Optical tweezers. An Introduction to Optical Tweezers. What Are Optical Tweezers?

Transcription

1 An Introduction to Optical Tweezers PD Dr. Martin Hegner Universität Basel Optical tweezers Optical tweezers Optical tweezers use forces of laser radiation pressure to trap small objects This technique is 0 years old, and used in biophysics the last 10 years Single molecule applications 1 What Are Optical Tweezers? 3 Matter can be influenced by light Wavelength selection Intensity of beam Optics Single beam tweezers Double beam tweezers Application in atom trapping UHV, low temperature (few K) Biological applications in a liquid environment Spectrum of Light Approximate wavelength (in vacuum) and frequency ranges for the various colors 4 Color Red Orange Yellow Green Blue Wavelength (nm) Frequency (THz) Violet µm 1 terahertz (THz) = 10 3 GHz = 10 6 MHz = 10 1 Hz, 1 nm = 10-3 µm = 10-6 mm = 10-9 m. The white light is a mixture of the colors of the visible spectra. Visible Light Region of the Electromagnetic Spectrum 0.7µm 0.6µm 0.5µm Infrared Ultraviolet

2 Single-beam optical tweezers Adsorption Spectrum of Water NIR diode laser Solid state diode pumped laser Notice the two scales on vertical axis 5 6 Matter Is Influenced by Light Diode Laser Θ Θ 7 8

3 Can We Build an Optical Tweezers With a Diode Laser? Beam Shaping Beam injection (LASER A) Kinematic mirrors Shutters L ¾ Beam Shaping ¾ Laser Power ¾ Single mode vs. multimode Laser Pinholes L Faraday isolators Anamorphic prisms Diode lasers (830 nm) Optical Diode Laser Beam Single Mode Expander Isolator λ=830nm Pinhole Lenses 00mW 9 10 Anamorphic Prisms Lenses Collimated diode laser beam Symmetric Bioconvex Lens Identical Plano-convex Lenses After Anamorphic prisms CCD image of laser beam Beam After Isolator Before Lens and Pinhole CCD image of laser beam 11 1 Identical Achromat Lenses

4 Spatial Filter Spatial filters provide a convenient way to remove random fluctuations from the intensity profile of a laser beam. Laser beams pick up intensity variations from scattering by optical defects and particles in the air. A pinhole centered on the axis can block the unwanted noise annulus while passing most of the laser's energy. The fraction of power passed by a pinhole of diameter D is: Spatial Filter remember there is high energy of pinhole After Pinhole CCD image of laser beam I (r ) = I 0 e r a where I 0 = I ACTUAL = I (r ) + I NOISE 13 Pt πa Where F=Objective Lens Focal Length l = Laser Wavelength r = Radius Distance within OPS â = Radius of OPS Gaussian at I(r) =Î0e- Polarizing Beam Splitter Bars 10 µm 14 Quarter Wave Plate Quarter-wave plates are used to turn plane-polarized light into circularly-polarized light and vice versa. To do this, we must orient the wave plate so that equal amounts of fast and slow waves are excited. We may do this by orienting an incident plane-polarized wave at 45 to the fast (or slow) axis 15 16

5 Double Beam Laser Tweezers White light spatial filter psd pbs diode laser Faraday isolator L1 0.1 atten. obj pbs qwp x-y-z transl. flow chamber obj x-y-z transl. diode laser Faraday isolator qwp pbs psd L1 pbs 0.1 atten. blue filter ccd camera Layout of the Core of the Instrument Beam conditioning (LASER A) Beam conditioning (LASER B) Linear translation stage Chamber D CCD L FI PBS-D PBS-D DM C L L F F PBS-I QW QW Detector A Detector B PBS-I Beam conditioning (LASER C) LED The physics behind optical tweezers Radiation pressure is the force per unit area on a object due to change in light momentum The physics behind optical tweezers Applying this formula to a 100% reflecting mirror reflecting a 60W lamp gives a pressure of: The light momentum of a single photo is: = The change is momentum can be calculated by the difference is momentum flux between entering and leaving a object Gravity pulls on a 1 kg mirror with 9.8 N so the force of the photos is negligible. However, if the same light is reflected by a object of 1 µg it can t be ignored! 19 Using a laser on a microscopic particle will realize this situation. 0

6 A particle in a laser beam A particle in a laser beam Light profile Force A Net Force B Light profile Force A Net Force B Force B Force B Force develops when rays of light act on objects with different index of refraction compared to the surrounding media. The particle gets push towards the highest light intensity. A Force develops when rays of light act on objects with different index of refraction compared to the surrounding media. The particle gets push towards the highest light intensity. A However there are also reflections pushing the bead forward 1 A particle in a laser beam But using a high NA objective, the refractive force can overcome the forces due to reflections. A particle in a laser beam lens Reflected photons Net Force What is a high NA objective? ( ) NA = n sin θ max Force Reflection Force Result: A particle can get sucked into the focus of a laser bundle and be stably trapped. Thus highly focused laser beam acts as a three-dimensional potential minimum. Therefore it takes force the dislodge a bead out of the laser focus. 3 4

