This grant supports an interdisciplinary team of three investigators using mathematical modeling, computer simulations, and experiments to develop improved predictive models for the behavior of cell membranes in certain contexts. This research project concerns the mathematical modeling of the interaction between a cell membrane and a solid particle, a physical process that is essential to cell adhesion to a solid surface and cellular uptake (endo/exocytosis) of colloidal nanoparticles (e.g., drug carriers). Advances in nano- and biomedical engineering have made it possible to design smart materials for more effective medical treatments (e.g., targeted drug delivery). These technical developments are based on understanding how a cell membrane interacts with colloidal particles in a fluid environment filled with ions and macromolecules. It is imperative to better understand the physical processes that underpin such ubiquitous membrane-solid interactions in a complex fluid environment.This project aims to develop new mathematical models and numerical algorithms to describe quantitatively the particle-membrane interactions by considering random thermal fluctuations, electrokinetic effects, and nanoscale phenomena (e.g., molecular layering) that are commonly ignored in conventional continuum-based approaches. Microfluidic experiments will be developed in parallel to guide the mathematical and computational modeling of a membrane interacting with solid surfaces with curvature and/or localized features. This project will advance the mathematical modeling of a lipid bilayer membrane (LBM) interacting with solid surfaces and particles by considering the presence of the thin liquid film filling the gap between the LBM and other solid surfaces. It is hypothesized that, through physically consistent effective interaction potentials, a continuum-based thin film equation can capture the macroscopic spreading dynamics of LBMs on surfaces with variable wetting properties and zeta potentials, under different ionic strengths. One of the main results from the mathematical modeling will be the stochastic nonlinear lubrication equation for the height of the thin liquid film between the LBM and a solid surface. Theoretical predictions, such as LBM adhesion and spreading time, will be compared against experimental results for validation and model refinement. The developed model will be employed to investigate the adhesion of a LBM (1) under different ionic concentrations in the liquid and (2) on solid surfaces with curvature and localized features.
|Effective start/end date||9/1/16 → 8/31/19|
- National Science Foundation