Introduction
GHB will be detected by measuring a capacitance change when the drug enters the sensor. When GHB binds to the transcription factor BlcR, a conformational change results in the disassembly of the tetrameric structure into two dimers, thereby causing its dissociation from the DNA binding sequence [1] . The dissociation of BlcR leads to a change in capacitance, a more detailed explanation of which can be found here. As GHB is present in certain drinks and endogenously in the human body, the sensor should be able to differentiate quickly between low and high GHB concentrations. Herein, we simulated a model based on the theory of the binding of substrate to surface-bound ligands [2]. By analyzing this model we determined the optimal conditions in the sensor, as well as the bioengineering steps that could improve its function. An overview of the input, the steps taken, and the output of the model can be seen in Figure 1.
Figure 1. An overview of the modeling done by SPYKE. We used lab data and literature to create the model. The results of the modelling provided the basis for the experiments which aim is to improve the binding affinity of BlcR to DNA.
Biomolecular workings
Figure 2 shows a graphical representation of the biomolecular workings of the sensor. Our model simulates the output signal of our sensor by calculating the portion of BlcR bound to DNA in equilibrium. Our sensor is similar to the one described by Sankar et al. [3] , wherein DNA is bound to one of two metal plates in a chip. When a transcription factor binds to this DNA, the transport of charge-carrying molecules is inhibited, thereby raising the capacitance. We calculated the fraction of bound BlcR at equilibrium which corresponds to a capacitance value. We assume that the capacitance would change in a few seconds when BlcR is bound to or released from the DNA, as indicated in the UTI experiments and in Sankar et al. The model works in two steps:
- Calculating the active concentration of BlcR dimers. The active concentration of BlcR dimers is represented by the part that is not bound to its substrate, GHB. Only this fraction of BlcR is able to bind to DNA. To calculate this we subtracted the amount of BlcR bound to GHB in equilibrium from the total amount of BlcR in the sensor. When the concentration of GHB increases, the amount of active BlcR dimers decreases.
- Calculating the fraction of DNA bound by BlcR. The fraction of DNA bound by BlcR is the output of the model. Active BlcR dimers form tetramers when binding to DNA.
Our sensor’s response to GHB can be summarized as follows: an increase in GHB concentration decreases the active concentration of BlcR dimers, thereby decreasing the fraction of DNA bound by BlcR, resulting in a capacitance change.
Figure 2. A graphical representation of the sensor’s biomolecular workings. Firstly, GHB converts the active dimer BlcR concentration into non-active BlcR dimers. The remaining fraction of BlcR binds to DNA. The capacitance of the electrode is proportional to the fraction of BlcR bound to DNA.
Modeling of the biosensor
We used the theory of the binding of substrate to surface-bound ligands to create our model [2] . This theory can be used to calculate the relative output signal of biosensors with surface-bound ligands for different substrate concentrations.
Calculating the active concentration of BlcR dimers
We first calculate the active concentration of BlcR dimers. The concentration of active BlcR in solution follows this equation:
where BlcR is the concentration of active BlcR dimers. The concentration of bound BlcR over time follows these equations:
When equilibrium is reached, the rate of formation of BlcR-GHB complexes is equal to its decay and the thermodynamic dissociation constant can be calculated as:
At t0, GHB gets added to the solution with BlcR and DNA, however, the amount of BlcR bound to GHB is still zero here. After some time, a new equilibrium is reached, where also the rates of formation and decay of GHB-BlcR complexes are equal:
| Time |
[BlcR] |
[GHB] |
[BlcR-GHB] |
| t0 |
[BlcR0] |
[GHB0] |
0 |
| tequilibrium |
[BlcR0]-x |
[GHB0]-x |
x |
At this new equilibrium with the presence of GHB, equation (4) becomes:
With this information, the active concentration of BlcR can be determined by calculating the GHB-bound fraction of BlcR (x). Afterward, this fraction can be subtracted from the original BlcR concentration resulting in the active BlcR concentration:
Calculating the fraction of DNA bound by BlcR
Following the calculation of the active fraction of BlcR, we can calculate the fraction of DNA bound by BlcR. The concentration of DNA bound by BlcR follows this equation:
where BlcR2 are BlcR tetramers formed from two dimers. When equilibrium is reached, the following equation holds:
In this equation, the Kd value is actually the concentration of BlcR needed to bind half of the DNA squared as two BlcR molecules bind one DNA molecule. Whenever we mention the Kd value of BlcR to DNA we mean the unsquared Kd value. In the sensor, the concentration of DNA is much lower compared to the concentration of BlcR:
The total amount of BlcR does not change over time:
The fraction of DNA bound by BlcR is calculated with the following equation:
Substituting equation (8) into equation (11) and simplifying using equation (9), we get:
BlcR dimers bind DNA cooperatively by forming tetramers. This process changes their overall structure, function, and response, which can be corrected by using a so-called Hill coefficient. The Hill coefficient is a measure of the degree of cooperative binding. A Hill coefficient of 1 means non-cooperative binding and a hill coefficient of 2 means strong cooperative binding [4] .
