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1. Overview

1.1 Why do we build this model？

The sophorolipid(SL) produced by wild-type

*Starmerella bombicola*was a random mixture of acid and lactone types. We constructed a CRISPR/Cas9 gene-editing system in*S. bombicola*to produce sophorolipids with different ratios in our project. The metabolic pathway of*S. bombicola*is shown in Fig. 1. The lactone sophorolipid is generated by the acid sophorolipid under the catalytic of esterification enzyme*SBLE*.Fig. 1 | Metabolic pathways of sophorolipid.

In order to precisely regulate different ratios of sophorolipid, we plan to replace the promoters of different key genes to control metabolic flow.
In the early stage of the experiment, we have gained 14 promoters from

*S. bombicola*and two natural promoters of*UGTB*and*SBLE*genes. If we randomly combine these promoters in pairs, there will be 225 (15×15) combinations (Fig. 2). Although the more accurate model for predicting metabolic flow is GSMM (Genome-Scale Metabolic Model),the*S. bombicola*genome information is not complete. It is difficult to construct an accurate GSMM. Therefore, we intended to construct a more convenient linear pathway model, which is a qualitative model based on Michaelis–Menten kinetics.Fig. 2 | Random combination of promoters. We added different promoters in front of the genes of the two key enzymes to regulate the proportion of metabolites.

1.2 What's impressive about our model？

What is impressive about our model is that we drove the model based on the real data obtained from the experiment [the fluorescence intensity of different promoters and relative mRNA levels of green fluorescent protein (GFP)], using the model for qualitative analysis to eliminate the most unlikely combinations, narrowing the experimental scope, and finally conducted quantitative experimental verification. Therefore, this model can not only relieve the experimental pressure, but also provide reference for the biosynthesis based on synthetic biology in the selection of regulatory parts (e.g., promoters and RBS) that regulate the expression of functional genes.

Of course, the highlight of our model lies in its high universality and fault tolerance. For different metabolic pathways, it is very easy to improve the model, including the use of Hill coefficient, the introduction of feedback regulation and so on.

Of course, the highlight of our model lies in its high universality and fault tolerance. For different metabolic pathways, it is very easy to improve the model, including the use of Hill coefficient, the introduction of feedback regulation and so on.

2. How to design

As shown in Fig. 3, we firstly normalized the promoter transcription level and translation level data, and then weighted them to obtain the promoter equivalent parameters μ.
Because of the complexity of membrane transport process and the qualitative nature of the model, we mainly used Michaelis-Menten equation as the theoretical basis of membrane transport dynamics in the design of linear pathway model.
The relationship between transporters and substrate concentration and substrate affinity is mainly considered.
The promoter equivalent parameters μi and μj were added to reaction 𝒗4 to generate acid-type SL and reaction 𝒗5 to generate lactone-type SL, respectively.
Then, by virtue of the law of conservation of mass, we constructed a set of ordinary differential equations, and used ODE45 in MATLAB R2020a to solve the equations numerically. When the simulated results entered the metastable state (a typical steady-state, as shown in Fig. 4), we can calculate the ratio of acid and lactone sophorolipids in a particular promoter combination. Then, according to the predicted trend of the model and the requirement of acid and lactone type ratio in the actual production process, a certain number of promoter combinations were selected for quantitative experimental verification.

Fig. 3 | Design of model. The whole modeling idea is "Quantitative Experiment – Qualitative Model – Quantitative Experiment". We process the experimental data of transcriptional level and translation level to get the promoter equivalent parameter, then we use this parameter to drive the establishment of the model.We use the qualitative results of the qualitative model to guide the experiment, and then use the experimental calibration model to get a standard curve, so as to reduce the number of trial and error, and provide a reference for the epidemic situation and the situation that all experiments can not be carried out due to various reasons.

Fig. 4 | The simulation result of μ7 and μ13.
a, we chose promoter equivalent parameters μ7 added to V4 and μ13 added to V5 as an example to display simulation results.
b, with the extension of the simulation time, the change rate of metabolite concentration tends to be a very small value, which provides a basis for our metastable state selection and ratio calculation.

3. How to simulate

①The mapminmax function in MATLAB R2020a was used to normalize the data at transcription level and translation level to 0-1, and 50% weights were assigned respectively.
The weighted data were equivalent parameters of the promoter.

