Team:TAS Taipei/Model
Introduction
In our project, mathematical modeling helps us understand how our constructs can be used to detect agricultural residues, whether they be pesticides or heavy metals.
For pesticide detection, we identified two potential enzymes that would break down a representative pesticide, malathion, in a predictable way. LC cutinase breaks down malathion producing acids that result in a measurable change in pH. OpdA breaks down malathion and produces a thiol-containing by-product that can be detected by a reaction that produces a yellow color. We used modeling to characterize the behavior of both proteins, identify which was working best, and relate the intensity of the signal after a certain amount of time to the concentration of pesticide we could detect.
For heavy metal detection, we decided to use proteins that bind metal ions, and engineer them to produce a detectable red color. Ultimately, we used modeling to understand how much red corresponded to how much metal ion concentration we could detect. We were also able to use modeling to understand how much metal-binding protein was being produced by our cells, so we would know how much bacteria to include if we wanted to detect a certain concentration of metal ions.
Detection of Pesticide
Based on what we learned in our surveys(click hereto look at the results of the survey), we wanted our method of detection for pesticides to be fast and convenient for consumers. We envisioned a prototype that can produce a visual signal or pH change when our constructs break down pesticides. Through research, we found two potential enzymes that can break down pesticides into products detectable by a pH change or the naked eye: LC cutinase and OpdA. We decided to model the efficiency of our enzyme using Michaelis–Menten kinetics (Michaelis & Menten, 1913). In order to determine which of the two enzymes to use, we needed to determine the efficiency of the system (i.e. the Vm/Km for our bacteria), which depends on the kinetic efficiency of the enzyme and the amount of enzyme produced. We can determine the efficiency of the system by collecting data over set time intervals (time-point data). A bacterial system that produces more efficient enzymes will have a higher overall system efficiency, which will then be chosen for our prototype. Since we needed to gather data through intervals of time, the majority of our pesticide detection experiments had to be time-dependent.
Our first candidate enzyme was LC cutinase. LC cutinase degrades malathion to produce two acidic byproducts: malathion monoacid and malathion diacid. These acids can then be detected through a pH change. Preliminary analysis of the time-based data at room temperature suggested that the enzyme was either not functioning correctly due to its inefficiency (indicated by a very low Vm/Km as shown in Figure 1), or not present at all. Through more research, we discovered that the optimal conditions for LC cutinase are a pH of 8.5 and a temperature of 50°C. We repeated our experiments under these optimal conditions, but we still did not see an improvement in function. This suggested that the enzyme was not actually present in our construct. To further investigate, we fit our data to a first order reaction exponential decay model, which models a non-functional LC cutinase, and compared it to a Michaelis-Menten fit, which models a functional LC cutinase. The results of this analysis are also shown in Figures 1 and 2. Unfortunately, the exponential model turned out to fit just as well or better than the Michaelis-Menten fit, suggesting that the enzyme was most likely not present in our experiments. Furthermore, when we checked for the presence of our protein by SDS-PAGE, we did not see bands at the expected size, suggesting that LC cutinase might not have been expressed in the cells.
Figure 1. We added malathion to LC cutinase at room temperature. We collected experimental data on
the pH change over time, then fit the data to the unknown efficiency of the system (Vm/Km) and an
unknown equilibrium constant (Ka). As shown below, exponential decay either fits just as well or
better than a Michaelis-Menten fit.
Experimental Data (Black Dots)
Michaelis–Menten Kinetics (Blue Line):
Vm/Km= 5.870×10-5 M-1*h-1
Standard Error = 1.415×10-6
Ka = 2.174×10-6
Standard Error = 9.391×10-7
R2 = 0.992
Exponential (Red Line with Crosses):
R2 = 0.991
Figure 2. We added malathion to LC cutinase at pH 8.5 and 50°C. We collected experimental data on
the pH change over time, then fit the data to the unknown efficiency of the system (Vm/Km) and an
unknown equilibrium constant (Ka). As shown below, exponential decay either fits just as well or
better than a Michaelis-Menten fit.
Experimental Data (Black Dots)
Michaelis–Menten Kinetics (Blue Line):
Vm/Km= 6.734×10-5 M-1*h-1
Standard Error = 3.218×10-6
Ka = 6.251×10-8
Standard Error = 5.552×10-9
R2 = 0.994
Exponential (Red Line with Crosses):
R2= 0.998
Our second candidate enzyme, OpdA, breaks down malathion into two products, one of which contains a thiol group. Ellman’s reagent detects the thiol product and turns the solution containing the degraded malathion yellow (Ellman 1959). After adding Ellman’s reagent into the OpdA-malathion solution, we were able to use spectroscopy to detect the yellow color. Since the intensity of the yellow color is proportional to the amount of product, we were able to convert this absorbance into the concentration of the product. In order to test the functionality of OpdA, we conducted preliminary tests to compare the intensity of the yellow color in solutions of OpdA with and without malathion. In every test of OpdA with malathion, the reaction happened in under one minute and showed consistently more yellow than the OpdA without malathion. This suggested that the enzyme is very kinetically efficient. Therefore, we diluted the enzyme one to one million with a starting concentration of 2.8 mg/mL (measured by A280). This allowed us to obtain data before all the malathion was converted into products. The time point data then allowed us to characterize OpdA, and the results suggested that OpdA is greater than six orders of magnitude more efficient than LC cutinase (Figure 3). By fitting OpdA to Michaelis-Menten kinetics, we were able to predict the intensity of the yellow color according to different concentrations of malathion given a fixed waiting time. This helped us achieve the end goal of predicting the pesticide concentration based on the breakdown of malathion.
