Question

DNA Comparisons A cell of the bacterium Escherichia coli has about \(4.2 \times 10^{6}\) base pairs of DNA, whereas each human cell has about \(3 \times 10^{9}\) base pairs of DNA. What percentage of the size of the human genome does the E. coli DNA represent?

Short answer

The E. coli DNA represents approximately 0.14% of the size of the human genome.

Step-by-step solution

Write down the given information

E. coli genome size: \(4.2 \times 10^{6}\) base pairs Human genome size: \(3 \times 10^{9}\) base pairs

Calculate the proportion of the E. coli genome to the human genome

To find the proportion, divide the size of the E. coli genome by the size of the human genome: \[\frac{E.\,coli\,genome\,size}{Human\,genome\,size} = \frac{4.2 \times 10^{6}}{3 \times 10^{9}}\]

Simplify the expression

Now, let's simplify the expression: \[\frac{4.2 \times 10^{6}}{3 \times 10^{9}} = \frac{4.2}{3} \times \frac{10^{6}}{10^{9}}\]

Perform the calculations

Calculate the quotient and the exponent subtraction: \[\frac{4.2}{3} \times \frac{10^{6}}{10^{9}} = 1.4 \times 10^{-3}\]

Convert the proportion to a percentage

To convert the proportion to a percentage, multiply the result by 100: \[1.4 \times 10^{-3} \times 100 = 0.14\%\] The E. coli DNA represents approximately 0.14% of the size of the human genome.

Key concepts

DNA Base Pairs

The fundamental unit of the double-stranded DNA molecule is the base pair, which is a pairing of nitrogenous bases — Adenine (A) with Thymine (T) and Cytosine (C) with Guanine (G). These pairs are the building blocks of genetic information, forming the rungs of the DNA 'ladder'.

With approximately 3 billion DNA base pairs in the human genome and 4.2 million in the E. coli genome, our understanding of the vast difference in genome sizes is paramount in genetics. Our focus on E. coli and human DNA serves to highlight the diversity in the genome sizes of living organisms. The significant difference in the number of base pairs between these two entities showcases the complexity and evolutionary characteristics of humans compared to smaller, simpler organisms like E. coli.

Proportion Calculation

Understanding proportions is essential in many scientific computations, such as comparing genome sizes. When we talk about proportions, we are looking at the relative size of one quantity to another. In our exercise, calculating the proportion involves dividing the genome size of E. coli by that of the human genome. This calculation gives us an insight into how large E. coli DNA is when measured against human DNA.

To put this into perspective using our example, if we imagine the human genome to be a vast library of information, the E. coli genome would represent just a single bookshelf within that library. Knowing how to calculate proportions helps us quantify such comparisons, making it easier to understand and communicate the scale of the differences.

Scientific Notation

Scientific notation is particularly useful in genetics, where numbers can be extremely large or small. This method of notation allows us to express these numbers in a compact, easy-to-understand form. For example, the number of base pairs in a human cell, which is 3 billion, can be expressed as \(3 \times 10^{9}\).

When we compare numbers in scientific notation, like the genome sizes of E. coli and humans, we simplify the calculation by aligning the powers of ten. In this specific exercise, we demonstrated how to divide numbers in scientific notation and then subtracted the exponents to determine the proportion in a more digestible format. Understanding scientific notation not only helps in making calculations feasible but also in appreciating the scale of genomic differences between organisms.