Category: Research

Force-clamp feedback for optical tweezers

A ~16 um long DNA-molecule is tethered between optically trapped plastic beads. Beads are held by a stationary trap (lower blue cross-hairs) and a steerable trap (upper green cross-hairs). The graphs on the right show the measured force (red) and the force set-point (blue) (top), the distance between the traps (middle), and the force-extension curve with a green cross indicating the current value (bottom). A force-extension curve of the tether is first obtained manually, before force-clamp feedback is switched on at t=24 s. The force set-point is first at 5.5 pN, then increased to 11.4 pN at 30 s and finally increased to 17.4 pN at 35 s. Scale-bar 5 µm. Anders Wallin et al. University of Helsinki, Finland, 2011.

Michelson interferometer

Tried this simple Michelson interferometer for measuring the error of a 100mm translation stage yesterday. The interferometer and stage are mounted to the same optical table, but there's still a fair amount of vibration of the measurement corner-cube which causes instability in the signal when the stage is not moving.

interf

Some sample data here: interf_data. One channel is an encoder signal from the motor which should come every 5 um, the other channel is the interferometer output. Analysis will follow...

Fluorescent DNA

Some very early testing of fluorescence imaging in our optical tweezers instrument. A 10 kb long piece of DNA (ca 3 um long when stretched) is held between two optically trapped microspheres. The DNA is coated with a fluorescent dye (SYBR-gold) which is exited by a 488 nm blue laser and the fluorescence signal is collected with a CCD camera looking through a narrow-band filter centered on the emission spectrum of SYBR-gold.

At around 1:10 in the video there's a double-tether (two DNA-molecules between the beads). We don't want that but there is not much that we can do about it, except discard the data. At the very end there's an image of QDots on the coverglass surface.

Fluorescent DNA

I'm testing an EMCCD camera. This is a video of fluorescently labeled DNA through a 100x epi-fluorescence microscope.

Or you can try a slightly better quality wmv-download (82 Mb)

Once we've had time to practice some more, it should look much cooler, something like these DNA-curtains, or DNA-ejection from bacteriophage lambda. But it's a start.

Also on a youtube near you: molecular motors, TIRFM, optical tweezers setup animation,

Uniform random points in a circle using polar coordinates

I need this seldom enough to forget how it's done - but then it's annoying to have to think/google for the solution again when I do need it... So I'll document here.

The task is to generate uniformly distributed numbers within a circle of radius R in the (x,y) plane. At first polar coordinates seems like a great idea, and the naive solution is to pick a radius r uniformly distributed in [0, R], and then an angle theta uniformly distributed in [0, 2pi]. BUT, you end up with an exess of points near the origin (0, 0)!  This is wrong because if we look at a certain angle interval, say [theta, theta+dtheta], there needs to be more points generated further out (at large r), than close to zero. The radius must not be picked from a uniform distribution, but one that goes as

pdf_r = (2/R^2)*r

That's easy enough to do by calculating the inverse of the cumulative distribution, and we get for r:

r = R*sqrt( rand() )

where rand() is a uniform random number in [0, 1]. Here is a picture:

fig2

some matlab code here.

The thinking for generating random points on the surface of a sphere in 3D is very similar. If I get inspired I will do a post on that later, meanwhile you can go read these lecture notes.

Testing an optical force-clamp

Here a DNA-molecule is being stretched between two optically trapped polystyrene micron-sized beads. We're using an FPGA-based real-time controller for steering the upper trap. It's programmed with a PI-loop which aims to keep the force acting on the lower bead constant. Around 10s into the video we switch on the feedback-loop and we see the actual force on the bead rise to the set-point.