Question

Suppose that \(E .\) coli synthesizes DNA at a rate of 100,000 nucleotides per minute and takes 40 minutes to replicate its chromo- some. (a) How many base pairs are present in the entire \(E .\) coli chromosome? (b) What is the physical length of the chromosome in its helical configuration-that is, what is the circumference of the chromosome if it were opened into a circle?

Short answer

(b) What is the physical length of the E. coli chromosome in its helical configuration (considering the circumference of the chromosome if opened into a circle)? Calculations: Step 1: Calculate the total number of nucleotides synthesized Total nucleotides synthesized = synthesis rate × replication time Total nucleotides synthesized = 100,000 nucleotides/min × 40 min Total nucleotides synthesized = 4,000,000 nucleotides Step 2: Calculate the total number of base pairs Total base pairs = total nucleotides synthesized Total base pairs = 4,000,000 base pairs Answer (a): The total number of base pairs in the entire E. coli chromosome is 4,000,000 base pairs. Step 3: Calculate the physical length of the chromosome (circumference) Number of turns = total base pairs / base pairs per turn Number of turns = 4,000,000 base pairs / 10.5 base pairs per turn Number of turns ≈ 380,952 turns Length of helix = number of turns × length of one turn Length of helix = 380,952 turns × 3.4 nm/turn Length of helix ≈ 1,295,237 nm Circumference of the chromosome = length of helix Circumference of the chromosome ≈ 1,295,237 nm Answer (b): The physical length of the E. coli chromosome in its helical configuration is approximately 1,295,237 nm (nanometers).

Step-by-step solution

Calculate the total number of nucleotides synthesized

To find the total number of nucleotides synthesized, multiply the synthesis rate (100,000 nucleotides per minute) by the time it takes to replicate the chromosome (40 minutes): Total nucleotides synthesized = synthesis rate × replication time

Calculate the total number of base pairs

Since there is one base pair per nucleotide, the total number of base pairs is equal to the total number of nucleotides synthesized: Total base pairs = total nucleotides synthesized

Calculate the physical length of the chromosome (circumference)

To find the physical length of the chromosome, first we need to know how many base pairs there are per turn of the helix. In the B-DNA form, which is the most common form of DNA, there are 10.5 base pairs per turn of the helix. Each turn of the helix has a length of 3.4 nm (nanometers). Thus, we can find out the number of turns in the helix and then calculate the circumference. First, find the number of turns in the helix: Number of turns = total base pairs / base pairs per turn Next, find the total length of the helix: Length of helix = number of turns × length of one turn Finally, since the helix has a cylindrical shape, the circumference is equal to the length of the helix: Circumference of the chromosome = length of helix Now, let's perform the calculations.

Key concepts

Nucleotides Synthesis Rate

To understand the concept of nucleotides synthesis rate, it's essential to grasp what nucleotides are. They are the basic building blocks of DNA and RNA, composed of a sugar, a phosphate group, and a nitrogenous base. In bacteria like E. coli, DNA replication is a carefully orchestrated process where enzymes synthesize new strands of DNA at remarkable speeds. For our bacteria in question, the rate is stated to be 100,000 nucleotides per minute. Imagine this as a miniature construction site, where the workers (enzymes) are adding 100,000 tiny bricks (nucleotides) to a growing structure (DNA strand) every single minute. This rate is not just a random number; it is a reflection of the efficiency and adaptability of the bacterial cell to replicate its genetic material swiftly, ensuring quick cell division and reproduction.

In context, if the speed of nucleotides addition were a car's speed and the DNA strand a road, the enzyme machinery in E. coli would be covering 100,000 units of road length each minute, an impressive feat considering the intricate nature of the task.

Chromosome Replication Time

The chromosome replication time relates to how long it takes for an organism to duplicate its entire set of DNA. For E. coli, the process takes approximately 40 minutes. This is a very short timeframe, especially when comparing it to human DNA replication, which can take several hours. During these 40 minutes, E. coli must ensure that its single chromosome—a circular DNA molecule—is accurately copied once and only once. It's akin to a timed photography session, capturing every detail precisely within a predetermined span. This quick replication ensures rapid growth and division, which is a hallmark of bacterial survival and proliferation. When we think about this process, it's not only the speed but also the precision that's noteworthy; any errors could result in faulty genetic information being passed on to the next generation.

Base Pairs Calculation

Understanding how to perform base pairs calculation is like doing the math to determine the length of a story told in a genetic alphabet. With the information that E. coli synthesizes DNA at a rate of 100,000 nucleotides per minute and completes its replication in 40 minutes, we can calculate the total number of base pairs. Since each nucleotide corresponds to one base pair, we simply multiply the two figures: 100,000 nucleotides/minute × 40 minutes, yielding a total of 4,000,000 base pairs. This calculation gives us the size of the entire E. coli chromosome—a sizable novel of life's instructions meticulously encoded in a microscopic space.

Physical Length of DNA

To illustrate the physical length of DNA, we can think of a long thread tightly coiled up into a compact form. For the E. coli chromosome, when we say 'physical length', we refer to the actual distance covered by this biological thread. Since we have already calculated the total number of base pairs, we can use the known values for B-DNA to estimate the physical length. DNA coils into a helical structure with 10.5 base pairs per turn, and each turn spans about 3.4 nm. Multiplying the number of turns by the length per turn gives the entire length of the helix. Converting this length into more tangible units like micrometers or millimeters allows us to better visualize this nearly invisible entity. This physical length is crucial for understanding how such a large amount of genetic information packs into such small cellular spaces.

DNA Helical Structure

Lastly, let's delve into the mesmerizing world of the DNA helical structure. DNA is not just a random string of molecules; it's a precisely coiled masterpiece that takes the shape of a double helix. The staircases of this spiral are the base pairs, and it takes about 10.5 of these steps to make a complete turn in the helix. Each base pair is linked like the rungs of a ladder, with complementary nitrogenous bases bonding together. The beauty of this structure is not just visual but functional; the helical nature of DNA allows for incredible compactness while still being able to unzip for processes like replication and transcription. The helix can be likened to a coiled spring or zipped up for safety and stretched out to access the genetic information it holds. This architecture is crucial for fitting lengthy DNA molecules into tiny cellular spaces and is an amazing example of nature's ingenuity in design and efficiency.