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Laser trapping and pN force measurement | |
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Introduction Single-beam laser-trapping (LT, also called optical tweezers or optical trapping), pioneered by Ashkin (1986), has been widely used in many research areas as a force measurement technique as well as a manipulator of nano/micro-particles under a microscope. The force measurement has been used for measuring the kinetic forces of protein motors such as kinesin, mydosin and dynesin, the dynamics during transcription of RNA polymerase from DNA, and the unzipping force of the DNA double helix, and so on since the LT force is the order of the 10 pN, equivalent with the forces of these biomolecules. In these applications, the lateral force in the laser trap balanced with the force of these biomolecules was measured as the lateral displacement of the particle from the initial equilibrium position. This configuration, however, is not easily applied to more general system such as force probe and substrate that is achieved by an atomic microscope (AFM). Therefore we have developed a system that measures the vertical force by using laser trapping [1], and related techniques [2,3]. The force measurement by LT is preferable to by the AFM in terms of the force sensitivity. The detection limit of LT is 10 fN while that of the AFM is 10 pN. Force measurement on substrate The trapping force Ftrap is measured as the displacement as follows; Ftrap = ktrap Δz , where ktrap is the spring constant of laser trap and Δz is the displacement of the particle due to an external force. To measure the vertical position with 1-nm resolution, we suggest evanescent field illumination and scattering detection. The particle held by LT in evanescent field generated around the vicinity of the substrate scatters the light of the field. Because the intensity of the field obeys exponential decay as the distance from the surface of the substrate, the intensity of the scattered light gives the particle position or particle displacement Δz on the substrate.Δz = -(1/&beta) [log I - log I0] , where I and I0 is the scattered light intensity after/before displacement and &beta is the decay constant of the evanescent field. The resolution of this method is achieved to 1 nm since the decay constant &beta is typically several hundreds nanometer and the intensity changes sensitively enough as the distance in nanometer scale. Fig.2 shows an example of the forces measured with our method; surface forces between a polystyrene particle of 1-μm diameter and glass substrate. In this measurement, the force always worked repulsively. The logarithm plot revealed the exponential property of the forces and from the decay constants, we determined the forces were mainly due to the electrostatic double-layer force and their Debye lengths were 29.5 nm, 17.9 nm and 10.4 nm in pure water , 0.01M-tris solution and 0.1M-tris solution. The force sensitivity is about a few tens fN.Wavefront controlled LT in optical axis The trapping properties such as the spring constant, the maximum force, the range of trapping, and the trapping position highly depend to the quality of the focus spot of the trapping beam. We developed a technique to control these trapping properties by modifying the wavefront of trapping beam, and consequently, the intensity distribution of the focus spot. The wavefront which should be induced is expressed as the Zernike polynomials ΣajZj, where Zj is jth m Zernike mode and aj is its expansion coefficient. To generate the desired wavefront, we utilize a membrane deformable mirror (OKO technologies, Netherlands). We control the trapping position in optical axis by inducing the 4th mode. Fig.3(a) shows the relation between the trapping position shift and the magnitude of 4th mode, a4. Fig. 3(b) shows the frequency response when the position of the trapped particle is modulated in a sinusoidal manner. The laser trapping force and the spring constant are sometimes deteriorated by aberrations due to systematic errors in optics or smaple conditions such as spherical aberration caused by refractive index mismatch between a sample slide glass and solvent for trapping medium. We compensate the deterioration of the force and the spring constant due to the spherical aberration by inducing 11th mode (1st spherical) or higher modes. Fig.5 shows the how well the deterioration is compensated. These calculation results are coincident with the experimental results. References
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 Fig.1 Configuration of force measurement.  Fig.2 Surface forces between a 1-μm polystyrene particle and galss substrate in different solutions.  Fig.3 Wave-front controlled LT system.  Fig.4 Trapping position control in optical axis. (a) The trapping position shift as a4. (b) Frequency response when the position of the particle is modulated in a sinusoidal manner.  Fig.5 Trapping force enhancement due to the spherical aberration correction. |