Team:NPU-China/Model

Introduction

This year our project is the introduction of acrylic synthetic routes in Escherichia coli or Saccharomyces cerevisiae to produce acrylic acid.

Primitive metabolic path map

We have a rational new design and transformation of the core enzyme ceaS2, at the same time, we also want to be optimized to improve the acrylic acid production in the metabolic flow.
We know that for Escherichia coli, the carbon flow rate of its original glycerol metabolic pathway may not be sufficient, and if the new glycerol metabolic pathway can be used to increase the carbon flow of DHAP or G3P, the substrate of the core enzyme ceaS2 can be increased Concentration to increase acrylic acid production.
Therefore, through the literature review, we found two enzymes which can achieve efficient conversion of glycerol to generate DHAP the same way.
In our new approach, Glycerol dehydrogenase (Gly DH) is capable of efficiently converting glycerol to 1,3-Dihydroxyacetone (DHA) and then phosphorylates DHA to DHAP via Dihydroxyacetone kinase (DAK).

New route map
Before the implementation of the formal experiment, we need to model it to analyze the impact of the introduction of new routes on the original metabolic flow, especially the two intermediates of DHAP or G3P. Specifically, we care about the following two issues:
1. Has the DHAP or G3P's carbon flow improved after the introduction of new metabolic pathways? Is it compared to the previous increase in production?
2. The introduction of new pathways after the entire metabolic pathway is stable and robust. How is it?
In order to answer these two questions, we established a carbon metabolic flow model.

The overall workflow is as follows:

Parameter estimation

There are many parameters to be determined in the model. Most of these kinetic parameters can be found in the literature or in the database, but at the same time, there are some kinetic parameters of the enzyme we are looking for. Its organic matter, or the temperature and ph of the enzyme are different. Therefore, we need to re-estimate this part of the parameters.

In the process data link, we cited the method using the data point weighting of University of Manchester in year 2016 . The weighting of the samples is as follows:
1. When the sample PH is the same, the sample is weighted by 4 .2 when they are close. 1 when they differ much.
2. When the sample temperature is the same, the pH is the same.
3. When the samples are from the same species , the weight of the sample is 4.When they are the non-identical species and are the prokaryotes，or the corresponding species mutated to the corresponding species, the weight is 2. When they are the non-identical species and are the eukaryotes, the weight is 1.
4. Try to delete the missing data. If there are some essential samples of the temperature and PH missing, then the corresponding weight is 2.

1.kernel density estimate 2. Gaussian mixed model.

The fourth point reflects our point of view of Bayesian. In the absence of prior knowledge of the case, we take as much as possible the weight of neutrality.
Based on the points above, we get a new parametric vector after weighting.In our model, we do the fitting of the probability density according to the two methods of the parameter vector.
1.kernel density estimate 2. Gaussian mixed model.

The basic workflow of parameter estimation：

The Gaussian mixture model can be approximated to any real probability distribution in theory. The EM algorithm is used to estimate the parameters required for the model. And we use the Gaussian mixture model to estimate the probability density of the possible distribution of parameters.
After making the probability distribution, we select Bin randomly, which meet the conditions of width = len / 10.And we select the most possible bin based on the CDF, and estimate the corresponding parameters when the bin reach average value.
Finally, we get the estimated parameter values, as well as the corresponding parameters of the original PDF. The specific form and parameter values are as follows:
The reaction path of the original pathway is Gly to Gly-3-p and then to DAHP
The original pathway belongs to the reaction of a single channel, and there is a random bibi reaction and an irreversible Mickey equation reaction. The reaction involves two enzymes paticipating - glpk and glpD. We assume that the reaction concentration of these two enzymes is 0.01 mM, assuming that the initial [Gly] concentration is 10 mM, the initial concentration of ATP 10 mM, Gly-3 The concentration of -p 0 mM and the concentration of DHAP 0 mM at the same time.

