7.4 Evolution and Entropy

Before we look at the entropy cost of a string of DNA or its protein we need to make an important observation about our accounting of logical improbability. When we examine the 3 dice in the box the macrostate {123} without order has 6 microstates by noting the identity of individual dice. The Boltzman-Gibbs thermodynamic probability 'W' also uses the identification of each particle in a system to account for all possible microstates. That is why W is such a huge number for any real system (ie for each macrostate every particle is swapped with every other particle creating a massive logical phase space). Effectively the value of 'W' for the {123} macrostate is 6 whereas for {666} it is just 1. But now if order is significant the macrostate {123} has like {666} only one microstate and hence the least possible probability and the smallest 'W'. Just one of a total 216 possibilities in this very simple case.

Now every string of codes being semantic information has three essential properties: They are

1. Non repeating
2. Non random
3. Ordered

Notwithstanding the fact that number 2 would appear to preclude any random process from assembling semantic information what we are really interested in is number 3. DNA being semantic information is ordered. Which means any meaningful string of DNA (such as codes for a specific protein) has the maximum improbability possible for any string of the same length (W = 1). Which means a string of DNA represents one out of the total logical phase space available when we identify each particle or in this case nucleic acid base. Allowing for redundancy in the human genome we may conservatively speak about a billion or 10^9 uniquely identified bases in the human genome!

Remembering that an increase in improbability is also a decrease in entropy we may now do some entropy accounting. We recall there are just 4 nucleic acid bases making up the alphabet of DNA, {A, T, C, G}. These molecules are also handed but in life only the R Form (right handed) is used even though roughly speaking both are equally likely and chemically equivalent. So just like our 3 dice a string of 3 DNA bases has a total number of possibilities or microstates of 4^3 x 2^3 = 8^3 = 512. Three DNA bases is called a codon and happens to code for one amino acid in a protein and being ordered it is a macrostate with only one microstate and an improbability of 512.

The calculation of the improbability (negative entropy) of any protein is now straight forward but some would ask, is it really improbable?

Have a cracking day..