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Considering the non-affine-in-control system governing the motion of a spherical particle trapped inside an optical tweezer, this paper investigates the problem of stabilization of the particle position at the origin through a control Lyapunov function (CLF) framework. The proposed CLF framework enables nonlinear optimization-based closed-loop control of position of tiny beads using optical tweezers and serves as a first step towards design of effective control algorithms for nanomanipulation of biomolecules. After deriving necessary and sufficient conditions for having smooth uniform CLFs for the optical tweezer control system under study, we present a static nonlinear programming problem (NLP) for generation of robustly stabilizing feedback control inputs. Furthermore, the NLP can be solved in real-time with no need for running computationally demanding algorithms. Numerical simulations demonstrate the effectiveness of the proposed control framework in the presence of external disturbances and initial bead positions that are located far away from the laser beam.
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Lyapunov-Based Nonlinear Control Strategies for Manipulation of Particles and Biomolecules Using Optical Tweezers
Tweezers-based nanorobots, optical tweezers in particular, are renowned for their exceptional precision, and among their biomedical applications are cellular manipulation, unzipping DNAs, and elongating polypeptide chains. This thesis introduces a series of Lyapunov-based feedback control frameworks that address both stability and controlled instability for biological manipulation, applied within the context of optical tweezers. At the core of this work are novel controllers that stabilize or destabilize specific molecular configurations, enabling fine manipulation of particles like polystyrene beads and tethered polymers under focused laser beams. Chapter 1 covers the foundational principles and surveys existing literature on the modeling and control of optical tweezers, emphasizing gaps in the stability and instability control of molecular systems. Chapter 2 presents a robust Control Lyapunov Function (CLF) approach, designed to stabilize spherical particles under optical trapping. By formulating a smooth, norm-bounded feedback controller, we achieve lateral stabilization despite external disturbances, using a real-time, static nonlinear programming (NLP) solution. Simulations verify the effectiveness of this CLF framework, even with significant initial displacements from the laser focus and under thermal forces modeled as a white Gaussian noise. Chapter 3 addresses controlled instability through a Control Chetaev Function (CCF) framework, specifically targeting protein unfolding applications. Linearization with respect to the control input facilitates the application of destabilizing universal controls for affine- in-control system dynamics. The resulting CCF-based norm-bounded feedback controller induces system instability by laterally extending the trapped DNA handle, thereby increasing the molecular extension and providing insights into protein denaturation and unfolding pathways. This controller is robust to stochastic thermal forces and optimized for real-time computational efficiency. These Lyapunov and Chetaev-based control designs collectively expand the capabilities of optical tweezers, advancing single-molecule manipulation under both stable and unstable conditions. These findings advance precision nanomanipulation, opening new avenues for exploring the molecular mechanics of protein unfolding and DNA elasticity.
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- Award ID(s):
- 2153744
- PAR ID:
- 10616689
- Publisher / Repository:
- UTD Theses and Dissertations
- Date Published:
- Subject(s) / Keyword(s):
- Control Lyapunov Function (CLF), Nonlinear control, Feedback control, Control Chetaev Function (CCF), Molecular biology, Protein unfolding, Optical tweezers, Closed-loop control
- Format(s):
- Medium: X
- Institution:
- University of Texas at Dallas
- Sponsoring Org:
- National Science Foundation
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Considering the non-affine-in-control system governing the motion of a spherical particle trapped inside an optical tweezer, this paper investigates the problem of stabilization of the particle position at the origin through a control Lyapunov function (CLF) framework. The proposed CLF framework enables nonlinear optimization-based closed-loop control of position of tiny beads using optical tweezers and serves as a first step towards design of effective control algorithms for nanomanipulation of biomolecules. After deriving necessary and sufficient conditions for having smooth uniform CLFs for the optical tweezer control system under study, we present a static nonlinear programming problem (NLP) for generation of robustly stabilizing feedback control inputs. Furthermore, the NLP can be solved in real-time with no need for running computationally demanding algorithms. Numerical simulations demonstrate the effectiveness of the proposed control framework in the presence of external disturbances and initial bead positions that are located far away from the laser beam.more » « less
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Understanding the process of protein unfolding plays a crucial role in various applications such as design of folding-based protein engines. Using the well-established kinetostatic compliance (KCM)-based method for modeling of protein conformation dynamics and a recent nonlinear control theoretic approach to KCM-based protein folding, this letter formulates protein unfolding as a destabilizing control analysis/synthesis problem. In light of this formulation, it is shown that the Chetaev instability framework can be used to investigate the KCM-based unfolding dynamics. In particular, a Chetaev function for analysis of unfolding dynamics under the effect of optical tweezers and a class of control Chetaev functions for synthesizing control inputs that elongate protein strands from their folded conformations are presented. Based on the presented control Chetaev function, an unfolding input is derived from the Artstein-Sontag universal formula and the results are compared against optical tweezer-based unfolding.more » « less
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Optical traps can measure bead motions with Å-scale precision. However, using this level of precision to infer 1-bp motion of molecular motors along DNA is difficult, since a variety of noise sources degrade instrumental stability. In this chapter, we detail how to improve instrumental stability by (1) minimizing laser pointing, mode, polarization, and intensity noise using an acousto-optical-modulator mediated feedback loop and (2) minimizing sample motion relative to the optical trap using a three-axis piezo-electric-stage mediated feedback loop. These active techniques play a critical role in achieving a surface stability of 1 Å in 3D over tens of seconds and a 1-bp stability and precision in a surface-coupled optical trap over a broad bandwidth (Δf = 0.03–2 Hz) at low force (6 pN). These active stabilization techniques can also aid other biophysical assays that would benefit from improved laser stability and/or Å-scale sample stability, such as atomic force microscopy and super-resolution imaging.more » « less
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Accepted Manuscript1.0
- Dissertation:
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