Qixuan Wang, Postdoctoral Scholar

I am a postdoctoral scholar in Dr. Qing Nie’s lab since 2012. I am in the job market this year looking for assistant professorship in the department of mathematics or interdisciplinary research.

Education

  • Ph.D. in Mathematics at University of Minnesota, Minneapolis, MN, USA, 2006-2012.
    Advised by Dr. Hans G. Othmer.
    Dissertation: Modeling of Amoeboid Swimming at Low Reynolds Number.
  • M.S. in Mathematics at University of Minnesota, Minneapolis, MN, USA, 2006-2010.
  • B.S. in Mathematics at Peking University, Beijing, China, 2002-2006.

Research

Research Interests: Computational Biology, Early Embryo Development, Hair Follicle Morphogenesis and Regeneration, Stochasticity in Pattern Formation, Cell Sorting and Cell Motility, Bio-Mechanics, Dynamical System, Partial Differential Equations.

Modeling of Hair Follicle Growth Dynamics and Spatio-Temporal Patterns

Hair follicle (HF) is a skin mini-organ in mammals that undergoes cyclic bouts of regeneration throughout its lifetime. This ability is in part related to its distinct stem cell populations, making the HF a model to study the mechanisms of stem cell regulation and tissue regeneration. At single HF level, cyclic growth is regulated both by signaling within the HF, and long-range interactions between neighboring HFs and other skin components. At population level, the co-option of these signals into skin macro-environment produces wave-like coupled hair growth.

Multi-scale model with HF growth mediated reaction-diffusion dynamics. We developed a multi-scale model that accounts for the realistic HF morphology, where hair-to-hair growth coordination emerges based on shared signaling. Individual HFs are modeled as an expanding or contracting 1-dimensional line, with activator and inhibitor signals produced and received at different locations of the HF and modeled using reaction-diffusion equations. With the signaling coupled with the movements of a HF along its axis, we are able to simulate cyclic HF growth and to induce communication between neighboring HFs. Our modeling and experiments confirm that WNT and BMP serve as the core hair cycle activator/inhibitor pair, affecting both telogen and anagen phase duration within the biologically excitable regime. Using the model we also show that skin behaves as a heterogeneous excitable medium, where dorsal-ventral interactions produce bilaterally symmetric hair growth patterns.

Hybrid model for single HF growth dynamics with discrete/continuum framework for cellular/genetic dynamics. We are developing a hybrid-model for single HF growth dynamics, where cell dynamics are modeled within a discrete framework and gene network regulation within a continuum framework using the stochastic reaction-diffusion PDEs. Implemented together, this hybrid-model suggests that interactions between proliferation- and differentiation-enhancing pathways coordinate to control HF growth during anagen.

Pattern Formation During Early Embryo Development

During early embryonic development, cells make fate specifications instructed by various chemical gradients, which give rise to the formation of gene expression domains that go on to form different tissues and structures. These chemical gradients are noisy and it is crucial that developing systems be able to cope with stochasticity and generate well-defined boundaries between different segmented domains.

Hybrid model for zebrafish rhombomere boundary sharpening with sub-cellular element method for cellular mechanics and stochastic PDE model for plasticity. We developed a hybrid model to study the influences of gene expression noise and cell sorting in zebrafish rhombomeres boundary sharpening. We use the sub-cellular element method (SCEM) to model the inter-cellular mechanical interactions, while the influence of morphogens and gene regulation on cell identity is described by a spatial stochastic model of cell fate regulation. Using the hybrid model, we show that adhesion, repulsion, and noise all have a role in the boundary sharpening process, none of which sharpens boundaries efficiently on its own: while cell sorting is only effective when transition regions are narrow, noise effectively narrows wide transition regions but is less effective at refining boundaries. Instead, noise and cell sorting work synergistically to accomplish sharpening. We also apply this computational framework to multiple boundaries to study the development of rhombomere 3-5 in zebrafish.



Mechanics of Cell Motility at Low Reynolds Number (LRN) Fluids

Locomotion of cells, both individually and collectively, is an important process in development, tissue regeneration, cancer metastasis, etc. Recent studies show that Dictyostelium discoideum (Dd) can swim by propelling themselves through a fluid using only fluid-cell interactions. We look into how complicated shape changes lead to locomotion in low LRN flows which is gov-erned by the Stokes equations.

