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Dual-‐Func)on Epi-‐Fluorescence Op)cal Tweezers to Characterize Single Polymer Interac)ons in Complex Polymeric Fluids
Kent Lee1, Cole D. Chapman2, & Rae M. Anderson1 University of San Diego1, University of California San Diego2
Introduc)on and Mo)va)on Apparatus Details
• A highly modified inverted fluorescence microscope is used as the base for this instrument. • A 1064 nm Nd:Yag DPSS laser is used to form the two op)cal traps. • Two beam expanders, a variable beam expander and a two-‐lens Keplerian beam expander, are used to increase the beam diameter from 4 µm to 80 µm to fully fill the back focal aperture of the objec)ve. • Two polarizing beam spliZers (PBS) are used to split the beam into two orthogonally polarized beams to allow forma)on of the two op)cal traps. The first PBS splits the beam towards a fixed mirror and a piezoelectric mirror. The second PBS recombines the beams. • A 1.2 NA, 60X water immersion objec)ve is used to magnify the sample and )ghtly focus the laser to form the two op)cal traps. • A 1.4 NA oil immersion condenser collects and collimates the exi)ng trapping beams for force detec)on. • Each two-‐axis PSD will track the laser deflec)on along both axes from each trap, which is used to determine the force exerted on a trapped object. • A flipper mirror controls whether the sample is being viewed using brigh_ield or fluorescence imaging.
Important Features Dual Imaging Capabili)es
20 µm
Dual Traps With One Movable Trap
Precise Movement of Sample Chamber
20 µm
The microsphere circled in blue is trapped in the fixed op)cal trap while the microsphere circled in green is trapped in the movable op)cal trap that is steered by a piezoelectric mirror, allowing precise movements. In the sequence to the leb, the piezoelectric mirror is steered from 0 V (first image) to 10 V (fibh image) to allow the trap (and the trapped microsphere) to move 14.7 µm (1.47 µm/V). The movable trap is able to move along both the x and y axes, allowing for easy manipula)on of samples.
The microsphere circled in pink is trapped in an op)cal trap while the microspheres circled in orange are free in solu)on, represen)ng the environment of the trapped microsphere. During this sequence of images (top), the piezoelectric stage is driven sinusoidally according to the equa)on displayed in the graph (boZom). Note that the trapped microsphere does not move with the other microspheres. This func)onality allows for precise movements of the trapped object rela)ve to the sample chamber/environment in both the x and y direc)ons. From the first to third image displayed, the environment moves approximately 29.7 µm in 1.6 seconds.
Stage
Posi)o
n (µm)
Two light sources and two cameras allow for both brigh_ield and fluorescence imaging. The two images to the leb are of fluorescently labeled microspheres (2 µm diameter) viewed using either the brigh_ield (top) or the fluorescence (boZom) light source and camera. Fluorescence imaging allows us to view fluorescently labeled DNA molecules to visualize single-‐molecule conforma)ons and dynamics during a given experiment while simultaneously measuring the force exerted on the molecule by surrounding entangled molecules (using the op)cal tweezers). However, fluorescence imaging for extended periods of )me can destroy the fluorescent dye and/or degrade the DNA. Therefore, brigh_ield imaging can be used to set up the condi)ons for data collec)on (e.g. trapping the desired molecule, moving the traps to the desired separa)on, etc.). This can extend the possible dura)on of an experiment. Brigh_ield imaging can also be used to conduct experiments in which we are only interested in the force exerted on a trapped molecule.
Time (s)
y(t)=14.85sin(2t)
1. Pecora, R., Science 1991, 251 (4996), 893-‐898. 2. Shaqfeh, E. S. G., Journal of Non-‐Newtonian Fluid Mechanics 2005, 130 (1), 1-‐28. 3. Rickgauer, J. P.; Smith, D. E., Single-‐Molecule Studies of DNA: Visualiza)on and Manipula)on of Individual DNA Molecules with Fluorescence
Microscopy and Op)cal Tweezers. In So< Ma=er: Sca=ering, Imaging, and ManipulaDon, Pecora, R.; Borsali, R., Eds. Springer: New York, 2007; Vol. 4.
4. Neuman, K. C.; Block, S. M., Review of ScienDfic Instruments 2004, 75 (9), 2787-‐2809. 5. Lang, M.; Fordyce, P.; Engh, A.; Neuman, K.; Block, S., Biophysical Journal 2003, 84 (2), 301A-‐301A. 6. Perkins, T. T.; Quake, S. R.; Smith, D. E.; Chu, S., Science 1994, 264 (5160), 822-‐6. 7. Robertson, R.M.; Smith, D. E., Macromolecules 2007, 40 (9), 3373-‐3377. 8. Robertson, R.M.; Smith, D. E., Physical Review Le=ers 2007, 99 (12).
