Since the engineered bacteria in the team need to grow and function in an environment of high arginine concentration, the team constructed the bacterial growth curve by mathematical modeling method and analyzed the influence of arginine concentration on bacterial growth, so as to provide a reference for the future application of engineered bacteria. At the same time, we found some problems that need more research.


First, the team initially designed Model 1 (Fig 1) based on the following assumptions.


Figure 1 – The exponential growth model with limited resources and linear decay



Figure 2 – The analytical expression of Model 1

Hypothesis 1 The net growth rate of bacteria is a linear summation of the growth rate obtained from resource consumption and bacterial mortality.


Hypothesis 2 Bacteria can only consume a certain proportion of the remaining resources, so the growth rate of bacteria depends on the remaining amount of resources available.


Hypothesis 3 The bacterial mortality rate is linear to its population (i.e. the number of individuals dying over a period of time is a constant proportion of the total population).


Hypothesis 4 The resources available to bacteria are a part of the total resources in the system and may vary according to the experimental conditions (such as the concentration of arginine presented).


Hypothesis 5 The consumption rate of available resources is linearly related to the number of bacteria.


Among them, the  is the function of the total resources available to bacteria in the environment, and its initial value  reflects the maximum capacity of bacteria under certain experimental conditions. The  is the bacterial mortality rate. When using this model to fit our experimental data, we found:



1. When the concentration of Arginine increases, the resources available to bacteria decrease, that is, the upper limit of the number of bacteria that can be present decreases (refer to the numerical change in ).


Figure 3 – The change of  with respect to the concentration of Arginine


 2. With the increase of Arginine concentration, the death rate of bacteria decreased (refer to the numerical change of ).


Figure 4 – The change of  with respect to the concentration of Arginine


Therefore, the inhibition of bacterial growth by arginine is not by increasing the rate of bacterial death, but by other means, possibly by reducing the utilization of nutrients by bacteria.


Moreover, our team found that the distribution of the original data was close to the form of the classical Logistic growth model, and this was used as the analytical expression as in Model 2(Fig 5). As the logistic growth model proposed, the model assumes that the population growth rate depends on both the current population size and the proportion of remaining environmental capacity.

In Model 2,  represents the maximum capacity of a species in the environment under certain conditions (similar to  in Model 1).  is the coefficient of the growth rate.


Figure 5 – The Classic Logistic growth function

Note that despite the same name of variable , they have different meanings in model 1 and model 2.

With Model 2 fitting for our experimental data, we found that the  and decreased simultaneously with increasing arginine concentration (Fig 6, 7).



Figure 6 – The change of  with respect to the concentration of Arginine



Figure 7 – The change of  with respect to the concentration of Arginine



Conclusion: Through comparison, the team chose the Logistic growth model as the final modeling of experimental data, because it fits significantly better than our original model as seen in the gap between the  of the models (Fig 8, 9).


Figure 8 -  values of Model 1 with respect to the Arginine concentration



Figure 9 -   values of Model 2 with respect to the Arginine concentration


It is worth mentioning that when the concentration of arginine is between 1000 and 40000 micrograms per milliliter, the experimental data start to fluctuate significantly, and the fitted results are poor under both models. This may be because the high concentration of arginine affects other aspects of the experiment that cannot be captured by our models. Therefore, the team filtered the final result based on the  yield from fittings, as we would only consider the effect of arginine on model parameter where the model is well-fit.


Figure 10 - An example of the poorly-fitted result of Model 1


Figure 11 - An example of the poorly-fitted result of Model 2

Since both  values in Model 1 and  values in Model 2 tended to decrease with increasing arginine concentration, we consider this conclusion plausible. However,  in Model 1 shows that increasing arginine concentration reduces bacteria mortality, while  in Model 2 shows that the net growth rate of the bacteria decreases. This seemingly contradictory phenomenon suggests that how arginine affects bacterial growth may be complex and requires further investigation.


With mathematical models of experimental data, we can draw conclusions that, the optimum growth environment for engineered bacteria is not recommended to contain arginine of a concentration higher than 1000 MCG/ml. Meanwhile, how arginine affects the growth of engineered bacteria at the molecular and metabolic levels should be the direction of future improvement, which will help settle down the controversial conclusions of decreased bacterial mortality and decreased net growth rate.



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