MODELING

Introduction

Due to the unknown nature of some of the turnover rates of enzymes and structures in the cell, the model was mainly used for explaining some of the poor results received from characterization of our nitrite reductase BioBrick. The specific structure and reactant explored in the modeling was heme. Heme is toxic in large quantities to E. coli, but is also very useful to the metabolic functions of the cell (Anzaldi & Skaar, 2010). This interaction causes heme to become highly regulated and the average concentration of free heme to decrease. The coding sequence in our plasmid design is being constantly produced and codes for a multiheme enzyme.

The refectory period for the enzyme (nrfHA_heme) after it reacts with the nitrite was modeled using a loop with a degradation rate. This was done in place of a reaction that produces a reactant as a product due to extraneous results

The key reactant, nitrite, is a charged molecule and does not pass the membrane of the cell easily. The model starts with 100 molecules of nitrite to analyze the effect of the system on nitrite at a low concentration. For the purposes of this model, diffusion of nitrite into the cell is not expressed. It can be assumed that if the rate of diffusion is greater than the rate of reduction to ammonia, there will be an excess of nitrite and the cell will likely die.

The formate/H₂ molecules are also modeled. These molecules are a reactant for the last reaction to ammonia. These molecules are readily abundant in the rumen of the cow but could be variable in broth.

Assumptions

1. An average cell volume of 0.66 µm³ is used (Kubitschek, 1990).
2. This model’s reaction rate is based on molecules per second per molecule of reactant(s).
3. Because pSB1C3 is a high copy count plasmid, promoter (pConst_nrfHA) is set to a concentration of 100 units to model 100 plasmids in a single cell.
4. Average heme concentration was not able to be found for the strain of E. coli used. A concentration of 0.1 uM is used. This is the average concentration in a human cell (Runyen-Janecky, 2013).This, when converted to molecules per second and the volume of an E. coli cell was considered, is estimated to be 40 molecules of heme.
5. The rate at which heme could be incorporated into the structure of the enzyme, when factoring in diffusion of heme through the cell (≈0.004 seconds) was estimated to be 227.27 reactions per second (Hagen et. al, 1997).
6. The rate at which heme degrades was assumed to be 0.147/second. This was taken as an abstraction of the average oxidation rate of heme in human cells (Liu & Montellano, 2000).
7. The reaction rate of the nitrite reductase protein used in our experiments is not known. A functional analog is modeled instead with a peak activity rate of 1050 micromoles of product per min per mg of enzyme (Einsle & Kroneck, 2007). This was estimated to be 1010 molecules per second per molecule of enzyme. It should be noted that this conversion was done using the weight of the analog (57.6 KDa). Whereas our protein has a weight of 50.6 kDa.
8. The degradation rate of the enzyme after it binds to the heme is estimated to be 0.13248/second as taken from the average degradation rate of a cytochrome protein in yeast cells (Janecky, 2013). This rate is also assumed for the degradation of the enzyme before it incorporates heme.
9. 𝛿-ALA is a precursor to heme production in the E. coli cell. For the sake of this model the actual rate of heme production by the presence of 𝛿-ALA is not used. It is simply used to input heme at a variable rate.
10. The DNA transcription rate is assumed to be 45nt/second (Vogel & Jensen, 1994).
11. The translation rate is assumed to be 20AA/second (Bremer & Dennis, 1996).
12. The degradation rate of the messenger RNA (mRNA) is assumed to be .147/second(Roberts et al., 2006).

In the above graph (graph 1), the heme is shown to start at 40 molecules and quickly drop off to almost zero. This is due to the enzyme quickly incorporating it into its structure. As a result, the ammonia production and nitrite reduction quickly drop off around 30 seconds. Ammonia levels still increase. This is due to the slow production of heme and the remnant enzyme.

In the above graph (graph 2), the heme is again shown to start at 40 molecules and drop off quickly, note the increase of simulation time from 90 seconds to 500 seconds compared to graph 1. There is no input of heme into the system. Because of this, the production of ammonia drops off much more quickly. In this system not all nitrite will be reduced to ammonia.

Values Used

Differential Equations

Flux Equations

This model was created and simulated using MathWorks SimBiology.

Works Cited

• Anzaldi, L. L., and Skaar, E. P. (2010) Overcoming the Heme Paradox: Heme Toxicity and Tolerance in Bacterial Pathogens. Infection and Immunity 78, 4977–4989.
• Bremer, H., and Dennis, P. P. (2008) Modulation of Chemical Composition and Other Parameters of the Cell at Different Exponential Growth Rates. EcoSal Plus 3.
• Einsle, O., and Kroneck, P. (2007) Cytochrome c Nitrite Reductase from Wolinella succinogenes with bound substrate nitrite.
• Hagen, S. J., Hofrichter, J., and Eaton, W. A. (1997) Rate of Intrachain Diffusion of Unfolded Cytochromec. The Journal of Physical Chemistry B 101, 2352–2365.
• Janecky, L. R. (2013) Quantification of protein half-lives in the budding yeast proteome. Front Cell Infect Microbiol 3.
• Kubitschek, H. E. (1990) Cell volume increase in Escherichia coli after shifts to richer media. Journal of Bacteriology 172, 94–101.
• Liu, Y., and Montellano, P. R. O. D. (2000) Reaction Intermediates and Single Turnover Rate Constants for the Oxidation of Heme by Human Heme Oxygenase-1. Journal of Biological Chemistry 275, 5297–5307.
• Runyen-Janecky, L. J. (2013) Role and regulation of heme iron acquisition in gram-negative pathogens. Frontiers in Cellular and Infection Microbiology 3.
• Vogel, U., and Jensen, K. F. (1994) The RNA chain elongation rate in Escherichia coli depends on the growth rate. Journal of Bacteriology 176, 2807–2813.
• Roberts, C., Anderson, K. L., Murphy, E., Projan, S. J., Mounts, W., Hurlburt, B., Smeltzer, M., Overbeek, R., Disz, T., and Dunman, P. M. (2006) Characterizing the Effect of the Staphylococcus aureus Virulence Factor Regulator, SarA, on Log-Phase mRNA Half-Lives. Journal of Bacteriology 188, 2593–2603.