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While the improbable may occur given long enough, it is wise to calculate just how improbable the event is before we commit ourselves to the idea of its certainty in any given time.
The core of biology can be said to be information, which is coded into the DNA of living things in the form of genes. The genes determine the construction of proteins, and the proteins are the machines that build and regulate our bodies. In a sense the genes are like the blueprints for some man made machine, so where did this genetic information come from? Did it arise by chance in some primitive geological environment on earth billions of years ago?
DNA is a polymer made up of a selection of four different nucleotide monomers. A gene is a long stretch of DNA whose nucleotides are arranged into a specific code that can be translated by the cell into a protein. An example of an average sized protein is "permease", which as its name partly suggests makes the otherwise relatively impermeable cell able to allow the entry of glucose for use in metabolism. Permease is a polymer composed of 275 monomers called amino acids, which are arranged from a pool of 20 different types of amino acid in a specific order determined by the sequence of the DNA for the permease gene. What is the probability that this information could have arisen by chance?
We can answer this by first making a simple analogy with the game scrabble. Imagine what the probability is, after taking your turn and putting your hand into the bag of letters, of pulling out, in the correct order, all the letters you need to make up a specific 7 letter word. If we say that this is a special bag with equal numbers of all the letters and no blanks and also an unlimited supply of tiles (maybe like a richly concentrated primordial soup with billions of chemicals floating around ready for reacting together to make life) then if you were after say a "c" for the first letter the chance of getting it would be 1 in 26, and to get the second letter correct would also be 1 in 26.
The probability of both letters being correct and in order is thus:
1/26 x 1/26,
which can be represented in scientific notation as 1/262 (said one over twenty six to the power of 2); for the complete word we get 1/267, which may not look like too much but this represents
1 chance in 26 x 26 x 26 x 26 x 26 x26 x 26: that is 1 chance in 8,031,810,176 or 1 chance in just over 8 billion.
The earth is 4.5 billion years old, so please don't hold your breath waiting for the 7 letter word of your dreams to arrange itself on your scrabble board.
Now we can apply these simple rules of probability to the molecule of permease. At each position in the protein chain there is an alphabet of 20 amino acids to choose from, and so the probability of chance occurrence of this molecule is 1/20 x 1/20 and so on till we multiplied 1/20 by itself 275 times. In scientific notation we write 1/20275. This is clearly an improbable number, but we are used to thinking of probability over the very short timescales of our own lives: what about the timescale of the earth or even the universe?
The universe is estimated to be 15 billion years old, which can be written as 15x109 years. 1/20275 over this time scale means that if you took one turn at chemical scrabble each year it would take you 20275 years to have a probability of 1 of success.
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