Dry Lab

OptKnock Calculation

Algorithm Principles

\( \begin{aligned} \underset{y_i}{maximize}\ \ \ &v_{chemical}\\ subject\ to\ \ \ &\underset{v_j}{maximize}\ v_{biomass}\\ &\begin{bmatrix} subject\ to\ \sum_{j=1}^MS_{ij}v_j=0,&\\ &v_{pts}+v_{glk}=v_{glc-uptake}\\ &v_{atp}\geq v_{atp-main}\\ &v_{biomass}\geq v_{biomass}^{target}\\ &v_j^{min}\cdot y_j\leq v_j\leq v_j^{max}\cdot y_j, \forall j\in M\\ \end{bmatrix}\\ &y_j=\{0,1\},\ \forall j\in N\\ &\sum_{j\in M}(1-y_j)\leq K \end{aligned} \)

The core idea of this algorithm is to use mathematical optimization methods to find the best combination of gene knockouts to increase the production rate of the target product without affecting normal cell growth and metabolic activities. This approach can assist teams in designing more efficient metabolic engineering strategies to improve the production efficiency of target products.

Candidate Reaction Set Determination

Simulation Calculations

OD-t Curve Verification

Our goal is to evaluate the impact of gene deletion on yeast growth based on the in vitro experiments.

In the experiment, we measured the optical density of yeast mutant strains ∆gal4 , ∆gal4∆gal80, and ∆gal4∆gal80∆SPE4 at 600 nm (OD₆₀₀)^[13]. To minimize random errors, we performed duplicate measurements, and the final results are shown in Table 6 and Figure 1.

From the above graph and data, it can be roughly observed that the actual differences in optical density among the three samples are small. However, for rigorous analysis, we used a more precise function to fit the growth curves. For the choice of the fitting function, we have opted for the commonly used logistic function^[14] and performed the fitting based on the average of the two measurements for each group in the software Origin. The fitted curve results are as follows:

As shown in Figure 2, it can be seen that the three curves align with our initial rough conclusion, as they all exhibit similar trends. We conducted pairwise two-sample t-tests for the three curves, considering both equal and unequal variances. The results support our observation: at the 0.05 significance level, there is no significant difference among the three curves.

In conclusion, based on the modeling work using the OD curves, we have demonstrated that the deletion of the target gene SPE4 had no significant impact on the growth of the yeast chasis itself .

