To begin the modeling process, we required an in-depth understanding of the reaction mechanisms involved in heparin synthesis. In conjunction with our design team, our modeling team searched related literature and identified 7 enzymatic reactions to isolate and model individually ( 2 reactions involved the synthesis and reduction of PAPS, 5 were involved in the sulfation of heparosan). 

Using the MathWorks provided webinars and practice modules, we began studying MATLAB and SimBiology, the two programs we would use to simulate the heparin synthesis pathway. We used primarily Simbiology for its accessibility, beginner resources, and simplistic format.

With an understanding of both the pathway and the programs we would use, the modeling team once again dived into the literature to search for useful model equations and parameters from other wet lab experiments. Of the modeling equations that we discussed ( Michaelis-Menten, Ordered Bi-Bi, Mass Action) we settled on Michaelis-Menten kinetics for its wide applicability and simplicity. Without data from the wet lab, our initial model is heavily based from assumptions of concentration taken from the literature. The kinetic parameters we used were pulled directly from research papers that measured reaction kinetics in various conditions and organized on a master document with their sources. Many of these parameters were in near-ideal conditions and were not organized by condition in our master document. These place-holder parameters were likely to vary between the literature and the experiments carried out in our lab, but they were important for making models that ran smoothly with units and in creating predictions for the product concentrations of the enzymatic reactions as well as for developing the models.

With the information we needed properly organized, we began taking steps toward building a functional model. Modeling team members were each assigned to two enzymes. Each enzymatic reaction was first modeled individually, with only the substrate, products, and any ions/compounds necessary that are known to boost effectiveness. Some models formed intermediate enzyme-substrate complexes. In cases like this, such as C5-epimerase’s reaction with N-Sulfoheparosan, the enzyme was originally modeled with the second enzyme, which breaks it down to establish a clear understanding of the pathway, and then both are eventually modeled individually for troubleshooting. Each model was first tested for effectiveness without units. To test without units we plugged in the concentrations and parameters found in the literature without the units that are associated with them. If the literature did not provide initial concentrations, random reasonable numbers were used. If the model ran correctly, produced a graph, and did not return any error messages, we moved on to the second next step. If not, we would address the errors in troubleshooting, and try again.

Each model was then prepared with units assigned to each of the variables involved.  The testing process was very similar.  If the model ran correctly, produced a graph, and did not return any error messages, we moved on to the second next step. If not, we would address the errors in troubleshooting, and try again. We troubleshoot by tracking the units by writing all of the initial units on paper, carrying out the equation to understand what the final unit of the product should be and performing the proper unit conversions on paper. Once each model was finalized, we were able to begin putting each of them back together. This was the extent of what we were able to accomplish while waiting for wet lab data. 

To put each of the models together, we planned to connect each pathway one by one to each other in order. Between each attachment, we would troubleshoot to make the model still function properly. In the event of more issues with the model units, we would have to go through the same troubleshooting process as the previous step. The final goal was to create a model that matched the data produced by the wet lab. After the Wet Lab Team transformed the bacteria and measured the amount of proteins produced, the initial concentrations of reactants, and the final concentrations of the products, the Modeling Team planned to use the data to approximate the experimental parameters. With accurate parameters, the model would be able to more accurately predict the changes in concentration over time. 

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The purpose of making a large model is to be able to visualize the approximate concentrations of all the chemical species involved in the reaction mechanism as time progresses. Modeling is incredibly useful for process engineering. With the information from a complete model, we would be able to point out the most rate-limiting reactants and and the slowest reaction.
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Regarding the testing cycle of our project, we would’ve greatly benefitted from comparing actual wet lab data to the data and predictions formed by the model. Unfortunately, the wet lab data came too far down the line to incorporate it into our model, but this was the main goal we were striving for. If there were any results that were problematic with the Wet Lab, such as there being significantly lower concentrations of a particular product than what was predicted, the model would’ve allowed us to identify potential causes. These could be factors like substrate depletion, an insufficient concentration of enzymes, or other conditions that were not accounted for initially. The ability to troubleshoot these problems would allow us to make adjustments that are targeted towards these issues like increasing enzyme concentrations or adjusting the amount of substrate.

Additionally, we could’ve also been able to produce sensitivity analyses by tweaking various parameters to see how sensitive the model is and system is to these changes, and examine the margin of error. Finally with the learning cycle, we would’ve been able to strongly fix our own model using data from the wet lab, deriving our own parameters, while also helping troubleshoot. Each step that we would take would get our model closer to the actual and complete mechanism that was happening in E. Coli strain. However, we just didn’t have enough time in the season to accomplish all these goals.

