Control Theory

Control theory is an engineering concept that describes dynamic input-output systems with feedback. Using control theory, we have four steps in our automation setup: Measure, Compute, Compare, and Correct. Each step describes what our system must accomplish, and creates feedback in order to create a desired outcome.

Figure 1. Control theory schematic.


We specifically chose the violacein pathway in order to exploit the unique self-colorimetric properties of its metabolic products. Each product in the pathway has a certain pigment, thus providing us a way to potentially measure its concentration akin to performing a colorimetric analysis. This can be implemented if each concentration of product (or mix of products) relates to only one unique RGB value set.

Image Processing

The image processing and response system handles the implementation of control theory in our system. To control products being made, a camera controlled by a Raspberry Pi computer will continuously capture images of our yeast culture with metabolites.

Through processing RGB values, it will determine the amount of metabolites in the solution, and send feedback signals to the culture management system to change inducer concentration levels. To explain it as a set of mathematical expressions, we want to establish a relationship between:

  1. Inducer concentration and metabolite concentration
  2. Metabolite production and RGB values

Figure 2. Vector I represents inducer inputs, and vector P represents concentrations of metabolite products. The matrix of RGB values are the points to generate each color intensity graph for each color, where the subscript term determines where on the x-axis it lies.

Machine Learning: Determining IP

The relationship between inducers and metabolite products can be solved with machine learning.

Inducible promoters work by having the inducer substance bind to a repressor on the gene binding site. By binding to it, the inducer changes the conformation of the repressor, making it detach from the DNA. In this way, inducible promoters “turn on” by “taking the plug off” the DNA.

The relationship between inducer concentration and metabolite production depends on inducer binding mechanisms to the repressor. These mechanisms have experimentally proven formulas to determine the binding rate, and thus can determine the relationship between inducer concentration and metabolite concentration. But, mutations in the binding region or the DNA making associated proteins can change the associated energies and kinematics of the binding process, making these theoretical models imprecise. Machine learning can overcome this issue by identifying the patterns that make up this relationship through repetition, which our automated system would be able to do once fully implemented. Since each specific experiment would have different mutations and issues, machine learning can figure out the relationship between inducer input concentration and the resulting metabolite product concentration.

Colorimetry: Determining P[RGB]

The second relationship can be determined through applied colorimetry.

The solution has an average RGB value. The camera takes a picture in fast succession with the solution illuminated with one of each RGB color. This will generate three graphs that can determine the intensity and purity of the solution. These graphs would be composited to make a big range of colors, which would be compared with control standard curves mapping each pure color at different concentrations.

Assuming that each color truly only maps to one specific RGB combination, this would give us the percentages of each metabolite color in the solution. Since we know the average amount of yeast we have in our solution, we can generate concentrations of each metabolite.

Culture Management

As explained on the Hardware page, we can control the growth rate of the yeast culture in our culture management setup, effectively keeping the density of cells to a controlled level. Thus, we can dilute our culture to prevent oversaturation of colors in the solution. With this setup, we can input inducers into the culture automatically.

Moreover, with the information obtained through image processing, we can automatically create the product levels we need by inputting inducers as needed.

Figure 3. Initial sketch including major components for our autonomous control system.