Research

Modeling of Hair Follicles and Skin

Our rearch in follicle & skin modeling is funded by NSF DMS 1951184 (Supplement DMS-2127265), UC Irvine NIAMS P30 skin seed grant.

Hairs have evolved in mammals for thermoregulation, camouflage, display, and mechanical protection. In humans, facial, scalp and body hair can signify social status, and various hair states are critical social clues. Importantly for science, hair follicles (HFs) have emerged as a leading system for studying general mechanisms of stem cell control, tissue patterning during morphogenesis, would-induced regeneration, and tissue aging. HFs are stem cell-rich skin mini-organs that can undergo oscillation-like cycles of regeneration throughout their lifetimes. At the cellular level, regeneration cycles occur as consecutive events of: stem cell activation, progenitor proliferation, differentiation, and coordinated apoptosis.  Morphologically, the HF growth cycle includes phases of active proliferation (anagen), apoptosis-driven involution (catagen), and stem cell quiescence (telogen).  In our lab, we develop mathematical models on hair follicles to answer questions in the following directions: 

1. Growth control. Two major questions: 1) spatial control: during anagen, how does a HF "know" that it has reached its maximum length therefore stops from further expanding? 2) temporal control: how does a HF know when to activate stem cell upon the telogen-to-anagen transition, and when to start degenerating upon the anagen-to-categen transition? With our biology collaborators, we develop multi-scale models to test theories on HF growth control mechanisms.
   Current collaborations: Dr. Makism Plikus (UC Irvine), Dr. Qing Nie (UC Irvine).  

2. Cell fate decisions. At the beginning of each anagen, HF stem cells get activated, giving rise to different compartments of the HF and leading to the downward HF expansion. How do HF cells make correct cell fate decisions along the way so to maintain the HF homeostasis and guarantee the well-functioning of the HF? We develop models on both single- and multi-cell levels to understand the regulation mechansims on HF cell fate decisions.
   Current collaborations: Dr. Makism Plikus (UC Irvine), Dr. Qing Nie (UC Irvine).  

3. HF regeneration in radio- and chemo-therapy. Recent experiments reveal that dose-dependent, HFs may exhibit different regenerative dynamics. We develop mathematical models to study the key factors that drive the HF regeneration after radiation, which may benefit research and treatment on hair recovery after radio- or chemo-therapy.
   Current collaborations: Dr. Sung-Jan Lin (National Taiwan U).  

4. Self-organizing of cat skin patterns. Fetal cat skin may develop periodic morphologic patterns, ranging from stripes to spots as can be found in domestic cats. In collatoration with our biology collaborators, we are developing both continuum and discrete types of mathematical models to study the Turing process on growing cat skin pattern formation. Model results will be used to predict novel skin color patterning mechanisms, and compared with experimental results collected from our collaborators' labs.
   Current collaborations: Dr. Greg Barsh (HudsonAlpha Institute for Biotechnology), Dr. Makism Plikus (UC Irvine).  

Microswimming

Swimming by shape changes at low Reynolds number (LRN) presents widely in biology and micro-robotic design. In this flow regime, inertial effects are negligible, and the micro-organisms or micro-robots propel themselves by exploiting the viscous resistance of the fluid. To fight viscous resistance, different micro-organisms adopt various propulsion mechanisms and directed locomotion strategies to search for food and to run from predators. It is important to understand how cells, micro-organisms and micro aquatic robots interact with surrounding viscous fluids, and how swimming performance depends on the geometric patterns of shape deformations of micro-swimmers. 

1. 3D flagellum beating. Flagella and cilia are common features of a wide variety of biological cells and play important roles in locomotion and feeding at the microscale. The beating of flagella is controlled by molecular motors that exert forces along the length of the flagellum and are regulated by a feedback mechanism coupled to the flagella deformation. We develop a flagellum beating model based on sliding-controlled motor feedback, and by applying computational simulations and mathematical analysis on the model, we investigate the flagellum beating dynamics.
   Current collaborations: Dr. Bhargav Rallabandi lab, Dr. Mykhailo Potomkin lab.  

2. Gait design of micro-swimming models. A micro-swimming gait design is a sequence of shape deformations of a micro-swimmer. An efficient design allows the micro-swimmer to fight the viscous resistance of the LRN fluid and thus swim faster and consume less energy. By applying asymptotic analysis and numerical simulations, we design the optimal gaits for micro-swimmer models.

3. Amoeboid cell swimming. Cells and microorganisms adopt various strategies to migrate in response to different environmental stimuli. To date, much modeling research has focused on the crawling-based Dictyostelium discoideum (Dd) cells migration induced by chemotaxis, yet recent experimental results reveal that even without adhesion or contact to a substrate, Dd cells can still swim to follow chemoattractant signals. We develop a modeling framework to investigate the chemotaxis induced amoeboid cell swimming dynamics. 

Embryonic 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 noise and generate well-defined boundaries between different segmented domains. We use tools from differential equations and sub-cellular element method to develop multiscale models, and use them to explore the roles of cellular plasticity and mechanical movement in pattern formation during embryonic development.