Worldshaper-HZBIOX
Background
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.