Growth Curve for E.coli

We carried out a practical demonstration of the logistic population growth we had learnt in our Ecology classes. Like always, it was our best friend E.coli who had to stay in the incubator.

November 23rd, 2010
Saturday 8:00 am
A handful of students walk into the Bio lab. Along with Nilesh Sir they prepare nutrient broth for ten side-arm flasks, 50ml in each. I don’t know how but they do prepare different kinds of the broth. Three for each of pH 6, pH 7 and pH 8. Of the three, one contains 0.5 g% of salt, another contains 1 g%, another contains 2 g%. Then they put E.coli into each of these flasks. That makes three into three: nine flasks. The tenth flask is the ‘standard’ against which all the other flasks will be compared during the course of the experiment.

It’s time=zero. The beginning of the experiment.

The colorimeter is turned on. The flask containing our standard solution is turned to its side, carefully, so that the liquid flows into the side-arm without spilling. This side arm is now lowered into the colourimeter, which is then set to zero.
Each of the other flasks are then analysed, one by one, with the help of the colourimeter and the values for “absorbance” at 545nm (normal yellow light) is noted down in the sheets of paper provided. I hope you did not miss the apostrophes. “Absorbance” here does not really mean absorbance, as with chemical compounds. We are using this just as a test for transparency of the broth. As our E.coli will expand its colony and grow in numbers, we need to be able to measure the population without having to count every individual. A good way of doing this is to use the fact that the presence of a larger number of E.coli will reduce the transparency of the broth and make it turbid. This it will do by the virtue of its opaqueness, which is not the same as absorbance. However, this hardly matters since all we are interested in is the relative amount of resistance to the passage of light in order to determine the relative number of E.coli population.
After noting down the readings, the students leave.

Saturday 8:30 am
A fresh handful of students enter. They take each of the side flasks out of the incubator and measure their ‘absorbance’ in the same way. Data is recorded.

At 9:00am, another group of students come in and repeat the process. This happens again after another half-an-hour. And then again and again.

Saturday 8:00 pm
It’s the last batch of students to enter the laboratory. They fill up the bottom-most row on the papers and disappear into the darkness outside.

Within a couple of days, we get the whole data set on our webmail. And we are to plot it.



Sitting back and smiling at the S-shaped curve on my laptop screen, I proceed to the theory. It’s easy and we have all been learning it in the class.

In the environment, in general, any sustainable food source can be increased linearly. This, however, causes the population to expand exponentially. This is known as the Malthusian Growth pattern (from the scientist Mall Thust). We shall write the following equation to represent the rate of population growth at a given instance of time.



Where ‘N’ is the population number, ‘b’ represents the birth rate and ‘d’ represents the death rate. If these two are constant, which is true in most cases, (b-d) can be replaced by another constant ‘r’, which is the intrinsic growth rate.



The dotted line represents the approximate instance of time when competition sets in. At this point, resource becomes scarce as compared to the population and a struggle for existence arises. The number of deaths increases. Only the fittest survive. So, beyond the dotted line, our graph above is incorrect. The population can’t continue to grow exponentially once competition sets in. We need to modify our equation.

We realize that the intrinsic growth rate ‘r’ is not a constant. In fact, it is a function of the population number. We can approximate this function as:




This is known as the logistic growth equation. The constant ‘K’ appearing in this equation is known as the Carrying Capacity.

The following graph shows how ‘r’ varies with the population number.



The population growth curve should now look like this.



Good news for us, our E.coli graphs look very much similar to this one.

We found that the carrying capacity of E.coli was higher in the broth with lower salt concentrations. This is, perhaps, because the possibility of bacterial death via exosmosis is higher in environments with high salt concentration.