In the simulation process, we referred to Liu 's [1] selection of parameter ranges in similar models. In order to simulate the transition from low pathway activity to high pathway activity, the initial concentrations of the first two intermediates were randomly selected from the supersaturated concentration range (between 0% and 10% of the average Km). The initial concentrations of the other three metabolites were randomly sampled from a concentration range close to saturation (50% and 150% of the average Km). All reactions were described by Michaelis-Menten kinetics, Km values were randomly sampled between 0 and 2, and the average Km of was 1. The concentration of metabolites and Km parameters are arbitrary units, but their ranges determine the conditions of low saturation and high saturation of the enzyme. In our model, except for the internal flow rate V1max of 0.5, all the maximum reaction rates are fixed at 1 to ensure that no reaction in the path is limited. At the same time, in order to enhance the simulation effect, according to the ratio of acid and lactone sophorolipids reported in the existing result, reaction 𝒗4 and reaction 𝒗5 confirm to the ratio of 13.12:34.36 .

In the simulation process, we referred to Liu 's [1] selection of parameter ranges in similar models. In order to simulate the transition from low pathway activity to high pathway activity, the initial concentrations of the first two intermediates were randomly selected from the supersaturated concentration range (between 0% and 10% of the average Km). The initial concentrations of the other three metabolites were randomly sampled from a concentration range close to saturation (50% and 150% of the average Km). All reactions were described by Michaelis-Menten kinetics, Km values were randomly sampled between 0 and 2, and the average Km of was 1. The concentration of metabolites and Km parameters are arbitrary units, but their ranges determine the conditions of low saturation and high saturation of the enzyme. In our model, except for the internal flow rate V1max of 0.5, all the maximum reaction rates are fixed at 1 to ensure that no reaction in the path is limited. At the same time, in order to enhance the simulation effect, according to the ratio of acid and lactone sophorolipids reported in the existing result, reaction 𝒗4 and reaction 𝒗5 confirm to the ratio of 13.12:34.36 .

②After the ordinary differential equations were established according to the conservation of mass, the promoter equivalent parameters μi and μj were added to the reaction 𝒗4 and the reaction 𝒗5 respectively.

③The ODE45 in MATLAB R2020a was used to solve 225 ordinary differential equations.

④Finally, the ratio of acid and lactone sophorolipids were calculated when the simulation reached metastable state.

Table 1 |Parameters List

4. How to feedback

According to our demand for the ratio of acid and lactone sophorolipids, promoter combinations within a certain range were selected for experimental verification (Fig. 5).

Fig. 5 | The simulation result of 225 combinations.
We chose different promoter equivalent parameters μi and μj (𝒊,𝒋⊂[𝟏,𝟏𝟓] and 𝒊,𝒋⊂𝐙) combinations to simulate linear pathway model. We used ODE45 to solve 225 ordinary differential equations and get the results of 225 solutions, so we could calculate the ratio of acid-type SL to lactone-type SL.

From Fig.4 b, it can be found that after a period of simulation (which is related to the step size of the simulation), the change rate of metabolites tends to be stable, which is what we think of as metastable state. We calculate the scale when we select the simulation 2000 steps (that is, 20 in Fig.4b) to get the heat map shown in Fig.6. Then several groups of promoters are selected for quantitative experimental determination, and a standard curve can be obtained by linear regression with our simulation results. It is the ‘standard curve’(Fig.7) that enables us to choose different time(only in the metastable state) to calculate the ratio of acid-type SL to lactone-type SL in the qualitative model. In the future, according to the trend of simulated data and the mapping relationship of real data, we can choose the several appropriate promoter combinations to achieve the desired ratio.

Fig. 6 | The ratio of acid-type SL to lactone-type SL calculated from simulation result of 225 combinations. The numerical values in the heat map represent the ratio of acid-type SL to lactone-type SL in the simulation.

Fig. 7 | Making ‘standard curve’. According to the trend simulated by the qualitative model, the several combinations of promoters are selected for experimental verification, and then a standard curve is drawn, which can correspond to the simulated data. In the future, according to the trend of simulated data and the mapping relationship of real data, we can choose the several appropriate promoter combinations to achieve the desired ratio.

