Related papers: A geometrical framework for thinking about protein…
The process of protein folding from an unfolded state to a biologically active, folded conformation is governed by many parameters e.g the sequence of amino acids, intermolecular interactions, the solvent, temperature and chaperon…
Folding and aggregation of proteins, the interaction between proteins and membranes, as well as the adsorption of organic soft matter to inorganic solid substrates belong to the most interesting challenges in understanding structure and…
Background: Many attempts have been made to resolve in time the folding of model proteins in computer simulations. Different computational approaches have emerged. Some of these approaches suffer from the insensitivity to the geometrical…
Numerous cellular functions rely on protein$\unicode{x2013}$protein interactions. Efforts to comprehensively characterize them remain challenged however by the diversity of molecular recognition mechanisms employed within the proteome. Deep…
Protein structure prediction can be shown to be an NP-hard problem; the number of conformations grows exponentially with the number of residues. The native conformations of proteins occupy a very small subset of these, hence an exploratory,…
Natural protein sequences that self-assemble to form globular structures are compact with high packing densities in the folded states. It is known that proteins unfold upon addition of denaturants, adopting random coil structures. The…
Generative modeling has become a central paradigm in protein research, extending machine learning beyond structure prediction toward sequence design, backbone generation, inverse folding, and biomolecular interaction modeling. However, the…
The protein design problem involves finding polypeptide sequences folding into a given threedimensional structure. Its rigorous algorithmic solution is computationally demanding, involving a nested search in sequence and structure spaces.…
This paper develops a complete foundational treatment of simplicial complexes from Euclidean spaces through geometric realizations, emphasizing concrete computations, examples, and practical verification methods. Beginning with finite point…
One of the molecular properties most intuitive to the human perception is the geometrical shape. However, when exploring a large chemical space the determination of shape needs to be automated. We present a fast and simple approach to…
Applying kernel methods to matchings is challenging due to their discrete, non-Euclidean nature. In this paper, we develop a principled framework for constructing geometric kernels that respect the natural geometry of the space of…
Protein folding, peptide aggregation and crystallization, as well as adsorption of molecules on soft or solid substrates have an essential feature in common: In all these processes, structure formation is guided by a collective, cooperative…
Geometrical properties of protein ground states are studied using an algebraic approach. It is shown that independent from inter-monomer interactions, the collection of ground state candidates for any folded protein is unexpectedly small:…
Collective behavior of proteins on biomembranes is usually studied within the spontaneous curvature model. Here we consider an alternative phenomenological approach, which accounts consistently for partial ordering of proteins as well as…
Protein flexibility is crucial for understanding protein structures, functions, and dynamics, and it can be measured through experimental methods such as X-ray crystallography. Theoretical approaches have also been developed to predict…
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.…
Shape had been intuitively recognized to play a dominant role in determining the global motion patterns of bio-molecular assemblies. However, it is not clear exactly how shape determines the motion patterns. What about the local…
The ability of a protein to recognise multiple independent target conformations was demonstrated in [1]. Here we consider the recognition of correlated configurations, which we apply to funnel design for a single conformation. The maximum…
Proteins are macromolecules responsible for essential functions in almost all living organisms. Designing reasonable proteins with desired functions is crucial. A protein's sequence and structure are strongly correlated and they together…
Computational protein design facilitates discovery of novel proteins with prescribed structure and functionality. Exciting designs were recently reported using novel data-driven methodologies that can be roughly divided into two categories:…