Team:Wash U/Biological Parts

Our group seeks to assess the optimality of the synthetic system that modulates pucB/A gene expression and LH2 complex assembly in Rhodobacter sphaeroides. Here we employ a mathematical model of this system to generate predictions about the behavior of the active system in response to light input. Features of the system that the model may help investigate include the time scale of response to light signals, the robustness of the system in response to fluctuations in light intensity, and the translation between changes in gene expression and the absorbance spectrum of the engineered cells.

Though the context of the model can extend back to the transcription of PrrA/B genes involved in integration oxygen and light signals, a preliminary testing model was developed using assumptions of certain initial conditions to isolate the light signal's effect. Since Cph8 and OmpR are located on the same transcript downstream of the puc promoter region, it was assumed that their associated protein and mRNA had already reached steady state concentrations, and the phosphorylation reaction had already reached steady state. Moreover, the concentrations of the factors were assumed to be equal at this state. The model whose diagram was constructed in the Simbiology Toolbox distributed by MathWorks details key reactions leading to the translation of the pucB/A genes. The reaction rate equation used for the lack of phosphorylation of OmpR when the light signal reaches Cph8 bound to OmpR is captured in a modified form of Michaelis-Menten kinetics. A logic function that corresponds to light ON/OFF (1/0) multiplies the maximum reaction rate in the numerator of the phosphorylation equation. Thus, the model assumes that no phosphorylation occurs by this mechanism in the presence of light. The OmpC promoter binding equation was based on the Hill Equation for an Activator(1).

Component characterization steps and literature searches are underway in order to obtain quantitative parameters for the reaction rates. In order to simulate behavior of the system, putative values were included that exaggerate true concentrations and time scales. OmpR was given an initial concentration normalized to one, and all other components were assumed insignificant initially to this value. An ideal light pulse was introduced at an instant and removed thirty simulation seconds later. From this rudimentary simulation it can be drawn that the nonlinearities of the phosphorylation and transcription factor binding kinetics effectively smooth the sharp light input. By design, the light switch ON yields no phosphorylation of OmpR and repression of the pucB/A genes which would give rise to LH2. Conversely, when left OFF, the concentration of pucB/A recovers and increases until the steady state determined by its translation and degradation rates.

References

1. Alon, Uri. Introduction to systems biology and the design principles of biological networks. Boca Raton, FL: Chapman & Hall, 2006.
2. Bower, James M. Computational Modeling of Genetic and Biochemical Networks (Computational Molecular Biology). New York: M.I.T. PRESS, 2001.
3. System modeling in cellular biology from concepts to nuts and bolts. Cambridge, MA: MIT P, 2006.

Simulating A Bioreactor

Nonlinear least squares estimation of wild type saturation curve

Problem:
In a typical reactor, cells at the surface absorb more than enough light to saturate their photosynthetic apparatus, transmitting less energy to deeper layers. Cells operating past the saturation point waste incident photons by non-photochemical quenching and possibly undergo photodamage. For wild type cells, the “saturation curve” is assumed to be approximately the same for all cells in all layers, regardless of their incident light intensity. This means that layers of cells on the exterior of the reactor nearest a light source receive an overabundance of photons and in turn block the interior layers from receiving enough light. In an optimal reactor, all layers would operate near their respective saturation points to maximize the photosynthetic channeling of incident light energy.

The total saturation curve for wild type R. Sphaeroides was fit with a nonlinear least squares regression of the form in the corresponding equation. Data points were generated from calculating absorbance as the negative logarithm of the ratio of the absolute irradiance detected on the next layer to incident absolute irradiance on a layer of cells. A logistic form was chosen to account for the diminishing returns to absorption of further photons past a threshold operating capacity of the photosynthetic apparatus. (1)

Exponential response curve for mutant LH2 saturation coefficients

Simulating our Mutant's advantage in a Bioreactor
For our mutant cells, the LH2 saturation curve for each layer scales as a function of light intensity. This predicted behavior in the mutant is due to negative regulation of LH2 complex production as incident light intensity increases. The scalar of the magnitude of the saturation curve was altered according to a predicted exponential curve of LH2 production in repsone to changes in incident light. It was assumed that the system could vary expression levels such that at high light intensities, the saturation curve is scaled to 25% of that of the wild type. At low light intensities, LH2 production was assumed to have the potential to be up-regulated to 150% of wild type expression levels.
The advantage this mutant would confer stems from the adaptive nature of the saturation curve heights. Cells receiving the most light on the outside of the bioreactor saturate at low absorption levels. This allows more light to transmit to further layers, which have elevated saturation curves due to lower incident light.

Model Assumptions

- Light intensity at next layer is given by transmittance from previous layer (assumes no backscattering).
- Total energy funneled to photosynthetic pathways is estimated as the sum of light absorbed by each layer. This generalizes to the optical density measurement of cell culture density.






- The constant wild type saturation curve inherently includes both LH2 and LH1 contributions to absorbance. The mutant's variable saturation curve only accounts for LH2 absorbance, since this is the only complex under the light-sensing regulation. To account for the component of absorbance provided by LH1, the proportion of total optical density due strictly to LH1 was investigated by comparing the growth of wild type and LH2-knockout (dbcOmega) cultures. It is evident that by day three the proportion of Optical Density accounted for by LH1 absorption converges to a value near 0.2. In other words, at the phase the layers of cells have grown in the model, 20% of total optical density can be attributed to LH1. To account for this, the absorption in the mutant was divided by the factor (1-0.2) = 0.8. Then, the total optical density of the mutant cultures reflects total absorption by both LH1 and LH2.



Relative growth of DBComega to WT in Flask 2 at OD600

- The model was revised upon gathering optical density data from the five layers of the bioreactor setup. (See Results Figure 2a.) In the wild type, the optical density of the first flask of cells was much lower than predicted, a phenomenon that was attributed to photodamage of the cells due to exposure to a large quantity of light past the saturation point of the LH2 complexes. In the optical density data for the flasks, both the dbcOmega knockout and the wild type logistically grew to an absorbance value of 1. This gave reason to put a hard limit of 1 on the first flask's potential optical density. Any light left over from this cutoff was transmitted to the next layer, as evidenced by in the increased growth of the second wild type flask in the Optical Density data. - The response curve for the coefficient of saturation for the mutant due to changes in light intensity was modeled as an inverse exponential form. In other words, the system reacts to increasing light intensity by exponentially tapering the coefficient of saturation.

Wild Type vs. Mutant Photobioreactor Simulation

The sequence of figures above shows the behavior of the static wild type saturation curve and the mutant variable saturation curve in response to incident light intensity. The dotted lines indicate the point of incident intensity and the associated absorbance with that point. The center stacked bar graph shows the accumulation of optical density given by the absorbance readings from the saturation curve. Recall that the mutant curve includes only LH2 adaptation, while the curve on the left is the total of LH1 and LH2 contributions to absorbance. Throughout the entire five layers of the bioreactor, it is evident from the simulation that the mutant achieved higher overall growth as indicated by OD. Also, the mean OD for the mutant exceeds that of wild type, and there is less variation in the levels about the mean (indicated by standard deviation).

References

1. Steven, Spilatro R. "Photosynthesis Investigation Study." Photosynthesis Investigation Study. Department of Biology, Marietta College, Marietta, Ohio, 1998. Web. 21 Oct. 2009. <http://www.marietta.edu/~spilatrs/biol103/photolab/photosyn.html>.

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