Cancer Technologies
Emma Bi (she/her/hers)
Undergraduate Student
University of California Berkeley
Berkeley, California, United States
Qi Wang
Professor
University of South Carolina, United States
Diffusion Experiment Methods:
To model the cell migration, we need to experimentally measure the osmotic pressure gradient. For this reason, Coumarin-102 dye at concentrations between 0 – 200 μmol were captured using the IX-70 microscope camera and the software ImageJ was used to analyze the fluorescence intensity of the dye at different concentrations. Injections were performed with a 100 μL syringe needle into a petri dish. The computational data and code was written in Matlab and Python for the diffusion experiment and for the calculation of the osmotic pressure gradient.
Theoretical Methods:
We developed a three phase cell migration model with charged ions, G-protein, and F-actin. In addition, we propose a reduced model for cell migration in 2-D driven by osmotic pressure.
Three Phase Model:
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Interfacial Boundary Conditions:
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We modeled the solute distribution of osmotic shock critical to cell migration. This was done through fitting the diffusion equation by the least square method to image data of Coumarin-102 fluorescent dye diffusing in water. The solute distribution was calculated and converted to capture the distribution of water diffusion. The results show that concentration of water is high upon initial injection and diffuses radially. Additionally, the osmotic pressure gradient was modeled from experimental data of the solute distribution in 2-D. This measures the driving force on cell migration as a result of the osmotic shock at a given time and space. There is high osmotic pressure at the initial location of injection and when t = 0, and the gradient gradually dissipates across time and space.
We have developed a mathematical model that distinguishes G-actin as separate from solute and details its interaction with F-actin. For each phase, we establish the forces, diffusion and convection of molecular particles, flux and boundary conditions. Equations for resistive forces such as body forces of the actin network by focal adhesion are defined. We primarily explore the conservation of G-actin from actin polymerization in the cell during migration. Cells placed in the PBS buffer migrated linearly along the concentration gradient once induced in a 2-D environment. To model the observed movement of the cell, we thereby reduce the three phase model to 1-D with a coordinate line consistent with the path the cell takes along the osmotic pressure gradient. These modifications to the model along with the establishment of the osmotic pressure gradient is the critical foundation for computational cell simulations that can model the behavior of cell migration in free space.
Experimental data depicts evidence of possible cell deformation upon osmotic shock. Further studies would incorporate such behaviors into the model, and G-actin distribution within a migrating cell. We next plan to simulate the models using the osmotic pressure gradient and reduced model. Computationally modeling the three-phase model could lead to further insights on cell propagation and a deeper understanding of cell movement through the mechanisms of actin polymerization and osmotic pressure.
This material is based upon work supported by the National Science Foundation under Grant No. 1852331
Special thanks to Professor Guiren Wang and Professor Qi Wang. Also supported by Anna Jiang, Anzhelika Kolinko, and in collaboration with Muriel Moon.
Stroka, K. M., Jiang, H., Chen, S. H., Tong, Z., Wirtz, D., Sun, S. X., & Konstantopoulos, K. (2014). Water permeation drives tumor cell migration in confined microenvironments. Cell, 157(3), 611–623. https://doi.org/10.1016/j.cell.2014.02.052
Li, Y., Yao, L., Mori, Y., & Sun, S. X. (2019). On the energy efficiency of cell migration in diverse physical environments. Proceedings of the National Academy of Sciences of the United States of America, 116(48), 23894–23900. https://doi.org/10.1073/pnas.1907625116
Yao, L., & Li, Y. (2022). Effective Force Generation During Mammalian Cell Migration Under Different Molecular and Physical Mechanisms. Frontiers in cell and developmental biology, 10, 903234. https://doi.org/10.3389/fcell.2022.903234
