Team:DTU-Denmark/Model
Substrate Set
Our substrate screening experiment produced a large number of interesting substrates for our detection assay. We looked at the raw fluorescence measurements, but we also applied statistical analysis to identify the peptides that had significant differences between the three venoms. In addition, we modelled the enzymatic activity of the venoms based on our measurements.
You can find the plots of logarithmic fluorescence signal and time of all the substrates here.
The relative signal of each substrate between the three snakes was also analyzed. You can find that part here.
Lastly, we looked at the fluorescence output in terms of enzymatic activity. We fit a non-linear model in the reactions and calculated their rates. You can find the models for all the substrates here.
LacZ Device
Purpose
If β-galactosidase is used as a reporter in our biosensor, we would have an output of our device that depends on two subsequent enzymatic reactions. We want to model how the enzymatic activity of the first reaction affects the kinetics of the secondary reaction, and find some optimal time for the first reaction to run, if we want the combined time of both enzymatic reactions to be as short as possible.
Background
In investigating if our prototype would be a viable option for in-field detection we decided to meet with Andreas Lausten, Co-founder of VenomAB, a producer of breakthrough solutions to modern antivenom monovalent production . As per his recommendation our system would ideally have to give a rapid response. As of yet, our assays had shown response time above 45 minutes for certain venoms, and we should seek to reduce the response time. In doing this we would have to amplify the output of our device compared to that of just using chromoproteins such as AmilCP.
Central assumptions
Ideally we would like to do this with different enzymes, especially enzymes with a high turnover rate and a robustness towards snake venom. However, due to time constraint we decided to establish a proof of concept for using β-galactosidase as an amplifier of the snake venom cleavage reaction, using the following assumptions
- Incubation times are static (no flow or dilution through the system)
- Volume is kept constant
- The concentration of ONPG in the secondary reaction is in great excess. This means that our released reporter enzyme from reaction 1 will be saturated with substrate throughout the secondary reaction, and will catalyse reactions at Vmax throughout the incubation period
Design of the Model
We imagine a device with two chambers (CH): CH1 and CH2 (See figure 4). When testing for snake envenoming, a blood sample will be loaded into CH1 with a set volume. CH1 will contain some sort of biotinylated surface e.g. biotinylated beads. Our biobrick testing device will attach to the biotinylated surface via the ScAvidin domain, and if venom is present, the linker peptide of the biobrick device will be cleaved, thereby releasing β-galactosidase. After a certain incubation time in venom, the sample is transferred from CH1 to CH2.
Primary reaction
As we needed a lot of kinetic parameters for our lacZ composite part, which would require a lot of kinetic experiments on our expressed part, we did a first iteration of our model, using a mixture of arbitrary values as well as values from literature to create a proof-of-concept that it would, in theory, be possible to determine an optimal timepoint for the incubation device to let the sample flow from CH1 to CH2.
In the first reaction, our expressed composite lacZ part (BBa_K2355313) is converted to ScAvidin and free enzyme by the reaction described in figure 5:
Besides the central parameter k1, which is the reaction rate constant for the reaction, both snake venom concentration and the concentration of the expressed composite part seems to have an influence on the rate of the reaction. As the snake venom proteases are not depleted during the reaction, no differential equation for concentration of venom is made. That leaves us with a very manageable set of ODE’s (Figure 6):
When simulating these ODE’s, the initial venom concentration is set to be 100 ug/mL, as this was the highest concentration of venom that we used in our experiments. The initial fusion protein concentration is set as being 2.47×10-6 mol/L (2.47 uM), as this is the maximum binding capacity of our biotinylated beads [1]. The reaction rate constant has been determined from the data of our protease substrate assay, where we calculated a rate constant of k1 = 0,014 on the basis of the data from Bitis gabonica venom on well O22 of the substrate set.
As can be seen in figure 7, the crossover time, where the concentration of released enzyme exceeds that of the substrate, is around 50 minutes. The time-scale seems to be realistic, and seems to be matching our experiences with our own substrate/venom reactions. For future calculations, the time used in this first reaction will be referred to as “T1” .
Secondary reaction
The secondary reaction is described in figure 8. ONPG is catalysed by β-galactosidase to ONP and galactose. As the reaction runs at Vmax due to the high substrate concentration, the rate constant for the conversion of ONPG can be described by kcat.
The goal was to see if an optimal incubation time for the primary enzymatic reaction could be identified. We calculated the concentration of ONP needed to give off an output signal that corresponds to what we would expect, if we had used amilCP as a reporter molecule, and incubated our device for 60 minutes. The theoretical absorbance of amilCP released after an hour of venom incubation can be calculated from the β-galactosidase function determined from the primary reaction above, and the molar extinction coefficient of amilCP, which is determined experimentally to be 87600 M−1×cm−1 [2] From the molar extinction coefficient of ONPG/ONP (21300 M−1⋅cm−1 ) [3], it was determined that a concentration of 5.8 uM released ONP would give off an absorbance value that corresponds to that of incubated amilCP.
Using a Vmax value of 142 mol/time/mg enzyme, the kcat rate constant of the secondary enzymatic reaction could be determined, using the calculated beta-gal concentration from the primary reaction. The kcat value was then used to determine the time (T2) it would take for the secondary reaction to reach the target concentration of 5.8 uM ONP, assuming that no ONP was present at the start of the reaction. The combined time of the two reactions (i.e. the time before sample is transferred from CH1 to CH2 plus the time for the secondary reaction to reach the target product concentration) can be plotted as a function of T1. With our arbitrary units of time, the plot appears as in figure 9.
From figure 9, it can be seen that there is a local minimum for the total time at T1= ~0.8 arbitrary time units. It thus seems like it is theoretically possible to determine an optimal time of incubation of our expressed composite part in snake venom, although more parameters has to be determined to give more reliable data. This is only our first iteration of the model, and in the second iteration we would like to input more real life values, to get away from working in a.u.
References
[1] TrueBlot® Biotin Magnetic Beads: https://rockland-inc.com/Product.aspx?id=53559
[2] Alieva, NO et al. (2008) Diversity and Evolution of Coral Fluorescent Proteins, PLOS ONE 3;7:e2680 (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2481297/pdf/pone.0002680.pdf)
[3] 2-Nitrophenyl b-D-galactopyranoside Product information: http://www.sigmaaldrich.com/content/dam/sigma-aldrich/docs/Sigma/Product_Information_Sheet/1/n1127pis.pdf
