Abusing Thermodynamics: Charles B. Thaxton

A great example of abusing thermodynamics can be seen in the book The Mystery of Life's Origin, by Charles B. Thaxton, Walter L. Bradley and Roger L. Olsen. Chapter 8 is available on-line here.

This chapter was written by Thaxton, who has a Ph.D. in physical chemistry, so really should know better. He considers the entropy when polypeptides form. A polypeptide is a sequence of amino acids, and he compares a random sequence with five each of the twenty biologically active amino acids to a specific sequence:

For a random polypeptide of 100 amino acids, the configurational entropy, Scr, may be calculated using eq. 8-2c and eq. 8-7 as follows:

Scr = k lncr

since cr = N! / n1!n2!...n20! = 100! / 5!5!....5! = 100! / (5!)20

= 1.28 x 10¹¹⁵ (8-8)

The calculation of equation 8-8 assumes that an equal number of each type of amino acid, namely 5, are contained in the polypeptide. Since k, or Boltzmann's constant, equals 1.38 x 10^-16 erg/deg, and ln [1.28 x 10¹¹⁵] = 265,

Scr = 1.38 x 10^-16 x 265 = 3.66 x 10^-14 erg/deg-polypeptide

If only one specific sequence of amino acids could give the proper function, then the configurational entropy for the protein or specified, aperiodic polypeptide would be given by

Scm = k lncm
= k ln 1
= 0
(8-9)

But wait... How does the polypeptide know? On the left hand we have a random polypeptide and in the right a specified one. But there is nothing special about the second one. If I pass them both to you, you cannot tell which is the specified one by doing any sort of experiment. Thermodynamically, they are the same (indeed, they may even be the same sequence).

The entropy in both sequences is the same, so clearly Thaxton has got it wrong.

In fact, calculating configuational entropy is far more complex than this, and as this article states, there is no proper way to do it yet.