Sheaf-theoretic representation of the proteolipid code

2025/12/29 by Troy A. Kervin · 1 voice
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #q-bio.MN #physics.bio-ph #q-bio.BM

paper · pdf

Abstract

Membrane particles such as proteins and lipids organize into zones that perform unique functions. Here, I introduce a topological and category-theoretic framework to represent particle and zone intra-scale interactions and inter-scale coupling. This involves carefully demarcating between different presheaf- or sheaf-assigned data levels to preserve functorial structure and account for particle and zone generalized poses. The framework can accommodate Hamiltonian mechanics, enabling dynamical modeling. This amounts to a versatile mathematical formalism for membrane structure and multiscale coupling.

Citations

• Learning Sheaf Laplacian Optimizing Restriction Maps
• Symplectic moduli space of 1-dimensional sheaves on Poisson surfaces
• Factorization algebra
• Sheaf Hypergraph Networks
• Emerging Patterns in the Continuum Representation of Protein-Lipid Fingerprints
• A Very Elementary Introduction to Sheaves
• Perspective: Coarse-grained models for biomolecular systems
• Sheaves, Cosheaves and Applications
• Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Environment and exposure to solvent of protein atoms. Lysozyme and insulin
• The interpretation of protein structures: Estimation of static accessibility

Discussions

• Troy A. Kervin: Sheaf-theoretic representation of the proteolipid code https://arxiv.org/abs/2512.23784 https://arxiv.org/pdf/2512.23784 https://arxiv.org/html/2512.23784 [bsky, 0 points, 0 comments]

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