Piezo tracking

Introduction

Piezo tracking allows the user to calculate the tether length using the position of the high-resolution trap and the displacement from the trap center.

Since this information is available with high temporal resolution, the resulting tether length data is also available at high resolution (as opposed to the distance data computed using video tracking, which is limited by the framerate of the Bright-field camera)

Workflow

  1. Use the regular mode of operation to catch two beads on the two traps and perform a force calibration in the same region of the field of view where the measurements will take place. It is more accurate to use same-sized beads, since using different sizes introduces a (constant) error.
  2. The relative-position trap should be on the left, and will remain fixed. The absolute-position trap should be on the right, and will be the one being moved.
  3. Ensure that both beads are being tracked correctly by choosing appropriate templates. Place the beads far enough (>5 μm) from each other.
  4. Ensure that the beads are at rest (no fluid flow or drag)
  5. Enable piezo tracking by pressing the following button located next to the bead tracking toolbar:

  1. Check that there are no errors in the notification center, and that Trap 1 Y and Trap 2 X and Y have been locked
  2. The tether length should now be visible in the timeline channel Distance/Piezo Distance

Explanation

The tether length is computed using the position of the traps and the bead displacement. This section explains the details for each parameter and how they are combined to calculate the tether length.

Bead displacement

This is the position of the trapped bead relative to the trap center. As long as the forces are within the linear regime of the optical traps, this distance can be calculated from Hooke’s Law:

Here, k is the trap stiffness (in pN/nm) that is calculated during Force Calibration. The displacement is computed for each bead individually from the force acting on that bead and the corresponding trap stiffness.

Initial trap separation

The initial trap separation is computed once when the Piezo Tracking is enabled, and it consists of the bead distance computed from video tracking plus the initial bead displacement for the two beads.

Fixed trap position

Assuming the fixed trap is on the left, and the moving (absolute-position) trap is on the right, the position of the fixed (left) trap can be computed by subtracting the initial trap separation from the initial position of trap on the right.

Current trap separation

Once the movement starts, the current trap separation is computed by subtracting the fixed trap position from the moving trap position. The fixed trap position comes from the previous section, while the moving trap position is the current mirror position of the absolute position trap.

Current tether length

Finally, the current tether length is calculated by taking the current trap separation and subtracting the bead displacements and the bead diameter.