The strength of OxyPonics lies in the integration of genetic engineering with optical engineering. A redox-sensitive fluorescent protein signals an external LED device, which can regulate the expression of an optogenetic cassette. We demonstrate the efficacy of this novel feedback system:
We provide evidence that the camera from our external LED device can interpret the ratiometric fluorescence changes in response to different levels of oxidative stress.
While we were not able to perform tests on rxRFP, we were able to conduct feasibility tests using mRFP.
First, we confirm that our setup is capable of detecting and quantifying the fluorescence produced. We use an LED with a 572 nm peak emission wavelength for excitation,and we used a 600 nm long-pass filter on our camera to preclude excess undesirable emission. For details on the setup, see Applied Design. Due to the broad emission of our LEDs, however, some of the excitation light is also detected. This effect was assumed to be linear. Next, we confirmed a linear relationship between excitation intensity and observed average emission intensity.
This means there will be a constant scaling factor between our ratios for rxRFP and the documented absorption ratios, but our measurements will be internally consistent. In addition, the contribution of the excitation light is incorporated into our model.
After confirming that we can collect data, we sought to determine data quality. There is inherent noise associated with the camera, which compounds with the natural noise present in biological fluorescence . To isolate in the camera, we took a generic red LED and recorded the average intensity across all of those samples. The resulting distribution reveals significant variation, with a smaller spread than a Gaussian of the same mean and standard deviation. This is shown in the following figure.
Figure 1: Distribution of observed emission levels for assessment of camera noise in well lit environment
Figure 2: Distribution of observed emission levels for assessment of camera noise in dark
To obtain information on the biological noise, we also recorded the average fluorescence intensity at 42% of maximum excitation intensity (a duty cycle of 42%). This distribution is heavily skewed towards higher values.
We noticed another peculiarity in our data; over a 1 hour time period with the same ambient light conditions, there was a clear upwards trend in the average intensity recorded. While we were unable to determine the cause, we hypothesize this may be due to bacterial sedimentation within the test tube. Since we illuminate and image from the bottom, this would increase the fluorescence we measured. For ratiometric readings, this will not be a problem, as this gradual increase will cancel out when we take a ratio. However, it is something to consider during practical application of our bacteria, and we envision a system that applies mechanical agitation to homogenize the culture.
We are ultimately interested in determining the oxidative stress of the environment by measuring fluorescence. The first step in doing this is determining the “true” fluorescence of our system based on our noisy values by using a Kalman filter. A Kalman filter is an estimator that combines predictions from a known model (in our case, the linear regression we obtained) with observed measurements in order to determine the true state of the measured system. The prediction provided by the Kalman filter is also the theoretical optimal prediction if the underlying process is linear [2,3]. A further advantage is that the Kalman filter can also predict its internal model parameters, allowing for greater flexibility if baselines cannot be obtained.
We compared the Kalman filter to a simple running average for our data at a 42% duty cycle. The predictions are very similar, varying slightly based on choice of parameters of the Kalman filter. Why is this the case?
It turns out that the expression for a running average is also a special case of a Kalman filter. For the case of estimating a constant, the running average is in fact the optimal configuration of the Kalman filter. However, in a real-world environment, our state is constantly changing, such as when we excite pDawn in order to alter the ROS level, or due to diffusion of ROS throughout the system. This can all be modeled theoretically and used as the model for a higher-order, more generalized Kalman filter, which would allow us to more accurately estimate the true ROS level in our system.
- Waters, J. C. (2009). Accuracy and precision in quantitative fluorescence microscopy. The Journal of Cell Biology, 185(7), 1135–1148. https://doi.org/10.1083/jcb.200903097
- Golcz (https://math.stackexchange.com/users/42957/rafal-golcz), R. (n.d.). Why use a Kalman filter instead of keeping a running average. Retrieved from https://math.stackexchange.com/q/206817
- Li (https://math.stackexchange.com/users/171352/wangyan-li), W. (n.d.). Why use a Kalman filter instead of keeping a running average. Retrieved from https://math.stackexchange.com/q/1137342