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How is growth rate an indicator of carbohydrate use? How do absorbance readings from a spectrophotometer show growth of bacteria if the absorbance readings are taken several times over the course of a day [and plotted on a graph]? If the second absorbance reading of a sample with bacteria and particular substrate is lower than its initial absorbance reading is there less bacteria present or more? Do the presence of substrates affect the absorbance reading in other words do carbohydrates have any turbidity?

context if needed - experiment determines if a species tested in the presence of a carbohydrate and combination of carbohydrates is able to use each as its sole carbon& energy source and if any are used preferentially to others

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How is growth rate an indicator of carbohydrate use?

Since carbohydrates are here the only carbon and energy source available, its assimilation is necessarly correlated to biomass production. The relation is most likely to be linear. Now, growth rate can be seen as the biomass production speed. So the fastest is carbohydrate use, the highest is the growth rate.

How do absorbance readings from a spectrophotometer show growth of bacteria if the absorbance readings are taken several times over the course of a day [and plotted on a graph]?

This is explained by the Beer-Lambert law. Simply put: the absorbance of an entity is proportionnal to its concentration - all else being equal. So, the more your bacterial population grows, the highest becomes its absorbance.

If you find a lower absorbance value at time $t+1$ in comparison to time $t$, yes it could mean that the bacterial cell number at time $t+1$ is lower than at time $t$. However, we know neither the protocole you have been following, nor the values you have been obtaining, so there could be other explanations, such as error of measurment.

Do the presence of substrates affect the absorbance reading in other words do carbohydrates have any turbidity?

Yes, molecules in the medium can impact your Optical Density (OD) values. However, that would only be true if these molecules absorb light at the wavelength you are using to measure absorbance (eg $600$ nm). This is why you should always blank with some filtered medium (or at least with some fresh medium).

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Turbidity (measured as absorbance) is direct indicator of numerical density of microbes in culture. The more microbe-cells: the more light is diffuse-reflected and scattered in the path of light; so the less amount light reach the photo-sensor given at colorimeter/ photometer.

Now; if with time the turbidity goes up; then it means with time the number of cell increasing.

Growth rate is an indicator of nutrient use. If certain nutrient is difficult to metabolize for that bacteria; the growth rate would decrease. So turbidity will not increase in that rate. Visit wikipedia that says

"The preferred sugar is consumed first, which leads to rapid growth, followed by a lag phase. During the lag phase the cellular machinery used to metabolize the second sugar is activated and subsequently the second sugar is metabolized."

Monod's original results on Diauxie. Time in hours is plotted on the horizontal axis. Optical density (equivalent to cell concentration) is plotted on the vertical axis.

(graphs from wikipedia)

Reference: Wikipedia.

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