Direct Measurement of Torque in an Optical Trap and Its Application to Double-Strand DNA

We present a method that offers the possibility to directly apply and measure torque on particles in an optical trap. It can be used to rotationally manipulate biopolymers attached to appropriate particles. A flat object is trapped and oriented in the focus of a linearly polarized laser light. The direction and power of the orientational trap are controlled by the polarization state of the light. As a demonstration of the capabilities of the method, we examined the torsional stiffness of dsDNA ($\lambda$-DNA) in its linear torsional regime by directly measuring the torque generated by the molecule.

Figure 1

Optical trapping arrangement. Notations: $P$, polarization plane of the trapping light; $M$, direction corresponding to the zero torsional strain of the molecule; EQ, equilibrium orientation of the disk.

Figure 2

Typical raw data showing the orientation of the disk during data collection at one twist extremum. The average of cumulative angles defines the equilibrium orientation EQ in the middle of the period. Calibration is based on the analysis of Brownian fluctuations (inset).

Figure 3

Torsional modulus of dsDNA as a function of the relative extension: ■, experimental values; ▴, torsional modulus measured in Ref. 16 at 15 and 45 pN tensions and represented by the model in Refs. 28, 30 fitted to our experimental values (solid line).