7 A particle in a laser beam Also the bead movement is measurable from the laser deflection. Why Can We Hold Particles by Light? A beam intensity net Force beam axis θ (A) A refractile bead is drawn into the intense part of a light beam but is also propelled away from the light source. B lens reflected reflected net force (B) A converging laser beam, focused by a lens, holds the bead at a constant axial position Microscope lens with high numerical aperture Gradient force must be greater than scattering force to allow stable trapping along the optical axis -> Overfill back aperture of the microscope lens 5 6 Momentum of a Photon Reaction force on bead: F = (W/c) n b sinθ Collector lens transforms exit angles into ray offsets (by Abbe sine conditions): X i = R L n b sinθ i Position sensitive light detector sums over all light rays to give a signal S = ΣX i W i External force is given by: F = S/R L c Regardless of the particle size or shape or the buffer refractive index 7 P 1 P = h/λ Bead F = dp/dt P Θ P P = momentum of a photon W = power of the laser c = speed of light n b = refractive index of medium R L = focal length of the lens Force measurement using the momentum of the light OBJ 8 buffer OBJ air Detector Maximum force on a trap F Max =(W/c)/(r back-aperture -r beam )/R L Wavelength: 830 nm Intensity: 00mW (per Laserdiode) OBJ external force OBJ R L Detector X R EX This measurement scheme should not be used in a single-beam trap because such a narrow cone of light (as depicted in the above figures) will not efficiently trap an object. But if a high-na beam were used instead, then the outermost exiting rays could not be collected by the analysis lens

8 Noise (OT, AFM) For an overdamped particle in liquid, thermal fluctuations of displacement reads as: x Noise = 0 S x ( f ) df = 0 γπ k T B ( f + f ) df c k B γt 4.1 RT S x ( f ) f c viscous drag coefficient corner frequency : Stiffness (K)/ πγ AFM lever is not overdamped S x ( f ) = cte f c 9 30 Using low-pass <fc and fs fs x Noise = Sx ( f ) df = 4γ 0 F Noise kbt K Independent of K!!!!! f s Optical Tweezers Fluid-Chamber Reducing Noise = reducing the size of the sensor Laser 830 nm OBJ OBJ F Noise = 4γ f k T, x Noise = 4γf k s B s B T / K, OT have a small force sensor, therefore a better force resolution Single Molecule resp. receptor/ligand Micropipette 31 3

9 Calibration of optical tweezers Virtual spring methods The optical trap is treated as though it were a linear spring pulling the bead toward the center of the trap 1. Stokes law method (viscous drag force) F = 6πrηv trap stiffness: κ = F / x. Corner frequency method 3. Equipartition method 4. Pulling dsdna LASER (1 + 9r/8d) Correction of wall effect in fluid chambers Corner Frequency Method Trap one bead record its motion on Position Sensitive Detector (PSD) 33 LASER suction Fluss Pipette Chamber Depth [µm] Using water immersion lenses with working distances of > 00 µm is enabling us to neglect surface effects. 34 Force (pn^/hz) Corner Frequency Method 1E-3 1E-4 1E-5 1E-6 1E-7 35 A*(B^/(B^+x^)) A=1.3768E-4 B= microns 00 ma f c Frequency (Hz) Frequency above which the bead doesn t feel the potential of the light any more. κ = πf c γ γ = 6πrη κ = trap stiffness γ = damping coefficient η = viscosity H O η = 1x10-9 pn. s/nm White Light Illumination for CCD? Choose the right filters to transmit the laser and reflect your illumination source Due to combination of optical elements within the OT measure the spectra of your combined optical components! 36

10 Manipulation of Micron Sized Beads by Optical Tweezers Optical IfP Bead in 3D movable trap Bead in the double-trap Bead placement on Pipette and in 1 st trap Bead manipulation with nd trap fixed in 3D molecule movable in 3D protein with affinity to DNA binding protein Bead held by suction on movable pipette 3 µm 3µm pipette movable in 3D Beam steering Power of the laser used Tilting the optical plane within the backaperture No loss of light (energy) within the trap 39 Moving the whole light beam within the back-apperture Loss of light (energy) within the trap asymmetric trapping 40 Remember that the laser light may affect the molecule of investigation. If the focal spot is within a fluid environment then the heat of high intensity light is dissipating into the liquid quickly. Loss of power from the source till the focal spot of the trap ~ 50% due to beam shaping Remember that the wavelength should be in the NIR to avoid damage of biology. With a power of ~ 80 trap we have a heating of ~1 C locally.

