Entropy-Driven Physical Amplification in Multivalent Biosensing

Sensitive detection of low-abundance molecular targets is widely assumed to require enzymatic amplification, such as PCR, to achieve low detection limits. In amplification-free platforms, sensitivity is traditionally constrained by equilibrium binding affinity. Here, we show theoretically that multivalent linker entropy provides a distinct physical route to exponential sensitivity enhancement in purely equilibrium-based sensing architectures. Using a statistical-mechanical theory supported by grand canonical Monte Carlo simulations, we demonstrate that redistributing a fixed total interaction strength over increasing linker valency exponentially lowers the adsorption threshold. This scaling emerges not from stronger energetic affinity, but from the rapid growth of combinatorial binding configurations, identifying entropy as a physical mechanism that amplifies the adsorption response. Crucially, this threshold shift requires no increase in total binding strength, enabling ultrasensitive responses without enzymatic replication. This prediction is consistent with the ultrasensitive, amplification-free detection demonstrated experimentally in DNA-functionalized colloidal systems [Proc. Natl. Acad. Sci. USA 120, (2023): e2305995120], whose physical origin had remained unexplained. Our theory identifies entropy-driven combinatorial effects as a plausible mechanism for this high sensitivity. More broadly, it establishes combinatorial linker entropy as a design principle for high-sensitivity, amplification-free detection.