Title: Single Molecule Studies Under Constant Force Using Model Based Robust Control Design,
Abstract: 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 article, we propose a mixed
objective H2-Hinfinity 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 Hinfinity norm for the
force regulation and error in step estimation while maintaining the H2 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 pico Newton with errors
below 10 percent is obtained while simultaneously providing real time estimates
of motor motion.