Thursday, April 9, 2015

The peculiar behavior of our GFP spectrum bleeding into the BFP spectrum

WARNING: Quantum Mechanics below.

Before we even started attempting to decipher our flow cytometry data, we were faced with a peculiar problem. As we've learned, there are various gates that we need to implement in order to control for proper cell size, healthiness and, in our particular experiment, fluorescence. But, upon looking at these gates (shown to the right), we noticed some odd behavior from the GFP gate. Unlike the blue gate, the green gate seems to 'curve upwards' just awkwardly spilling over into the blue region. The BFP gate is more tame. With increasing concentrations of BFP in the cells, we created a strict boundary that *most* cells do not cross. 

Fluorescence spectra 'bleeding over' is a common phenomenon. First, we see that these emission spectra are not just sharp peaks emitting at a single wavelength. Sadly, when GFP is expressed in cells, it emits light in a spectrum. It would make things much easier if it was just a single wavelength but we have thermal expansion to thank for that! Which, by the way, can be described as a Gaussian distribution of energy centered on mean wavelength.... bringing it back to lecture. But I digress.

The wavelength spectrum range (as shown below) can be anywhere from 50-150 nm. What is important, however, is that this width can 'bleed over' and excite the detectors reserved for other wavelengths. This phenomenon does not generally occur, however, with a lower energy spectrum 'bleeding over' into a higher energy state. Very simply, this makes sense from what we know about energy levels. From the "ground state" (the lowest energy level), we can emit a high-energy electron with a blue wavelength. This high-energy electron creates a cascade of lower energy electrons (green) to jump up to another unstable state and emit yet another, lower-energy light (red in the figure below). If we emit anything greater than a blue wavelength, then we just broke conservation of energy.

What is important it is fairly easy for a higher-energy light spectrum to 'bleed over' into the lower spectrum. This is why the GFP bleed over is so interesting because we see, at large intensities of GFP expression, GFP molecules having blue-like behavior.

How can lower energy light do this? You made me suffer through this description of energy levels and now you're telling me that this may not be the explanation? Welcome to science!

So before we go farther, let me say that my hypothesis for this phenomenon is not well studied, this is my speculation based on fundamental quantum mechanics. I'm going to walk you through some of the basic principles, which will elucidate my explanation.

Or in modern terms,
"Plugged it into Wolfram Alpha"
Quantum mechanics is the science of the very small, the body of principles that explains behavior of matter and interactions with energy on the scale of atoms. Most people know it as that weird realm of physics that where we stick a cat in a box and debate whether it's alive or dead. Well, it is weird but it's incredibly useful and has faced the test of science for a long time. 

Now, what we know from this 3D world is that if I throw a ball against a wall, usually it will bounce back. For those of you who played Red Butt (wall ball, butts up, rump rounders.... known by many different aliases) as a kid, you probably learned this in the most unfortunate matters. In quantum mechanics, there is a chance, a VERY small chance, but a change none the less that the ball will just go right through the wall. For those of you interseted, you can find the probability of this by calculating the DeBroglie wavelength of an object (

We all know the ball didn't hit the wall Johnny
go up and pay the price
No, we aren't throwing quantum balls either.
Unfortunately, in quantum mechanics one does not often model little balls bouncing off of walls (spoiler alert, particles aren't spherical but just energy fields, have fun visualizing atoms now) but rather waves propagating through space. In our case, think of an electron going to an energy state that is a higher energy than the particle. In quantum mechanics, this wave has a finite probability of penetrating this energy barrier but at the cost, however, of a smaller resulting amplitude. Think back to our original discussion, doesn't this sound familiar?

the black friday security guards
stand no chance
A particle penetrating an energy barrier greater than its own is just like our GFP 'bleed over' problem! What could be occurring that at high intensities of GFP, there is a finite probability that the GFP particles excite the blue photomultiplier tubes. This can only be possible at high intensities because the probability of a particle existing in some space is directly proportional to the intensity of its light. The electrons will have a higher probability of penetrating the barrier with a higher intensity of light emitted. For our GFP gate, this seems to occur for a Green Fluorescence of 10^4-10^5. The resulting green electrons that result are low intensity light, on the order of 10^3.

T = \frac{\displaystyle \exp\left(-2\int_{x_1}^{x_2} dx \sqrt{\frac{2m}{\hbar^2} \left( V(x) - E \right)}\,\right)}{\displaystyle \left( 1 + \frac{1}{4} \exp\left(-2\int_{x_1}^{x_2} dx \sqrt{\frac{2m}{\hbar^2} \left( V(x) - E \right)}\,\right) \right)^2}\ ,
just plug and chug!
It is entirely possible to calculate the intensity of GFP needed to penetrate the blue photomultiplier tubes. Given the energy level differences within the photodetectors, it is entirely possible to calculate the intensity of the incoming wave needed for the detector to pick it up as non-zero signal.

In sum, the GFP 'bleed over' problem may be an artifact of a quantum particle's ability to penetrate high-energy barriers. At high enough intensities, the GFP may be able to penetrate through the blue-green energy difference and excite the flow cytometry's photodetectors. This is only possible, as we see in the GFP diagram, only at high intensity GFP for it to 'bleed over' into a higher-energy spectrum, the BFP spectrum. Notice that it keeps steadily increasing at higher intensities! Hope that you enjoyed my little intro to QM, post any questions to the comment section below.


No comments:

Post a Comment

Note: Only a member of this blog may post a comment.