Single molecule measurements and biological motors

Calibration

An important issue in making single molecule measurements is precise calibration of position detectors (such as quadrant photodiodes) and active components such as piezoelectric stages and acousto-optic deflectors. There are many different ways of calibrating a setup, but a typical calibration chain might work as follows:

A stage micrometer or graticule is used to calibrate the magnification of the video images. Typically this would give x and y calibrations in nm per pixel (most video equipment has a nonunit aspect ratio).
The piezoelectic stage motion is then calibrated against the video, e.g. using the stage micrometer. If the stage is not feedback controlled, non-linearities and hysteresis will need to be taken into account. This should give a calibration in nm/V or nm/bit.
The AODs are also calibrated against the video image. For example, a trapped bead can be moved across the field of view and its position measured in video pixels. Again a calibration in nm/V or nm/bit should be obtained.
The detector can then be calibrated against the active components. Ideally the calibration between the stage and AODs should be cross-checked. The linearity of the detector can also be characterised at this time. Typically the detector's linear range is sufficient for most work; the nonlinearities do not need to be taken into account. The x and y calibrations should be similar and again be in nm/V or nm/bit.
1. to calibrate against stage motion, a bead immobilised by being stuck to the cover slip or in an acrylamide gel is used. Typically a stage triangle wave would then be used. This method has the advantage that it will work with detectors that measure position relative to the trap, as well as with imaging detectors. However since the object is not actually trapped, careful focus adjustment may be necessary to ensure the same detector sensitivity.
2. To calibrate against trap motion, a trapped bead is moved, typically in a triangle wave (see example below). This will work with imaging detectors, but not those that measure position relative to the trap.

Additionally, the power spectrum can be used to provide an independent calibration method, i.e. one that is not dependent on the stage or AOD calibrations.

AOD Triangle wave used to calibrate or cross-check detector. The upper panel shows the input waveform, a 1.25 μm, 3 Hz triangle wave imposed on the trap position. The lower panel shows the detector response with a 1 μm bead in the trap. Note that the low frequency ensures that the effect of viscous drag on the bead position is minimised, so that there is negligible hysteresis in the detector response. Ideally also the measurement is made at high trap stiffness to minimise the thermal motion of the bead. The amplitude used deliberately exceeds the linear range of the detector (see next figure).

Linearity of Quadrant Photodiode detector. This plot shows the analysis of the records in the previous figure. The detector response over 1000 nm of trap motion is shown, with successive cycles averaged together to reduce the effect of thermal motion and other noise sources. The detector shows good linearity over approximately the central 600 nm of the range; a linear fit to this portion of the data confirms that the detector and AOD calibrations cross-check correctly.

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