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We utilize a multiscale modeling framework to study the effect of shape, sizeand ligand composition on the efficacy of binding of a ligand-coated-particleto a substrate functionalized with the target receptors. First, we show howmolecular dynamics (MD) along with Steered MD calculations can be used toaccurately parameterize the molecular binding free energy and the effectivespring constant for a receptor-ligand pair. We demonstrate this for two ligandsthat bind to the $\alpha_5\beta_1$-domain of integrin. Next, we show how theseeffective potentials can be used to build computational models at the meso- andcontinuum- scales. These models incorporate the molecular nature of thereceptor-ligand interactions and yet provide an inexpensive route to study themultivalent interaction of receptors and ligands through the construction ofBell potentials customized to the molecular identities. We quantify the bindingefficacy of the ligand-coated-particle in terms of its multivalency, bindingfree energy landscape and the losses in the configurational entropies. We showthat (i) the binding avidity for particle sizes less than $350$ nm is set bythe competition between the enthalpic and entropic contributions while that forsizes above $350$ nm is dominated by the enthalpy of binding, (ii) anisotropicparticles display higher multivalent binding compared to spherical particlesand (iii) variations in ligand composition can alter binding avidity withoutaltering the average multivalency. The methods and results presented here havewide applications in the rational design of functionalized carriers and also inunderstanding cell adhesion.

Computational investigation of multivalent binding of a ligand coated  particle: Role of shape, size and ligand heterogeneity from a free energy  landscape perspective