Anael Verdugo

Assistant Professor of Applied Mathematics

About Me

I am an assistant professor at the California State University Fullerton Mathematics Department, working in the area of mathematical biology at the interface between applied mathematics and the biological sciences.

Research Interests

The main focus of my research is to build mathematical models of cellular regulatory networks to gain a deeper understanding of cell physiology. The interdisciplinary nature of my work has allowed me to cross boundaries between traditional fields in applied mathematics and the biological sciences. As a result, my work relies on a tight integration of theoretical and empirical results and it can be summarized in the following three areas:

  1. Dynamic modeling of stress responses
  2. Mathematical analysis of small biological networks
  3. Computational studies of biological oscillators

I am currently collaborating with biologists to build, analyze, and validate dynamic models of cellular pathways, which are then used to predict novel physiological behavior. I also work on mathematical questions inspired by biological systems. Some of my current and previous projects include the use and study of nonlinear differential equations, dynamical systems and bifurcation theory.

CV

Education

2009 Ph.D. Applied Mathematics, Cornell University
2007 M.S. Applied Mathematics, Cornell University
2003 B.S. Mathematics, California Institute of Technology

Professional Experience

2013-Present Assistant Professor, Department of Mathematics, Cal State University Fullerton
2012-2013 Postdoctoral Associate, Virginia Bioinformatics Institute, Virginia Tech
2011-2012 NSF Postdoctoral Fellow, Department of Biochemistry, Oxford University
2009-2011 NSF Postdoctoral Fellow, Department of Biological Sciences, Virginia Tech

Publications

  1. Verdugo A, Vinod PK, Tyson JJ, Novak B. “Molecular mechanisms creating bistable switches at cell cycle transitions.” Open Biology, 3:120179 (2013)
  2. Tyson JJ, Baumann WT, Chen C, Verdugo A, Tavassoly I, Wang Y, Weiner LM, Clarke R. "Dynamic modelling of oestrogen signalling and cell fate in breast cancer cells." Nature Rev Cancer, 11(7):523-532 (2011)
  3. Clarke R, Shajahan AN, Wang Y, Tyson JJ, Riggins RB, Weiner LM, Baumann WT, Xuan J, Zhang B, Facey C, Aiyer H, Cook K, Hickman FE, Tavassoly I, Verdugo A, Chen C, Zwart A, Wärri A, Hilakivi-Clarke LA. "Endoplasmic reticulum stress, the unfolded protein response, and gene network modeling in antiestrogen resistant breast cancer." Hormone Molecular Biology and Clinical Investigation , 5(1):35-44 (2011)
  4. Bridge J, Mendelowitz L, Rand R, Sah S, Verdugo A. “Dynamics of a ring of three coupled relaxation oscillators.” Commun Nonlin Sci Numer Simul, 14:1598-1608 (2009)
  5. Mendelowitz L, Verdugo A, and Rand R. "Dynamics of three coupled limit cycle oscillators with application to artificial intelligence." Commun Nonlin Sci Numer Simul, 14:270-283 (2009)
  6. Verdugo A. and Rand R. "DDE model of gene expression: a continuum approach." Proceedings of the 2008 IMECE-ASME International Mechanical Engineering Congress, paper no. IMECE2008-66321 (2008)
  7. Verdugo A and Rand R. "Center manifold analysis of a DDE model of gene expression." Commun Nonlin Sci Numer Simul, 13:1112-1120 (2008)
  8. Verdugo A and Rand R. "Hopf bifurcation in a DDE model of gene expression." Commun Nonlin Sci Numer Simul, 13:235-242 (2008)
  9. Verdugo A. and Rand R. "Delay differential equations in the dynamics of gene copying." Proceedings of the 2007 ASME International Design Engineering Technical Conferences, paper no. DETC2007-34214 (2007)
  10. Rand R and Verdugo A. "Hopf bifurcation formula for first order differential-delay equations." Commun Nonlin Sci Numer Simul, 12:859-864 (2007)

Research

Overview

The main focus of my research is to build mathematical models of cellular regulatory networks. The interdisciplinary nature of my work has allowed me to develop a variety of interdisciplinary expertise and skills some of which include: (1) use of nonlinear ordinary differential equations to build realistic models of gene-protein networks based on biological literature and experimental data, (2) use of dynamical systems and bifurcation theory to understand the intrinsic dynamic properties of these networks, and (3) use of computer software tools such as Matlab, Copasi, Xppaut, and R to simulate and predict novel network behavior and its implications for cell physiology.

Dynamic modeling of cancer treatment

The focus of this research is to build mathematical models of cell growth and division, programmed cell death, and stress responses in breast cancer cells. Current projects are focused on the pathways involved in iron signaling (Figure 1) and estrogen signaling (Figure 2) and its effects on cell proliferation and tumor growth in breast cancers. These two research enterprises are aimed at understanding the underlying mechanisms and responses of cancer cells to drug therapies (iron therapies or estrogen therapies, respectively). Quantitative mathematical models can shed light on the dynamics of how these pathways and mechanisms collaborate to overcome drug treatment in cancer cells.


Figure 1

Figure 2

Mathematical analysis of small biological networks

Realistic networks of cellular processes are usually relatively large. Fortunately, they generally exhibit smaller recurrent sub-networks that repeat significantly enough to motivate their independent study. The ubiquitous role of these sub-network “motifs” in the biological literature (e.g. Figure 3) indicates the importance of having a clear and thorough understanding of their dynamic properties. My research is focused on using dynamical systems and bifurcation theory to study these motifs in order to gain a deeper understanding of their dynamic behavior.



Figure 3

Computational studies of biological oscillators

Figure 4 Computational models of biological oscillators are frequently used to study repetitive phenomena such as circadian rhythms, cardiac heartbeats, neuronal firing, and even firefly blinking patterns. The theoretical study of how these oscillators behave as part of a larger collective ensemble (e.g. Figure 4) has become an area of active research in the field of applied mathematics. My research is focused in trying to understand how the overall dynamics depends on the network topology, coupling strengths, natural frequencies, and nonlinearities. To this end, I use computational techniques and computer simulations to explore the rich behavior exhibited by these networks.

Teaching

  1. Spring 2014, Numerical Analysis (Math 340)
  2. Spring 2014, Short Course in Calculus (Math 130)
  3. Fall 2013, Numerical Analysis (Math 340)
  4. Fall 2013, Short Course in Calculus (Math 130)

Contact

Anael Verdugo
MH 182L
657-278-5829
averdugo@fullerton.edu