Spring 2012:Vincent Lee Lab 1

Objectives

• Familiarization with optical trapping theory and practice.
• Preparing and trapping E Coli to measure flagella strength/speed

Calibrations

• Calibrations done with 0.97µm silica beads

Trap Stiffness

• PSD data taken at ~70mW, ~80mW, and ~90mW
• Stokes drag data taken at 80mW and 70mW

Finding R

PSD: R=V/µ

$ \beta =3\pi \eta D=9.14203\times 10^{-9} $

$ f_0=\frac{\alpha }{2\pi \beta } $

$ f_0=312.4740 $

$ p_0=4.394\times10^{-7} $

$ \alpha=1.795\times10^{-5} $

$ R=\sqrt{\frac{\pi ^2\beta f_0^2P_{0,V}}{K_BT}}R=973486 $

QPD R=V/µ

$ R=\frac{(-0.04352)-(0.02416)}{(11.51)-(11.39)}*10^6=564000 $

Method 1: Equipartition

There are multiple values of R found.

• For R=973486, $ \left\langle x^2\right\rangle =2.1956\times 10^{-27} $
  • $ \alpha =1.83504\times 10^{-5} $
• For R=564000, $ \left\langle x^2\right\rangle =6.5411\times 10^{-27} $
  • $ \alpha =6.1595\times 10^{-6} $

Method 2: Noise PSD roll-off

$ Calculated Subscript[f, 0]=312.474 $

$ \alpha=2\pi f_0\beta $

$ \alpha=1.79488\times10^{-5} $

Method 3: Stokes drag

Stokes drag produced results varying more than two orders of magnitude from the other methods. This is probably a result of the

Position

• Position calibration done with beads stuck in 10M Aqueous NaCl

Measured ratio: ≈0.66µm/V

E Coli

The E Coli were genetically modified to stick to the cover glass of the microscope slide and to spin their flagella in only one direction. The intent of the experiment was to measure the force behind velocity of an average E Coli flagellum.

Findings

E Coli 2

Stopped spinning at 9.5mW trap strength.

This is one of the datasets from this experiment. It clearly shows that the E Coli No. 2 had a rotational frequency of around 5 revolutions per second. This falls within Appleyards findings, but the bacteria I observed seemed to be spinning faster than Appleyard's:

• Mean frequency = 7.28571
• Variance of spinning frequencies = 4.7381

Issues

• Initially, camera was not fast enough to see the quickly spinning E Coli, need at least a camera of 20FPS
• Flushing the slide proved delicate, ended up working best with very light suction and water feed
• Population density of E Coli sometimes became an issue, really need a maximum of ~15 bacteria per slide, otherwise they really impinge on each other's movement
• Bacteria that stop are annoying