Kang-Ling Liao
                              Update: 12/11, 2013
Mathematical Biosciences Institute 
The Ohio State University                                             
376 Jennings Hall
1735 Neil Ave.
Columbus, OH 43210 U.S.A.
Phone (Office): (614) 688-0427  
E-mail: liao.92@mbi.osu.edu
Research Statement
Mathematical Research Interests                                
l Dynamical Systems 
Ø  oscillation, oscillation-arrested, coupled oscillator
l Delayed Differential Equations: 
Ø  how transcription and translation delays affect the dynamics in somitogenesis and gene regulation
Ø  how delay affects the dynamics in patch model
l Bifurcation Theory
Ø  how parameters affect the dynamics in somitogenesis, gene regulation, and patch model
l  Reaction-Diffusion Systems
Ø   traveling wave pattern
Ø   the existence of the upper and lower solutions in delayed reaction-diffusion systems
Ø   how delays affect the stability of the positive steady state  
Biological Research Interests
l   Somitogenesis
Ø   synchronous/asynchronous oscillation, oscillation-arrested, and the traveling wave pattern 
Ø   normal/abnormal somite formation 
Ø   coupling strength and coupling delays 
Ø   coupling structure
l   Gene Regulation
Ø   synchronous/asynchronous oscillation, oscillation-arrested, and the traveling wave pattern 
l   Cancer Immunoediting
Ø   CD200-CD200R-complex
Ø   Interleukin-27
Ø   Interleukin-35
l   Ecology
Ø   dynamics of discrete-space and continuous-time model
l   Modeling on Biological Process

I am a Postdoctoral Fellow at the Mathematical Biosciences Institute (MBI). My research interests are in differential equations, delayed differential equations, and bifurcation theory. I have been working on many interesting mathematical biological problems, such as somitogenesis, modeling in cancer immunoediting, and evolution in ecology.


Somitogenesis is the process that vertebrate embryos develop somites. This process depends on gene expressions which have the interesting phenomena: synchronous oscillation with period around 30 minutes in the tail bud, traveling wave pattern, oscillation-arrested in the anterior of presomitic mesoderm. In order to investigate these phenomena, we used sequential-contracting technique to derive conditions for oscillation-arrested and applied delay Hopf bifurcation theorem, center manifold theory, and the normal form method to analyze the existence of the stable synchronous/asynchronous oscillation in the tail bud. We also used numerical simulation to find some suitable gradient for degradation rates of cells to generate normal traveling wave pattern. 


For cancer immunoediting, we constructed mathematical models to study some important factors, such as CD200-CD200R-complex, Interleukin-27 (IL-27), and Interleukin-35 (IL-35) cytokines, in cancer immunoediting. For CD200-CD200R-complex, recent experiments indicated that CD200-CD200R-complex has two opposite effects of tumor growth: inhibition and promotion. In order to investigate the functions of CD200-CD200R-complex in tumor growth, we constructed a mathematical model to simulate how CD200-CD200R-comples affects tumor growth. Furthermore, we demonstrated that whether blocking CD200 is a good therapy in cancer treatment depends on the "affinity" of the macrophages to form this complex with tumor cells. On the other hand, IL-12 cytokine family is regarded as pro-inflammatory cytokine that inhibits tumor growth. Recently, two new members were found. One is IL-27 which promotes immune system to kill tumor cells. The other is IL-35 which promotes tumor growth and inhibits immune response. However, it still lacks of strong evidence for their functions in tumor growth. Hence, we constructed two mathematical models for these two cytokines to demonstrate their functions. Our numerical results quantitatively fit the experimental data. By using our numerical simulations, we also provided some practicable dozing schedule on these two cytokines in cancer treatment.


In evolution in ecology, if we consider a reaction-diffusion equation with time delay, there exists a critical value of delay such that if delay is smaller than this value, then the positive steady state is stable. But, if delay is larger than the critical value, then the steady state is unstable. However, this result only holds in a narrow range of parameter values. In order to extend this range, we used a patch model with time delay to study this question. By using delayed Hopf bifurcation theorem, center manifold theorem, and the normal form method, we obtained similar results for the patch model under a wider range of parameter values.