Reference

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2. [2] Lu, H. et al. A consensus S. cerevisiae metabolic model Yeast8 and its ecosystem for comprehensively probing cellular metabolism. Nature Communications 10, 3586 (2019). doi:10.1038/s41467-019-11581-3.
3. [3] The yeast consensus genome-scale model [Lu et al. 2019], version 8.3.4 [Sánchez et al. 2019], was used.
4. [4] Orth, Jeffrey D et al. “What is flux balance analysis?.” Nature biotechnology vol. 28,3 (2010): 245-8. doi:10.1038/nbt.1614.
5. [5] Feldmann, and Horst. "Yeast (Molecular and Cell Biology) || Yeast Metabolism." (2012):25-58. DOI:10.1002/9783527659180.ch3.
6. [6] Manina, Alessia Shelby, and Fabio Forlani. “Biotechnologies in Perfume Manufacturing: Metabolic Engineering of Terpenoid Biosynthesis.” International journal of molecular sciences vol. 24,9 7874. 26 Apr. 2023, doi:10.3390/ijms24097874.
7. [7] Ruiz-Villafán, Beatriz et al. “Carbon catabolite regulation of secondary metabolite formation, an old but not well-established regulatory system.” Microbial biotechnology vol. 15,4 (2022): 1058-1072. doi:10.1111/1751-7915.13791.
8. [8] Burgard, Anthony P et al. “Optknock: a bilevel programming framework for identifying gene knockout strategies for microbial strain optimization.” Biotechnology and bioengineering vol. 84,6 (2003): 647-57. doi:10.1002/bit.10803.
9. [9] = Vlassis N, Pacheco MP, Sauter T (2014) Fast Reconstruction of Compact Context-Specific Metabolic Network Models. PLoS Comput Biol 10(1): e1003424.
10. [10] Laurent Heirendt & Sylvain Arreckx, Thomas Pfau, Sebastian N. Mendoza, Anne Richelle, Almut Heinken, Hulda S. Haraldsdottir, Jacek Wachowiak, Sarah M. Keating, Vanja Vlasov, Stefania Magnusdottir, Chiam Yu Ng, German Preciat, Alise Zagare, Siu H.J. Chan, Maike K. Aurich, Catherine M. Clancy, Jennifer Modamio, John T. Sauls, Alberto Noronha, Aarash Bordbar, Benjamin Cousins, Diana C. El Assal, Luis V. Valcarcel, Inigo Apaolaza, Susan Ghaderi, Masoud Ahookhosh, Marouen Ben Guebila, Andrejs Kostromins, Nicolas Sompairac, Hoai M. Le, Ding Ma, Yuekai Sun, Lin Wang, James T. Yurkovich, Miguel A.P. Oliveira, Phan T. Vuong, Lemmer P. El Assal, Inna Kuperstein, Andrei Zinovyev, H. Scott Hinton, William A. Bryant, Francisco J. Aragon Artacho, Francisco J. Planes, Egils Stalidzans, Alejandro Maass, Santosh Vempala, Michael Hucka, Michael A. Saunders, Costas D. Maranas, Nathan E. Lewis, Thomas Sauter, Bernhard Ø. Palsson, Ines Thiele, Ronan M.T. Fleming, Creation and analysis of biochemical constraint-based models: the COBRA Toolbox v3.0, Nature Protocols, volume 14, pages 639–702, 2019 doi.org/10.1038/s41596-018-0098-2.
11. [11] Hamasaki-Katagiri, N et al. “Spermine is not essential for growth of Saccharomyces cerevisiae: identification of the SPE4 gene (spermine synthase) and characterization of a spe4 deletion mutant.” Gene vol. 210,2 (1998): 195-201. doi:10.1016/s0378-1119(98)00027-4.
12. [12] Amaradio, Matteo N et al. “L-lactate production in engineered Saccharomyces cerevisiae using a multistage multiobjective automated design framework.” Biotechnology and bioengineering vol. 120,7 (2023): 1929-1952. doi:10.1002/bit.28391.
13. [13] Aho, Ken et al. “Model selection for ecologists: the worldviews of AIC and BIC.” Ecology vol. 95,3 (2014): 631-6. doi:10.1890/13-1452.1.
14. [14] G. F. Gause (1932), Experimental studies on the struggle for existence. I. Mixed populations of two species of yeast, J. Exp. Biol. 9, p. 389.
15. [15] Johnson, Valen E. “Revised standards for statistical evidence.” Proceedings of the National Academy of Sciences of the United States of America vol. 110,48 (2013): 19313-7. doi:10.1073/pnas.1313476110.

Appendice

1. ⚫If the yeast8-model does not exist in Matlab, the instructions used when reading the model are:
2. model=xls2model('model-eth-santalol.xlsx')



