Team:GA State SW Jiaotong/SGCM

Strain growth competition model

Model overview

In the final product of the project, the Bacillus Subtilis engineered bacteria (Bacillus Subtilis WB600), which can secrete Gas6 protein and EGF protein, was applied to the user's scalp for use. To verify that Bacillus Subtilis can survive in the scalp microenvironment and does not cause significant disruption to the scalp microflora balance, we designed the following model for this project.

To make the study general and operational at the same time, the microbial population of the human scalp was analyzed, and the two strains with the most extensive survival in the scalp microenvironment, Marassezia, restricta and Staphylococcus epidermidis, were selected to represent the scalp microenvironment flora. Then a series of experiments such as strain monoculture and strain co-culture were used (see Experimental protocol 1) to measure the growth status between strains under different conditions. Finally, regarding the literature [1], the growth data of the strains were analyzed according to logistic growth curves to deduce the growth status of each strain under co-culture conditions to study the relationship of growing competition between strains under co-culture.

Establishment and analysis of logistic growth models for single strains

Analysis of monoculture growth characteristics of Bacillus Subtilis WB600

Before exploring the competition mechanism of co-culture of different strains, the monoculture growth characteristics of each strain need to be analyzed. Referring to the literature [1], it was found that the growth characteristics of the strains can be described by the logistic formula, namely:

Since continuous data are not available for the experiment, equation (2) can be approximated and modified to the form of equation (3).

Equation (1) is a common ordinary ordinary differential equation model (ODE), for which a direct numerical solution was applied based on the experimental data (see Table 1), and the results were obtained as shown in Figure 1. From the figure, it can be seen that the logistic model simulates the growth process of Bacillus Subtilis WB600 very well, and the average relative error at the corresponding point is 8.75%, which has a certain significance, which indicates that the logistic model has a good application effect on the growth curve of the strain.

Fig.1. Logistic modeling of growth of Bacillus Subtilis WB600

Analysis of growth characteristics of S. epidermidis monoculture

Fig.2. Logistic modeling of growth of S. epidermidis

Analysis of growth characteristics of M. restricta monoculture

The preliminary observation of the growth data of M. restricta in Table 1 showed that the growth rate of M. restricta was extremely fast, reaching an OD600 of 2.52 at 2.5 h and breaking the maximum value of absorbance of 3.0 at 5 h. Because of this characteristic, the growth curve could not be analyzed by logistic model, and it is assumed here that the maximum growth rate of M. restricta is infinite. The maximum growth rate μMm is infinite and the maximum loading capacity is also infinite.

Development and analysis of logistic growth models for two strains

Analysis of growth characteristics of M. restricta co-cultured with S. epidermidis

After obtaining the growth characteristics of each strain after monoculture, the analysis of the growth characteristics between the strains co-cultured was started. Also according to the literature [1], the growth process under co-culture of different strains can be equally described by a logistic model, i.e.

Due to the limitations of the experimental conditions, the experiment could only obtain the overall growth concentration of the strains under co-culture conditions (see Table 1). With reference to the logistic model, the parameters must be obtained to obtain the growth curves of each strain under co-culture conditions. Without access to the previous scientific literature, the logistic model was first decomposed by numerical solution. Then the least-squares method was used to estimate the target parameters' parameters and based on the experimental data of co-culture. The overall solution model is shown in equation (6):

Where denotes the overall growth concentration of M. restricta and S. epidermidis measured by the experiment at the time i under co-culture conditions. The initial growth concentration OD600 values of M. restricta and S. epidermidis under co-culture conditions, i.e., boundary conditions.

The above equation (6) was solved and the results were obtained as shown in Figure 3. From Figure 3, it can be seen that the overall strain growth concentration variation predicted by the logistic model has outstanding results with the experimental data, with a general average relative error of only 2.28%, reaching the significance level. In addition, the estimated target parameters of maximum growth rate =0.5366 for M. restricta, maximum growth rate for S. epidermidis and maximum carrying capacity for M. restricta and S. epidermidis under co-culture can be seen that the conditions of co-culture with M. restricta, S. epidermidis The maximum growth rate of S. epidermidis was the same as that of the monoculture condition, i.e., indicating that there was no inhibition effect. Still, only the maximum carrying capacity was reduced due to the co-culture. In contrast, M. restricta showed some competitive inhibition under the co-culture condition, but the overall growth was still better, with OD600 values up to 1.5. This is consistent with the actual situation, i.e., the fact that M. restricta and S. epidermidis can coexist harmoniously in the scalp.

