Optical tweezers stiffness

The optical tweezers stiffness is set to about 0.02 pN nm (adjusting the laser power), which is about 10000 times less stiff than an AFM cantilever. This is sufficient to hold the beads stably trapped but still about 10 100 times less stiff than the acto-myosin complex. This means that myosin can undergo its conformational change essentially unhindered by the tweezer. 

Since most of the variance in the data arises from thermal motion of the beads held in the optical tweezers, the standard deviation (a) is governed by the optical tweezer stiffness (Figure 12.7). Therefore, if for example experiments are carried out at a combined laser tweezer stiffness of 0.04 pN nm, the standard deviation of the thermal noise will be 15 nm, so if 100 events are collected the step size estimate will have a standard error of the mean of (15/vT00) =1.5 nm. 

Brownian movement of the bead held in the optical tweezers serves as a useful probe of the tweezer stiffness. The variance of bead position along one axis, (x), is inversely proportional to the stiffness of the optical tweezers and is directly proportional to absolute temperature. 

Figure 12.6 Calibration of trap stiffness using Stokes drag. The stiffness of the trap can be determined using Stokes drag force. A triangle wave is applied to the stage which holds the specimen chamber while a bead is held in the optical tweezer. The rapid movement of the stage creates a force, F, on the bead caused by the motion of the surrounding fluid. This causes the bead to be displaced a distance, x, from the trap centre the greater the system stiffness the less the bead is displaced. f/X= stiffness of the tweezers K) (inset)...

Figure 12.7 CaLibration of trap stiffness by thermal noise analysis. A single 1.1 jim bead is held in the optical tweezers and data is collected at 2 kHz. (a) The graph shows the bead position vs time -solid lines denote 1 standard deviation of bead position, (b) The same data plotted as a histogram. The mean displacement is 0 nm and the variance is determined by the vibration due to brownian noise, (c) The trap stiffness can be determined from this information using the equipartition principle lf2Ktrsj, x ) = l/2ksT, where Ktrap trap stiffness, (x ) = variance, /fB= Boltzman constant and T= absolute temperature...

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