Single Molecule Studies Enabled by Model-Based Controller Design

Optical tweezers have enabled important insights into intracellular transport through the investigation of motor proteins, with their ability to manipulate particles at the microscale, affording femto newton force resolution. Its use to realize a constant force clamp has enabled vital insights into the behavior of motor proteins under different load conditions. However, the varying nature of disturbances and the effect of thermal noise pose key challenges to force regulation. Furthermore, often the main aim of many studies is to determine the motion of the motor and the statistics related to the motion, which can be at odds with the force regulation objective. In this paper, we propose a mixed objective <inline-formula><tex-math notation="LaTeX">$H_2/H_\infty$</tex-math></inline-formula> optimization framework using a model-based design, that achieves the dual goals of force regulation and real-time motion estimation with quantifiable guarantees. Here, we minimize the <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math> </inline-formula> norm for the force regulation and error in step estimation while maintaining the <inline-formula> <tex-math notation="LaTeX">$H_2$</tex-math></inline-formula> norm of the noise on step estimate within user specified bounds. We demonstrate the efficacy of the framework through extensive simulations and an experimental implementation using an optical tweezer setup with live samples of the motor protein “kinesin”, where regulation of forces below 1 piconewton with errors below <inline-formula><tex-math notation="LaTeX">$\text{10}\%$</tex-math> </inline-formula> is obtained while simultaneously providing real-time estimates of motor motion.