Mariel Vazquez

Mariel Vazquez

Position Title

Department of Mathematics, College of Letters and Science
Department of Microbiology and Molecular Genetics, College of Biological Sciences
Center for the Advancement of Multicultural Perspectives on Science (CAMPOS)

Mathematical Sciences Building (MSB) 2150, and Briggs 09

Profile Introduction

My research lies at the interface of mathematics, polymer physics, and molecular biology. I specialize in the application of topological tools to study DNA. My work is currently focused on two lines of inquiry: (1) DNA Topology: the mechanism of site-specific recombination, topoisomerase action, and the packing of chromosomes in human cells and viral capsids; using mathematical tools including know theory, low-dimensional topology, and Monte Carlo simulations; and (2) Chromosomal Aberrations and Cancer: analysis of cancer genomic data and mechanisms of repair pathways; using biophysical models, graph theory, and topological data analysis.

I am Professor in the departments of Mathematics and of Microbiology and Molecular Genetics. I also serve as Faculty Director for the Center for the Advancement of Multicultural Perspectives on Science (CAMPOS). CAMPOS was established in 2012 with funding from the National Science Foundation (UC Davis ADVANCE), and is currently an initiative of the  Office of Diversity, Equity and Inclusion.

Grad Group Affiliations

  • Applied Mathematics (GGAM)
  • Mathematics
  • Integrative Genetics and Genomics (IGG)


  • BIS 10
  • MAT17 series
  • MAT108

Honors and Awards

  • 2018 Fellow of the Association for Women in Mathematics
  • 2016 Blackwell-Tapia Prize 
  • 2014 Mohammed Dahleh Distinguished Lectureship Award, UC Santa Barbara
  • 2012 Presidential Early Career Award for Scientists and Engineers PECASE ( White House)
  • 2011 CAREER Award (National Science Foundation)
  • 2014 CAMPOS Faculty Scholar, UC Davis
  • 2016 Blackwell Tapia Prize
  • 2017 Association for Women in Mathematics Fellow, inaugural class

    Professional Societies

    • American Mathematical Society
    • Society for Industrial and Applied Mathematics
    • Association for Women in Mathematics


    • 1994 B. Sc. Mathematics UNAM
    • 2000 PhD Mathematical Biology Florida State University


    Vazquez, M.E. Knots and DNA, Revista Situs (1995) IMATE, UNAM

    Trigueros, S.*, Arsuaga, J., Vazquez, M.E., Sumners, D.W., and Roca, J. Novel Display of knotted DNA molecules by two-dimensional gel electrophoresis, Nucleic Acids Research (2001) 29(13): e67

    Arsuaga, J., Vazquez, M., Trigueros, S.*, Sumners, D.W., and Roca, J. Knotting probability of DNA molecules confined in restricted volumes: DNA knotting in phage capsids, Proc. Natl. Acad. Sci. USA (2002) 99(8): 373-5377

    Saka, Y.†and Vazquez, M. TangleSolve: topological analysis of site-specific recombination, Bioinformatics (2002) 18: 1011-1012.

    Hlatky, L., Sachs, R.K., Vazquez, M., and Cornforth, M.N. Radiation-induced chromosome aberrations: insights gained from biophysical modeling, Bioessays (2002)24:714-723

    Sachs, R.K., Arsuaga, J., Vazquez, M., Hahnfeldt,  P., and Hlatky, L. Using Graph Theory to Analyze Chromosome Aberrations, Radiation Research (2002) 159(5): 556-567.

    Cornforth, M.N., Greulich-Bode, K.M., Loucas,  B.D., Arsuaga, J., Vazquez, M., Sachs,  R.K., Bruckner, M., Molls, M., Hahnfeldt, P., Hlatky, L., and Brenner,  D.J., Chromosomes are predominantly located randomly with respect to each other in interphase human cells, Journal of Cell Biology (2002) 159(2): 237-244. Accompanying commentary: Chromosomal Cliques by A.W. Dove, J. Cell Biology (2002) 159(2): 199.

    Vazquez, M., Greulich-Bode, K.M., Arsuaga, J., Cornforth, M.N., Bruckner, M., Sachs, R.K., Hlatky, L., Molls, M., and Hahnfeldt,  P. Computer analysis of mFISH chromosome aberration data uncovers an excess of very complex metaphases, International Journal of Radiation Biology (2002) 78:1103-1116.

    Arsuaga, J., Tam, R., Vazquez, M., Sumners, D.W., and Harvey, S. Investigation of viral DNA packaging using molecular mechanics models, Journal of Biophysical Chemistry (2002) 101-102(1): 475-484.

