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Protein structure and RNA aptamer structure

  1. 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)
  2. 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)
  3. 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)
  4. 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)
  5. 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

  1. N.Morikawa, Discrete differential geometry of proteins: A new method for encoding three-dimensional structures of proteins. ArXiv: math.CO/0506082 (2005).
  2. N.Morikawa, Discrete differential geometry of triangle tiles and algebra of closed trajectories. ArXiv: math.CO/067051 (2006).
  3. N.Morikawa, Discrete differential geometry of tetrahedrons and encoding of local protein structure. ArXiv: 0710.4596 (2007).
  4. N.Morikawa, Discrete differential geometry of N-simplices. (manuscript, 2008) [pdf] (60KB).
  5. N.Morikawa, Discrete differential geometry of n-simplices and protein structure analysis. Applied Mathematics, 5, 2458-2463. (2014) [link]
  6. N.Morikawa, Mathematics of a tetrahedron chain and the Hamiltonian cycle problem. (manuscript, 2015) [pdf] (2.4MB)
  7. N.Morikawa, Discrete Differential Geometry of Triangles and Escher-Style Trick Art, 6, 161-166. (2016) [link]
  8. N.Morikawa, Discrete Differential Geometry and the Structural Study of Protein Complexes. Open Journal of Discrete Mathematics, 7, 148-164. (2017) [link]

Protein complexes

  1. N.Morikawa, Sub(Z) implementation of biological activities conducted by proteins. (manuscript, 2004). [pdf] (164 KB)
  2. N.Morikawa, Toward Sub(Z^N) implementation of protein-protein interactions. (manuscript, 2004). [pdf] (804 KB)

Hetero numbers

  1. N.Morikawa, Polynomial representation of DNA and proteins. (manuscript, 2003). [pdf] (524 KB, gzipped)
  2. N.Morikawa, Research project: toward Galois theory of protein-like objects. (manuscript, 2003). [pdf] (1.2 MB)
  3. N.Morikawa, Research project: protein as numbers. (manuscript, 2004). [pdf] (272 KB)


  1. N.Morikawa, Algebra and analysis of proteins. (poster at GRC on theoretical biology & Biomathematics, 2004). [ppt] (1.5 MB)
  2. N.Morikawa, Polynomial representation of DNA and Proteins: hetero number theory. (picture book, 2004) [pdf] (1.4 MB, gzipped)
  3. N.Morikawa, Some mathematical problems in proteomics. (manuscript in japanese, 2006). [pdf] (192 KB)
  4. 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)
  5. 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)