This fraction of DNA bound by BlcR corresponds to the output of the sensor. To make the most accurate simulation of our sensor, we calculated the binding affinities of our produced BlcR to DNA and succinic semialdehyde (SSA), the analog of GHB. For this we used the results of the Electrophoretic Mobility Shift Assay (EMSA) experiments and the method described by Heffler et al [5] . We used ImageJ to do the image processing and analysis. We were mostly interested in estimating the degree of cooperative binding of BlcR as Pan et al. only reported that there was cooperative binding but not the exact degree. An overview of the species and parameters used in the model can be seen in Tables 1 & Table 2. Several assumptions had to be made to create the model, as shown in Table 3. They were adapted from literature and wet lab experiments.
To calculate the binding affinity of BlcR to DNA we used EMSA results shown in Figure 3.
Figure 3. EMSA study for the characterization of BlcR binding to the 51 bp Blc operator sequence. The concentration of Cy3 labeled DNA was maintained at 25 nM. Titration of dimeric BlcR from lanes 1 to 10. 1: 0 μM, 2: 0.1 μM, 3: 0.25 μM, 4: 0.4 μM, 5: 0.5 μM, 6: 0.6 μM, 7: 0.7 μM, 8: 0.8 μM, 9: 0.9 μM, 10: 1 μM.
- First, all the average fluorescence of the unbound DNA bands of the EMSA were calculated for different BlcR concentrations.
- Then, the background fluorescence was subtracted.
- The fraction of DNA bound to BlcR was calculated by dividing each fluorescence signal by the maximum fluorescence signal of the leftmost band.
- The fractions bound were fitted using excel to equation (13). Figure 4 shows the data and the best possible fit formula.
- The resulting binding affinity and hill coefficient were: Kd=395±32.5nM & Hill coefficient=1.79±0.528. The errors are the 95% confidence interval obtained from the curve fit.
Figure 4. The fraction of DNA bound with BlcR for different BlcR concentrations. The pink line represents the data obtained from EMSA and the purple line is the formula it was fitted to (R2=0.987).
The Kd value resembles the two binding affinities found by Pan et al.
[1] (120nM and 490nM). In the model, we use these values to closely mimic the conditions in our sensor.
As established before by Pan et al. [1] , one SSA molecule binds to one BlcR dimer. This means there cannot be cooperative binding. This simplifies the calculation of the binding coefficient as the Hill coefficient is one. To calculate the binding affinity of BlcR to SSA, we used the EMSA results shown in Figure 5.
Figure 5. EMSA study for the characterization of BlcR dissociating from the 51 bp Blc operator sequence in presence of SSA. The concentration of Cy3 labeled DNA and BlcR was maintained at 25 nM and 1.6 μM respectively. Titration of SSA from lane 1 to 9 . 1: 0, 2: 64 nM, 3: 320 nM, 4: 1.6 μM , 5: 08 μM, 6: 40 μM, 7: 0.2 mM, 8: 1 mM, 9: 25 nM DNA only.
- First of all, the average fluorescence of the bound DNA bands of the EMSA was calculated for different SSA concentrations. The first two bands were skipped as they showed an overall lower intensity.
- The background fluorescence was subtracted.
- The fraction of DNA bound to BlcR was calculated by dividing each fluorescence signal by the maximum fluorescence signal of the third band.
