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Therapeutic antibodies are an essential and rapidly expanding drug modality. The binding specificity between antibodies and antigens is decided by complementarity-determining regions (CDRs) at the tips of these Y-shaped proteins. In this…
Antibodies are Y-shaped proteins that protect the host by binding to specific antigens, and their binding is mainly determined by the Complementary Determining Regions (CDRs) in the antibody. Despite the great progress made in CDR design,…
We seek to understand the interplay between amino acid sequence and local structure in proteins. Are some amino acids unique in their ability to fit harmoniously into certain local structures? What is the role of sequence in sculpting the…
The complementarity-determining regions of antibodies are loop structures that are key to their interactions with antigens, and of high importance to the design of novel biologics. Since the 1980s, categorizing the diversity of CDR…
Local protein structure analysis is informative to protein structure analysis and has been used successfully in protein structure prediction and others. Proteins have recurring structural features, such as helix caps and beta turns, which…
In this paper, we systematically review weighted persistent homology (WPH) models and their applications in biomolecular data analysis. Essentially, the weight value, which reflects physical, chemical and biological properties, can be…
Amyloid fibrils are stable aggregates of misfolded proteins and polypeptides that are insoluble and resistant to protease activity. Abnormal formation of amyloid fibrils in vivo may lead to neurodegenerative disorders and other systemic…
Many structured systems admit locally consistent descriptions that nevertheless fail to globalize when constrained by an ambient reference or feasibility condition. Diagnosing such failures is naturally an evaluative problem: given a fixed…
Persistent homology (PH) is a popular tool for topological data analysis that has found applications across diverse areas of research. It provides a rigorous method to compute robust topological features in discrete experimental…
The 3-hinge gyrus (3HG) is a newly defined folding pattern, which is the conjunction of gyri coming from three directions in cortical folding. Many studies demonstrated that 3HGs can be reliable nodes when constructing brain networks or…
Every homomorphism $\varphi: B(G) \rightarrow B(H)$ between Fourier-Stieltjes algebras on locally compact groups $G$ and $H$ is determined by a continuous mapping $\alpha: Y \rightarrow \Delta(B(G))$, where $Y$ is a set in the open coset…
We inspect the geometry of proteins by identifying their backbones as framed polygons. We find that the left-handed helix region of the Ramachandran map for non-glycyl residues corresponds to an isolated and highly localized sector in the…
The electronic structure including energy bands, band weights, and local density of states (LDOS) of interfaces between hexagonal (AB) and rhombohedral (ABC) graphite has been has been calculated. The full-potential local-orbital code…
Let $\beta$ be a contact form on a compact smooth manifold $X$ and $v_\beta$ its Reeb vector field. The paper applies general results of different authors about Hodge structures that are transversal to a given foliation to the special case…
Antibodies are crucial proteins produced by the immune system in response to foreign substances or antigens. The specificity of an antibody is determined by its complementarity-determining regions (CDRs), which are located in the variable…
Variation of mixed Hodge structures(VMHS), introduced by P. Deligne, is a linear structure reflecting the geometry on cohomology of the fibers of an algebraic family, generalizing variation of Hodge structures for smooth proper families,…
The idea that structural disorder might be a novel mechanism of protein interaction is widespread in the Literature, although the number of statistically significant structural studies supporting this is surprisingly low. At variance with…
Antibody co-design represents a critical frontier in drug development, where accurate prediction of both 1D sequence and 3D structure of complementarity-determining regions (CDRs) is essential for targeting specific epitopes. Despite recent…
Antibodies are canonically Y-shaped multimeric proteins capable of highly specific molecular recognition. The CDRH3 region located at the tip of variable chains of an antibody dominates antigen-binding specificity. Therefore, it is a…
The adhesion zone of immune cells, the 'immunological synapse', exhibits characteristic domains of receptor-ligand complexes. The domain formation is likely caused by a length difference of the receptor-ligand complexes, and has been…