References
Force Detec)on and Calibra)on
Because op)cal traps behave similar to a spring, the force exerted on a trapped object can be described with Hooke’s Law, F = -kx, where x is the deflec)on of the laser forming the trap (measured using PSD). Before using a trap for force detec)on, it must be calibrated to find the trap s)ffness k along each axis. To do this, we need to relate a known force on a trapped object to the measured laser deflec)on along each axis. The drag force on a microsphere in water can be accurately calculated using Stoke’s Drag Theorem, F=8πrηv, where r is radius of the object, η is dynamic viscosity (10-‐3 Ns/m2 for water) , and v is the velocity of the object. The ra)o of this calculated force versus the measured trap deflec)on gives us the trap s)ffness (F/x = k) and thus the calibra)on for the trap. To use this method, we trap a microsphere (2-‐µm in diameter, in a water solu)on) and move the piezoelectric stage sinusoidally in either the x or y direc)on according to the equa)on s(t) = 14.85sin(5t) , where s is in µm and t is in seconds. The posi)on of the stage, the trap deflec)on, and the )me are recorded at a rate of 1 kHz using Labview. The stage velocity (and thus the velocity of the trapped microsphere) v(t) is calculated by differen)a)ng the stage posi)on (x(t) or y(t)) with respect to )me. The stage velocity and measured PSD signal (laser deflec)on) versus )me are ploZed for both the x-‐direc)on (top) and y-‐direc)on (boZom). Both stage veloci)es are reduced by a factor of 1000 to make the scales of velocity and laser deflec)on comparable. The average trap constants (using 10 trials of 10 seconds each for each axis) are kx = 94 pN/V and ky = 115 pN/V for x and y respec)vely. The two trap constants are very similar indica)ng the symmetry of the trap, and values are comparable to op)cal traps we have used in previous experiments that lack fluorescence detec)on and two-‐axis force measurement capabili)es. Thus, the novel features we have incorporated into this instrument do not detract from the trap’s func)onality.
0.05
0.04
0.03
0.02
-‐0.02
-‐0.03
-‐0.04
-‐0.05
0.01
0
-‐0.01
0 1 2 3 4 5 6 7 8 9 10
PSD X Signal (V)
Stage X Ve
locity (V
/s)
Time (s)
0.04
0.03
0.02
-‐0.02
-‐0.03
-‐0.04
-‐0.05
0.01
0
-‐0.01
0 1 2 3 4 5 6 7 8 9 10
0.05
PSD Y Signal (V)
Stage Y Ve
locity (V
/s)
Time (s)
kx = 94 pN/V
ky = 115 pN/V
When fluids consis)ng of many polymers are at high concentra)ons and the polymers are sufficiently long, the polymers may become entangled with each other, leading to highly complex and intriguing fluid proper)es that are s)ll not well understood. This situa)on could be compared to understanding how one strand of spagher in a pot of spagher would move and change shapes as it is being pulled through the pot of spagher. Experimental studies of entangled polymeric fluids have been focused predominantly on how entanglements affect fluid proper)es as a whole rather than the molecular proper)es of single polymer molecules in this environment that give rise to the overall fluid proper)es. Referring back to the spagher example, it would be as though many people studied how the whole pot of spagher behaves as it is poured out of the pot instead of studying how individual strands of spagher behave. Using DNA as a model for these polymer studies1,2 has allowed for newer methods to be used to directly understand single polymer dynamics3 within these complex fluids. Op)cal tweezers and epi-‐fluorescence microscopy are two such methods that have been used independently for force measurement and visualiza)on of DNA respec)vely. However, fluorescence microscopy and op)cal tweezers are rarely combined4,5, and even more rarely used to probe polymeric fluids6 . Thus, combining the capabili)es that these two individual instruments offer will allow for enhanced elucida)on of single polymer proper)es in a polymeric fluid because of the ability to simultaneously visualize the dynamics and conformaDonal responses of single molecules while quanDtaDvely measuring the forces exerted on these molecules by neighboring polymers. By building and using this unique apparatus, we hope to elucidate the perplexing nature of single polymers in complex entangled polymeric fluids.
Background
Fluorescence microscopy allows for clear visualiza)on of samples that are tagged with fluorescent dye. Having the fluorescence capability allows us to see conforma)onal changes of a sample as it is entangled and interacted with. In this figure, the green represents fluorescently labeled DNA while the black is unlabeled DNA and would not be visible under the fluorescence microscope. By combining fluorescence microscopy with op)cal tweezers, forces measured by op)cal tweezers can be aZributed to conforma)onal changes visualized by fluorescence microscopy.
Op)cal tweezers take advantage of the conserva)on of momentum of light par)cles to trap microscopic par)cles in place on a microscope slide with a laser. When there is no force ac)ng on the trapped par)cle (top leb), the deflec)on exi)ng the trap is centered on the PSD (top right). When there is a force ac)ng on the trapped par)cle (boZom leb), the deflec)on is off center of the PSD (boZom right). The force on the par)cle can be measured by this deflec)on. This will be useful in measuring the forces of other DNA pulling on a single strand of entangled DNA.
F = -‐ktx
Op)cal tweezers are comparable to springs. An op)cally trapped par)cle is analogous to a par)cle that is bound to a spring with one fixed end. When a force pushes the par)cle away from the equilibrium posi)on of the trap (or spring), there is a restoring force that pulls it back towards the equilibrium posi)on. Because op)cal tweezers can be modeled as a spring, different tweezers setups have different trap constants (similar to how different springs have different spring constants). As a result, in order to accurately measure force, the op)cal tweezers must first be calibrated to determine the trap constant.
