Multivalent adhesion of flexible nanocarriers to cell membranes: effects of architecture, subdivision, and length

Multivalent adhesion between ligand-functionalized nanocarriers and cell-surface receptors underlies targeted drug delivery, yet how the structure of flexible carriers regulates binding independently of stiffness remains poorly understood. We use a multiscale statistical mechanics-based framework coupling a deformable-membrane continuum model to coarse-grained models of flexible nanocarriers, ligands, and receptors. Monte Carlo simulations quantify multivalency and resolve binding free energies into enthalpic and entropic contributions. We compare star and linear architectures, subdivision of a fixed ligand budget among multiple carriers, and contour lengths across receptor densities and membrane excess areas. Bond number is receptor-limited at low receptor density and ligand-limited at high density, yielding similar multivalency among designs. Carrier structure instead controls the organization and thermodynamic quality of comparable bond populations through enthalpy-entropy compensation, with receptor translational entropy as the dominant penalty. Linear nanocarriers bind more favorably than star nanocarriers at matched stiffness and multivalency because they incur a smaller collective configurational penalty. Ligand-budget subdivision produces a nonmonotonic response: at high receptor density, the single-carrier system is most favorable and the two-carrier system least favorable because of entropic penalties and weaker receptor-ligand enthalpic stabilization. Contour length produces a weaker receptor-density-dependent crossover: shorter carriers are favored at low receptor density, longer carriers at intermediate density, and their binding free energies converge after ligand saturation. Membrane excess area modulates these balances without imposing a universal ordering. Similar bond numbers can therefore conceal substantial differences in adhesion free energy, providing design principles for matching carrier structure and ligand organization to receptor expression and membrane mechanics.