Fig.2. Logistic modeling of growth of S. epidermidis

Analysis of growth characteristics of M. restricta co-cultured with Bacillus Subtilis WB600

Prior to the analysis, observation of the experimental data revealed that the growth data of M. restricta co-cultured with Bacillus Subtilis WB600 had reached a maximum value of 3.0 in 12.5h of adoption, which initially indicated that there was no serious competitive inhibition between the two strains. To ensure the reliability and accuracy of the data, only five sample points between 0h and 10h were taken for the analysis of the data.

The analysis process was the same as step 3.1, and the experimental data of the co-culture of M. restricta and Bacillus Subtilis WB600 after screening in Table 1 were analyzed to obtain the results shown in Figure 4, where the growth concentration of Bacillus Subtilis WB600 is indicated by LWB . Analysis of Figure 4 revealed that the overall strain concentration growth curves showed a good fit with the experimental data, with an average relative error of 16.3%. In addition, the estimated maximum growth rate of M. restricta, μLMm=0.536, was essentially equal to the maximum growth rate of M. restricta and S. epidermidis when co-cultured, indicating that M. restricta was not inhibited by the effect. the maximum growth rate of Bacillus Subtilis WB600, μLWBm= 0.055, a decrease of about 54% compared to the maximum growth rate in monoculture, and a final growth density OD600 of 0.3, indicating that Bacillus Subtilis WB600 was strongly inhibited when co-cultured with M. restricta.

Fig.4. Logistic modeling of growth of M. restricta co-cultured with Bacillus Subtilis WB600

Analysis of growth characteristics of S. epidermidis co-cultured with Bacillus Subtilis WB600

The same analysis procedure as in 3.1 and 3.2 was used to analyze the experimental data of S. epidermidis and Bacillus Subtilis WB600 co-cultured in Table 1. The results were obtained as shown in Figure 5. The analysis revealed that the overall growth concentration variation of the predicted strains fitted well with the experimental data, with an average relative error of 7.85%. The maximum growth rate of S. epidermidis under co-culture conditions,=0.11, decreased by 36.1% compared with the maximum growth rate of 0.172 under co-culture of M. restricta and S. epidermidis, indicating that S. epidermidis was inhibited to some extent, but the overall growth was good. The maximum growth rate of Bacillus Subtilis WB600, =0.0749, was still inhibited to some extent compared to the monoculture. The degree of inhibition was reduced compared to the growth condition under the coculture conditions of M. restricta and Bacillus Subtilis WB600.

Fig.5. Logistic modeling of growth of S. epidermidis co-cultured with Bacillus Subtilis WB600

Analysis of results

After the above series of analyses, it was found that the engineered bacteria Bacillus Subtilis WB600 was co-cultured with M. restricta and S. epidermidis, M. restricta did not suffer from a strong inhibition effect. S. epidermidis suffered some inhibition effect, but the overall growth condition was good. At the same time, Bacillus Subtilis WB600 was strongly inhibited (maximum growth rate decreased by about 54%) but still survived for a long time.

Considering the actual medication situation, we that this situation is the best phenomenal support for medicine by applying. The normal growth (no significant inhibitory effect) of M. restricta and S. epidermidis ensured that the engineered bacteria used did not compete poorly with the native ecological flora of the scalp, resulting in a disruption of the scalp flora balance. The strong inhibitory effect of the engineered bacteria Bacillus Subtilis WB600 itself will not affect the stability of engineered bacteria's effect (because the drug only needs a very small concentration to have an effect) but let the number of engineered bacteria added to the scalp in a stable and controlled state, that is, will not grow on the scalp indiscriminately, but will eventually stabilize within a low concentration threshold. This will further reduce the aggressiveness of the engineered bacteria.

Reference

[1] Quinto EJ, Marín JM, Caro I, Mateo J, Schaffner DW. Bayesian modeling of two- and three-species bacterial competition in milk. Food Res Int. 2018 Mar;105:952-961. doi: 10.1016/j.foodres.2017.12.033. Epub 2017 Dec 14. PMID: 29433294.