Drawing in PDF: chamber_holder
Drawing in DXF: plate_v2.dxf

Here's a video from the paper. We are holding on to two micron sized plastic spheres with laser-beams (shown in the video as green/cyan cross-hairs). The lower beam/trap is stationary while the upper one is steerable. A ca 16um long DNA-molecule (invisible) is tethered between the beads.The experiment is performed in the presence of lambda exonuclease, an enzyme that "eats up" one strand of the DNA leaving just a single-stranded DNA-tether between the beads.

In the first part of the video a force-extension curve (bottom panel) is obtained using manual control. We stretch out the molecule by moving the upper trap upwards and check that the force-signal looks like it should when we have a single DNA-molecule of the right length between the beads.

In the second part, after t = 20 s, the tether is held force clamped at 3.4 pN (force shown in top panel). We're keeping the force constant with a PI-controller implemented on an FPGA that reads the force-signal from the lower bead and updates the position of the upper trap at around 200 kHz. As the molecule shortens the controller needs to move the upper trap/bead lower in order to maintain a 3.4 pN tension in the molecule. The video is at normal speed (1X) while the force extension curve is measured. During 13 min of force-clamp control the video is sped up 25-fold. During this time the exonuclease digests one strand of the double-stranded DNA molecule. When held at 3.4 pN of tension, single-stranded DNA is significantly shorter than double-stranded DNA. So the gradual conversion from a double-stranded tether to a single-stranded tether is seen as a decrease in the extension, i.e. a shortening of the distance between the plastic beads (middle panel). The tether broke at t = 880 s. Scale-bar 5 ?m.

The thesis looks like this, and is available online.

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.

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...

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.

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,

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:

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.