Fall 2010: Problem Set 3

Due 9/30/2010, 11:59 PM

Question 1

You are trying to image a 10 micron thick cell that expresses Enhanced Green Fluorescent Protein (EGFP) at a concentration of 1 µM using a Nikon Plan Apo 100X objective with an NA = 1.0 and a CCD camera with a pixel size of 7.5µm x 7.5µm that supports binning modes of 2x2, 4x4, and 8x8. The camera has a quantum efficiency of 0.8.

The excitation source is a laser with wavelength 395 nm that produces a flux density of $ 6 \frac{W}{cm^2} $ in the sample plane. The extinction coefficient of EGFP at this wavelength is about $ {\epsilon} = 55,000 M^{-1}cm^{-1} $, and its quantum yield is 0.6.

Recall that the Beer-Lambert law states that $ T = \frac{I}{I_0} = 10^{-{\epsilon}lc} $, where $ {\epsilon} $ is the molar absorption coefficient, $ l $ is the path length, and $ c $ is the concentration.

a) What binning mode should you use on the CCD camera? b) What fraction of the excitation photons passing through the center of the cell will give rise to fluorescence emission? c) How many excitation photons per second pass through a single pixel’s image in the sample plane? d) To make an image with a signal to noise ratio of > 100, what is the minimum exposure time? (Assume shot noise predominates.)

Qusetion 2

Two proteins (A and B) are tagged with fluorescent reporters. To study their spatial interaction dynamics, they are imaged repeatedly in rapid succession. Two lasers alternately excite the fluorophores in synchronization with a fast CCD camera. In this way, the camera captures an image of protein A in one frame and image of protein B in the next, so that the molecules are imaged almost simultaneously. Protein A is tagged with GFP.

a) Choose the reporter that you want to tag protein B with. b) Choose two laser wavelengths that will excite protein A and protein B fluorophores efficiently. c) Design the reflection/transmission curves of a single dichoric and emission filter set that will allow you to image both protein A and protein B.

You will likely find this website useful: http://www.invitrogen.com/site/us/en/home/support/Research-Tools/Fluorescence-SpectraViewer.html  

Question 3

Using the example code from the Simulating Brownian Motion in Matlab tutorial (or any other simulation environment you like):

a) Simulate particle trajectories for 5 particles with a sampling interval of 0.1 seconds and a length of 10 seconds – something that would be easy to achieve in the lab. b) Write some code to estimate the diffusion coefficient from a particle trajectory. Run the simulated trajectories through your code. c) What is the statistical uncertainty in your estimate? d) Now run at least ten simulations each for 10, 40, 160, 640, and 2560 seconds. Plot the viscosity estimate versus particle track length with error bars. e) In the lab, most scholars have been using the methodology from the Newburgh reference (http://scitation.aip.org/journals/doc/AJPIAS-ft/vol_74/iss_6/478_1.html) to estimate D, i.e. estimating the slope of the MSD versus time interval curve. Rerun the simulation using only the mean squared displacement for the shortest time interval to estimate D. How does the uncertainty compare?