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Research Papers

Improving Single-Molecule Experiments With Feedback Control of Optical Traps

[+] Author and Article Information
D. G. Cole

Department of Mechanical Engineering and Materials Science,
Swanson School of Engineering,
University of Pittsburgh,
Pittsburgh, PA 15261

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received July 8, 2010; final manuscript received May 16, 2012; published online November 7, 2012. Assoc. Editor: Nader Jalili.

J. Dyn. Sys., Meas., Control 135(2), 021001 (Nov 07, 2012) (9 pages) Paper No: DS-10-1193; doi: 10.1115/1.4007237 History: Received July 08, 2010; Revised May 16, 2012

This article explores various types of feedback control—position feedback, which was shown to be equivalent to force feedback, rate feedback, and integral feedback—for the purpose of improving instrument performance for single-molecule experiments. The ability of each of each types of feedback to lower the measurement signal-to-noise ratio (SNR) is evaluated and compared to the open-loop case. While position feedback does not result in any improvement in the SNR, the cases of rate feedback and integral feedback both resulted in improvements in the measurement's SNR. Rate feedback is shown to effectively “cool” the beads held in the optical trap, thereby limiting the effect that Brownian disturbances have on the beads’ motion. Integral feedback is shown to improve the SNR of the measured signal of interest and is robust and easy to implement. It is also shown that integral feedback acts as an exogenous force estimator. Ultimately, feedback does not provide better resolution as measured by SNR than an open-loop filtering approach can but does provide other advantages, including the ability to control other variables and to make a more robust instrument that can be easily adapted to changes in experimental conditions or the environment.

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Figures

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Fig. 2

The mobility matrix describes velocity–force interaction between the beads. The coupling between the beads, quantified by the off diagonal term YΔ, is significant in two-beam experiments.

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Fig. 1

A schematic of the two-beam trap showing the stiffness of each trap and the molecular forces of the molecule. The position of each trap is located by u1 and u2 and the absolute position of the microspheres by x1 and x2. The trapping force is determined by the trap stiffness k and the linearized molecular stiffness by km. Drag forces are not shown.

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Fig. 3

The measured molecular steps (solid) compared to actual steps (dashed) for open-loop and closed-loop rate feedback control simulation. The open-loop data were filtered at 3 Hz. The rate feedback gain is 1070, which results in a closed-loop cut-off similar to the open-loop filter. For an environmental temperature of 290 K, this rate feedback results in an effective temperature of 0.3 K.

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Fig. 4.

The measured molecular steps (solid) compared to actual steps (dashed) for open-loop and closed-loop integral feedback control simulation. The open-loop data were filtered at 3 Hz. The integral feedback gain is 1060, which results in a closed-loop cut-off similar to the open-loop filter.

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Fig. 5.

This is a block diagram of the force estimation scheme using feedback. The estimated force fest is compared with the real exogenous force fex to generate the estimation error fest. The integral feedback process makes the estimation error small across the bandwidth of interest.

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