The past few weeks I've been thinking a lot about optics. Too much. It's given me a headache. But we've characterized some really important details about how the Pioreactor works. Let's first talk about how microbial cells interact with light.
When a light ray (UV, visible, or near-IR) strikes a cell, a few things can happen: the light ray can be absorbed (and possibly re-emitted as fluorescence), the light ray can be scattered inelastically, or the light ray can be scattered elastically. For the Pioreactor, which uses 900nm light rays, the most relevant and most common behaviour is elastic scattering. The near-IR light ray will strike a cell, and reflect off it, without losing any energy. It turns out that the angle of the reflection is not uniform. Angles closer to 180° are more common. So positioning IR photodiodes, which measure IR light, at specific angles from the IR source means we can measure how much light is being scattered off cells. See Figure 1 for an example of this:
Under good conditions (which we will soon break), we make the assumption that the cell density is proportional to the amount of scattered light. However, eventually the cell density is so high the the scattered light rays strike another cell, and scatter unpredictably. See Figure 2:
When there are multiple scattering events, the assumption of proportionality isn't valid anymore. We call this saturation of the signal, and we expect to see a decreasing signal as the cell density continues to increase. However, the angle comes into play again: a decreasing angle between the photodiode and the IR LED will decrease the effects of multiple scattering events, albeit at the cost of less sensitivity. Here's an experiment we did that demonstrates this.
We prepared six vials of yeast with varying cell densities, and a blank (no yeast) vial. We placed the vials in a Pioreactor with four photodiodes at different angles: 45°, 90°, 135°, and 180°.
What we found was very surprising! Below is the data for the photodiodes at 45°, 90°, 135°:
We can see that the with increasing angle, the photodiodes are more sensitive (i.e. a small increase in cell density corresponds to a large increase in signal), however the point of saturation is lower. All the sensors are about-linear, but the 135° saturates the quickest and starts to fall sharply afterwards.
The 180° requires a negative-logarithmic transformation to make it linear, and hence isn't directly comparable to the sensors above. However, if we normalize all the data, we can compare all the sensors. See Figure 5.
The 180° signal is missing it's last point because it's raw signal was too small to detect (something we can fix with more amplification), however it is the least linear of the group. From this normalized perspective, the 45° stands out as being both linear, and having a very high saturation point. In hardware, we can amplify it as well to make it more sensitive, too.
Thus, going forward, for users who want to examine the entire growth curve, we recommend using the 45° pockets for the photodiodes. For users who are most interested in the early phases of growth, or in continuous culture where the density is somewhat low, we recommend using the 135° sensor. The 90° is useful for inbetween use cases, and provides the full growth curve only if the media is not too rich (< 3% sugars by weight).
💡 Also read our follow-up blog post on the Pioreactor optics system.
A side story of frustration and learning
After completing the above experiment, I wanted to test the different angles for actual growing cultures in rich media. My photodiodes were set up like so to be able to measure 135°, 90°, and 45°:
The results went as expected: the 135° signal was most sensitive, but saturated quickly and decreased.
However, if we zoom into the first few hours, the 45° was doing something strange. Ignoring the "blips", the culture's density seemed to be increasing, but then it slowed down before speeding back up again.
This didn't make any sense. The signal-response was linear, and the culture was growing exponentially, so the signal should also be increasing exponentially - but this isn't exponential!
Sadly, this kept happening, and caused me a lot of mental trouble. Only after taking a few hours off, did I think of what might be happening. Recall that lots of the scattered light ends up reflecting to 135°. What would happen if the photodiode positioned at 135° was reflecting light back? I tested this first by shining a light head-on onto an LED, and sure enough, there was a very small amount of light reflected directly backwards. So this was my theory: early in the culture, lots of light is scattered to the 135° photodiode, and a small fraction of this light is directly reflected backwards into the 45° sensor! See Figure 9. When the culture grows and becomes more dense, the reflected light no longer gets through. This means that the 45° is seeing too much early light on, and the corrects itself as the culture gets dense.
To test this, I set up a new experiment with the same configuration, but with another 45° with no LED opposite to it. And sure enough the new 45° photodiode looked perfect:
In conclusion, the specific configuration I chose above was the problem, and it's really really good to know that it can cause problems.