On Nonlinear Control of Optical Traps Using Pulling Trajectory Tracking for Single-Molecule Experiments

2011 ◽  
Author(s):  
Daniel G. Cole
Keyword(s):  
Single Molecule ◽  
Optical Trap ◽  
Static Condition ◽  
Optical Force ◽  
Optical Traps ◽  
Pi Control ◽  
Force Estimation ◽  
Integral Control ◽  
Servo Tracking ◽  
Additional Feedback

This article explores nonlinear position plus integral (PI) feedback for controlling an optical trap used in single-molecule experiments. In general, nonlinearities in the spatial dependence of the optical force complicate feedback control for optical traps. Furthermore, the extension of a molecule creates an additional feedback path that puts constraints on the PI control gains. The nonlinear PI control presented here is shown to provide all of the benefits of integral control: disturbance rejection, servo tracking, and force estimation. The ability of nonlinear PI control to lower the measurement SNR is evaluated. Finally, constraints on the pulling rate are given to ensure the system trajectory remains in a quasi-static condition, stable, and the bead remains held in the trap.

Nonlinear Proportional Plus Integral Control of Optical Traps for Exogenous Force Estimation

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
D. G. Cole ◽  
J. G. Pickel
Keyword(s):  
Optical Trap ◽  
Open Loop ◽  
Optical Force ◽  
Optical Traps ◽  
Pi Control ◽  
Force Estimation ◽  
Nonlinear Controller ◽  
Closed Loop System ◽  
Integral Control ◽  
Servo Tracking

This article explores nonlinear proportional plus integral (PI) feedback for controlling the position of an object held in an optical trap. In general, nonlinearities in the spatial dependence of the optical force complicate feedback control for optical traps. Nonlinear PI control has been shown to provide all of the benefits of integral control: disturbance rejection, servo tracking, and force estimation. The controller also linearizes the closed-loop system. More importantly, the nonlinear controller is shown to be equivalent to an estimator of the exogenous force. The ability of nonlinear PI control to lower the measurement SNR is evaluated and compared to the variational open-loop case. A simulation demonstrating the performance of the nonlinear PI control is presented.

Exogenous Force Estimation Using Disturbance Modeling for Optical Trap Experiments

2011 ◽  
Author(s):  
Jason G. Pickel ◽  
Daniel G. Cole
Keyword(s):  
Kalman Filter ◽  
Control Structure ◽  
Optical Trap ◽  
Relative Displacement ◽  
Optical Force ◽  
Force Estimation ◽  
Experimental Conditions ◽  
Hooke’S Law ◽  
Hooke's Law ◽  
Disturbance Model

In many optical trapping experiments, exogenous forces are estimated by assuming the exogenous force is balanced with the optical force. These optical forces are measured using Hooke’s law, and the displacement of the particle is low-pass filtered to minimize the effects of Brownian noise. This paper explores a different approach that uses a disturbance model approach for estimating exogenous forces using a Kalman filter. The state estimate is then used in a LQG structure to manipulate the relative position of a dielectric particle within an optical trap. The exogenous force estimate using a Kalman filter has been shown to have a higher SNR than the force estimation using Hooke’s Law. In addition to force estimation, the control structure can also manipulate the relative displacement of the particle to satisfy experimental conditions. A simulation is presented to demonstrate the performance of the LQG control structure.

scholarly journals Numerical Analysis of Optical Trapping Force Affected by Lens Misalignments

Photonics ◽  
2021 ◽  
Vol 8 (12) ◽  
pp. 548
Author(s):  
Hanlin Zhang ◽  
Wenqiang Li ◽  
Nan Li ◽  
Huizhu Hu
Keyword(s):  
Numerical Calculation ◽  
Numerical Analysis ◽  
Optical Trapping ◽  
Optical Trap ◽  
Geometrical Optics ◽  
Optical Force ◽  
Optical Traps ◽  
Trapping Force ◽  
Calculation Results ◽  
The Asymmetry

Geometrical optics approximation is a classic method for calculating the optical trapping force on particles whose sizes are larger than the wavelength of the trapping light. In this study, the effect of the lens misalignment on optical force was analyzed in the geometrical optics regime. We used geometrical optics to analyze the influence of off-axis placement and the tilt of the lens on the trapping position and stiffness in an optical trap. Numerical calculation results showed that lens tilting has a greater impact on the optical trap force than the off-axis misalignments, and both misalignments will couple with each other and cause a shift of the equilibrium point and the asymmetry of the optical trap stiffness in different ways. Our research revealed the asymmetry in optical traps caused by lens misalignment and can provide guidance for optimize lens placement in future experiments.

