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

## TL;DR

This paper introduces a robust control framework for optical tweezers that simultaneously regulates force and estimates motor protein motion, overcoming disturbances and thermal noise for precise single-molecule studies.

## Contribution

It presents a novel mixed H2-Hinfinity optimization approach for dual force regulation and motion estimation in optical tweezer experiments, with quantifiable guarantees.

## Key findings

- Force regulation below 1 pN with less than 10% error achieved
- Effective real-time motor motion estimation demonstrated
- Framework validated through simulations and live experiments

## 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.