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.