    Vazquez, M., and Sumners, D.W. Tangle Analysis of Gin Recombination, Math. Proc. Camb. Phil. Soc. (2004) 136: 565-582.

    Arsuaga, J., Greulich-Bode, K., Vazquez, M., Hahnfeldt, P., Brenner, J., Sachs, R.K., and Hlatky, L. Chromosome spatial clustering expressed through radiogenic aberrations, International Journal of Radiation Biology (2004) 80(7): 507-515.

    Levy, D.*, Vazquez, M., Cornforth, M., Loucas, B., Sachs, R.K., and Arsuaga, J., Comparing DNA damage processing pathways by computer analysis of chromosome painting data, J. Comp. Biol. (2004) 11(4): 626-641.

    Vazquez, M., Colloms, S.D., and Sumners, D.W. A unique mechanism for Xer recombination is suggested by tangle analysis, J. Mol. Biol. (2005) 346:493-504.

    Vives, S., Loucas, B., Vazquez, M., Brenner, D., Sachs, R.K., Hlatky, L., Cornforth, M., and Arsuaga, J., SCHIP: Statistics of Chromosome Interphase Positioning, Bioinformatics (2005) 21(14): 3181-3182.

    Arsuaga, J., Vazquez, M., McGuirck, P.†, Trigueros, S., Sumners,  D.W., and Roca, J., DNA knots reveal a chiral organization of DNA in phage capsids, Proc. Natl. Acad.Sci. USA (2005) 102(26):9165-9169.

    Ardanza-Trevijano, S., Arsuaga, J., Crespo J. A., Extremiana, J. I., Hernandez, L.J., Rivas, M. T., Roca, J., and Vazquez, M, Topological Invariants in DNA, Fullerenes and the Theory of Social Choice (Spanish), La Gaceta de la Real Sociedad Matematica Española (2007) 10(3): 611-632. 

    Hua, X.†, Raghavan, B.†, Nguyen, D.†, Arsuaga, J., and Vazquez, M., Random State Transitions of Knots: a first step towards modeling unknotting by type II topoisomerases, Topology and its applications 157(7):1381-1397

    Zheng, W.†, Galloy, C., Hallet, B., and Vazquez, M., The tangle model for site-specific recombination: a computer interface and the Tnpl-IRS recombination system, Proceedings of International Workshop on Knot Theory for Specific Objects, Ed. A. Kawauchi, OCAMI studies (2007) Vol. 1(2): 251-271.

    Blackstone, T.†, McGuirk, P.†, Liang, C.*, Roca, J., Arsuaga, J., and Vazquez, M., The role of writhe in DNA condensation, Proceedings of the International Workshop on Knot Theory for Scientific Objects, Ed. A. Kawauchi, OCAMI studies (2007) Vol. 1(2): 239-250.

    Grainge, I., Bregu, M., Vazquez, M., Sivanathan, V.*, Ip, S.Y.P., and Sherratt, D.J. Unlinking chromosome catenanes in vivo by site-specific recombination, EMBO Journal (2007) 26(19): 4228-38.

    Arsuaga, J., Diao, Y., and Vazquez, M., Mathematical Methods in DNA Topology: Applications to Chromosome Organization and Site-specific Recombination, In: Mathematics of DNA Structure, Function and Interactions (eds C.J. Benham, S. Harvey, W.K. Olson, D.W. Sumners, and D. Swigon), Springer Science + Business Media, LLC, New York, (2009) pp. 7-36. 

    Darcy, I., Luecke, J., and Vazquez, M., Tangle analysis of difference topology experiments: applications to a Mu protein-DNA complex, Algebraic and Geometric Topology (2009) 9: 2247-2309.

    Scharein, R., Ishihara, K.*, Arsuaga, J., Diao, Y., Shimokawa, K., and Vazquez, M., Bounds for minimal step number of knots in the simple cubic lattice, J. Phys. A : Math. Theor. (2009) 42: 475006.

    DeWoskin, D.*, Climent, J., Cruz-White, I., Vazquez, M., Park, C., and Arsuaga, J.,  Applications of computational homology to prediction of treatment response in breast cancer patients, Topology and its Applications (2010) 157 (1): 157-164.

    Shimokawa, K., and Vazquez, M., DNA and Knot Theory (Japanese), (2011) Sugaku 63(2): 237-242 Expository paper. 

