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Optical tweezers have enabled important insights into intracellular transportthrough the investigation of motor proteins, with their ability to manipulateparticles at the microscale, affording femto Newton force resolution. Its useto realize a constant force clamp has enabled vital insights into the behaviorof motor proteins under different load conditions. However, the varying natureof disturbances and the effect of thermal noise pose key challenges to forceregulation. Furthermore, often the main aim of many studies is to determine themotion of the motor and the statistics related to the motion, which can be atodds with the force regulation objective. In this article, we propose a mixedobjective H2-Hinfinity optimization framework using a model-based design, thatachieves the dual goals of force regulation and real time motion estimationwith quantifiable guarantees. Here, we minimize the Hinfinity norm for theforce regulation and error in step estimation while maintaining the H2 norm ofthe noise on step estimate within user specified bounds. We demonstrate theefficacy of the framework through extensive simulations and an experimentalimplementation using an optical tweezer setup with live samples of the motorprotein kinesin; where regulation of forces below 1 pico Newton with errorsbelow 10 percent is obtained while simultaneously providing real time estimatesof motor motion.

Single Molecule Studies Under Constant Force Using Model Based Robust Control Design