3. ⚫If the model does not exist in Excel format but in. xml format, the instructions used when reading the model are:
4. model=readCbModel('example.xml')
5. ⚫If using BiomassPrecursorCheck for precursor metabolism detection of Biomass function, it is necessary to revise the Linear programming solver as follows
6. ChangeCobraSolver(‘glpk’, ‘lp’) or ChangeCobraSolver(‘gurobi’,’lp’)
7. [missingMets,presentMets] =biomassPrecursorCheck(model)
8. ⚫If using Gap Analysis for gap detection of the entire network, it is necessary to first apply the Linear programming solver.Revise as follows:
9. ChangeCobraSolver(‘glpk’, ‘milp’)
10. [gaps]=gapAnalysis(model)
11. ⚫If the reaction in the result is A ->B ->C ->D, then 'A=product', 'D=substrate'
12. ⚫If you use GapFind to find gaps in the model, you also need to run it under the milp algorithm:
13. [allGaps,rootGaps,downstreamGaps]=gapFind(model)
14. ⚫If you want to add a reaction equation to the COBRA model that can be read into MATLAB, you can run:
15. [allGaps,rootGaps,downstreamGaps]=gapFind(model)
16. ⚫If you want to delete the reaction equation in the COBRA model that has been read into MATLAB, you can run:
17. class="text-center">modelOut = removeRxns(model,’Rxn###’)
18. ⚫If you want to change the objective equation in the GSMM model, you can run:
19. Model=changeObjective(model,’Rxn###’)
20. ⚫If you want to balance the reaction equation, you need to run the following command under lp:
21. [massImbalance,imBalancedMass,imBalancedCharge,imBalancedBool,Elements] = checkMassChargeBalance(model)
22. ⚫If you want to calculate the traffic of the target equation in the model, you need to run FBA:
23. FBAsolution=optimizeCbModel(model)
24. ⚫If you want to modify the objective equation after reading the model, you can run the following command:
25. model=changeObjective(model,’Rxn###’)
26. ⚫If you want to see the flow distribution of each reaction in the entire model, you need to first run the FBAsolution program, and then run the following instructions:
27. printFluxVector(model,FBAsolution.x,1,1)
28. ⚫If you need to convert a. mat file (MATLAB file) into an Excel or XML file, you need to upload it first.After reading the file on MATLAB, convert it to an xls or XML file. The specific instructions and steps are as follows:
29. load(‘example.mat’)
30. model=example
31. writeCbModel(model,’xls’,’***.xls’)
32. Then you can see the xls format of the model in the folder where ***.mat is located, and the XML file can be obtained similarly.
33. ⚫If you need to save an xls or XML file in. mat format, proceed as follows:Save the model in xls format as. mat.



34. Note: Calculate the Formula charge using Marvin beans software and a small plugin.
35. ⚫If you want to use Cytoscape to draw a network diagram of a model, you can run the following operations:
36. notShownMets=outputNetworkCytoscape(model,’iBH982’)
37. Among the obtained files is an iBH982. sif file, which is imported into the Cytoscape software (file>import>network)You can obtain the desired image.
38. ⚫If you want to determine the essential genes of the model, you need to run single gene knockout under FBA and LP planners.
39. [grRatio,grRateKO,grRateWT,hasEffect,delRxns,fluxSolution] = singleGeneDeletion(model)
40. Then open grRateKO from the workspace on the left, which is the growth rate of the model after gene deletion. In this list.The gene sequencing is consistent with the automatically generated gene sequence when reading the model. Gene name sequence in Workspace ->model ->genes.
41. ⚫If you want to simulate pairing knockout, you need to run the double knockout command:
42. [grRatioDble,grRateKO,grRateWT] = doubleGeneDeletion(model)
43. The Optknit instruction can be used to calculate on the model FBA algorithm that can maximize the production of a certain substance while generating.The gene knockout target with the largest possible volume needs to be converted from the planner to a milp (Mixed Integer) when running this command.Linear Programming, and then run the following command:
44. selectedRxns={model.rxns{[1:n]}}
45. #N represents the Rxn range used to search for targets, such as from Rxn1 toRxn1000; Note: The range cannot be too large and cannot include transport Rxn, exchange Rxn, Biomass Rxn, NGAM Equation)#
46. options.targetRxn=’Ex_lac-L[e]’
47. #Ex_ Lac L [e] is the objective equation, which refers to the location of the compound that needs to maximize yield Reaction#
48. options.vmax=1000
49. #Hoping the target equation has the maximum flow rate#
50. options.numDel=5
51. #Targeting to identify up to 5 targets#
52. options.numDelSense=’L’
53. constrOpt.rxnList={‘Biomass’,’ATPM’}
54. #Biomass is the name of the biomass equation, while ATPM is the Rxn name of the NGAM equation#
55. constrOpt.values=[0.01,1.52]
56. #In order to maximize the target product, the production of Biomass will inevitably decrease, but it cannot be lower than a certain value, otherwise the cell will not grow and synthesize substances Here, the minimum flow rate for the biomass equation is set to not be less than 0.01, and the flow rate for the NGAM equation is set to not be less than 1.52#
57. constrOpt.sense=’GE’
58. OptKnockSol=OptKnock(model,selectedRxns,options,constrOpt)
59. From the instructions, it can be seen that the target product that wants to be maximized needs to be a growth coupled compound.