The chromosomes in the nucleus of a cell contain all the information a cell needs to carry on its life processes. They are made up of a complex chemical (a nucleic acid) called deoxyribonucleic acid, or DNA for short. Scientist's decoding of the chemical structure of DNA has led to a simple conceptual understanding of genetic processes. DNA is the hereditary material of all cells. It is a double-stranded helical macromolecule consisting of nucleotide monomers with deoxyribose sugar and the nitrogenous bases adenine (A), cytosine (C), guanine (G), and thymine (T). In the chromosomes of a cell, DNA occurs as fine, spirally coiled threads that in turn coils around another, like a twisted ladder. The DNA molecule is threaded so fine that it is only possible to see it under high powerful electron microscopes.
On May 10, 2006 an article entitled "Unravel your DNA and it would stretch from here to the moon" appeared on the WNET-DT blog1. This post mentions that uncoiled DNA extracted from all cells in the human body measures something like $$3,85 \times 10^8\,\text{m}$$. But is this correct? To get a sense of exactly how long the uncoiled DNA molecules are, we first need to know a) the total number of base pairs per cell, b) the length of a single base pair, and c) the total number of cells in the human body.
The human genome is a concept that refers to the complete set of human genetic information stored within a single cell of the human body. Such a cell contains 46 chromosomes (22 autosome pairs + 2 sex chromosomes), containing about 3 billion base pairs (bp) of DNA in total. Below we quote some sources that give an estimate for the total length of a human genome.
reference | quote | length |
---|---|---|
N.A. Campbell, et al. Biology: Concepts & Connections2. California, 2009. | At actual size, a human cell's DNA totals about 3 meters in length. | $$3,0\,\text{m}$$ |
McGraw-Hill Encyclopedia of Science and Technology3. New York, McGraw Hill, 2012. | If stretched out, would form very thin thread, about 6 feet (2 meters) long. | $$2,0\,\text{m}$$ |
H.R. Matthews. DNA Structure Prerequisite Information. 1997. | The length is (length of 1 bp)(number of bp per cell) which is $$(0.34\,\text{nm})(6 \times 10^9)$$. | $$2,0\,\text{m}$$ |
A.L. Leltninger. Principles of Biochemistry. New York, Worth, 1975. | Chromosome 13 contains a DNA molecule about 3.2 cm long. | $$1,5\,\text{m}$$ |
The World Book Encyclopedia4. Chicago, World Book, 1999. | On the average, a single human chromosome consists of DNA molecule that is about 2 inches long. | $$2,3\,\text{m}$$ |
If we then know that the body of an adult contains some $$10^{13}$$ cells, we can calculate the total length of DNA in one adult human as \[(\underbrace{2 \times 3 \times 10^9}_{a})(\underbrace{0,34 \times 10^{-9}\,\text{m}}_{b})(\underbrace{10^{13}}_{c}) = 2,0 \times 10^{13}\,\text{m}\] That is the equivalent of nearly 70 trips from the earth to the sun and back. \[ \begin{eqnarray} 2,0 \times 10^{13}\,\text{m} & = & 136,37\,\text{AU} \\ \\ \frac{136,37}{2} & = & 68,18 \times \text{round trips to the Sun} \end{eqnarray} \]
The input contains the following three floating point numbers, each on a separate line:
estimate of the total number of base pairs per cell
estimate of the length of a single base pair, expressed in nanometer (nm)
estimate of the total number of cells in the human body
Compute the total length of all DNA in the human body from the estimates given in the input. This length must be printed three times, each time on a separate line:
length expressed in meter
length expressed in astronomical units ($$1\,\text{AU} = 149.597.870,691\,\text{kilometer}$$)
length expressed in number of round trips to the Sun
Input:
6e+9
0.34
1e+13
Output:
2.04e+13
136.365577302
68.1827886512