A mathematical model of cell adhesion on soft surfaces.
basic_science · Level V
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- Record sourced from PubMed, PMID 42385568.
- Also identified by DOI 10.1016/j.jmbbm.2026.107527.
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Abstract
Cell adhesion is a fundamental process influenced by the interplay between cellular mechanics and substrate properties. Experimental studies have shown that substrate stiffness can influence adhesion, proliferation, and migration in a highly context-dependent manner, with both stiffness-enhanced and compliance-enhanced responses reported under different biological and mechanical conditions. While several theoretical frameworks have examined membrane adhesion and mechanobiology, a simplified mechanical description capable of systematically exploring the coupled role of membrane rigidity and substrate compliance across broad stiffness ranges remains of interest. Here, we develop a mathematical model that predicts cell adhesion on soft surfaces by integrating key physical parameters: the flexural rigidity of the cell membrane, the elastic modulus of the substrate, and the binding energy density at the interface between the two. The model describes the equilibrium shape of the cell membrane, computes the total adhesion energy, and identifies the conditions under which adhesion is favored. Simulations spanning substrate stiffness from 1 kPa to 1 MPa and membrane rigidity from 1k<sub>B</sub>T to 5000k<sub>B</sub>T reveal that adhesion is optimized on soft surfaces for sufficiently large values of substrate stiffness (E<sub>s</sub>>10kPa) and low values of membrane rigidity (D<15k<sub>B</sub>T). In contrast, for low values of both membrane rigidity and substrate stiffness, adhesion increases for increasingly higher values of substrate stiffness. Conversely, at higher bending rigidities, adhesion behavior shifts depending on the stiffness regime. These predictions remain consistent with diverse experimental observations reported in the mechanobiology literature and support the view that adhesion behavior emerges from the coupled interplay between membrane mechanics and substrate compliance. Our framework provides design maps for tuning cell-substrate interactions and highlights the potential of nanostructured surfaces to modulate adhesion through control of local curvature and mechanical coupling.