11 Wave length of choice for OT Single Mode Laser Vs. Multi Mode Laser From Characterization of Photodamage to Escherichia coli in Optical Traps K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman and S. M. Block Biophys. J. 77 (1999) Newer paper on that topic: Stress Response in Caenorhabditis elegans Caused by Optical Tweezers: Wavelength, Power, and Time Dependence G. Leitz, E. Fällman, S. Tuck and O.Axner Biophys. J. 8 (00) Fluid delivery Optical Tweezers Without / With Fluid Chamber vacuum-pressure automatic syringe Expansion bottles automatic valves Microscope Lens: Olympus N.A. 1,; 60x Water Immersion Working Distance 80 µm Fluid-Chamber: Two Cover-slides with Parafilm Channel for Micropipette 43 44

12 Combining two powerful techniques for single-molecule studies Optical tweezers: nanoscale manipulation & sub-piconewton sensitivity + Single-molecule fluorescence: measuring nanoscale structural changes Combination: correlating structural changes & biomechanical transitions Trapped bead biotin streptavidin Excitation & collection volume Current development of the instrument Motivation: Biosensor with sub pn sensitivity for biological investigations on single molecules in buffer solutions Optical path allows combination with light spectroscopy Simultaneous Single Molecule Mechanics and Fluorescent Resonance Energy Transfer (FRET) Measured by Optical Tweezers A Exitation Exitation D D A A Emission A F 45 The complete chamber is placed on a closed-loop piezoelectric element such that nanometer displacements can be applied. Also shown are donor and acceptor dyes. 46 Inter or intra protein rearrangement upon ligand interaction within filament protein-complexes (Actin; Intermediate filaments) Emission Visualization of Local Motion e.g. on RNAP or DNAP on DNA Applying an External Load The Optical Tweezers Setup (Combining Static (Counter-propagating) Double Beam Trap With steerable Micropipette and steerable Second Trap) M M Slid M AOM DM PBS ICCD DM APDs Lasers Trap FRET detection 47 48

13 New single photon detection setup Pulling Single DNA Fragments With Optical Tweezers 1 b Instrument today Excitation with 488 nm b b b b b 49 Epi-luminescent in-coupling iccd + APD detectors 50 Elasticity of single DNA fragments Overstretch Transition of dsdna Force [pn] inextensible worm like chain (WLC) elastic Modulus of B-DNA Entropic regime extensible WLC Enthalpic regime 0% S-DNA transition G Extension [µm] 100% ssdna extensible WLC S-DNA Lebrun A et al. NAR (1996) 4, 60 Biomechanics on DNA with FRET detection The Fields of Application 5 Mechanical Properties of a single dsdna Scanning Probe ( F ~ 10 pn) Molecular Recognition Mechanical Deformation Unfolding of single molecules Optical Tweezers ( F ~ 00 fn) Mechanical Properties Molecular Motors Unfolding of single molecules Optical Spectroscopy

14 DNA pulling with AFM Is there a DNA in-between the beads? Force [pn] Extensible WLC model Experimental data overstretch plateau S-form DNA Extension [nm] Rief et al. Sequence-dependent mechanics of single DNA molecules Nature Struct. Biol (1999) Essevaz-Roulet, B. et al Mechanical separation of the complementary strands of DNA Proc. Natl. Acad. Sci. USA (1997) Data Fitting to the Worm-Like Chain P F k T B x 1 L Manipulation of a single dsdna molecule Detection of a single fluorophore label Persistence Length (nm) ( pn / ) 1 1 Force Laser Magnetic Extension ( µm) Science (199) 58, 11 Science (1996) 71,

15 Attachment of organelles to polystyrene spheres for future molecular motor experiments 57 GFP labeled Mitochondria trapped in steerable OT Aldehyde activated Polystyrene sphere Ø3 µm In collaboration with W. Voos Uni Freiburg Optical tweezers references [1] A.Ashkin "Optical trapping and manipulation of neutral particles using lasers", Proc. Natl. Acad. Sci. USA, vol. 94, pp , May [] "The Optical Tweezers and Laser Scalpel Home Page", Internet ref. [3] Karel Svoboda & Steven M. Block "Biological Applications of Optical Forces", Ann. Rev. Biophys. Biomol. Struct. 3, p , [4] R. H. Austin et al. "Stretch Genes", Physics Today, p. 3-38, Feb [5] Prentiss Group... "Simple Optical Tweezers", Internet ref. Feb [6] K. Visscher & S. M. Block "Versatile Optical Traps with Feedback Control", Academic Press, Methods in Enzymology. Vol 98, p , [7] W. Grange et al. Rev. Sci. Instr. (00) Optical tweezers system measuring the change in light momentum flux. Rev. Sci. Instr. 73, (Handout)