- The data was plotted and can be seen in Figure 6. The fraction of DNA bound follows equation (13). When the fraction bound is 0.5, the active concentration of BlcR is the same as the binding affinity thus 390 nM. This means 1210 nM of BlcR is bound to SSA. The following equation can then be used to calculate the binding affinity of BlcR to SSA.
The resulting Kd value is around 500 nM.
Figure 6. The fraction of DNA bound to BlcR for different SSA concentrations.
It is hard to estimate the binding affinity of BlcR to SSA as there are not enough data points. The binding affinity can be estimated to be in the same range as the one found by Pan et al. (700nM)[1] . As Pan et al. uses a more accurate ITC measurement to calculate the binding affinity and we don’t have many data points we choose to use the value found by Pan et al. in the model.
Table 1. The species used in the model
| Species [concentration unit] |
Description |
| DNA [μM] |
Immobilized DNA, able to bind two BlcR dimers |
| BlcR [μM] |
Dimerized transcription factor able to bind a specific sequence present on DNA |
| DNA-BlcR2 [μM] |
Two BlcR dimers bound to DNA |
| GHB [μM] |
Inhibitor of BlcR |
| BlcR-GHB [μM] |
GHB molecule bound to a BlcR dimer, making it inactive |
Table 2. The parameters used in the model
| Parameter |
Description |
Value (if not specified otherwise) |
Literature/experiment |
| Max_BlcR |
The maximum concentration of BlcR possible before aggregation occurs |
7.9*10-6[M] |
aggregation experiments (Notebook 4, 26/09/2022) |
| GHB_drink |
The average concentration of GHB in a spiked drink |
5*10-2[M] |
[5] |
| Cutoff |
The recommended cutoff value for GHB detection. Below this value, the GHB can be endogenously present in drinks. |
5*10-5[M] |
Interview NFI |
| Hill coefficient |
Shows the degree to which BlcR dimers cooperatively bind (1=fully independent, 2=strongly cooperative) |
1.79 |
EMSA experiments (Notebook 1, 27/09/2022) |
| Kd_BlcR_GHB |
Dissociation constant of GHB from BlcR |
700*10-6 |
[1] |
| Kd_BlcR_DNA |
Dissociation constant of BlcR from DNA |
395*10-6 |
EMSA experiments (Notebook 1, 27/09/2022) |
| Surface |
Surface area of electrode |
2*10-5 [m2] |
[7] |
| Volume |
Volume between electrodes |
5*10-9 [m3] |
[7] |
| Max_surface_coverage_DNA |
Maximum surface coverage of electrode with DNA |
3*10-7[m-2] |
[3] |
| DNA_total |
Maximum amount of DNA immobilized on electrode |
3*10-11 mol |
Max_surface_coverage_DNA * Surface |
| C_DNA_0 |
Concentration of DNA between electrodes |
6*10-3 M |
DNA_total/Volume |
Table 3. The assumptions used to create the model
| Assumption |
Description |
Consequence |
Literature |
| The model is in equilibrium conditions. |
The maximum concentration of BlcR possible before aggregation occurs. |
We assume that our system quickly establishes and can maintain equilibrium after the addition of molecules, thereby making all equilibrium equations used for the model valid. |
[3] |
| BlcR binds with the same binding affinity to GHB as DNA. |
The binding affinity of BlcR to the ligand GHB is similar to the binding affinity of BlcR to SSA. |
We use the binding affinity of BlcR to SSA found in the literature as the binding affinity of BlcR to GHB when running the model. |
[8] |
| BlcR binds as a tetramer and is present in the solution as a dimer. |
BlcR monomers will associate with each other strongly to form dimers. |
In equilibrium, only loose BlcR dimers and BlcR tetramers bound to DNA exist. |
[1] |
| One BlcR tetramer binds to one DNA molecule. |
In our model we use the wild-type oligo. This contains two BlcR binding sequences, to each of which one dimer can bind. The two dimers then form a DNA-bound tetramer. |
There is an equilibrium between 2 dimers + 1 DNA and 1 DNA-bound tetramer. |
[1] |
| BlcR bound to GHB can’t bind to DNA. |
When GHB binds to BlcR, it causes a conformational change that makes a tetramer fall back into two dimers, which cannot bind back to DNA as long as GHB remains bound. |
When GHB is added to the model, the equilibrium of BlcR forms shifts to favour unbound, inactive dimers. The inactive dimers are also in equilibrium with active BlcR + GHB. |
[1] |
| One GHB molecule binds to one BlcR dimer. |
If GHB is present in the solution, it may bind BlcR. Although each dimer has two GHB binding sites theory suggests one BlcR dimer can bind at most one GHB molecule. |
