Introduction

In our design, we hope EcN will eventually colonize the ileum. To verify that the modified EcN can form an independent ecological niche at the ileum after erythritol consumption, we simulated the co-culture of the modified EcN with 24 species of ileal microbiota based on the dFBA algorithm, and designed a recipe for the average Chinese population using the Scientific Research Report on the Chinese Dietary Guidelines (2021). We simulated the intestinal environment of the average Chinese population based on the recipe, predicting the growth of multiple intestinal microbiota in co-culture, and verified that the modified EcN has better competitiveness in the microbiota. Meanwhile, the framework we developed can also be applied to other co-culture simulations, which can be promoted as a toolbox.

Data Accession

GEMs collection

GEMs of 773 microbiota species in the gut have been constructed in the literature (Magnúsdóttir, S., et al., 2017), and we collected the GEMs of microbiota in the ileal terminus and obtained the abundance of each strain (Stolaki, M., et al., 2019). Since the samples used for the construction of these models are intestinal microorganisms, it is no longer necessary to specifically adjust them to the state in an anaerobic environment.

Micro-community

The total amount of microbiota in ileal is approximately to be 10^10 cfu/L. Hence, if we assume that one cfu is produced by one microbial, we can calculate the total biomass of the ileal micro-community is about 0.1g/L. The relevant abundance of the ileal micro-community is from Stolaki, M., et al., 2019.

Here we roughly set the relevant abundance of EcN to be 0.0678%. While the others are based on the paper mentioned above.

Growth Medium Design

The environment of the human gut is closely related to a person's dietary habits and food intake and thus varies from person to person. To ensure that the model is both general and has Chinese characteristics, we entered the recipes recommended by Scientific Research Report on the Chinese Dietary Guidelines (2021) into the vmh website, which will return the fluxes that these foods can provide to the intestine, and use these data to approximate the concentrations of each substance in the human intestine.

Model Description

Assumptions

1, microbiota is uniformly distributed at the ileum
2, the absorption coefficient of different substances by the same microbial is the same
3, the absorption rate of these substances by the body does not change with time
4, the model only simulates the existence of competing substances, that is, it is considered that in addition to erythritol only one microbial can use the substance is sufficient, the concentration will not be affected with time
5, there is no exchange of signal molecules between intestinal microbials, the competitive relationship only through Competing substances in the form of expression
6, the intestinal microbiota dilution rate is the same
7, the goal of the growth of intestinal microbiota is to make the maximum Biomass
8, the intestinal material flow uniform rate

Algorithm

$I_j$: indexes of metabolites in organism j
$J$: indexes of the organism
$K_j$: the coupled metabolites of organism j
$X_j$: the biomass of organism j
$C_i$: the indexes of metabolites
$v_{lb j}^{i}$: uptake flux of an exchange reaction related to metabolites I in organism j
$v_{max,j}^i$: max uptake flux of an exchange reaction related to metabolites I in organism js
$k_{i,j}$: Monod constantss
$v_{s,j}^i$: the solution flux of an exchange reaction related to metabolites I in organism js
$S_j$: Stoichiometric matrix of organism js
${\mu}_j$: Growth rate of organism js
$d_j$: dilution rate of organism js
$U_{human}^i$: uptake rate of ileals

\begin{equation} \frac{dX_j}{dt}={\mu}_jX_j=d_jX_j \label{(1)} \end{equation}

The biomass of each organism is determined by the growth rate and dilution rate. The growth rate is solved by the (3), the LP problem, while the dilution rate is constant with the specific microbial strain, won’t be affected by time or other factors.

\begin{equation} v_{lb j}^i=v_{max,j}^i\frac{C_i}{k_{i,j}+C_i} \label{(2)} \end{equation}

In constrain-based modelling(cobra), the lower bound of an exchange reaction means the ability for a microbial to uptake a specific metabolite i. And refers to the maximum ability to uptake a metabolite, the value of this term is set by the lower bound value in the GEMs accessed from AGORA. And the monod constant is set to 0.1mM, which is used in previous work(Popp, D., et al., 2020).

\begin{equation} max:{\mu}_j \label{(3)} \end{equation} \begin{equation} subject\ to: S_jv_j=0 \label{(4)} \end{equation} \begin{equation} v_{lb,j}^i \le v_{j}^i \le v_{ub,j}^i \label{(5)} \end{equation}

The lines above are the FBA. The object in each organism is set to be the biomass reaction, referring that the microbial will always try its best to grow. This object is widely used in cobra model. As the (4) shown, it is the expression of the constrain based on the conservation of mass theorem while the (5) is the constrain for the extent of reaction specific in the microbial.

\begin{equation} ({\exists}j' \in J, j' \neq j, i_j \in K_j \bigwedge i_j \in K_{j'})\longrightarrow i_j \in K_j \label{(6)} \end{equation} \begin{equation} \frac{dC_i}{dt}=\sum_{j=1,i\in K_j}^{n}v_{s,j}^iX_j-U_{human}^iC_i \label{(7)} \end{equation}

The (6) explains the concept of the coupled metabolites in math. By considering coupled metabolites, the algorithm can avoid some single metabolites that only utilized by single strain. We would rather assume these single metabolites to be adequate instead of the method used in (2) in order to keep the model stable. The single metabolites may arise from the inconsistency of the SBML files, and the coupled metabolites have an overwhelming amount compared to the single ones.

