Team:NCTU Formosa/Proof Of Concept
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Introduction
Concept
DenTeeth can produce antimicrobial peptides, LL-37 when the concentration of bacteria in the mouth is higher. After the growth of bacteria is inhibited, STATH and BMP2 will express, maintaining a high calcium level in saliva, and repairing soft tissues in the oral cavity. Therefore, oral problems, especially periodontal disease can be successfully prevented.
How do we prove it?
We proved our concept with a meticulous process which can be roughly divided into three parts: Model, Lab Work, and Device design. Combining modeling results and predictions with our lab work, we enable to make DenTeeth work as we imagined. We could further prove that DenTeeth can be implemented in the real world for daily usages.
Bacteria Growth Simulation with DenTeeth
Considered the previous growth model plus the killing formula of LL37. We could write down the growth model of E. coli and P.gingivalis under the sterilization action of DenTeeth(Eq.3):
$$\frac{d[E. coli]}{dt}= g_{E. coli}(1-\frac{[E. coli]}{[E. coli_{Max}]})-k_{k}[B][LL-37]$$
$$\frac{d[P]}{dt}= g_{P}[P](1-\frac{[P]}{P_{Max}})-N⋅k_{k} [B][LL-37] $$
As we can see above, the concentration of P.gingivalis and E. coli are reduced. And finally they will achieve dynamic balance.
LL-37 tetR mRFP Production Simulation
Next, in order to know how P.gingivalis grew under the inhibition of our dental bones, we used logical ODEs again to stimulate the growth curves of P.gingivalis. [2]All the situations were the same as E. coli. Thus, the final ODE system(Eq.2) and its parameters (Tab2) of P.gingivalis can be seen below:
$$\frac{d[P]}{dt}= g_{P}[P](1-\frac{[P]}{P_{Max}})$$
| Parameters | Description | Values | Units |
|---|---|---|---|
gP
| growth rate of P.gingivalis [3]
| 0.0025
| min-1 |
|
| PMax | Maximum P.gingivalis concentration [3] | 0.7 | O.D. |
BMP2 STATH GFP Production Simulation
To know how the bacteria in dogs’ oral cavities grow under the effect of our dental bones, we needed to calculate the inhibition amount of LL-37.
LL-37 killed growing bacteria with a rate kk, and afterwards each dead cell quickly took up N [LL-37]. These [LL-37] were bound to the membrane as well as to the cytoplasm of the cell and are not recycled to attack other cells. The killing formula of LL-37 (1) and the time evolution of concentrations of available [LL-37] (2) was described by the following equations:
$$(1)\frac{d[B]}{dt}= −k_{k}⋅[B][LL-37]$$
$$(2)\frac{d[LL-37]}{dt}= −N⋅k_{k}[B][LL-37]$$
And the parameters (Tab3) of this system can be seen below:
| Parameters | Description | Values | Units |
|---|---|---|---|
| kk | killing rate [4] | 0.04 | 1/μM·min |
| N | LL-37 absorbed per dead cell [4] | 0.35 | μM/O.D |
Model Validation
Considered the previous growth model plus the killing formula of LL-37. We could write down the growth model of E. coli and P.gingivalis under the inhibition action of DenTeeth(Eq.3):
$$\frac{d[E. coli]}{dt}= g_{E. coli}(1-\frac{[E. coli]}{[E. coli_{Max}]})-k_{k}[B][LL-37]$$
$$\frac{d[P]}{dt}= g_{P}[P](1-\frac{[P]}{P_{Max}})-N⋅k_{k} [B][LL-37] $$
As we can see above, the concentration of P.gingivalis and E. coli are reduced. And finally they will achieve dynamic balance.
Protein Functional Test
Because E. coli itself would also be affected by LL-37, in order to test whether this will further affect the concentration of the target product, we then used the analysis above to predict the concentration of these products over time.
The total amount of AHL was composed of the initial AHL from the quorum sensing model. The AHL-LuxR complex would activate the Plux promoter , which could lead to the production of LL-37, tetR and mRFP.
