(237c) Generalized Langevin Dynamics for Adhesion of a Polymer-Grafted Nanoparticle to Cell

Stealth nanoparticles (SNP) [1] are a promising material for nanocarriers in vascular targeted drug delivery. Biocompatible polymers such as polyethylene glycol (PEG) are grafted to the particle surfaces to avoid unwanted immune clearance and improve the stability of nanoparticles in the blood circulation. Targeting ligands are linked to the free ends of polymers to achieve desirable antigen-antibody recognition. Once such nanocarriers reach the target cells, the delivery efficiency is expected to be influenced by various physiological factors such as vessel-wall-mediated hydrodynamic interactions, specific binding between targeting agents and membrane receptors, and cell membrane morphology. In this work, we model the SNP as a composite nanoparticle consisting of a hard core coated with a porous polymeric brush with end-ligands. In the vicinity of the vessel wall, the nanoparticle center-of-mass motion is resolved using a Langevin equation (LE) incorporating near-cell lubrication force [2], and the conformational relaxation of the coated polymer is described using a generalized Langevin equation (GLE) with a time-correlated viscous resistance and a Hookean-type internal elastic force. Concurrently, the evolution of membrane configuration subjected to thermal effects and external binding forces is explored using Fourier space Brownian dynamics (FSBD) [3] simulation to achieve more satisfactory statistics. In the presence of the membrane-mediated binding potential between the functionalizing ligands and membrane receptors, the nanoparticle center-of-mass motion, structural relaxation of the coated polymers, and membrane thermal undulations are simultaneously resolved using these coupled equations. The mean squared displacement, velocity autocorrelation function, and position autocorrelation function of the SNP for various distances from the vessel wall, coated brush heights, and strengths of binding potential are examined. We demonstrate that the interplay between the thermodynamic effects and hydrodynamic interactions substantially impacts the transient relaxation of both the velocity and position of the SNP, as evidenced by the distinct behaviors observed from the autocorrelation functions at different characteristic time scales.

References:

[1] C.-M. J. Hu, R. H. Fang, B. T. Luk, and L. Zhang, Nanoscale 6, 65 (2014).

[2] H.-Y. Yu, D. M. Eckmann, P. S. Ayyaswamy, and R. Radhakrishnan, Phys. Rev. E 91, 052303 (2015).

[3] L. C.-L. Lin and F. L. H. Brown, Phys. Rev. Lett. 93, 256001 (2004).