Feedback Control and Exogenous Force Estimation for Improved Single-Molecule Experiments

2010 ◽  
Author(s):  
Daniel G. Cole
Keyword(s):  
Feedback Control ◽  
Single Molecule ◽  
Force Feedback ◽  
Open Loop ◽  
Optical Traps ◽  
Measured Signal ◽  
Force Estimation ◽  
Position Feedback ◽  
Integral Feedback

This article explores two types of feedback used to control optical traps: position feedback, which was shown to be equivalent to force feedback, and integral feedback. The ability of each of these types of feedback to lower the measurement SNR in single molecule experiments is evaluated and compared to the open-loop case. While position feedback did not result in any improvement in the SNR, the case of integral feedback results in an improvement. Integral feedback is shown to improve the SNR of the measured signal of interest, and is relatively robust and easy to implement. It is also shown that integral feedback acts as an exogenous force estimator.

Development of Precision Optical Traps for Single Molecule and Motor Protein Research

2004 ◽  
Author(s):  
Kurt D. Wulff ◽  
Daniel G. Cole ◽  
Robert L. Clark
Keyword(s):  
Angular Momentum ◽  
Laser Beam ◽  
Orbital Angular Momentum ◽  
Single Molecule ◽  
Optical Trap ◽  
Motor Protein ◽  
Optical Traps ◽  
Position Sensing ◽  
Intensity Field ◽  
Increased Sensitivity

Optical traps have become an important instrument for investigating systems and processes at the micro- and nanoscale, particularly within biology where manipulation of biological systems from DNA to cells has offered new insights to cellular processes. Using the inherent momentum of light, particles are trapped in the high intensity field of a focused laser beam thus allowing for the manipulation of microscopic particles. This paper discusses the current development of a state-of-the-art optical trap with increased sensitivity for the measurement of single molecule and motor protein mechanics. A common position sensing technique uses quadrant photodiodes to detect motion on the order of tens of nanometers. However, the measurement of positions and forces on a smaller level than previously attempted requires increased precision. Interferometric techniques provide one method to improve the spatial resolution to the order of nanometers or less. Furthermore, the use of feedback control offers the ability to easily adapt the optical trap to the particular experiment being conducted. In addition, optical traps can apply torque to trapped objects for the study of rotary mechanics when the trapping laser has orbital angular momentum. Methods for generating a laser beam with orbital angular momentum will be discussed.

scholarly journals Polarization effects and the calibration of a donut beam axial optical tweezers for single-molecule force spectroscopy

2017 ◽  
Author(s):  
Russell Pollari ◽  
Joshua Milstein
Keyword(s):  
Optical Tweezers ◽  
Single Molecule ◽  
Optical Trap ◽  
Force Spectroscopy ◽  
Index Of Refraction ◽  
Optical Force ◽  
Practical Implementation ◽  
Single Molecule Force Spectroscopy ◽  
Polarization Effects ◽  
Axial Forces

ABSTRACTAdvances in light shaping techniques are leading to new tools for optical trapping and micromanipulation. For example, optical tweezers made from Laguerre-Gaussian or donut beams display an increased axial trap strength and can impart angular momentum to rotate a specimen. However, their application to precision, biophysical measurements remains limited as their are a number of challenges to applying this tool to optical force spectroscopy. One notable complication, not present when trapping with a Gaussian beam, is that the polarization of the trap light can significantly affect the tweezers’ strength as well as the precise location of the trap. In this article, we provide a practical implementation of a donut beam optical tweezers for applying axial forces. We show how to precisely calibrate the height of the optical trap above the coverslip surface while accounting for focal shifts in the trap position that arise due to radiation pressure, mismatches in the index of refraction, and polarization induced intensity variations.

Optimal trap velocity in a dynamic holographic optical trap using a nematic liquid crystal spatial light modulator

2022 ◽  
Author(s):  
Karuna Sindhu Malik ◽  
Bosanta Ranjan Boruah
Keyword(s):  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
Spatial Light Modulator ◽  
Optical Trap ◽  
Optical Element ◽  
Optical Traps ◽  
Light Modulator ◽  
Step Size ◽  
Microscopic Object ◽  
Optimal Velocity

Abstract A dynamic holographic optical trap uses a dynamic diffractive optical element such as a liquid crystal spatial light modulator to realize one or more optical traps with independent controls. Such holographic optical traps provide a number of flexibilities and conveniences useful in various applications. One key requirement for such a trap is the ability to move the trapped microscopic object from one point to the other with the optimal velocity. In this paper we develop a nematic liquid crystal spatial light modulator based holographic optical trap and experimentally investigate the optimal velocity feasible for trapped beads of different sizes, in such a trap. Our results show that the achievable velocity of the trapped bead is a function of size of the bead, step size, interval between two steps and power carried by the laser beam. We observe that the refresh rate of a nematic liquid crystal spatial light modulator is sufficient to achieve an optimal velocity approaching the theoretical limit in the respective holographic trap for beads with radius larger than the wavelength of light.

