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Published on: June 4, 2015
Application of Population Dynamics to Study Heterotypic Cell Aggregations in the Near-Wall Region of a Shear Flow
Yanping Ma1, Jiakou Wang, Shile Liang
1Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA.
Abstract:
Our research focused on the polymorphonuclear neutrophils (PMNs) tethering to the vascular endothelial cells (EC) and the subsequent melanoma cell emboli formation in a shear flow, an important process of tumor cell extravasation from the circulation during metastasis. We applied population balance model based on Smoluchowski coagulation equation to study the heterotypic aggregation between PMNs and melanoma cells in the near-wall region of an in vitro parallel-plate flow chamber, which simulates in vivo cell-substrate adhesion from the vasculatures by combining mathematical modeling and numerical simulations with experimental observations. To the best of our knowledge, a multiscale near-wall aggregation model was developed, for the first time, which incorporated the effects of both cell deformation and general ratios of heterotypic cells on the cell aggregation process. Quantitative agreement was found between numerical predictions and in vitro experiments. The effects of factors, including: intrinsic binding molecule properties, near-wall heterotypic cell concentrations, and cell deformations on the coagulation process, are discussed. Several parameter identification approaches are proposed and validated which, in turn, demonstrate the importance of the reaction coefficient and the critical bond number on the aggregation process.
Insights
This study models how polymorphonuclear neutrophils (PMNs) and melanoma cells aggregate near blood vessel walls, crucial for understanding cancer metastasis. The findings highlight key factors influencing this cell aggregation process.
Area of Science:
- Biophysics
- Cell Biology
- Mathematical Modeling
Background:
- Tumor cell extravasation during metastasis involves cell adhesion to vascular endothelium.
- Polymorphonuclear neutrophils (PMNs) play a role in facilitating tumor cell adhesion and aggregation.
Purpose of the Study:
- To develop and validate a multiscale near-wall aggregation model for heterotypic cell interactions.
- To investigate the influence of cell deformation and cell ratios on aggregation dynamics.
- To understand the process of melanoma cell emboli formation mediated by PMNs.
Main Methods:
- Applied a population balance model based on the Smoluchowski coagulation equation.
- Utilized an in vitro parallel-plate flow chamber simulating near-wall cell-substrate adhesion.
- Combined mathematical modeling, numerical simulations, and experimental observations.
Main Results:
- Developed a novel multiscale near-wall aggregation model incorporating cell deformation and heterotypic cell ratios.
- Achieved quantitative agreement between model predictions and experimental data.
- Identified intrinsic binding molecule properties, cell concentrations, and cell deformation as significant factors in coagulation.
Conclusions:
- The developed model accurately predicts cell aggregation dynamics in shear flow.
- Cell deformation and heterotypic cell ratios are critical parameters influencing metastasis.
- Parameter identification approaches validated the importance of reaction coefficient and critical bond number.
