We have theoretically studied the resonant radiation force exerted on single-walled carbon nanotubes (SWCNs) by taking into account the excitonic effect under the effective-mass approximation. When a light frequency is close to an exciton level, the radiation force becomes significantly large even at room temperature for conventional laser intensities in optical manipulation. The peak positions in radiation force spectra are sensitive to the tube diameter and light polarization. Furthermore, the chirality dependence on exciton for similar diameter is relatively large. Therefore, the selective sorting and trapping of SWCNs with a desired specific structure is possible by tuning the applied field frequency.
Friday, October 16, 2009
Size- and orientation-selective optical manipulation of single-walled carbon nanotubes: A theoretical study
Hiroshi Ajiki, Takuya Iida, Takahiro Ishikawa, Seiji Uryu, and Hajime Ishihara
We have theoretically studied the resonant radiation force exerted on single-walled carbon nanotubes (SWCNs) by taking into account the excitonic effect under the effective-mass approximation. When a light frequency is close to an exciton level, the radiation force becomes significantly large even at room temperature for conventional laser intensities in optical manipulation. The peak positions in radiation force spectra are sensitive to the tube diameter and light polarization. Furthermore, the chirality dependence on exciton for similar diameter is relatively large. Therefore, the selective sorting and trapping of SWCNs with a desired specific structure is possible by tuning the applied field frequency.
We have theoretically studied the resonant radiation force exerted on single-walled carbon nanotubes (SWCNs) by taking into account the excitonic effect under the effective-mass approximation. When a light frequency is close to an exciton level, the radiation force becomes significantly large even at room temperature for conventional laser intensities in optical manipulation. The peak positions in radiation force spectra are sensitive to the tube diameter and light polarization. Furthermore, the chirality dependence on exciton for similar diameter is relatively large. Therefore, the selective sorting and trapping of SWCNs with a desired specific structure is possible by tuning the applied field frequency.
Minimum-variance Brownian motion control of an optically trapped probe
Yanan Huang, Zhipeng Zhang, and Chia-Hsiang Menq
This paper presents a theoretical and experimental investigation of the Brownian motion control of an optically trapped probe. The Langevin equation is employed to describe the motion of the probe experiencing random thermal force and optical trapping force. Since active feedback control is applied to suppress the probe's Brownian motion, actuator dynamics and measurement delay are included in the equation. The equation of motion is simplified to a first-order linear differential equation and transformed to a discrete model for the purpose of controller design and data analysis. The derived model is experimentally verified by comparing the model prediction to the measured response of a 1.87 μm trapped probe subject to proportional control. It is then employed to design the optimal controller that minimizes the variance of the probe's Brownian motion. Theoretical analysis is derived to evaluate the control performance of a specific optical trap. Both experiment and simulation are used to validate the design as well as theoretical analysis, and to illustrate the performance envelope of the active control. Moreover, adaptive minimum variance control is implemented to maintain the optimal performance in the case in which the system is time varying when operating the actively controlled optical trap in a complex environment.
This paper presents a theoretical and experimental investigation of the Brownian motion control of an optically trapped probe. The Langevin equation is employed to describe the motion of the probe experiencing random thermal force and optical trapping force. Since active feedback control is applied to suppress the probe's Brownian motion, actuator dynamics and measurement delay are included in the equation. The equation of motion is simplified to a first-order linear differential equation and transformed to a discrete model for the purpose of controller design and data analysis. The derived model is experimentally verified by comparing the model prediction to the measured response of a 1.87 μm trapped probe subject to proportional control. It is then employed to design the optimal controller that minimizes the variance of the probe's Brownian motion. Theoretical analysis is derived to evaluate the control performance of a specific optical trap. Both experiment and simulation are used to validate the design as well as theoretical analysis, and to illustrate the performance envelope of the active control. Moreover, adaptive minimum variance control is implemented to maintain the optimal performance in the case in which the system is time varying when operating the actively controlled optical trap in a complex environment.
