Problem 8 - Campbell Biology

Question

SCENTIFIC INQUIRY When bacteria infect an animal, the number of bacteria in the body increases in an exponential fashion (graph A). After infection by a virulent animal virus with a lytic replicative cycle, there is no evidence of infection for a while. Then the number of viruses rises suddenly and subsequently increases in a series of steps (graph B). Explain the difference in the curves.

Step-by-Step Solution

Answer

Bacterial growth is continuous and exponential, while viral growth has a latent phase, a sudden spike, and a stepwise increase due to the lytic cycle.

Step 1: Identify Graph A Pattern

Graph A represents the exponential growth of bacteria in an animal's body. The curve rises smoothly and continuously, illustrating how bacterial populations double over regular intervals.

Step 2: Understand Exponential Growth

Exponential growth means that the number of bacteria increases rapidly over time. Mathematically, this can be described by the function \( N(t) = N_0 \times e^{kt} \)where \( N(t) \) is the number of bacteria at time \( t \), \( N_0 \) is the initial number of bacteria, \( e \) is the base of the natural logarithm, and \( k \) is the growth rate constant.

Step 3: Identify Graph B Pattern

Graph B shows the viral infection process with three stages: a latent period, a sudden increase, and a stepwise increase in virus numbers. The initial flat region indicates no apparent infection, followed by a burst of viral particles, leading to the stepwise increase in virus count.

Step 4: Understand Viral Growth

Viral growth, particularly with a lytic cycle, involves a latent period where the virus is replicating inside host cells but not yet releasing new particles. Once replication is complete, viruses burst out of the host cells at once, causing a sudden spike in numbers. Continuing infection of new cells leads to the stepwise increase pattern observed.

Step 5: Compare and Contrast

Bacterial growth shows a smooth, exponential increase because bacteria continuously divide. In contrast, viral growth exhibits a delay (latent period), followed by a sudden spike due to the synchronized release of viral particles from host cells, and then a stepwise increase as new rounds of infection occur.

Key Concepts

Exponential Growth

Bacteria exhibit exponential growth when they infect an animal's body. This means that the bacterial population grows at a constant rate, doubling over regular intervals. For example, if you start with 2 bacteria, after one interval, there will be 4, and after another interval, there will be 8. This continuous multiplication leads to rapid increases in bacterial numbers.

Mathematically, this can be expressed as: \( N(t) = N_0 \times e^{kt} \)where:

• \( N(t) \): Number of bacteria at time \( t \)
• \( N_0 \): Initial number of bacteria
• \( e \): Base of the natural logarithm
• \( k \): Growth rate constant

This formula shows how the bacteria will grow exponentially over time.

Lytic Replicative Cycle

Viruses that follow the lytic cycle exhibit a different pattern from bacteria. The lytic cycle involves the virus infecting a host cell, taking over the cell's machinery to create new viral particles, and then bursting out of the cell.

Here are the key stages:

• The virus attaches to a host cell.
• It injects its genetic material into the cell.
• The viral DNA or RNA takes over, directing the host cell to produce viral components.
• New viral particles are assembled.
• The host cell bursts, releasing new viruses ready to infect other cells.

These steps result in a sudden increase in the number of viruses, followed by a stepwise increase as more host cells are infected and burst.

Viral Latent Period

The latent period is a phase during a viral infection when there is no apparent increase in virus numbers. This happens while the virus is inside the host cells, replicating its genetic material and constructing new viral particles.

During this period:

• The virus is not yet releasing new particles.
• There may be no signs of infection, making it hard to detect.
• Host cells are being used to produce new viruses.

Once the replication is complete, the latent period ends, and there is a sudden burst in virus numbers as host cells release the newly formed viral particles. This can cause the infection to spread rapidly across the host organism.

Bacterial Population Doubling

Bacterial population growth follows a predictable pattern called 'population doubling.' Each bacterium reproduces by binary fission, resulting in two daughter cells.

Here is how bacterial doubling works:

• One bacterium divides into two.
• Each new bacterium divides again, creating four.
• This process continues, doubling the population each time.

The time it takes for the bacteria to double their population is called the 'doubling time.' This time can vary depending on the type of bacteria and environmental conditions but can lead to large populations very quickly.

Host Cell Burst

During a lytic viral infection, the host cell burst is a critical phase. After the virus has hijacked the host cell's resources to produce new virus particles, the cell will eventually burst, releasing these particles.

This process is essential for viral proliferation and involves:

• The accumulation of new viruses inside the host cell.
• The host cell's membrane breaking down.
• Releasing a large number of virus particles at once.

The burst leads to a sudden increase in virus numbers, helping the infection to spread rapidly to new host cells. This can cause significant damage to the host organism, depending on the type of virus and the cells affected.