Conditions on length of Ligand-Receptor pairs for nanoparticle adhesion influenced by plasma membrane surface charge

Nanoparticle (NP) adhesion with a plasma membrane typically occurs through the formation of a receptor-ligand (R-L) bond. For this binding to occur the ligand-functionalized NP need to come within a minimum distance of separation, equal to the length of the R-L complex (d_RL). Here we develop a theory to establish the significant influence of the membrane surface charges and the surrounding electrolyte environment on this process of the approach of the NP towards the membrane within the R-L complex length. The negatively charged membrane induces a negative electrostatic potential on the NP surface thereby repelling the NP from the membrane, whereas the thermal fluctuations assist the NP to come closer to the membrane. This balance leads to a critical NP-membrane separation length d_g,c. Our theory establishes a design criterion on the length of the R-L complex such that to facilitate the NP-membrane adhesion, we need to have d_RL> d_g,c. This leads to a design space for engineering the ligands for the NPs such that the process of adhesion can be ensured in a given electrostatic environment.