2D analysis of Dd swimming performance with coupled approach of Schwarz-Christoffel transformation and complex analysis on Goursat functions. In 2-dimensional LRN swimming problem, techniques from complex analysis can be used. One can introduce a stream function, which leads to a biharmonic equation, and the general solution of the Stokes problem is expressed in terms of the Goursat functions that are determined by the motion of the boundary of the swimmer. Using the Schwarz-Christoffel transformation, we approximate the shape changes of Dd, and reduce the problem to the solution of a linear system of equations for basis functions on the boundary of the unit disk. Using this framework, we show that realistic propagating shape deformations can produce propulsion at speeds in the range observed experimentally. We also explore how Dd cell shape and its protrusion shape affect the speed and performance of swimming.

Hydrodynamic interaction analysis for single and multi 3D linked-sphere models. Various 3D linked-sphere models have been developed by different groups including ours in studying LRN swimming behaviors. We apply asymptotic analysis on some of these models, showing that one adopting a mixed modes of shape changes outperforms others adopting unitary modes. Next we use the reflection method on this mixed-mode model to investigate the effect of higher-order hydrodynamic interactions. Simulation results are compared with data from swimming Dd cells. Using the same approach, we also analyze the hydrodynamic interactions among multiple swimmers, which will benefit the study of swarm swimming.



Teaching

Lecture Instructor, at Department of Mathematics, University of California, Irvine, CA, 2012-2015.

  • Undergraduate, lower division:
    Linear Algebra: Fall 2012, 70 students; Fall 2013, 54 students; Spring 2014, 51 students; Spring 2015, 17 students.
    Infinite Series and Linear Algebra: Winter 2013, 115 students.
    Elementary Differential Equations: Winter 2014, 119 students.
    Introduction to Linear Algebra: Fall 2014, 60 students; Winter 2015, 53 students.
  • Undergraduate, upper division:
    Linear Algebra: Spring 2013, 50 students.

Publications

  • 7. Qixuan Wang# and Hans G. Othmer. "Analysis of a model microswimmer with applications to blebbing cells and mini-robots." Under minor revision of Journal of mathematical biology (2016).
  • 6. Qixuan Wang*, Ji Won Oh*, Hye-Lim Lee, Anukriti Dhar, Tao Peng, Raul Ramos, Christian Fernando Guerrero-Juarez, Xiaojie Wang, Ran Zhao, Xiaoling Cao, Jonathan Le, Melisa A Fuentes, Shelby C Jocoy, Antoni R Rossi, Brian Vu, Kim Pham, XiaoyangWang, Nanda Maya Mali, Jung Min Park, June- Hyug Choi, Hyunsu Lee, Julien Legrand, Eve Kandyba, Jung Chul Kim, Moonkyu Kim, John Foley, Zhengquan Yu, Krzysztof Kobielak, Bogi Andersen, Kiarash Khosrotehrani, Qing Nie#, Maksim V Plikus#. "A multi-scale model for hair follicles reveals heterogeneous domains driving rapid spatiotemporal hair growth patterning." eLife, 6 (2017): e22772.
    eLife Insight: Tissue Regeneration: Regional differences.
    PEW Analysis: The Mystery of Hair Growth, Untangled.
    UCI News: UCI study sheds light on regulation of hair growth across the entire body.
    News coverage by University of California.
    Related press coverage in New Scientist, Medical News Today , Laboratory Equipment Magazine , Esquire , OC Register , Daily Mirror , Daily Mail , Birmingham Mail .
  • 5. Qixuan Wang*, William R. Holmes*, Julian Sosnik, Thomas Schilling, Qing Nie#. "Cell sorting and noise-induced cell plasticity coordinate to sharpen boundaries between gene expression domains." PLoS computational biology, 13.1 (2017): e1005307.
  • 4. William R. Holmes*, Nabora Soledad Reyes de Mochel*, Qixuan Wang, Huijing Du, Michael Chiang, Olivier Cinquin, Ken W.Y. Cho# and Qing Nie#. "Gene Expression Noise Enhances Robust Organization of the Early Mammalian Blastocyst." PLoS computational biology, 13.1 (2017): e1005320.
  • 3. Qixuan Wang# and Hans G. Othmer. "Computational analysis of amoeboid swimming at low Reynolds number." Journal of mathematical biology, 72.7 (2016): 1893-1926.
  • 2. Qixuan Wang# and Hans G. Othmer. "The performance of discrete models of low Reynolds number swimmers." Mathematical Biosciences and Engineering, 12.6 (2015): 1303-1320.
  • 1. Qixuan Wang#, Jifeng Hu and Hans G. Othmer. "Models of Low Reynolds Number Swimmers Inspired by Cell Blebbing." Natural Locomotion in Fluids and on Surfaces, Springer New York, 2012. 185-195.

*: Equal contribution. #: Corresponding author(s).