In silico prediction of the relationships between the protein structure and its physiological activity is an important research topic for drug design. Broad picture of my research is to construct a topological model to clarify the antibody-antigen recognition system, since immunotherapy is applied to wide range of severe diseases such as cancer .
To achieve the goal, we focus on a topological method called “Fatgraph models of proteins” . Fatgraph models of proteins are topological two-manifold with boundary components (surface) which have one to one correspondence with three-dimensional protein structures listed on Protein Data Bank (PDB)  with only a few exceptions. The traits of each surface for each protein are described by the following invariants; Euler characteristics, number of boundary components, and genus. Fatgraph is also called ribbon graph and has already proven their utility in theoretical physics including string theory .
In this research, we constructed fatgraph models of antibodies and investigated the traits of antigen-binding fragments (Fab). Then, we topologically examined the transformations of the fatgraphs of the proteins due to the changes of protein sequences or existence of ligands.
 Patel, Shetal A. et al. (2018) Combination Cancer Therapy with Immune Checkpoint Blockade: Mechanisms and Strategies, Immunity, Volume 48, Issue 3, 417 - 433
 R. C. Penner, et al., (2010) Fatgraph models of proteins, Communications on Pure and Applied Mathematics. Volume 63 , Issue 10 , 1249 - 1297.
 H.M. Berman, et al. (2000) The Protein Data Bank, Nucleic Acids Research, 28: 235 - 242. http://www.rcsb.org/
 R. C. Penner, (2016) Moduli spaces and macromolecules. Bull. Amer. Math. Soc. 53, 217 - 268.