Optical manipulation of microtubules for directed biomolecule assembly
Cerasela Zoica Dinu, Tania Chakrabarty, Elaine Lunsford, Christopher Mauer, Joseph Plewa, Jonathan S. Dordick and Douglas B. Chrisey
Optical trapping provides the ability to directly manipulate nano-objects in synthetic environment and hold the potential to produce the next generation of nanodevices. We report a computer-controlled strategy based on dynamic holographic optical trapping to efficiently capture and optically manipulate individual microtubules (25 nm in diameter and several µm in length) as well as hybrid complexes formed from microtubules and quantum dots, with nanometer spatial resolution (15 nm), in three dimensions (over distances exceeding 50 µm in thex–y plane and 10 µm in the z direction), in stationary flow and on engineered surfaces. We also show that individual hybrid complexes can be captured and manipulated for the assembly of user-directed architectures. This strategy can be used for the automated nanofabrication of complex macromolecular architectures and development of novel hybrid materials.
Optical trapping provides the ability to directly manipulate nano-objects in synthetic environment and hold the potential to produce the next generation of nanodevices. We report a computer-controlled strategy based on dynamic holographic optical trapping to efficiently capture and optically manipulate individual microtubules (25 nm in diameter and several µm in length) as well as hybrid complexes formed from microtubules and quantum dots, with nanometer spatial resolution (15 nm), in three dimensions (over distances exceeding 50 µm in thex–y plane and 10 µm in the z direction), in stationary flow and on engineered surfaces. We also show that individual hybrid complexes can be captured and manipulated for the assembly of user-directed architectures. This strategy can be used for the automated nanofabrication of complex macromolecular architectures and development of novel hybrid materials.
Tuesday, October 13, 2009
Generation and Mixing of Subfemtoliter Aqueous Droplets On Demand
Jianyong Tang, Ana M. Jofre, Rani B. Kishore, Joseph E. Reiner, Mark E. Greene, Geoffrey M. Lowman, John S. Denker, Christina C. C. Willis, Kristian Helmerson and Lori S. Goldner
We describe a novel method of generating monodisperse subfemtoliter aqueous droplets on demand by means of piezoelectric injection. Droplets with volumes down to 200 aL are generated by this technique. The droplets are injected into a low refractive index perfluorocarbon so that they can be optically trapped. We demonstrate the use of optical tweezers to manipulate and mix droplets. For example, using optical tweezers we bring two droplets, one containing a calcium sensitive dye and the other calcium chloride, into contact. The droplets coalesce with a resulting reaction time of about 1 ms. The monodispersity, manipulability, repeatability, small size, and fast mixing afforded by this system offer many opportunities for nanochemistry and observation of chemical reactions on a molecule-by-molecule basis.
We describe a novel method of generating monodisperse subfemtoliter aqueous droplets on demand by means of piezoelectric injection. Droplets with volumes down to 200 aL are generated by this technique. The droplets are injected into a low refractive index perfluorocarbon so that they can be optically trapped. We demonstrate the use of optical tweezers to manipulate and mix droplets. For example, using optical tweezers we bring two droplets, one containing a calcium sensitive dye and the other calcium chloride, into contact. The droplets coalesce with a resulting reaction time of about 1 ms. The monodispersity, manipulability, repeatability, small size, and fast mixing afforded by this system offer many opportunities for nanochemistry and observation of chemical reactions on a molecule-by-molecule basis.
Optical mirror trap with a large field of view
Maximilian Pitzek, Ruth Steiger, Gregor Thalhammer, Stefan Bernet, and Monika Ritsch-Marte
Holographic optical tweezers typically require microscope objectives with high numerical aperture and thus usually suffer from the disadvantage of a small field of view and a small working distance. We experimentally investigate an optical mirror trap that is created after reflection of two holographically shaped collinear beams on a mirror. This approach combines a large field of view and a large working distance with the possibility to manipulate particles in a large size range, since it allows to use a microscope objective with a numerical aperture as low as 0.2. In this work we demonstrate robust optical three-dimensional trapping in a range of 1mm x 1mm x 2mm with particle sizes ranging from 1.4 μm up to 45 μm. The use of spatial light modulator based holographic methods to create the trapping beams allows to simultaneously trap many beads in complex, dynamic configurations. We present measurements that characterize the mirror traps in terms of trap stiffness, maximum trapping force and capture range.
