Optical Tweezers as an Application of Electrodynamics

Transcription

1 Optical Tweezers as an Application of Electrodynamics Edda Klipp Humboldt University Berlin Institute for Biology Theoretical Biophysics

2 Yeast Cell as an Osmometer Media 1 Media 2 50µm Eriksson, Lab on Chip, 2006

3 Optical Tweezer l What is it? Optical Tweezers use light to manipulate microscopic objects as small as a single atom. The radiation pressure from a focused laser beam is able to trap small particles. In biological sciences, these instruments have been used to apply forces in the pn-range and to measure displacements in thenm rangeof objects ranging in size from 10 nm to over 100 mm.

4 History First demonstration of optical tweezer: A. Ashkin, J.M. Dziedzic, J.E. Bjorkholm and S. Chu "Observation of a Single-Beam Gradient Force Optical Trap for Dielectric Particles." Opt. Lett. 11 (5) optical trap: a tightly focused beam of light capable of holding microscopic particles stable in three dimensions 1997: Nobel Prize in Physics for Steven Chu for trapping neutral atoms (0.1 nanometer in diameter) using resonant laser light and a magnetic gradient trap Ashkin was able to trap larger particles (10 to 10,000 nanometers in diameter): an individual tobacco mosaic virus and an Eschericha coli bacterium.

5 Optical tweezers are capable of manipulating nanometer and micrometer-sized dielectric particles by exerting extremely small forces via a highly focused laser beam. The beam is typically focused by sending it through a microscope objective. The narrowest point of the focused beam, known as the beam waist, contains a very strong electric field gradient. It turns out that dielectric particles are attracted along the gradient to the region of strongest electric field, which is the center of the beam. The laser light also tends to apply a force on particles in the beam along the direction of beam propagation. General Description It is easy to understand why if one considers light to be a group of particles, each impinging on the tiny dielectric particle in its path. This is known as the scattering force and results in the particle being displaced slightly downstream from the exact position of the beam waist, as seen in the figure.

6 Laser Light Amplification by Stimulated Emission of Radiation ein sehr enges Frequenzspektrum (d. h. das Licht hat nur eine Farbe, ist also monochromatisch), die Parallelität der Strahlung, die den Laserstrahl auch über große Entfernung kaum breiter werden lässt, und eine große Kohärenzlänge (Strecke über die die Wellen phasengleich sind).

7 More Optical traps are very sensitive instruments and are capable of the manipulation and detection of sub-nanometer displacements for submicrometer dielectric particles. For this reason, they are often used to manipulate and study single molecules by interacting with a bead that has been attached to that molecule. DNA and the proteins and enzymes that interact with it are commonly studied in this way. For quantitative scientific measurements, most optical traps are operated in such a way that the dielectric particle rarely moves far from the trap center. The reason for this is that the force applied to the particle is linear with respect to its displacement from the center of the trap as long as the displacement is small. In this way, an optical trap can be compared to a simple spring, which follows Hooke's law. Federgleichung F=-kx F Rückholkraft x Entfernung aus Gleichgewichtsposition k Federkonstante

8 Particle Size Dependence Proper explanation of optical trapping behavior depends upon the size of the trapped particle relative to the wavelength of light used to trap it. In cases where the dimensions of the particle are much greater than the wavelength, a simple ray optics treatment is sufficient. If the wavelength of light far exceeds the particle dimensions, the particles can be treated as electric dipoles in an electric field. For optical trapping of dielectric objects of dimensions within an order of magnitude of the trapping beam wavelength, the only accurate models involve the treatment of either time dependent or time harmonic maxwell equations using appropriate boundary conditions.

9 Optical Trap Ray Optics Explanation When the bead is displaced from the beam center, as in (a), the larger momentum change of the more intense rays cause a net force to be applied back toward the center of the trap. When the bead is laterally centered on the beam, as in (b), the net force points toward the beam waist.

10 Principles In cases where the diameter of a trapped particle is significantly greater than the wavelength of light, the trapping phenomenon can be explained using ray optics. As shown in the figure, individual rays of light emitted from the laser will be refracted as it enters and exits the dielectric bead. As a result, the ray will exit in a direction different from which it originated. Since light has a momentum associated with it, this change in direction indicates that its momentum has changed. Due to Newton's third law (actio = reactio), there should be an equal and opposite momentum change on the particle.

11 Newton s laws of motion Newton's laws of motion are three physical laws that form the basis for classical mechanics. They are: 1 In the absence of a net force, a body either is at rest or moves in a straight line with constant speed. 2 A body experiencing a force F experiences an acceleration a related to F by F = ma, where m is the mass of the body. Alternatively, force is equal to the time derivative of momentum. 3 Whenever a first body exerts a force F on a second body, the second body exerts a force F on the first body. F and F are equal in magnitude and opposite in direction.