scholarly journals Bio-Molecular Applications of Recent Developments in Optical Tweezers

Biomolecules ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 23 ◽  
Author(s):  
Dhawal Choudhary ◽  
Alessandro Mossa ◽  
Milind Jadhav ◽  
Ciro Cecconi
Keyword(s):  
Photonic Crystal ◽  
Optical Tweezers ◽  
Single Molecule ◽  
Continuous Wave ◽  
Imaging Techniques ◽  
Resolving Power ◽  
Optical Traps ◽  
Laser Source ◽  
One Dimensional

In the past three decades, the ability to optically manipulate biomolecules has spurred a new era of medical and biophysical research. Optical tweezers (OT) have enabled experimenters to trap, sort, and probe cells, as well as discern the structural dynamics of proteins and nucleic acids at single molecule level. The steady improvement in OT’s resolving power has progressively pushed the envelope of their applications; there are, however, some inherent limitations that are prompting researchers to look for alternatives to the conventional techniques. To begin with, OT are restricted by their one-dimensional approach, which makes it difficult to conjure an exhaustive three-dimensional picture of biological systems. The high-intensity trapping laser can damage biological samples, a fact that restricts the feasibility of in vivo applications. Finally, direct manipulation of biological matter at nanometer scale remains a significant challenge for conventional OT. A significant amount of literature has been dedicated in the last 10 years to address the aforementioned shortcomings. Innovations in laser technology and advances in various other spheres of applied physics have been capitalized upon to evolve the next generation OT systems. In this review, we elucidate a few of these developments, with particular focus on their biological applications. The manipulation of nanoscopic objects has been achieved by means of plasmonic optical tweezers (POT), which utilize localized surface plasmons to generate optical traps with enhanced trapping potential, and photonic crystal optical tweezers (PhC OT), which attain the same goal by employing different photonic crystal geometries. Femtosecond optical tweezers (fs OT), constructed by replacing the continuous wave (cw) laser source with a femtosecond laser, promise to greatly reduce the damage to living samples. Finally, one way to transcend the one-dimensional nature of the data gained by OT is to couple them to the other large family of single molecule tools, i.e., fluorescence-based imaging techniques. We discuss the distinct advantages of the aforementioned techniques as well as the alternative experimental perspective they provide in comparison to conventional OT.

scholarly journals The mechanochemistry of the kinesin-2 KIF3AC heterodimer is related to strain-dependent kinetic properties of KIF3A and KIF3C

2020 ◽  
Vol 117 (27) ◽  
pp. 15632-15641
Author(s):  
Brandon M. Bensel ◽  
Michael S. Woody ◽  
Serapion Pyrpassopoulos ◽  
Yale E. Goldman ◽  
Susan P. Gilbert ◽  
...  
Keyword(s):  
Single Molecule ◽  
Mechanical Load ◽  
Optical Trap ◽  
Kinetic Properties ◽  
Dependent Manner ◽  
Force Sensitivity ◽  
Mammalian Neuron ◽  
Kinetics Of ◽  
Strain Dependent ◽  
Transport Potential

KIF3AC is a mammalian neuron-specific kinesin-2 implicated in intracellular cargo transport. It is a heterodimer of KIF3A and KIF3C motor polypeptides which have distinct biochemical and motile properties as engineered homodimers. Single-molecule motility assays show that KIF3AC moves processively along microtubules at a rate faster than expected given the motility rates of the KIF3AA and much slower KIF3CC homodimers. To resolve the stepping kinetics of KIF3A and KIF3C motors in homo- and heterodimeric constructs and determine their transport potential under load, we assayed motor activity using interferometric scattering microscopy and optical trapping. The distribution of stepping durations of KIF3AC molecules is described by a rate (k1= 11 s−1) without apparent kinetic asymmetry. Asymmetry was also not apparent under hindering or assisting mechanical loads in the optical trap. KIF3AC shows increased force sensitivity relative to KIF3AA yet is more capable of stepping against mechanical load than KIF3CC. Interestingly, the behavior of KIF3C mirrors prior studies of kinesins with increased interhead compliance. Microtubule gliding assays containing 1:1 mixtures of KIF3AA and KIF3CC result in speeds similar to KIF3AC, suggesting the homodimers mechanically impact each other’s motility to reproduce the behavior of the heterodimer. Our observations are consistent with a mechanism in which the stepping of KIF3C can be activated by KIF3A in a strain-dependent manner, similar to application of an assisting load. These results suggest that the mechanochemical properties of KIF3AC can be explained by the strain-dependent kinetics of KIF3A and KIF3C.

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