Team:Athens/Background
BACKGROUND
Preservation of the optical properties of Flavobacteriia
In order to predict the optical properties of our biomaterial, we have to simulate it’s interaction with light and quantify the results. Finite Element Method (FEM) modeling using COMSOL was implemented to solve the Maxwell Equations. The output of the modeling process is reflectance data for wavelengths between 300 nm to 900 nm. The simulation was inspired by [1] and the advice of Dr. Pete Vukusic.
TEM cross-section images can provide information about the spatial arrangements of the bacteria colonies. Based on those, a simplified geometry can be built. The main observations linked to optical properties are as follows:
Flavobacteriia can produce structural colouration due to their bodies forming a 2D close-packed hexagonal lattice as schematically shown in Figure 1. As such, if the periodicity is preserved along a considerable domain, the Flavobacteria will reflect light only at certain angles, but with a very strong intensity. It should be noted that for some strains (e.g. M17 [2]) that showcase longer distances in their hexagonal lattice, structural coloration is diminished.
The close-packed structures observed do not appear in a continuous uniform single structure but differentiate into large domains. The orientation of this close-packed structure differs for every domain. This should be taken into consideration when building the model protocol, since the bacteria macroscopically do not have a preferred orientation with respect to in-plane rotation and the visual appearance is independent of rotation along this axis [2].
Lastly the distances observed in the hexagonal lattices are not constant and can influence the optical properties of the system. As shown in [1], this intra domain periodicity has an effect on the estimated results of the simulation. However experimental data for the distribution of periodicities observed in the hexagonal lattice has not been documented for the particular strain we use. Consequently, the model will only include periodicities of 357 nm [2].
Based on the above observations, a brief description of the geometry used will be presented:
Firstly the periodicity observed should be implemented using a large enough domain which will represent the agar medium (refractive index is 1.34). The smallest “speckle” that is capable of producing iridescence is around 50 μm² for Cellulophaga lytica bacteria [1]. However, computations in such order of magnitude are prohibited with the tools in our disposal, so we opted for a smaller 3.5 μm² domain. This is expected to influence the results but it has been shown that a 10 μm² domain also produces acceptable results.
The bacteria is placed in a hexagonal lattice with a periodicity of 357 nm (refractive index is 1.38). Their assigned diameter is fixed at 295 nm which is the mean average based on experimental data ([2], Supporting Information).
The intra domain geometry was rotated from −30° to + 30° degrees with a 5° step, so as to replicate the domain’s different orientations, and the results of simulation were averaged. A weighted average is expected to provide a better estimation since bacteria may show a preference of orientation in the micron scale but experimental data were not available. The
This simulation must be edited to provide data for the biomaterial’s optical properties. It is important to address one key assumption our simulation is based upon; The secretion of cellulose from the bacteria will be spatially axisymmetric and the end geometry of the substance will be continuous and will contain the bacteria. In order to simplify the simulation, the domain that represents the agar medium as mentioned above, will now represent the cellulose product.
We distinguish between two possible geometries; one which the bacteria will remain in their periodic positions and another which will have the bacteria be replaced by air. The latter geometry is supposed to simulate the possible state in which the acellular material will be, once the bacteria are removed.
Estimating the cellulose production over time
A kinetic modeling of cellulose production is essential to predict the time period needed to create the desired material. The bcs genes can be designed as a gene circuit and a kinetic model that computes a dynamic ODE system based on this gene circuit has already been proposed by the literature [3].
This model introduces mRNA and protein expression alongside bacterial growth kinetics. The model also proposes the quantification of plasmid stability through the inclusion of plasmid bearing and plasmid free biomass in the system. However the experimental procedure regarding the cellulose production will include a substrate that contains antibiotics which target and eliminate cells that are plasmid free. In addition after the conjugation experimental procedure, it is expected to have a liquid batch that contains mostly plasmid bearing cells. Taking these facts into consideration, our model is based on the assumption that all biomass will contain the cellulose operon so plasmid stability will not be taken into consideration. This might affect the results, particularly the estimation of the growth of biomass. The combination of mRNA, protein expressions and growth kinetics should capture the dynamics of bacterial cellulose production effectively.
