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Protein structure and RNA aptamer structure
- N.Morikawa, Number sequence representation of protein structures based on the second derivative of a folded tetrahedron sequence. ArXiv: q-bio.BM/0610017 (2006). [pdf] (1.4 MB)
- N.Morikawa, Local feature detection in protein and RNA aptamer structures based on differential geometry of tetrahedron sequences (manuscript, 2007). [pdf] (14 pages with 5 figures and 3 tables, 532 KB)
- N.Morikawa, Systematic analysis of local flexibility of multiple-structure proteins (manuscript, 2008).
[pdf (rev.0)] (19 pages with 9 figures and 3 tables, 1.3 MB, 2008)
[pdf (rev.1)] (6,600 words with 8 figures, 6 tables, and 3 supplements, 1.3 MB, 2009)
- L.Mavridis, V.Venkatraman, D.W.Ritchie, N.Morikawa, R.Andonov, A.Cornu, N.Malod-Dognin,
J.Nicolas, M.Temerinac-Ott, M.Reisert, H.Burkhardt, A.Axenopoulos, and P. Daras, SHREC’10 Track: Protein Models, Eurographics Workshop on 3D Object Retrieval (Editors: I. Pratikakis, M. Spagnuolo, T. Theoharis, and R. Veltkamp) (2010). [pdf] (2.4MB)
- N.Morikawa, A novel method for identification of local conformational changes in proteins.
ArXiv: q-bio.BM/1110.6250 (2011). [pdf] (6 pages with 5 figures, 528 KB) [Supplement]
Discrete differential geometry of N-simplices
- N.Morikawa, Discrete differential geometry of proteins: A new method for encoding three-dimensional structures of proteins. ArXiv: math.CO/0506082 (2005).
- N.Morikawa, Discrete differential geometry of triangle tiles and algebra of closed trajectories. ArXiv: math.CO/067051 (2006).
- N.Morikawa, Discrete differential geometry of tetrahedrons and encoding of local protein structure. ArXiv: 0710.4596 (2007).
- N.Morikawa, Discrete differential geometry of N-simplices. (manuscript, 2008) [pdf] (60KB).
- N.Morikawa, Discrete differential geometry of n-simplices and protein structure analysis. Applied Mathematics, 5, 2458-2463. (2014) [link]
- N.Morikawa, Mathematics of a tetrahedron chain and the Hamiltonian cycle problem. (manuscript, 2015) [pdf] (2.4MB)
- N.Morikawa, Discrete Differential Geometry of Triangles and Escher-Style Trick Art, 6, 161-166. (2016) [link]
- N.Morikawa, Discrete Differential Geometry and the Structural Study of Protein Complexes. Open Journal of Discrete Mathematics, 7, 148-164. (2017) [link]
- N.Morikawa, Global Geometrical Constraints on the Shape of Proteins and Their Influence on Allosteric Regulation. Applied Mathematics, 9(10), 1116-1155. (2018) [link]
- N.Morikawa, Design of Self-Assembling Molecules and Boundary Value Problem for Flows on a Space of n-Simplices. Applied Mathematics, 10(11), 907-946, November 2019. [link]
Protein complexes
- N.Morikawa, Sub(Z) implementation of biological activities conducted by proteins. (manuscript, 2004). [pdf] (164 KB)
- N.Morikawa, Toward Sub(Z^N) implementation of protein-protein interactions. (manuscript, 2004). [pdf] (804 KB)
Hetero numbers
- N.Morikawa, Polynomial representation of DNA and proteins. (manuscript, 2003). [pdf] (524 KB, gzipped)
- N.Morikawa, Research project: toward Galois theory of protein-like objects. (manuscript, 2003). [pdf] (1.2 MB)
- N.Morikawa, Research project: protein as numbers. (manuscript, 2004). [pdf] (272 KB)
- N.Morikawa, On the Defining Equations of Protein's Shape from a Category Theoretical Point of View. Applied Mathematics, 11(9), 907-946, September 2020. [link]
- N.Morikawa, Two Mathematical Approaches to Inferring the Internal Structure of Proteins from their Shape. Global Journal of Science Frontier Research: F, Mathematics and Decision Sciences, Volume 21 Issue 3 Version 1.0 Year 2021. [link]
- N.Morikawa, Discrete Exterior Calculus of Proteins and Their Cohomology. Open Journal of Discrete Mathematics , 12, 47-63., July 2022. [link]
- N.Morikawa, A Novel Design Method for Protein-Like Molecules from the Perspective of Sheaf Theory, 13(3), 63-85, July 2023, [link]
Miscellaneous
- N.Morikawa, Algebra and analysis of proteins. (poster at GRC on theoretical biology & Biomathematics, 2004). [ppt] (1.5 MB)
- N.Morikawa, Polynomial representation of DNA and Proteins: hetero number theory. (picture book, 2004) [pdf] (1.4 MB, gzipped)
- N.Morikawa, Some mathematical problems in proteomics. (manuscript in japanese, 2006). [pdf] (192 KB)
- N.Morikawa, Discrete differential geometry of tetrahedron tiles and local protein structure. The slides and manuscript of the lecture at the 4th Int'l conf. of app. math. and computing, Aug. 12-18, 2007, Plovdiv Bulgaria. [html], [pdf] (656KB), [ppt] (2.2MB)
- N.Morikawa, Algebra of affine closed trajectories of triangles - Introduction to Hetero numbers (1) -. The slides and manuscript of a talk, Oct. 21, 2007. [html], [pdf] (424KB), [ppt] (3.3MB)