    Portillo, J.*, Diao, Y., Scharein, R., Arsuaga, J., and Vazquez, M., On the mean and variance of the writhe of random polygons,  J. of Phys. A: Math Theor. (2011) 44: 275004.

    Soteros, C., Ishihara, K., Shimokawa, K., Szafron, M., and Vazquez, M., Signed Unknotting Number and Knot Chirality Discrimination via Strand Passage, Progress of Theoretical Physics Supplement (2011) 191: 78-95.

    Arsuaga, J., Diao, Y., Kaplan, T., and Vazquez, M., The effects of density on the topological structure of the mitochondrial DNA from trypanosomes, Journal of Mathematical Biology (2012) 64(6): 1087-1108.
    Ishihara, K., Scharein, R., Diao, Y., Arsuaga, J., Vazquez, M., and Shimokawa, K., Bounds for the minimum step number of knots confined to slabs in the simple cubic lattice, J. of Phys. A: Math Theor. (2012) 45: 065003.
    Darcy, I.K. and Vazquez, M., Determining the topology of stable protein-DNA complexes (2013) Biochemical Society Transactions 41(2): 601-605.
    Brasher, R. Scharein, R.G., and Vazquez, M., New biologically motivated knot table (2013) Biochemical Society Transactions 41(2): 606-611.

    Ishihara, K., Shimokawa, K., and Vazquez, M., Site-specific recombination modeled as a band surgery: Applications to Xer Recombination (2013) in Discrete and Topological Models in Molecular Biology (Eds. Jonoska Nataša; Saito, Masahico) Natural Computing Series, Springer ISBN 978-3-642-40192-3  [peer- reviewed Book Chapter].

    Shimokawa, K., Ishihara, K., Grainge, I., Sherratt, D., and Vazquez, M., FtsK-dependent XerCD-dif recombination unlinks replication catenanes in a  stepwise manner (2013) Proceedings of the National Academy of Sciences USA 110 (52) 20906-20911; Accompanying commentary: Jayaram, M., Mathematical validation of a biological model for unlinking replication catenanes by recombination (2013) PNAS 110 (52) 20854-20855.

    Segal, M., Xiong, H., Capurso, D., Vazquez, M., and Arsuaga, J., Reproducibility of Three-Dimensional Chromatin Configuration Reconstructions (2014) Biostatistics, Epub ahead of print, Feb 11.


    Javier Arsuaga, Reyka Jayasinghe, Robert Scharein, Mark Segal and Vazquez, M., Current theoretical models fail to predict the topological complexity of the human genome, Frontiers in Molecular Biosciences 2, pp.48, 2015

    Ishihara, K., Pouokam, M., Suzuki, A., Scharein, R., Vazquez, M., Arsuaga, J., Shimokawa, K. Bounds for minimum step number of knots confined to tubes in the simple cubic lattice, Journal of Physics A: Mathematical and Theoretical, 50 (21), pp. 215601, 2017.

    Stolz, R., Yoshida, M., Brasher, R., Flanner, M., Ishihara, K., Sherratt, D.-J., Shimokawa, K., Vazquez, M. Pathways of DNA unlinking: A story of stepwise simplification, Scientific Reports, 7 (1), pp. 12420, 2017, ISBN: 2045-2322.

    Witte, S.*, Flanner, M., and Vazquez, M. (2018) A symmetry Motivated Link Table. Symmetry 10: 604 .

    Pouokam, M.*, Cruz, B., Burgess, S., Segal, M., Vazquez, M., and Arsuaga, J. (2019) The Rabl configuration limits topological entanglement of chromosomes in budding yeast. Scientific Reports. 9 (1): 6795.

    Lidman, T., Moore, A.H. and Vazquez, M. Distance one lens space fillings and band surgery on the trefoil knot. In press.  arXiv:1710.07418v2  [math.GT]

    Moore, A., and Vazquez, M. (2019) Recent advances on the non-coherent band surgery model for site-specific recombination, AMS Contemporary Mathematics. In press. [math.GT]

    Moore, A.H., and Vazquez, M. (2019). A note on band surgery and the signature of a knot.  arXiv:1806.02440.

    Cruz, B., Calderer, M.C., Arsuaga, J., Vazquez, M. (2019). Computer simulations show that the bacteriophage packaging motor induces a chiral organization of the genome. Biophysical Journal. Submitted.

    Walker, S., Arsuaga, J., Vazquez, M., Hiltner, L.*, Calderer, M.C. (2019). Liquid crystal model of viral DNA encapsidation. Submitted. arXiv: 1902.09188