The (7) describes the time derivative of the coupled metabolites, the consumption of them is arisen from the microbial and human. Here, we assume the human uptake rate to be constant.(see code)

Results

Growth Curve

We simulated the growth of the above-mentioned 25 species of microbial in the ileal terminal environment, and the change of substances in the starting 12 hours. The starting concentrations of microbiota concentrations were set according to the concentration of ileal microbiota and the relative abundance of various microbials, while the concentrations of various substances in the environment were set according to the data in Table1. The results showed that the growth trend of most microbials gradually leveled off within 12 hours, reflecting that the provided nutrients were going to be depleted within 12 hours, and the specific substance change trend is shown in Fig3. Within 12 hours, we can see the growth of EcN is negligibly low compared to other microbials, and the reason for this result is that the initial abundance of provided EcN is low, only 0.0678%. Therefore, it is obviously difficult to see the promoting effect of erythritol on EcN in terms of population density.

But when considering the growth rates of ileal microbials in ileum, the advantage of EcN manifests. With erythritol, the extra-carbon source, existing, EcN maintains relatively low growth rate under the condition of nutrition-rich environment. However, given enough time, EcN is capable surpassed the grow-slow strain (such as ClostridiumsymbiosumATCC14940, etc.) under such condition.

The right half of the curve in FIG. 4 shows the growth rates of each microbial in the gut when glucose and other major carbon sources are no longer sufficient.

As you can see, the growth rate of Bacteroides vulgatus ATCC 8482 decreased greatly under the condition of insufficient nutrition. However, in contrast, under the same condition of insufficient main carbon source, EcN was supported by erythritol (as an independent carbon source, erythritol could only be absorbed by EcN, so it was relatively sufficient), and the decrease of growth rate was not so drastic as that of other microbials It was also noted that when the main carbon source was insufficient, the growth rate of EcN was above the medium level in the population, which further indicated the possibility of EcN colonization supported by erythritol as an independent carbon source.

MICOM Verification

MICOM has been mentioned in the previous section. In this section, we still use MICOM to do a simple verification of the results of our model. The construction of growth medium in MICOM was realized by the method mentioned in this section (see Table1). For unmodified EcN, its growth rate in intestinal microbiota was the lowest (Fig5A), which also reflects the background on which our project is based -- EcN is often difficult in the process of colonization.

After the transformation, the growth rate of EcN that could utilize erythritol was increased to a certain extent (Figure 5B). Comparing the growth rate of EcN before and after being modified, it could be found that the growth rate of some microbials would change with the growth of EcN.

The initial abundance of engineered EcN largely determines the outcome of the competition. If the initial abundance of EcN is too low, it will lead to a decline in the competitiveness of major carbon sources (such as glucose, etc.), resulting failure in competition. Only by ensuring that the initial abundance of engineering EcN reaches a specific proportion in the population, can EcN be competitive enough. (FIG. 7).

This conclusion will also guide us to increase the abundance of EcN as much as possible in the actual design process, such as the use of wrapping pods or other wrapping materials.

Source Code

Reference

1. Kumar, M., Ji, B., Babaei, P., Das, P., Lappa, D., Ramakrishnan, G., Fox, T.E., Haque, R., Petri, W.A., Bäckhed, F., Nielsen, J., 2018. Gut microbiota dysbiosis is associated with malnutrition and reduced plasma amino acid levels: Lessons from genome-scale metabolic modeling. Metabolic Engineering 49, 128–142. https://doi.org/10.1016/j.ymben.2018.07.018

2. Magnúsdóttir, S., Heinken, A., Kutt, L., Ravcheev, D.A., Bauer, E., Noronha, A., Greenhalgh, K., Jäger, C., Baginska, J., Wilmes, P., Fleming, R.M.T., Thiele, I., 2017. Generation of genome-scale metabolic reconstructions for 773 members of the human gut microbiota. Nat Biotechnol 35, 81–89. https://doi.org/10.1038/nbt.3703

3. Popp, D., Centler, F., 2020. μBialSim: Constraint-Based Dynamic Simulation of Complex Microbiomes. Front. Bioeng. Biotechnol. 8, 574. https://doi.org/10.3389/fbioe.2020.00574

4. Stolaki, M., Minekus, M., Venema, K., Lahti, L., Smid, E.J., Kleerebezem, M., Zoetendal, E.G., 2019. Microbial communities in a dynamic in vitro model for the human ileum resemble the human ileal microbiota. FEMS Microbiology Ecology 95, fiz096. https://doi.org/10.1093/femsec/fiz096

5. https://vmh.life