The modeling approach we used is extremely helpful for synthetic biology research as it both simplifies the simulation of complex biochemical reactions and allows for flexibility and adaptability. Future teams can utilize our model to troubleshoot issues more efficiently, predict rate-limiting steps, and revise their experimental designs. Furthermore, the scalability of our model enables other teams to be able to expand on it by incorporating additional enzymatic reactions or metabolic pathways. By converging the process of reaction modeling and parameter integration, our work contributes to a more standardized approach to modeling in synthetic biology, ultimately speeding up project timelines and improving experimental outcomes. This model could also serve as an invaluable educational tool for new teams looking to grasp foundational concepts in computational modeling and enzyme kinetics, and undoubtedly has the potential to benefit the community if utilized. While we didn’t quite have the time to fully integrate our model with the design. We have clear plans for how we would’ve utilized it had we had more time to fully integrate the model. During the design phase, the model would’ve allowed us to predict enzyme and substrate concentrations and see the rates, helping guide our decisions on which components of the full pathways that we should optimize and prioritize. For instance, if the model clearly outlined any sort of rate-limiting reactions or any inefficiencies, we could tailor our designing efforts to also incorporate those engineering efforts in those areas. Instead, in this area we used particular places that needed modification that were exemplified in previous literature. Additionally, in the build cycle we would’ve used this to likely test different plasmids and the possibility of breaking our plasmid into arrangements similar to our modeling compartments, given how the data turned out. It could’ve helped us choose optimal plasmids, enzymes, and reaction conditions to make more precise modifications with building the actual sort of designs.

Our model serves as a strong example for many other teams in the future projects. Any type of team doing projects around these types of sulfation enzymes or any sort of enzymatic pathways, particularly in synthetic biology will find our model particularly useful. By organizing kinetic parameters and creating a step-by-step modeling process (from individual enzyme reactions to the full pathway integration), we provide a template that other teams can adapt by looking through our project. Additionally, through using our model, other teams will be able to tell the speed at which their reactions will take place as well as what sort of results to expect from their Wet Lab data, and to better adjust their real-time project concentrations to make the results stronger, more visible, and more optimized. Finally, these models could also be used in the real-world impact for those who are looking to do research on this sort of topic and use our model as a basis to help support their proposal. It could also attract more investors into this research field and proposal by displaying the strong impact that these enzymes have on the production of heparin.

Deng, JQ., Li, Y., Wang, YJ. et al. Biosynthetic production of anticoagulant heparin polysaccharides through metabolic and sulfotransferases engineering strategies. Nat Commun 15, 3755 (2024). https://doi.org/10.1038/s41467-024-48193-5

James R Myette, Zachary Shriver, Jian Liu, Ganesh Venkataraman, Robert Rosenberg, Ram Sasisekharan, Expression in Escherichia coli, Purification and Kinetic Characterization of Human Heparan Sulfate 3-O-Sulfotransferase-1, Biochemical and Biophysical Research Communications, Volume 290, Issue 4, 2002, Pages 1206-1213, ISSN 0006-291X, https://doi.org/10.1006/bbrc.2001.6268.

Presto, J. (2006). N-Sulfation and Polymerization in Heparan Sulfate Biosynthesis (PhD dissertation, Acta Universitatis Upsaliensis). Retrieved from https://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7162

‍S. D. Vallet, T. Annaval, R. R. Vives, E. Richard, J. Hénault, C. Le Narvor, D. Bonnaffé, B. Priem, R. Wild, H. Lortat-Jacob, Proteoglycan Res. 2023, e8. https://doi.org/10.1002/pgr2.8

‍Sterner, Eric et al. “Assays for determining heparan sulfate and heparin O-sulfotransferase activity and specificity.” Analytical and bioanalytical chemistry vol. 406,2 (2014): 525-36. doi:10.1007/s00216-013-7470-4

Vaidyanathan, Deepika et al. “Elucidating the unusual reaction kinetics of D-glucuronyl C5-epimerase.” Glycobiology vol. 30,11 (2020): 847-858. doi:10.1093/glycob/cwaa035

Xintong Xi, Litao Hu, Hao Huang, Yang Wang, Ruirui Xu, Guocheng Du, Jian Chen, Zhen Kang, Improvement of the stability and catalytic efficiency of heparan sulfate N-sulfotransferase for preparing N-sulfated heparosan, Journal of Industrial Microbiology and Biotechnology, Volume 50, Issue 1, 2023, kuad012, https://doi.org/10.1093/jimb/kuad012