Design of a constant force clamp and estimation of molecular motor motion using modern control approach

Since its inception, optical traps have become an important tool for single molecule investigation because of its precise ability to manipulate microparticles and probe systems with a force resolution of the order of fN. Its use as a constant force clamp is of particular importance in the study of molecular motors and DNA. The highly nonlinear nature (specially the presence of hysteresis) of the force-extension relationships in such biomolecules is traditionally modelled as a linear Hookean spring for small force perturbations. For these linear models to hold, high disturbance rejection bandwidths are required so that the perturbations from the regulated values remain small. The absence of systematic design and performance quantification in the current literature is addressed by designing an optimized PI and a H_∞ controller, that significantly improve the force regulation and its bandwidth. A major application of constant force clamps is in step detection of biomolecules, where due to the presence of thermal noise, one has to extract the stepping data via postprocessing. In this paper, a real time step-detection scheme, currently lacking in literature, is achieved via a mixed objective H₂/H_∞ synthesis. In the design, the H _∞ norm for force regulation and stepping estimation error is minimized while keeping the H₂ norm of the thermal noise on the stepping estimate is kept bounded.