# Genomic Scale Metabolic Model

After analyzing the localized genetic circuit design, we want to put our synthetic circuit into our model organism PCC 7942 and model its growth. This is done via a genome-scale metabolic model [1], a computer model that contains all the identified metabolic reactions and all the identified genes that code for the proteins associated with the reaction. All reactions have a metabolic flux and experimentally measured upper boundary and lower boundary of such steady state reactions are also in the model. Thus, by knocking out or incorporating certain genes, thus deleting or adding some production pathways and their associated properties, we can simulate the best possible configuration of the system provided that the cell functions normally - the optimal production yield.

Theoretically, the model is comprehensive by including all reactions and genes based on established high accuracy rate, which ensures the model is very reliable and can serve as a good guide for experimental procedures. For the PCC 7942 strain that is used in our project, there is a second-generation metabolic model already constructed and published [2]. Thus, simulations and computations with the synthetic genome-scale metabolic model are reliable ways to design and test the blueprints of our production strain.

The genomic-scale model does nothing more than solving this linear optimization program, except for this time, there are thousands of constraints that need to be considered at the same time. For the standard optimal yield simulation, a mathematical representation can be formulated in this way:

Objective function: Demand reaction flux

Under constraints:

*(1) lb(1) ≤ rxn(1) ≤ ub(1)...(n) lb(n) ≤ rxn(n) ≤ ub(n)(n + 1) Nutrient uptake rate = const*

Note that the demand reaction is an imaginary reaction that constantly draw our desired product out of the system. In this way, we use the demand reaction flux to represent the overall production rate. By giving a fixed value of nutrient uptake rate (constraint n+1), we are defining the cell states and see how it affects our production yield.

We use COBRApy: COnstraints-Based Reconstruction and Analysis for Python to build our genomic-scale metabolic model because the open source PCC 7942 model is readily provided matching the required format [3].

- Load the constructed model for PCC 7492 to the system and perform the flux to steady state under relevant constraints
- Perform flux balance analysis (FBA), which considers each reaction as a metabolic flux and balances all the fluxes to steady state under relevant constraints
- Because PCC 7942 is a photosynthetic organism, light and CO2 are the key parameters to determine the organism’s growth rate. We can manipulate this intake and see how it affects usage of the biochemical pathway. Specifically, light uptake is represented as the exchange rate of photon650nm and CO2 uptake is represented as the exchange rate of bicarbonate (HCO3-) in the organism.
- Upper and lower bounds of these two reactions serve as the constraints of the model and are tailored accordingly.

First, robustness analysis is performed with a fixed CO2 uptake and a varying light intensity. Namely, it tests how “robustly” the change of a given substrate affects the organism growth, or how an organism reacts to a change of substrate. The result is shown in Figure.1, where growth remains at 0 hr-1 until a photon uptake rate of about 14.1 mmol gDW-1 hr-1, because with such a small amount of photon, the system cannot make enough carbohydrates to sustain its growth. Growth also reaches a plateau as photon uptake increases, because the CO2 now becomes the limiting substrate of the system.

**Keep in mind as the upper and lower bounds are set arbitrarily, the result represents an overall trend of growth rate rather than the exact value. This applies for all the results obtained by such models. *

This time, light intensity is fixed with a varying CO2 uptake. The result is shown below. With photon uptake fixed at 35 mmol gDW-1 hr-1, growth rate increases steadily as CO2 uptake increases. At an CO2 uptake of about 2.40 mmol gDW-1 hr-1, growth, however, begins to decrease as CO2 uptake increases. This is because photon becomes limiting at this point, and photon that would have been used to produce biomass must instead be used to reduce excess CO2. This phenomenon matches the result of several published paper [4]. **Both of the above results indicate the reliability of the PCC 7942 model, which is ready to accept our synthetic genetic circuit**.

After configuring the model organism, we started incorporating our synthetic module. Seven new reactions and the genes associated with these reactions as well as four new metabolites are added to the system. To check the viability of our system, we needed to determine if integrating the synthetic genes into the model organism would be disrupting in any way. With a fixed carbon uptake, the optimized growth rate is calculated. This growth rate is then divided into increments and a demand reaction flux (a flux that constantly draws the demanded product out of the system, in our case, tagatose) is set as the new objective function.

We plot tagatose production rate against organism growth rate under pre-defined CO2 and photon uptake. At first glance, the result seems counterintuitive – as growth rate increases, production rate decreases. However, it is adequately presented because the biomass accumulation flux uses the same pool of resources and nutrients as the dement reaction flux; once the fixed amount of nutrition is drawn to one flux, the other flux will be compromised, hence the inversed relationship. **This is to prove that our newly added metabolic pathways interact and are dependent on the existing system, that the increased flux of these reactions will compromise one another**.

After the synthetic circuit is successfully incorporated to the organism, the models can be studied to guide us in terms of designing directions. As the metabolically engineered cyanobacteria aimed to produce tagatose will sit in a bioreactor with constant light sources (the excess light source is proved to not compromise organism growth), optimal CO2 concentration needs to be determined. The tagatose production rate is plotted against organism’s CO2 uptake. It has shown the system collapses once the CO2 uptake rate reaches a certain high value and this may be due to excessive CO2 affecting organism growth (Figure.2). **In summary, the CO2 concentration needs to be tweaked around in final bioreactor designs in order to find the optimal condition**.

Here we again perform the gene knockout (STS) to see if the results match our enzymatic kinetic model. The difference in tagatose production of the two systems is directly compared via gene deletion. The similar viability test is performed, while at this time both systems are tested under different CO2 uptake rate. The results are discussed as follows. When CO2 uptake is small, the systems do not experience any differences. However, the production rate of the one-cycled system starts to reach a plateau while that of the two-cycled system continues to arise. Eventually, as CO2 uptake keeps increasing, the production rate of the two-cycled system reaches its limit as well and it starts to decrease. Thus, the two models converge again. A video is generated to better demonstrate such differences. **It can be shown that the two-cycled system does not significantly improve on the production rate, confirming our results from the enzymatic kinetic model** (however, further investigation needs to be made because, again, these theoretical constraints are set arbitrarily).

#### Reference

[1] J. D. Orth, I. Thiele and B. Ø. Palsson, *Nature Biotechnology*, 2010, **28**, 245-248.

[2] J. T. Broddrick, B. E. Rubin, D. G. Welkie, N. Du, N. Mih, S. Diamond, J. J. Lee, S. S. Golden and B. O. Palsson, *Proceedings of the National Academy of Sciences*, 2016, **113**.

[3] A. Ebrahim, J. A. Lerman, B. O. Palsson and D. R. Hyduke, *BMC Systems Biology*, 2013, **7**, 74.

[4] H. M. Khairy, N. A. Shaltout, M. F. El-Naggar and N. A. El-Naggar, *The Egyptian Journal of Aquatic Research*, 2014, **40**, 243-250.