BlcR dimers exist in a normal active form and an inactive form in which one GHB molecule is bound. In our model, no BlcR dimers exist with two GHB molecules bound. |
[1] & [9]
|
| BlcR is present in a significantly higher concentration than DNA. |
The molarity of BlcR in our system is multiple orders of magnitude higher than that of DNA. For every DNA molecule in the system, many more BlcR dimers are present. |
If BlcR binds to DNA the concentration of BlcR is largely unaffected. |
- |
| BlcR, GHB, and DNA don’t degrade. |
The BlcR proteins, GHB molecules, and surface-bound oligonucleotides don’t degrade. |
The total number of BlcR dimers, GHB molecules, and DNA strands, meaning loose + in any complex with other components, remains constant. |
(GHB) [10], (DNA) [11] & (BlcR) [12] |
| All reaction components are present in high copy numbers. |
BlcR, DNA and GHB (if applicable) are all present in significant enough concentrations to make the system work as intended. |
Any change in equilibrium is not rate-limited by a lack of any of the components. |
- |
Overview of binding model
We implemented our model in Python, as it is an open-source programming language [13] and thus contributes to the core values of iGEM [14]. For our first implementation, we programmed the model with a combination of pure Python and NumPy, a commonly used expansion for Python that gives more methods for scientific computing. We ran the model for different conditions (see below) to get an idea of how our sensor behaves.
Model without GHB
To find out how our sensor behaves without the addition of GHB, we ran our model over a large range of BlcR concentrations. Figure 7 shows the fraction of DNA bound by BlcR plotted against the BlcR concentration. The fraction of DNA bound to BlcR corresponds to the capacitance of the electrode. The capacitance is at its minimum when all DNA is bound and at its maximum when no DNA is bound. The model was run for a Hill coefficient of 1 and 1.79 to see differences between independent and cooperative binding of BlcR dimers to DNA.
Figure 7. The fraction of DNA bound to BlcR over a range of BlcR concentrations without GHB in the system. Hill coefficient = 1, no cooperative binding of two BlcR dimers to DNA. Hill coefficient = 1.79, strong cooperative binding of two BlcR dimers to DNA.
- The fraction of DNA bound by BlcR highly depends on the concentration of BlcR;
- The model gives a sigmoidal response curve, as expected from literature [2];
- When we take into account the cooperative binding (we increase the hill coefficient from 1 to 1.79), the curve increases in steepness;
- Both with and without cooperative binding, more than 1 μM BlcR is needed to cover more than 95% of the DNA.
Model with varying GHB concentrations
The model was run over a range of GHB concentrations to get an understanding of what the behavior of our sensor would look like in the presence of GHB. For every GHB concentration, the fraction of DNA bound by BlcR was calculated over a range of BlcR concentrations. Again, a Hill coefficient of either 1 or 1.79 was used to study the differences induced by cooperative binding. The results are shown in Figure 8 .
Figure 8. The fraction of DNA bound per BlcR concentration over a range of GHB concentrations. (a) Hill coefficient=1, no cooperative binding of two BlcR dimers to DNA. (b) Hill coefficient=1.79, strong cooperative binding of two BlcR dimers to DNA.
- With GHB present we need a larger concentration of BlcR to bind most of the DNA.
- Differences in GHB concentrations have a large impact on the sensor.
- Switch-like behavior is expected to occur when GHB concentrations increase, meaning that instead of a gradual increase or decrease in BlcR bound to DNA, the system jumps between states where either almost nothing or almost everything is bound.
Sensitivity of our sensor
An important characteristic of our sensor is its sensitivity. The sensitivity here is defined as the amount of GHB which is needed to dissociate 99% of BlcR from the DNA. We ran the model over a range of concentrations of BlcR. We calculated the concentration of GHB necessary for dissociation of 1% and 99% of BlcR from the DNA. The results are shown in Figure 9.
Figure 9. The sensitivity of our sensor for a range of BlcR concentrations.