Holographic optical tweezers typically require microscope objectives with high numerical aperture and thus usually suffer from the disadvantage of a small field of view and a small working distance. We experimentally investigate an optical mirror trap that is created after reflection of two holographically shaped collinear beams on a mirror. This approach combines a large field of view and a large working distance with the possibility to manipulate particles in a large size range, since it allows to use a microscope objective with a numerical aperture as low as 0.2. In this work we demonstrate robust optical three-dimensional trapping in a range of 1mm x 1mm x 2mm with particle sizes ranging from 1.4 μm up to 45 μm. The use of spatial light modulator based holographic methods to create the trapping beams allows to simultaneously trap many beads in complex, dynamic configurations. We present measurements that characterize the mirror traps in terms of trap stiffness, maximum trapping force and capture range.
Force and Premature Binding of ADP Can Regulate the Processivity of Individual Eg5 Dimers
Megan T. Valentine and Steven M. Block
Using a high-resolution optical trapping instrument, we directly observed the processive motions of individual Eg5 dimers over a range of external loads and ATP, ADP, and phosphate concentrations. To constrain possible models for dissociation from the microtubule, we measured Eg5 run lengths and also compared the duration of the last step of a processive run to all previous step durations. We found that the application of large longitudinal forces in either hindering or assisting directions could induce Eg5-microtubule dissociation. At a constant moderate force, maintained with a force clamp, the premature binding of ADP strongly promoted microtubule release by Eg5, whereas the addition of ATP or phosphate had little effect on dissociation. These results imply that run length is determined not only by the load, but also by the concentration and type of nucleotides present, and therefore that the biochemical cycles of the two motor domains of the Eg5 dimer are coordinated to promote processive stepping.
Using a high-resolution optical trapping instrument, we directly observed the processive motions of individual Eg5 dimers over a range of external loads and ATP, ADP, and phosphate concentrations. To constrain possible models for dissociation from the microtubule, we measured Eg5 run lengths and also compared the duration of the last step of a processive run to all previous step durations. We found that the application of large longitudinal forces in either hindering or assisting directions could induce Eg5-microtubule dissociation. At a constant moderate force, maintained with a force clamp, the premature binding of ADP strongly promoted microtubule release by Eg5, whereas the addition of ATP or phosphate had little effect on dissociation. These results imply that run length is determined not only by the load, but also by the concentration and type of nucleotides present, and therefore that the biochemical cycles of the two motor domains of the Eg5 dimer are coordinated to promote processive stepping.
On the Origin of Kinesin Limping
Adrian N. Fehr, Braulio Gutiérrez-Medina, Charles L. Asbury and Steven M. Block
Kinesin is a dimeric motor with twin catalytic heads joined to a common stalk. Kinesin molecules move processively along microtubules in a hand-over-hand walk, with the two heads advancing alternately. Recombinant kinesin constructs with short stalks have been found to “limp”, i.e., exhibit alternation in the dwell times of successive steps. Limping behavior implies that the molecular rearrangements underlying even- and odd-numbered steps must differ, but the mechanism by which such rearrangements lead to limping remains unsolved. Here, we used an optical force clamp to measure individual, recombinant dimers and test candidate explanations for limping. Introducing a covalent cross-link into the stalk region near the heads had no effect on limping, ruling out possible stalk misregistration during coiled-coil formation as a cause. Limping was equally unaffected by mutations that produced 50-fold changes in stalk stiffness, ruling out models where limping arises from an asymmetry in torsional strain. However, limping was enhanced by perturbations that increased the vertical component of load on the motor, including increases in bead size or net load, and decreases in the stalk length. These results suggest that kinesin heads take different vertical trajectories during alternate steps, and that the rates for these motions are differentially sensitive to load.
