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 $H_2/H_\infty$ 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 $H_\infty$ norm for the force regulation and error in step estimation while maintaining the $H_2$ 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 $\text{10}\%$ is obtained while simultaneously providing real-time estimates of motor motion.

中文翻译：

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基于模型的控制器设计支持单分子研究

光学镊子通过研究运动蛋白已经使人们能够深入了解细胞内运输，它们具有在微观尺度上操纵微粒的能力，从而提供了毫微微牛顿力的分辨率。它用于实现恒力钳位，已使人们能够深入了解不同负载条件下运动蛋白的行为。然而，扰动的变化性质和热噪声的影响对力的调节提出了关键的挑战。此外，许多研究的主要目的通常是确定电动机的运动以及与运动有关的统计数据，这可能与力调节目标不一致。在本文中，我们提出了一个混合目标$ H_2 / H_ \ infty $使用基于模型的设计的优化框架，可实现可调节保证力和实时运动估计的双重目标。在这里，我们将$ H_ \ infty $ 维持步态估计中的力调节和误差规范 $ H_2 $用户指定范围内的步长估计噪声的范数。我们通过广泛的模拟和实验实施，通过使用光学镊子装置和运动蛋白“驱动蛋白”的实时样品，证明了该框架的有效性，其中运动蛋白的调节力低于1 piconewton，误差低于1 piconewton$ \ text {10} \％$ 可以同时提供电机运动的实时估计值。