In this reaction, we make the following assumptions about our model:
1. The ATP of the E.coil system is given externally completely, assuming that the culture conditions given externally are sufficient and ATP maintains a stable constant.
2. Assume that the substrate involved in the reaction does not participate in other reactions.
In order to determine the yield of the target product, we chose to observe the efficiency of the DHAP yield estimation system in view of the lack of basic Deas2 enzyme data.

Changes of metabolic flux before passage

We can observe that the DHAP stops growing close to 50 minutes.

Then, we need to test the carbon pathway through the modified pathway, And add a metabolic pathway enzyme-catalyzed by GlyDH enzyme and DAK in the original path, while the need for NOX enzyme and CAT enzyme from the role of NAD + supplement, resulting in DHA, and finally Phosphorylation produces DHAP.
metabolic flow after the transformation of the reaction model. According to the actual situation of the reaction, we make the following assumptions:
1. In the reaction , due to the process of hydrogen peroxide to the production of O2, that is, the process of generating acceptor, is faster, we will regard the reaction of NOX enzyme NADH catalytic as an ordinary Michael's equation, rather than ordered sequence reaction.
2. Random pairs of sequence reactions and ordered sequence reaction equations are identical. So we substrate which is identified as the [A] substrate depending on the integrity of the data.

Metabolic pathways after transformation

We can see that the rate of DHAP is faster after changing the metabolic pathway, which means that the higher the output per unit time after being put in use, the sooner the reaction is done. Compared to the pre-improved pathway ,the reaction finishes roughly five minutes ahead.
Sensitive analysis
In the previous pathway study, we noted that the Kcat values of glpK and GlyDH enzymes are unknown (we do not have a large deviation in the absence of a sample expressed in E.coil).
The Kcat value of the reaction of propanal is the Kcat value of the reaction of Gly and GlyDH. It is also assumed that the K63 ratio of the two enzymes is 2: 1.
We often use Kcat / Km to describe the catalytic efficiency of different enzymes for the same substrate, and as a result of our experiments, GlyDH exhibited higher catalytic efficiency than glpK. Thus we assume that the GlyDH enzyme and the glpK enzyme satisfy the following relationship:
GlyDH enzyme activity and the Km value for gly and the Km value of the glpk enzyme to gly have been known in previous studies. Next we adjust the alpha coefficient to study the effect of different ratios on the overall metabolic flow.

KATA Sensitivity Test before Modification

KATA Sensitivity Test after Modification

We show the highest ratio (1000) and the lowest ratio (0.001) in yellow and blue lines respectively. The pre-transformation pathway is most sensitive to the change of Kcat in glpK enzyme, and the metabolic pathway of the target substrate is transformed with the change of α Rate is always higher than the pre-transformation pathway, even when the glpK Kcat / Km value is 100 times the GlyDH, the reason may be DAK enzyme catalytic efficiency’s higher than glpD.
As we can see, the previous reaction is dependent on ATP, and in the previous hypothesis, we make ATP stable in the constant .In order to analyze the ATP concentration changes on the impact of glycerol conversion, we add a Standard deviation of 0.05, mean of the normal distribution of variables to disturb the timing of the concentration of ATP in ODE.
For the sake of us to observe the significant results, we assume that the initial concentration of ATP is 0 and is always greater than zero.
And the change curve of the concentration in 60min is shown below:

Before transformation

After trransformation

We found that the random change of ATP concentration had a significant effect on the pathway after transformation, and the rate of DHAP synthesis was lower than that before transformation.
But when we adjust the standard deviation of the normal distribution random variable to 0.05, the result is shown below.
Thus, we found that even if ATP had a greater perturbation, the overall level was relatively high in 0-60 min compared to the previous standard deviation of 0.02. While the transformation of the metabolic pathway also reflects a more stable curve of change. At this point the concentration of DHAP is not significantly affected by changes in ATP concentration.
Thus, in actual production, we only need to keep the ATP concentration at a slightly higher level, not only to ensure the production of the target product, but to increase the stability of the system as well.