Kinesin is a dimeric motor with twin catalytic heads joined to a common stalk. Kinesin molecules move processively along microtubules in a hand-over-hand walk, with the two heads advancing alternately. Recombinant kinesin constructs with short stalks have been found to “limp”, i.e., exhibit alternation in the dwell times of successive steps. Limping behavior implies that the molecular rearrangements underlying even- and odd-numbered steps must differ, but the mechanism by which such rearrangements lead to limping remains unsolved. Here, we used an optical force clamp to measure individual, recombinant dimers and test candidate explanations for limping. Introducing a covalent cross-link into the stalk region near the heads had no effect on limping, ruling out possible stalk misregistration during coiled-coil formation as a cause. Limping was equally unaffected by mutations that produced 50-fold changes in stalk stiffness, ruling out models where limping arises from an asymmetry in torsional strain. However, limping was enhanced by perturbations that increased the vertical component of load on the motor, including increases in bead size or net load, and decreases in the stalk length. These results suggest that kinesin heads take different vertical trajectories during alternate steps, and that the rates for these motions are differentially sensitive to load.
Flickering Analysis of Erythrocyte Mechanical Properties: Dependence on Oxygenation Level, Cell Shape, and Hydration Level
Young-Zoon Yoon, Ha Hong, Aidan Brown, Dong Chung Kim, Dae Joon Kang, Virgilio L. Lew and Pietro Cicuta
Erythrocytes (red blood cells) play an essential role in the respiratory functions of vertebrates, carrying oxygen from lungs to tissues and CO2 from tissues to lungs. They are mechanically very soft, enabling circulation through small capillaries. The small thermally induced displacements of the membrane provide an important tool in the investigation of the mechanics of the cell membrane. However, despite numerous studies, uncertainties in the interpretation of the data, and in the values derived for the main parameters of cell mechanics, have rendered past conclusions from the fluctuation approach somewhat controversial. Here we revisit the experimental method and theoretical analysis of fluctuations, to adapt them to the case of cell contour fluctuations, which are readily observable experimentally. This enables direct measurements of membrane tension, of bending modulus, and of the viscosity of the cell cytoplasm. Of the various factors that influence the mechanical properties of the cell, we focus here on: 1), the level of oxygenation, as monitored by Raman spectrometry; 2), cell shape; and 3), the concentration of hemoglobin. The results show that, contrary to previous reports, there is no significant difference in cell tension and bending modulus between oxygenated and deoxygenated states, in line with the softness requirement for optimal circulatory flow in both states. On the other hand, tension and bending moduli of discocyte- and spherocyte-shaped cells differ markedly, in both the oxygenated and deoxygenated states. The tension in spherocytes is much higher, consistent with recent theoretical models that describe the transitions between red blood cell shapes as a function of membrane tension. Cell cytoplasmic viscosity is strongly influenced by the hydration state. The implications of these results to circulatory flow dynamics in physiological and pathological conditions are discussed.
Erythrocytes (red blood cells) play an essential role in the respiratory functions of vertebrates, carrying oxygen from lungs to tissues and CO2 from tissues to lungs. They are mechanically very soft, enabling circulation through small capillaries. The small thermally induced displacements of the membrane provide an important tool in the investigation of the mechanics of the cell membrane. However, despite numerous studies, uncertainties in the interpretation of the data, and in the values derived for the main parameters of cell mechanics, have rendered past conclusions from the fluctuation approach somewhat controversial. Here we revisit the experimental method and theoretical analysis of fluctuations, to adapt them to the case of cell contour fluctuations, which are readily observable experimentally. This enables direct measurements of membrane tension, of bending modulus, and of the viscosity of the cell cytoplasm. Of the various factors that influence the mechanical properties of the cell, we focus here on: 1), the level of oxygenation, as monitored by Raman spectrometry; 2), cell shape; and 3), the concentration of hemoglobin. The results show that, contrary to previous reports, there is no significant difference in cell tension and bending modulus between oxygenated and deoxygenated states, in line with the softness requirement for optimal circulatory flow in both states. On the other hand, tension and bending moduli of discocyte- and spherocyte-shaped cells differ markedly, in both the oxygenated and deoxygenated states. The tension in spherocytes is much higher, consistent with recent theoretical models that describe the transitions between red blood cell shapes as a function of membrane tension. Cell cytoplasmic viscosity is strongly influenced by the hydration state. The implications of these results to circulatory flow dynamics in physiological and pathological conditions are discussed.
