Calibration?¶
Let’s say, you do an experiment with an optical tweezers. For example, a molecular motor, e.g. kinesin-1, is bound to a microsphere (=bead), which is made of polystyrene with a certain diameter. You trap bead, move it to a microtuble and it happens - because you are lucky - that the bead consumes the present ATP and starts walking along the microtuble. Because the bead is still held by the optical trap, the kinesin needs to pull the bead out of center of the trap and each step will lead to a little higher force that the trap excerts to the bead. You measure the displament of the bead interferometrically with a position sensitive device like a quadrant photodiode (QPD). The signal that you record will be given in Volts and will depend on many different physical parameters that are defined by the optical tweezers setup itself, the bead, the sample, etc. However, converting the signal into a physical quantity, such as the displacement of the bead in nanometers or the force that pulls the bead out of the center of the trap, is called calibration.
There are different approaches to calibrate an optical trap. An overview is given in [Jun et al.]
Common approaches calibrate by:
Method Prior known parameters Calibrating parameter Ref. equipartition theorem temperature, displacement sensitivity trap stiffness scanning through stuck bead – displacement sensitivity Boltzmann statistics temperature, displacement sensitivity trap stiffness viscous drag flow speed of medium displacement sensitivity passive power spectral density temperature, displacement sensitivity (via radius) trap stiffness [1] active power spectral density temperature trap stiffness displacement sensitivity [2]
| [1] | K. Berg-Sørensen & H. Flyvbjerg 2004 - doi |
| [2] | S. F. Tolić-Nørrelykke, et al. 2006 - doi |
Passive PSD analysis¶
In passive PSD analysis, the brownian motion of a trapped particle is monitored and its power spectral density is used to calibrate for the apperent trap stiffness. This is done by fitting a model to the PSD.
Power spectral density of a trapped microsphere.
Active PSD analysis¶
In active calibration you simultaneously calibrate for both, the trap stiffness and the displacement senitivity. While the former is done the same way as it is done in passive PSD analysis, the latter directly measures the displacement sensitivity. This is done by exciting the bead sinusoidially with a known amplitude and frequency and measuring the displacement at that frequency and comparing it to the theoretical value.
Power spectral density of a trapped microsphere with an additional sinusoidal movement at 32 Hz.
Height dependent calibration¶
A height-dependent calibration uses the height-dependence of the viscous drag close to a plane surface, which is well described by Faxen’s law. This can be used to determine:
- the exact height of the sphere
- the size of the sphere or
- the viscosity of the medium
Fit of the relative drag to Faxén’s law.