- The sensitivity of the sensor is expected to be high when exposed to the average concentration of GHB in drinks (5 mg/L≈50 mM).
- The system can not be optimally used below 1 μM BlcR concentration since below those concentrations less than 99% of BlcR is bound to the DNA in equilibrium.
- For every BlcR concentration above 1 μM and below 5 mM there is a window of GHB concentrations where a change in GHB concentration contributes to an output change, namely the area between both graphs.
Signal-to-noise
Free BlcR dimers between the plates of the capacitor are a cause of the noise. We call the ratio of bound to unbound BlcR between the plates the signal-to-noise ratio. The signal-to-noise ratio was calculated over a range of BlcR concentrations. The results are shown in Figure 10.
Figure 10. The signal-to-noise ratio of our sensor for a range of BlcR concentrations.
- There is an optimal BlcR concentration to minimize the noise, namely where the signal-to-noise ratio is highest (~0.5 μM).
Optimal model usability
With a clear overview of how the model behaves, we determined the optimal conditions for our sensor. We tested our model on the average GHB concentration found in spiked drinks (50 mM) [5] . As discovered during aggregation experiments (Notebook 4, 26/09/2022) the maximum BlcR concentration obtainable before aggregation occurs is 7.9 μM. To function properly, the BlcR concentration in the sensor should be below this value. We looked at possible ways of improving the entire system based on the simulation results.
Optimal model usability at standard conditions and values
In our sensor the most simple variable to change is the concentration of BlcR. We saw in the simulations mentioned above that the BlcR concentration plays a large role in the behavior of the system. We used the model to find the optimal BlcR concentration for the sensor. The following requirements need to be met for the system to be optimal:
- The fraction of DNA bound by BlcR should reduce from 99% to 1% when a GHB concentration of 5*10-2 mM , as found in spiked drinks, is added.
- The signal-to-noise ratio should be the maximum possible.
- The BlcR concentration should be below the maximum obtainable concentration of 7.9 μM.
The optimal BlcR concentration could be determined in three steps:
- We start by creating a range of BlcR concentrations in which we get the change of signal from 99% to 1% bound when 50 mM of GHB is added.
- We take the lower and upper bounds of this range and use them to plot the signal-to-noise curve between these values.
- We calculate the maximum signal-to-noise value and its corresponding BlcR concentration. The results are shown in Figure 11.
Figure 11. The signal-to-noise ratios for the possible concentrations of BlcR. The higher-bound GHB concentration is 50 mM.
- The optimal concentration of BlcR for the sensor is around 2 μM and results in a signal-to-noise ratio of around 7000.
- When used with a BlcR concentration of 2 μM the system meets all the requirements necessary for the sensor to function.
Optimal model usability at high GHB concentration in drinks and standard values
Unfortunately, alcoholic drinks can already contain a small concentration of GHB without being spiked
[15] . We introduced a cutoff value of 50 μM, as suggested by the NFI , to avoid false positives resulting from the endogenous concentration of GHB in certain alcoholic drinks. Below this cutoff value the sensor should not give a warning signal and thus most of the DNA should be bound. We ran the same analysis as before but used this already existing GHB concentration as the cutoff. The results of the simulations are shown in Figure 12.
Figure 12. The signal-to-noise ratios for the possible concentrations of BlcR. The cutoff GHB concentration is 50 μM.
- The maximum signal-to-noise value obtainable is very low when compared to previous simulations.
- Under these conditions, the lowest BlcR concentration possible is higher than the maximum possible BlcR concentration before aggregation occurs even with strong cooperative binding.
The last point is crucial for the success of our project. Without changing the properties of the system, our system would not work under normal conditions for all drinks due to the limited BlcR concentration. Thus, the sensor should be changed to some extent for it to be able to function as desired.
Optimal model usability at high GHB concentration in drinks and varying values
To get around the previously identified problems of a low signal-to-noise value and protein aggregation for drinks already containing GHB, we looked at all the variables of the system, to see if we could change them. The electrodes are made for optimal capacitance, and the DNA concentration is already optimized for maximum BlcR binding. The two variables we could possibly change without impacting the system in a negative way are the binding affinities of BlcR to DNA and the binding affinity of BlcR to GHB. To determine which of the two would improve the sensor’s response more when changed, and to see if the affinities should be increased or decreased, we ran the model over different dissociation constants (Kd) of BlcR to DNA or GHB. Note that a higher Kd translates to lower binding affinity.