5. Q & A

5.1 Why do you use the Michaelis-Menten equation？

①Michaelis-Menten equation is classical and has been thoroughly studied, which can explain the interaction between substrate and enzyme well.

②The kinetic modeling of Michaelis-Menten equation is easy to modify. For example, if it is found that enzymes in metabolic pathways have feedback inhibition in the future, we can consider using "Hill coefficient" to change the simple linear pathway model into feedback kinetic model. Therefore, the model has better compatibility with the team in Manufacturing track.

③The linear pathway model we constructed is a qualitative model, and it is not necessary to introduce complex quantitative processes, such as mRNA degradation and protein degradation.

calculate the ratio of acid-type SL to lactone-type SL in the qualitative model. In the future, according to the trend of simulated data and the mapping relationship of real data, we can choose the several appropriate promoter combinations to achieve the desired ratio.

②The kinetic modeling of Michaelis-Menten equation is easy to modify. For example, if it is found that enzymes in metabolic pathways have feedback inhibition in the future, we can consider using "Hill coefficient" to change the simple linear pathway model into feedback kinetic model. Therefore, the model has better compatibility with the team in Manufacturing track.

③The linear pathway model we constructed is a qualitative model, and it is not necessary to introduce complex quantitative processes, such as mRNA degradation and protein degradation.

calculate the ratio of acid-type SL to lactone-type SL in the qualitative model. In the future, according to the trend of simulated data and the mapping relationship of real data, we can choose the several appropriate promoter combinations to achieve the desired ratio.

5.2 Why do you use the method of setting equivalent parameters of the promoter？

In eukaryotes, the relationship between promoters and transcription is complex. At the same time, the uncertainty of the splicing process of RNA may also affect the level of translation, so we adopted a "grey box" method to normalize the transcription level and translation level of the promoters, and then weighted the data to obtain a parameterμ that can represent the equivalent strength of the promoter.

5.3 What is metastable state？ Why do you choose to calculate the simulated ratio of acid and lactone types of sophorolipid at metastable state？

Metastable state is a state between complete steady state and unsteady state. In fact, it is difficult to achieve true steady-state due to the limitations of various complex factors. Almost all experimental results are metastable. Moreover, it is difficult for the linear pathway model to reach the real steady state under the simulated conditions. Although extending the simulation time can make the simulation results tend to be in a steady state to a large extent, it is impossible to extend the fermentation time in the real experiment. On the other hand, the selection of the same time to calculate the ratio of acid and lactone sophorolipids has little influence on the stereotyped model using trend judgment, so we chose metastable state to calculate the ratio of acid and lactone sophorolipids.

5.4 Does this model have any implications for other possible teams？ Is it universal？

In particular, our model introduced the concept of promoter equivalent parameter. If a team is using different RBS combinations, it can also use GFP to represent the transcription and translation levels of different RBS, and then introduce an "RBS equivalent parameter", or even introduce feedback regulation to further improve the linear pathway model, and eliminate a large part of the combinations that are almost impossible in theory through simulation. Other cis-acting elements in synthetic biology can also be simulated by referring to this method to improve the efficiency of subsequent experiments.

5.5 Why is the kinetic process of product transport to extracellular expressed by Michaelis equation？

Because in eukaryotes, the kinetics of membrane transport is too complex, and the transport mechanism of our products is not clear. Therefore, in order to simplify the qualitative model, the transport process is also regarded as a reaction, and the Michaelis equation is used to reflect the interaction between the substrate and the transporter.

5.6 What’s the meaning of "Standard Curve"？

The standard curve is not necessarily a simple linear relationship, we need to go through a certain amount of experiments, and then regression fitting the simulation results and the real experimental results. We get a mapping interval in which we select a small number of promoter combinations to achieve the results closest to our desired results.

6. Summary

We use the traditional Michaelis-Menten equation to get a more general model, which can not only solve the problem of the number of trial and error in our experiments, but also provide a model that is easy to use and expand for more teams. (e.g., the manufacturing track).

1. Liu, Y.; Link, H.; Liu, L.; Du, G.; Chen, J.; Sauer, U., A dynamic pathway analysis approach reveals a limiting futile cycle in N-acetylglucosamine overproducing Bacillus subtilis. Nat Commun 2016, 7, 11933.