Question

Suppose that a mutation occurs in about 1 out of every 1 million bacterial cells, and suppose that you have a bacterial colony in a bottle like that described in cosmic Calculations 6.1 (in which the bacteria divide each minute). Given the number of bacteria in the bottle after 1 hour, approximately how many bacteria would have some type of mutation? What does this tell you about why bacteria often evolve resistance to new drugs?

Short answer

About \( 1.15 \times 10^{12} \) bacteria may mutate, facilitating drug resistance evolution.

Step-by-step solution

Understand the Growth of Bacteria

The bacteria in the bottle double in number every minute. After 1 hour (which is 60 minutes), the initial number of bacteria will have doubled 60 times.

Calculate the Number of Bacteria after 60 Minutes

If we let the initial number of bacteria be denoted by \( N_0 \), after 60 minutes, the number of bacteria will be \( N_0 \times 2^{60} \). However, for these problems, it's common to assume an initial number like 1 bacteria, so the calculation becomes \( 2^{60} \).

Calculate the Number of Mutant Bacteria

A mutation occurs in 1 out of every 1 million bacteria. Therefore, the number of bacteria with a mutation can be estimated by multiplying the total number by the mutation rate: \( \frac{2^{60}}{10^6} \).

Estimate the Value

Calculate \( 2^{60} \), which is approximately \( 1.15 \times 10^{18} \), and then divide by \( 10^6 \) to get \( 1.15 \times 10^{12} \) mutant bacteria.

Interpret the Result

Given approximately \( 1.15 \times 10^{12} \) mutant bacteria after 1 hour, this shows why bacteria can quickly evolve resistance to drugs: the vast number of mutations provide many opportunities for drug-resistant strains to appear.

Key concepts

Bacterial Growth

Bacterial growth refers to the process by which bacteria multiply and increase in number. This usually occurs through binary fission, a process where a single bacterial cell divides into two identical daughter cells. Each of these cells can continue to divide as well, leading to exponential growth. This growth pattern can be summarized as:

• Doubling the number of bacteria at regular intervals
• Under ideal conditions, growth is limited by factors like nutrient availability and space

In the context of the exercise, the bacteria in the bottle double every minute, resulting in a massive increase in their population over a short period. After just one hour (60 minutes), the number of bacteria effectively doubles 60 times, which is a staggering growth, producing up to \(2^{60}\) bacteria from a single initial bacterium.

Mutation Rates

The concept of mutation rates is crucial in understanding genetic variability in bacterial populations. Mutations are random changes in the DNA sequence and occur at a predictable rate. In many bacteria, mutations happen roughly in 1 out of every 1 million cells.This low probability might seem insignificant, but given the large population sizes that bacteria can reach, even a small mutation rate results in many mutated individuals. Considering the large number of bacteria after one hour in our exercise, this leads to a significant number of bacteria with mutations:

• Total number of bacterial cells potentially having mutations is \( \frac{2^{60}}{10^6} \)
• This results in approximately \(1.15 \times 10^{12}\) mutated bacteria in just 60 minutes

Drug Resistance

Drug resistance in bacteria arises when some bacteria survive the effects of a drug, often due to a genetic mutation, and continue to grow and multiply. This can happen quite rapidly in bacterial populations because of their high mutation rates and rapid growth.

• Mutations may lead to changes that confer survival advantages
• Specifically, some mutations may allow bacteria to neutralize or resist the drug's effects

In the scenario of our exercise, the large number of mutations occurring due to rapid bacterial growth provides numerous opportunities for drug-resistant strains to evolve, explaining why antibiotic resistance is a significant public health concern.

Evolution of Bacteria

The evolution of bacteria is a result of mutations accumulated over time. These genetic changes can lead to adaptations that increase the fitness of bacteria in their environments. The process generally involves:

• Variation from mutations providing a potential for new traits
• Natural selection acting on beneficial mutations to enhance survival and reproduction
• Genetic drift, where random changes also affect which traits become common

Given the rapid reproduction and vast numbers of bacteria, the rate of evolutionary change can be much faster than in organisms with slower reproduction rates. In just a short time, as in our exercise example, bacteria can develop significant resistance to drugs by evolving through many cycles of selection for resistant traits. This understanding of bacterial evolution is critical in managing the spread of drug-resistant bacteria.