91Ó°ÊÓ

A flask of nutrient broth, buffered to maintain pH, is inoculated with a strain of E. coli. The flask is placed in a constant temperature environment where it is aerated by shaking. A. Predict the effect of a change in energy availability over time. B. Represent the change graphically in terms of the number of cells as a function of time. C. In your graph as time progresses there is a change in the growth rate of the population. Add annotation to your graph to describe the time interval during which the growth rate is increasing linearly in proportion to the number of cells. Add annotation to your graph to describe another time interval during which the growth rate is decreasing in proportion to the square of the number of cells. Add a third annotation to describe an interval of time where the rate of growth is zero. D. Select and justify two measurements of the E. coli population that could be made at two different points in time during growth that would be sufficient to answer questions about the population size at any time. E. Describe the population of E. coli if the environment was continuously supplement by additional nutrient broth.

Step by step solution

01

Predicting Effect of Energy Availability

Over time, the availability of energy sources (nutrients) will initially support rapid growth of the E. coli population. As nutrient levels decline, energy availability will diminish, leading to slower growth, and eventually, growth will cease when energy sources are exhausted.

02

Graph of Cell Number vs. Time

Draw a graph where the x-axis represents time and the y-axis represents the number of cells. The initial phase should show an exponential increase in the number of cells, then a slowing growth rate, followed by a plateau where growth stops.

03

Annotating Graph - Linear Growth Phase

Annotate the initial phase of the graph as the 'exponential phase' where the growth rate is increasing linearly with the number of cells.

04

Annotating Graph - Decelerating Growth Phase

Annotate the mid-phase of the graph ('decay phase') where the growth rate begins to decrease in proportion to the square of the number of cells, due to the depletion of nutrients.

05

Annotating Graph - Zero Growth Phase

Annotate the final phase ('stationary phase') where the growth rate is zero, indicating that the number of cells remains constant due to lack of available nutrients.

06

Selecting Measurements for Population Size

select two measurements such as optical density (OD) and colony-forming units (CFU) at different time points. These measurements provide data on population size, which can be used to model growth trends.

07

Population with Continuous Nutrient Addition

Describe that with continuous nutrient replenishment, the E. coli population would continuously grow, potentially reaching a new steady state where the rate of nutrient addition matches the rate of consumption.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Nutrient Broth

Nutrient broth is a liquid medium used to grow bacteria like E. coli. It contains essential nutrients to support bacterial growth. Key components include:

• Proteins and peptides: Serve as nitrogen sources.
• Carbohydrates: Provide energy.
• Minerals: Essential for enzyme function and cellular processes.

Buffering agents help maintain a stable pH, ensuring optimal growing conditions. In an experiment, maintaining a constant temperature and aerating the broth also aid in consistent bacterial growth.

Exponential Growth Phase

During the exponential growth phase, bacteria rapidly multiply. Each bacterial cell divides into two, leading to exponential increase in population size, expressed mathematically as:
\ N(t) = N_0 e^{\text(kt)} \
where \(N(t)\) is the population size at time \(t\), \(N_0\) is the initial population size, and \(k\) is the growth rate constant. Initially, nutrient availability is high, supporting rapid growth. However, this phase cannot last indefinitely due to nutrient depletion and waste accumulation.

Growth Rate

Growth rate is a measure of how quickly the E. coli population increases. It can be quantified during the exponential phase using the following relationship:
\ \text(growth rate) = \frac{dN}{dt} = kN \
Here, \(\frac{dN}{dt}\) is the rate of change in population, \(N\) is the number of cells, and \(k\) is the growth rate constant. Factors that influence growth rate include:

• Availability of nutrients
• Temperature
• pH levels
• Oxygen supply

Managing these factors can optimize the growth rate in laboratory settings.

Stationary Phase

The stationary phase occurs when the growth rate equals the death rate, resulting in a stable population size. This phase is marked by:

• Depletion of nutrients
• Accumulation of waste products
• Limited space for expansion

Cells adapt to survive under stress conditions, often entering a dormant state. This phase can show little to no visible growth in cell numbers but is crucial for understanding bacterial survival mechanisms in adverse conditions.

Optical Density

Optical Density (OD) measures the turbidity or cloudiness of a bacterial culture. It's a quick and non-destructive method to estimate cell concentration. An OD reading is obtained using a spectrophotometer, which measures how much light is absorbed by the culture:

• OD measured at 600 nm is common for E. coli.
• Higher OD values indicate higher cell concentrations.

However, OD measurements must be calibrated to correlate with colony-forming units (CFU) for accurate population size estimation.

Colony-Forming Units

Colony-forming units (CFU) represent the number of viable bacteria in a sample. CFUs are determined through a plating method, where a diluted sample is spread on an agar plate and incubated:

• Each colony represents a single bacterial cell or a group of cells.
• CFU counts are expressed as CFU/mL.

This method provides a direct and reliable measure of the number of living cells in the culture, essential for validating OD readings and assessing bacterial growth under different conditions.