Model with varying dissociation constants
We wanted to test the impact of changing the dissociation constants on the behavior of the model. For this, we calculated the amount of BlcR needed to bind at least 99% of the DNA. We modeled how the concentration of BlcR changes for different Kd values of BlcR to DNA (Figure 13a) and BlcR to GHB (Figure 13b). The previously mentioned cutoff value of 50 μM was again used.
Figure 13. The concentration of BlcR needed to bind 99% of the DNA over a range of Kd values with [GHB]=50μM. (a) The Kd of BlcR to DNA was varied. (b) The Kd of BlcR to GHB was varied.
- Decreasing the Kd_BlcR_DNA clearly decreases the amount of BlcR needed to bind 99% of the DNA.
- Increasing the Kd_BlcR_GHB clearly decreases the amount of BlcR needed to bind 99% of the DNA.
- Increasing the binding affinity (decreasing Kd) of BlcR to DNA is the best way to decrease the necessary concentration of BlcR as this has more impact than decreasing the binding affinity of BlcR to GHB.
- To get to a usable BlcR concentration for all drinks, the Kd value between BlcR and GHB needs to be decreased around 10 fold.
To see how the sensitivity is affected by the increase in binding affinity between BlcR and DNA, we ran the model over a range of Kd values of BlcR to DNA. We calculated the concentration of GHB necessary to unbind 99% of BlcR at the maximum possible BlcR concentration before aggregation. The results are shown in Figure 14.
Figure 14. The sensitivity of our sensor for a range of Kd values of BlcR to DNA.
- Even with a Kd value 1000 times lower than the original Kd, the concentration of GHB found in most drinks is still enough to dissociate more than 99% of the BlcR from the DNA. Thus, decreasing the Kd value does not pose a risk to the sensitivity of the sensor.
To see how the signal-to-noise is affected by the increase of binding affinity between BlcR and DNA, we ran the model over a range of BlcR concentrations and Kd values of BlcR to DNA. We calculated the signal-to-noise of the DNA over a range of BlcR concentration for 3 Kd’s (3.95 nM, 39.5 nM, 395 nM). The concentration of GHB was the cutoff value (50 μM). The results are shown in Figure 15.
Figure 15: The signal-to-noise of our sensor for a range of BlcR concentrations for multiple Kd values (3.95, 39.5, 395 nM).
- Decreasing the Kd_BlcR_DNA increases the signal-to-noise ratio for lower concentrations of BlcR. Thus decreasing the Kd value does not pose a risk to the signal-to-noise ratio of the sensor.
Changing the binding affinity of BlcR to DNA
We again ran a simulation to find out how the optimal BlcR concentration changes with an increased binding affinity between BlcR and DNA. The results are shown in Figure 16.
Figure 16 An animation of the signal-to-noise ratios for the possible concentrations of BlcR changing because of a decreasing Kd value of BlcR to DNA. The cutoff GHB concentration is 50 μM.
- Increasing the binding affinity between DNA and BlcR increases the signal-to-noise ratio and lowers the minimum required BlcR concentration for the correct functioning of the sensor.
- With an increased binding affinity between DNA and BlcR, the system can work with all drinks.
Conclusion
From the data we obtained with modeling we came to the conclusion that the most effective way to optimize our sensor is to increase the binding affinity between BlcR and its DNA binding sequence. Increasing the binding affinity between BlcR and DNA has a larger impact on the signal-to-noise ratio and the required concentration of BlcR in the sensor than increasing the binding affinity between BlcR and GHB. The concentration of GHB that is used to spike someone's drink is very high compared to the concentration found in drinks normally, meaning the sensitivity of the sensor does not need improving. Lastly, lower BlcR concentration results in reducing the cost of our product and decreasing the noise such that our sensor can work with every drink. Because of the reasons named above, we aimed at decreasing the Kd_BlcR_DNA in modules 2 and 3.
Downloads
The model was created in the open-source programming language, Python, to make sure everyone can recreate and build upon it. We share the files for the software on our gitlab repository. Download links for Spyder and the required libraries are also included.
References
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