The differential equations have generally 4 different forms: time derivative of mRNA, enzyme concentrations, growth of biomass and glucose reduction. The equations are shown below:
\[\frac{d[\mathrm{cmcax}]}{d t}=b_{\operatorname{cmcax}}\left(\frac{I P T G^{3}}{I P T G^{3}+K_{I P T G}{ }^{3}}\right)\left(\frac{1^{0.8}}{1^{0.8}+\left(\frac{[G] u]}{K}\right)^{0.8}}\right)-a_{\operatorname{cmcax}}[\mathrm{cmcax}]\]
\[\frac{d[c c p A x]}{d t}=b_{c c p A x}\left(\frac{I P T G^{3}}{I P T G^{3}+K_{I P T G}^{3}}\right)\left(\frac{1^{0.8}}{1^{0.8}+\left(\frac{[G l u]}{K_{G l u}}\right)^{0.8}}\right)-a_{c c p A x}[c c p A x]\]
\[ \frac{d[b c s A]}{d t}=b_{b c s A}\left(\frac{I P T G^{3}}{I P T G^{3}+K_{I P T G}^{3}}\right)\left(\frac{1^{0.005}}{1^{0.005}+\left(\frac{[G l u]}{K_{G l u}}\right)^{0.005}}\right)-a_{b c s A}[b c s A]\]
\[ \frac{d[b c s B]}{d t}=b_{b c s B}\left(\frac{I P T G^{3}}{I P T G^{3}+K_{I P T G}^{3}}\right)\left(\frac{1^{0.005}}{1^{0.005}+\left(\frac{[G l u]}{K_{G l u}}\right)^{0.005}}\right)-a_{b c s B}[b c s B]\]
\[ \frac{d[b c s C]}{d t}=b_{b c s C}\left(\frac{I P T G^{3}}{I P T G^{3}+K_{I P T G}^{3}}\right)\left(\frac{1^{0.005}}{1^{0.005}+\left(\frac{[G l u]}{K_{G l u}}\right)^{0.005}}\right)-a_{b c s C}[b c s C]\]
\[ \frac{d[b c s D]}{d t}=b_{b c s D}\left(\frac{I P T G^{3}}{I P T G^{3}+K_{I P T G}^{3}}\right)\left(\frac{1^{0.005}}{1^{0.005}+\left(\frac{[G l u]}{K_{G l u}}\right)^{0.005}}\right)-a_{b c s D}[b c s D]\]
\[ \frac{d[C c p A x]}{d t}=b_{C c p A x}[c c p A x]-a_{C c p A x}[C c p A x]\]
\[ \frac{d[\operatorname{Bcs} A]}{d t}=b_{B c s A}[b c s A]-a_{B c s A}[\operatorname{Bcs} A]\]
\[ \frac{d[B c s B]}{d t}=b_{B c s B}[b c s B]-a_{B c s B}[B c s B]\]
\[ \frac{d[B c s A B]}{d t}=b_{B c s A B}\left(\frac{B c s A}{B c s A+K_{B c s A}}\right)\left(\frac{B c s B}{B c s B+K_{B c s B}}\right)\]
\[ \frac{d[C S]}{d t}=b_{C S}[B c s A B]-a_{C S}[C S]\]
\[ \frac{d[B c s C]}{d t}=b_{B c s C}[b c s C]-a_{B c s C}[B c s C]\]
\[ \frac{d[B c s D]}{d t}=b_{B c s D}[b c s D]-a_{B c s D}[B c s D]\]
\[ \frac{d[\text {cellulose}]}{d t}=\left(\frac{b_{C S, \text {cellulose}} C S}{C S+K_{\text {CS,cellulose}}}\right)\left(\frac{b_{\text {Cmcax}, \text {cellulose}} C \operatorname{mcax}}{C m c a x+K_{\text {Cmcax,cellulose}}}\right)\left(\frac{b_{C c p A x, \text {cellulose}} C c p A x}{C c p A x+K_{C c p A x, \text {cellulose}}}\right)\left(\frac{b_{B c s C, \text {cellulose}} B c s C}{B c s C+K_{B c s C, \text {cellulose}}}\right)\left(\frac{b_{B c s D, \text {cellulose}} B c s D}{B c s D+K_{\text {BcsD}, \text {cellulose}}}\right) X_{\text {total}} \]
\[\frac{d X}{d t}=\frac{\mu_{\max } \operatorname{Glu} X}{K_{G l u}+G l u}-\frac{d_{\max }}{K_{d}+[G l u]} X\]
\[\frac{d G l u}{d t}=-\frac{\mu_{\max } \operatorname{Glu} X}{Y_{X / G l u}\left(K_{G l u}+G l u\right)}\]
Initial values for the variables of the system have been set as follows, on Table 1.
| Variable | Initial Value | Unit | Variable | Initial Value | Unit |
|---|---|---|---|---|---|
| BcsA | 1 | mg/L | cellulose | 0 | mg/L |
| bcsA | 0 | mg/L | Cmcax | 1 | mg/L |
| BcsAB | 1 | mg/L | cmcax | 0 | mg/L |
| BcsB | 1 | mg/L | CS | 1 | mg/L |
| bcsB | 0 | mg/L | Glu | 4000 | mg/L |
| BcsC | 1 | mg/L | IPTG | 0.05 | mM |
| bcsC | 0 | mg/L | μ | 0 | 1/min |
| BcsD | 1 | mg/L | X | 0 | mg/L |
| bcsD | 0 | mg/L | CcpAx | 1 | mg/L |
| ccpAx | 0 | mg/L |
Lastly, the values of the parameters have been specified in the literature for a genetically engineered E. coli strain. The values accured from fitting experimental data to the ODE system. However, due to the lack of lab access, we were not able to replicate the experiments for our system and as such we did not have data to fit the parameters values to the system and the experimental conditions.
Results and discussion has been documented on the Engineering Success page.
[1] A unique self-organization of bacterial sub-communities creates iridescence in Cellulophaga lytica colony biofilms
[2] Genetic manipulation of structural color in bacterial colonies
[3] Linking Engineered Gene Circuit Kinetic Modeling to Cellulose Biosynthesis Prediction in Escherichia coli: Toward Bioprocessing of Microbial Cell Factories
"Monarch Butterfly Wing Scales" by David Illig is licensed under CC BY-NC-SA 2.0
