(162h) Generalized Langevin Dynamics for Functionalized Nanocarrier Adhesion to Cell Surfaces in the Presence of Hydrodynamic Interactions

Vascular delivery of antibody-functionalized nanocarriers (50 nm-1 µm in size) to selectively bind targeted receptors on the endothelial cells is a viable therapeutic strategy in systems pharmacology. However, the optimal design of such nanocarriers involves the appropriate selection of size, shape of nanocarriers and antibody density on the nanocarriers, and the choice of appropriate tethers/linkers bridging the antibodies to the nanocarrier surface depends on the physiological microenvironment including the hemodynamics and the rheological properties of the flow in the capillaries as well as the cellular state of the endothelial cells (which governs the expression of the targeted receptors such as the intracellular adhesion molecule-1 or ICAM-1). We have shown in recent work that a model-based optimization of this design can help guide the achievement of targeting selectivity and specificity in vivo [1,2]. Here we address the important aspects of nanocarrier adhesive dynamics in terms of how they impact binding selectivity and specificity.

The main premise of this work is the hypothesis that the efficiency of vascular targeted drug delivery using functionalized nanoparticles is affected simultaneously by several biophysical and biochemical factors such as the margination probability of the nanocarrier towards the red blood cell-free layer, hydrodynamic interactions due to the wall and the near-wall flow field, thermal fluctuations, and the specific ligand-receptor (or antibody-antigen) binding interactions. A complete description of hydrodynamic interactions for the system can be achieved by direct numerical simulations of the fluctuating hydrodynamic equations, which simultaneously resolve the velocities and the stresses of the fluid and the particles [3-5]. While such a model can be pursued for simple geometries for small systems such as short capillary segments not much longer than a few diameters of the blood cells, it is not realistic for a pharmacological model considering nanocarrier margination and binding in a vascular network tree. With the objective of developing a coarse-grained description of the hydrodynamics in complex geometries, we present a generalized Langevin dynamics aiming to capture the adhesive dynamics of the nanocarrier closed to the vessel wall in the presence of RBC-driven marginating potential, hydrodynamic, and Brownian forces. The functionalized nanoparticle is modeled as hard or soft sphere with surface-grafted ligands (antibodies) that interact with the receptors (such as ICAM-1) on the endothelial cells. To incorporate the memory effects of the nanocarirer due to coupling with the locally confined fluid and the relaxation of the ligand-receptor pair, a set of non-Markovian, generalized Langevin equations [6] for the nanocarrier motion (translational and rotational motion about the center of mass) and the stretching for each tether as well as antibody-antigen pair are solved simultaneously. The space-time dependent memory functions are obtained from independent experiments [7], microscopic simulations [8], or analytical theories [9]. We analyze the nanocarrier velocity autocorrelation function along suitable coordinates (center of mass translation/rotation, ligand-receptor bond, and tether coordinates) to characterize nanocarrier adhesive dynamics and the potential of mean force along a specified reaction coordinate to quantify the binding affinity [1] in the presence of various hydrodynamic couplings. We also discuss the generalization of the current theoretical framework to study the rolling motion and internalization of the nanocarrier.

References

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