Optimizing Binding among Bimolecular Tethered Complexes.

Tethered motion is ubiquitous in nature, offering controlled movement and spatial constraints to otherwise chaotic systems. The enhanced functionality and practical utility of tethers has been exploited in biotechnology, catalyzing the design of novel biosensors and molecular assembly techniques. While notable technological advances incorporating tethered motifs have been made, a theoretical gap persists within the paradigm, hindering a comprehensive understanding of tethered-based technologies. In this work, we focus on the characterization of the binding kinetics of two tethered molecules functionalized to a hard surface. Using a mean-field approximation, the binding time of such bimolecular system is determined analytically. Furthermore, estimates of the grafting site separation and polymer lengths which expedite binding are provided. These estimates, along with the analytical theories and frameworks established here, have the potential to improve efficacy in self-assembly methods in DNA nanotechnology and can be extended to more biologically specific endeavors including targeted drug-delivery and molecular sensing.