are determined by both geometric and chemical features.…
Proteins are a matter of dual nature. As a physical object, a protein molecule is a folded chain of amino acids with multifarious biochemistry. But it is also an instantiation along an evolutionary trajectory determined by the function…
This chapter deals with approaches for protein three-dimensional structure prediction, starting out from a single input sequence with unknown struc- ture, the 'query' or 'target' sequence. Both template based and template free modelling…
We study the fields of endomorphisms intertwining pairs of symplectic structures. Using these endomorphisms we prove an analogue of Moser's theorem for simultaneous isotopies of two families of symplectic forms. We also consider the…
This chapter discusses geometric models of biomolecules and geometric constructs, including the union of ball model, the weigthed Voronoi diagram, the weighted Delaunay triangulation, and the alpha shapes. These geometric constructs enable…
An In Silico model to relate the properties of proteins to the structure, sequence, function and evolutionary history of proteins is shown. The derived ideal sequences for amino acid residues in proteins can then be considered as attractors…
Spatially proximate amino acids in a protein tend to coevolve. A protein's three-dimensional (3D) structure hence leaves an echo of correlations in the evolutionary record. Reverse engineering 3D structures from such correlations is an open…
A new method for the Automated Protein Structure Analysis (APSA) is derived, which simplifies the protein backbone to a smooth curve in 3-dimensional space. For the purpose of obtaining this smooth line each amino acid is represented by its…
Proteins, chain molecules of amino acids, behave in ways which are similar to each other yet quite distinct from standard compact polymers. We demonstrate that the Flory theorem, derived for polymer melts, holds for compact protein native…
We consider six different secondary structures of proteins and construct two types of Go-type off-lattice models: with the steric constraints and without. The basic aminoacid-aminoacid potential is Lennard Jones for the native contacts and…
Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or…
Motivation: Thanks to the recent advances in structural biology, nowadays three-dimensional structures of various proteins are solved on a routine basis. A large portion of these contain structural repetitions or internal symmetries. To…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…
The ability to computationally generate novel yet physically foldable protein structures could lead to new biological discoveries and new treatments targeting yet incurable diseases. Despite recent advances in protein structure prediction,…
Protein-protein interactions (PPIs) are crucial in regulating numerous cellular functions, including signal transduction, transportation, and immune defense. As the accuracy of multi-chain protein complex structure prediction improves, the…