12 The Electric Dipole Approximation In cases where the diameter of a trapped particle is significantly smaller than the wavelength of light, the particle can be treated as a point dipole in an inhomogenous electromagnetic field. The force applied on a single charge in an electromagnetic field is the Lorentz force, The force on the dipole can be calculated by substituting two terms for the electric field in the equation above, one for each charge. The polarization of a dipole is p=qd where d is the distance between the two charges. For a point dipole, the distance is infinitesimal, x 1 -x 2 taking into account that the two charges have opposite signs, the force takes the form Notice that the E 1 cancel out. Multiplying through by the charge, q, converts position, x, into polarization, p,

13 The Electric Dipole Approximation, cont. wherein thesecond equality, ithas been assumed that the dielectric particle is linear (i.e. p= E ). In the final steps, two equalities will be used: (1) a Vector Analysis Equality, (2) one of Maxwell's Equations. First, the vector equality will be inserted for the first term in the force equation above. Maxwell's equation will be substituted in for the second term in the vector equality. Then the two terms which contain time derivatives can be combined into a single term.

14 The Electric Dipole Approximation, cont. The second term in the last equality is the time derivative of a quantity that is related through a multiplicative constant to the Poynting vector, which describes the power per unit area passing through a surface. Since thepowerof thelaserisconstantwhen sampling over frequencies much shorter than the frequency of the laser's light ~10 14 Hz, the derivative of this term averages to zero and the force can be written as Thesquareof themagnitudeof theelectricfield is equal to the intensity of the beam as a function of position. Therefore, the result indicates that the force on the dielectric particle, when treated as a point dipole, is proportional to the gradient along the intensity of the beam. In other words, the gradient force described here tends to attract the particle to the region of highest intensity. In reality, the scattering force of the light works against the gradient force in the axial direction of the trap, resulting in an equilibrium position that is displaced slightly downstream of the intensity maximum. The scattering force depends linearly on the intensity of the beam, the cross section of the particle and the index of refraction of the trapping medium (e.g. water).

15 Generic Optical Tweezer The most basic optical tweezer setup will likely include the following components: a laser, a beam expander, some optics used to steer the beam location in the sample plane, a microscope objective and condenser to create the trap in the sample plane, a position detector (e.g. quadrant photodiode) to measure beam displacements and a microscope illumination source coupled to a CCD camera.

16 Applications cell sorting probe the cytoskeleton, measure the visco-elastic properties of biopolymers, and study cell motility Optical Tweezers have been used to trap dielectric spheres, viruses, bacteria, living cells, organelles, small metal particles, and even strands of DNA. Applications include confinement and organization (e.g. for cell sorting), tracking of movement (e.g. of bacteria), application and measurement of small forces, and altering of larger structures (such as cell membranes). Two of the main uses for optical traps have been the study of molecular motors and the physical properties of DNA. In both areas, a biological specimen is biochemically attached to a micron-sized glass or polystyrene bead that is then trapped. By attaching a single molecular motor (such as kinesin, myosin, RNA polymerase etc.) to such a bead, researchers have been able to probe motor properties such as: Does the motor take individual steps? What is the step size? How much force can the motor produce? Similarly, by attaching the beads to the ends of single pieces of DNA, experiments have measured the elasticity of the DNA, as well as the forces under which the DNA breaks or undergoes a phase transition.

17 Cell Sorting Fluorescence-activated cell sorting - FACS One of the more common cell-sorting systems makes use of flow cytometry through fluorescent imaging. In this method, a suspension of biologic cells is sorted into two or more containers, based upon specific fluorescent characteristics of each cell during an assisted flow. By using an electrical charge that the cell is "trapped" in, the cells are then sorted based on the fluorescence intensity measurements. The sorting process is undertaken by an electrostatic deflection system that diverts cells into containers based upon their charge. List of measurable parameters: volume and morphological complexity of cells cell pigments such as chlorophyll or phycoerythrin DNA (cell cycle analysis, cell kinetics, proliferation, etc.), RNA chromosome analysis and sorting (library construction, chromosome paint) protein expression and localization, protein modifications, phospho-proteins transgenic products in vivo, particularly the Green fluorescent protein or related fluorescent * cell surface antigens Intracellular antigens (various cytokines, secondary mediators, etc.) nuclear antigens enzymatic activity, ph, intracellular ionized calcium, magnesium, membrane potential membrane fluidity, apoptosis (quantification, measurement of DNA degradation, mitochondrial membrane potential, permeability changes, caspase activity) cell viability monitoring electropermeabilization of cells oxidative burst characterising multidrug resistance (MDR) in cancer cells glutathione,..

18 Movies Movie 1, Fig3 Repositioning spores Movie 2, Fig4 Rotating a germling Movie3, Fig6 Movinga woroninbody Movie 4, Fig7A- Vacuolar repulsion Movie 7, Fig8 Redirection of growth Movie 8, Fig9 Hyphal tip growht force Movie 9, Fig10 Germling growth force Movie 10, Fig11 Hyphal beating

19 Applications, cont.

20 Applications, cont. Controlled release of encapsulated agents Concentration profile around particle

21 Comparison of Techniques