A novel mathematical model of protein interactions (2): The mathematics behind the model
Abstract
This article is a sequel to ``A novel mathematical model of protein interactions from the perspective of electron delocalization (2025)'', where protein molecules are modelded as loops of triangles with no singular holes inside. Here we consider two questions: (1) How can we define the shape of a molecule? (i.e., how can we define the shape of a loop with no singular holes inside?), and (2) Is the given loop a molecule? (i.e., are the holes within a loop are singular?). These questions are answered by (1) giving a defining system of equations for the shape of a molecule using concepts from category theory, and (2) giving a equation that determines whether holes within a loop are singular using concepts from cohomology theory, respectively. No prior knowledge of the previous paper, category theory, or cohomology theory is required.
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BibTeX
@misc{morikawa2026novel,
title = {{A novel mathematical model of protein interactions (2): The mathematics behind the model}},
author = {Naoto Morikawa},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29086},
eprint = {2608.29086},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29086},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A novel mathematical model of protein interactions (2): The mathematics behind the model
AU - Naoto Morikawa
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29086
UR - https://arxiv.org/abs/2608.29086
AB - This article is a sequel to ``A novel mathematical model of protein interactions from the perspective of electron delocalization (2025)'', where protein molecules are modelded as loops of triangles with no singular holes inside. Here we consider two questions: (1) How can we define the shape of a molecule? (i.e., how can we define the shape of a loop with no singular holes inside?), and (2) Is the given loop a molecule? (i.e., are the holes within a loop are singular?). These questions are answered by (1) giving a defining system of equations for the shape of a molecule using concepts from category theory, and (2) giving a equation that determines whether holes within a loop are singular using concepts from cohomology theory, respectively. No prior knowledge of the previous paper, category theory, or cohomology theory is required.
ER -