Figure 3. We added malathion to purified OpdA and we allowed the reaction to proceed for over 10
minutes. We took out an aliquot from the reaction at different time points and added Ellman’s reagent.
We collected experimental data on the change in absorbance of the liquid over time and converted the
absorbance to the moles of the product produced. We then fit the data to the unknown efficiency of the
system (Vm/Km).
Vm/Km= 11.703 M-1 s-1
Standard Error = 2.298
R2 = 0.930
Detection of Heavy Metals
Our goal for heavy metal detection is to have a visual detection of heavy metals. In order to implement this goal, our approach was to take an existing metal-binding protein (MBP) and attach a chromoprotein on it. This will allow us, in principle, to visualize, through color, where the heavy metals are located on the surface of the produce. Out of many different possible metal-binding proteins that we tested, we found that OprF and Met are the most suitable for prototyping because they do not release metal ions after binding them. In order to visualize the location of the heavy metal, we fused these MBP’s with a chromoprotein. Preliminary testing on vegetables soaked with heavy metals demonstrated that the MBP solutions formed droplets on the surface of vegetables. However, it was not apparent whether the MBPs were actually binding to metals on the surface of vegetables, as a water rinse removed much of the fusion protein.
Since the fusion protein was not successful, we moved on to explore spectroscopic methods of detection. In principle, the metal-binding proteins in cells will form complexes with heavy metal ions that diffuse into the cell, removing heavy metal ions from the solution. Normally, it is difficult to use light spectroscopy to detect heavy metals in real samples because of the potential presence of contaminants, such as other heavy metals. However, since the proteins we used are specific to one type of heavy metal, the decrease in absorbance that we detect will only come from the decrease in concentration of the heavy metal we are targeting. Hence, contamination from other heavy metals should not interfere with our results. Consequently, the decrease in the absorbance of the solution before and after the cells are added indicates the amount of heavy metals bound to the cells. After removing the cells, we were able to find the amount of heavy metals removed by the proteins through Beer’s law. This calculation will be valid because the difference in absorbance is only caused by the removal of the heavy metal we want to detect. From an equilibrium model, we were able to derive a relationship between the concentration of heavy metals and the amount of heavy metals bound to the proteins in or on the bacteria. Assuming that our MBP’s have high specificity for a certain heavy metal, and as the equilibrium constant approaches a high value, we can demonstrate that the initial concentration of heavy metal in the solution will be equal to the concentration of metals bound in or on the cells until there are more heavy metals than MBPs (Figure 4). When this happens, the amount of metals bound to the MBP will no longer change. This relationship will, therefore, allow us to detect heavy metal concentrations up to the concentration of proteins or to the limits of our spectrometer.
Figure 4. The concentration of the nickel bound and the concentration of nickel will be the same until the
amount of nickel exceeds the protein concentration, where it plateaus.
Our equilibrium model also suggests that, as long as we are able to find the maximum amount of protein that is present, we are able to accurately find the amount of heavy metals in a sample using the method described above. As shown in Figure 4, the amount of metals bound will be equal to the amount of heavy metals in high concentrations. Thus, by conducting an experiment using a very high concentration (>1 mM) of heavy metals, we were able to interpolate the amount of protein expressed by the cells based on the amount of metals bound to the cells. We determined experimentally that at OD600=0.7 the protein concentration is 0.0038M. This allowed us to make a model on how much nickel will be bound to the protein according to different concentrations of heavy metal, as shown in Figure 5. This model assumes the high-binding-constant limit discussed above and illustrated in Figure 4, resulting in a linear fit regime, followed by a sharp plateau when all metal-binding proteins are bound to metal ions.
Figure 5. The graph shows the concentration of metals (0.0038M) bound to the cell at OD600=0.7
and 15 mM nickel.
References
Michaelis, L., & Menten, M. L. (1913). Die Kinetik der Invertinwirkung [The Kinetics of Invertase Action], Biochemische Zeitschrift, 49, 333–369.
Elmman, G. (1959). Tissue sulfhydryl groups, Archives of Biochemistry and Biophysics, 82, 70-77.
All fitting was performed using Python and packages from the SciPy and NumPy distributions:
Python Core Team (2019). Python: A dynamic, open source programming language. Python Software Foundation. URL https://www.python.org/.
Oliphant, T.E. (2007) Python for Scientific Computing, Computing in Science & Engineering, 9, 10-20 (2007), DOI:10.1109/MCSE.2007.58
Millman, J.K, & Aivazis, M. (2011). Python for Scientists and Engineers, Computing in Science & Engineering, 13, 9-12, DOI:10.1109/MCSE.2011.36
Oliphant, T.E. (2006). A guide to NumPy, USA: Trelgol Publishing.
Van der Walt, S., Colbert S.C., & Varoquaux, G. (2011). The NumPy Array: A Structure for Efficient Numerical Computation, Computing in Science & Engineering, 13, 22-30, DOI:10.1109/MCSE.2011.37