The prediction formula of LL-37 tetR RFP are shown below(Eq.4) [6]:
$$\frac{d[mLL-37]}{dt}= K_{mLuxI}·β·[(A-R)_{2}]-deg_{mLL-37}[mLL-37]$$
$$\frac{d[mtetR]}{dt}= K_{mLuxI}·β·[(A-R)_{2}]-deg_{mtetR}[mtetR]$$
$$\frac{d[mRFP]}{dt}= K_{mLuxI}·β·[(A-R)_{2}]-deg_{mRFP}[mRFP]$$
$$\frac{d[LL-37]}{dt}= k_{LL-37}·[mLL-37]-deg_{LL-37}[LL-37]$$
$$\frac{d[tetR]}{dt}= k_{tetR}·[tetR]-deg_{tetR}[tetR]$$
$$\frac{d[RFP]}{dt}= k_{RFP}·[RFP]-deg_{RFP}[RFP]$$
$$β=\frac{k_{a}+α[LuxR-AHL_{in}]_{2}}{k_{a}+[LuxR-AHL_{in}]_{2}}$$
And the parameters (Tab.5) can be seen below [6]:
| Parameters | Description | Values | Units |
|---|---|---|---|
| KmLuxI | Plasmid copy number times LuxI transcription rate | 23.3230 | nM*min-1 |
| ka | Dissociation rate of LuxR-AHLin2 | 200 | nM |
| α | Basal expression of LuxI | 0.01 | - |
| kLL-37 | translation rate of mLL-37 | 6.52 | min-1 |
| ktetR | translation rate of mtetR | 0.14 | min-1 |
| kRFP | translation rate of mRFP | 0.54 | min-1 |
| dmLL-37 | degradation rate of mLL-37 | 0.24 | min-1 |
| dmtetR | degradation rate of mtetR | 0.35 | min-1 |
| dmRFP | degradation rate of mRFP | 0.258 | min-1 |
| dLL-37 | degradation rate of LL-37 | 0.011 | min-1 |
| dtetR | degradation rate of tetR | 0.1386 | min-1 |
| dRFP | degradation rate of RFP | 0.498 | min-1 |
Efficiency Optimization Model
When the concentration of bacteria was low, DenTeeth would start to produce BMP2, STATH and GFP. Thus, we wanted to predict the production of these proteins. Considering the Quorum Sensing Model, we could write down the formula(Eq.5) [7]:
$$\frac{d[BMP2]}{dt}= C_{ptet} ·({l_{ptet}+\frac{1-l_{ptet}}{1+(\frac{[tet]}{k_{tet}})^{n_{tet}} } })-(d_{BMP2} ·[BMP2])$$
$$\frac{d[STATH]}{dt}= C_{ptet} ·({l_{ptet}+\frac{1-l_{ptet}}{1+(\frac{[tet]}{k_{tet}})^{n_{tet}} } })-(d_{STATH} ·[STATH])$$
$$\frac{d[GFP]}{dt}= C_{ptet} ·({l_{ptet}+\frac{1-l_{ptet}}{1+(\frac{[tet]}{k_{tet}})^{n_{tet}} } })-(d_{GFP} ·[GFP])$$
And the parameters (Tab.5) can be seen below [7]:
| Parameters | Description | Values | Units |
|---|---|---|---|
| Ctet | maximum transcription rate of ptet | 2.79 | min-1 |
| Iptet | leakage factor of ptet | 0.002 | - |
| ktet | dissociation constant of ptet | 6 | - |
| ntet | hills coefficient | 3 | - |
| dBMP2 | degradation rate of BMP2 | 0.05 | min-1 |
| dSTATH | degradation rate of STATH | 0.0000248 | min-1 |
| dGFP | degradation rate of GFP | 0.347 | min-1 |
In order to observe the switching between inhibition and restoration of DenTeeth, we added RFP after the inhibition sequence and GFP after the restoration sequence. Next, we simulated the relative fluorescence intensity of RFP and GFP to know the actual operation of DenTeeth. The result is shown in the figure below. (Fig.6):
DenTeeth-bone
Concept
DenTeeth can produce antimicrobial peptides, LL-37 when the concentration of bacteria in the mouth is higher. After the growth of bacteria is inhibited, STATH and BMP2 will express, maintaining a high calcium level in saliva, and repairing soft tissues in the oral cavity. Therefore, oral problems, especially periodontal disease can be successfully prevented.
How do we prove it?
We proved our concept with a meticulous process which can be roughly divided into three parts: Model, Lab Work, and Device design. Combining modeling results and predictions with our lab work, we enable to make DenTeeth work as we imagined. We could further prove that DenTeeth can be implemented in the real world for daily usages.
Reference
- Schink, S. J., et al. (2019). "Death rate of E. coli during starvation is set by maintenance cost and biomass recycling." 9(1): 64-73. e63.