Removal of the cardiac myosin regulatory light chain increases isometric force production
Kiran Pant, James Watt, Michael Greenberg, Michelle Jones, Danuta Szczesna-Cordary, and Jeffrey R. Moore
The myosin neck, which is supported by the interactions between light chains and the underlying alpha-helical heavy chain, is thought to act as a lever arm to amplify movements originating in the globular motor domain. Here, we studied the role of the cardiac myosin regulatory light chains (RLCs) in the capacity of myosin to produce force using a novel optical-trap-based isometric force in vitro motility assay. We measured the isometric force and actin filament velocity for native porcine cardiac (PC) myosin, RLC-depleted PC (PCdepl) myosin, and PC myosin reconstituted with recombinant bacterially expressed human cardiac RLC (PCrecon). RLC depletion reduced unloaded actin filament velocity by 58% and enhanced the myosin-based isometric force similar to 2-fold. No significant change between PC and PCdepl preparations was observed in the maximal rate of actin-activated myosin ATPase activity. Reconstitution of PCdepl myosin with human RLC partially restored the velocity and force levels to near untreated values. The reduction in unloaded velocity after RLC extraction is consistent with the myosin neck acting as a lever, while the enhancement in isometric force can be directly related to enhancement of unitary force. The force data are consistent with a model in which the neck region behaves as a cantilevered beam.
The myosin neck, which is supported by the interactions between light chains and the underlying alpha-helical heavy chain, is thought to act as a lever arm to amplify movements originating in the globular motor domain. Here, we studied the role of the cardiac myosin regulatory light chains (RLCs) in the capacity of myosin to produce force using a novel optical-trap-based isometric force in vitro motility assay. We measured the isometric force and actin filament velocity for native porcine cardiac (PC) myosin, RLC-depleted PC (PCdepl) myosin, and PC myosin reconstituted with recombinant bacterially expressed human cardiac RLC (PCrecon). RLC depletion reduced unloaded actin filament velocity by 58% and enhanced the myosin-based isometric force similar to 2-fold. No significant change between PC and PCdepl preparations was observed in the maximal rate of actin-activated myosin ATPase activity. Reconstitution of PCdepl myosin with human RLC partially restored the velocity and force levels to near untreated values. The reduction in unloaded velocity after RLC extraction is consistent with the myosin neck acting as a lever, while the enhancement in isometric force can be directly related to enhancement of unitary force. The force data are consistent with a model in which the neck region behaves as a cantilevered beam.
Radiation forces on dielectric and absorbing particles studied via the finite-difference time-domain method
Lin Jia and Edwin L. Thomas
Using the three dimensional finite-difference time-domain (FDTD) method, we calculate the radiation force from an incident plane wave on both dielectric and absorbing particles in the Lorentz-Mie regime via the Maxwell stress tensor approach. We find that the radiation force changes with particle permittivity, and we categorize the force into three regions: increasing, fluctuating, and constant. We discuss how particle size, shape, orientation and absorption affect the radiation force. A nanoscale solar sail is proposed based on our calculation. A detailed understanding of the optical force of a plane wave on particles in the Lorentz-Mie regime is fundamental for designing nanoscale solar sail systems and optical traps from a set of interfering plane waves.
Using the three dimensional finite-difference time-domain (FDTD) method, we calculate the radiation force from an incident plane wave on both dielectric and absorbing particles in the Lorentz-Mie regime via the Maxwell stress tensor approach. We find that the radiation force changes with particle permittivity, and we categorize the force into three regions: increasing, fluctuating, and constant. We discuss how particle size, shape, orientation and absorption affect the radiation force. A nanoscale solar sail is proposed based on our calculation. A detailed understanding of the optical force of a plane wave on particles in the Lorentz-Mie regime is fundamental for designing nanoscale solar sail systems and optical traps from a set of interfering plane waves.
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