New trends in physics teaching, v.4; The ... - unesdoc - Unesco

Entropy and Information
the starting point of a new copying process. In this process, an identical copy of the original
molecule results.
In order to preserve the genetic information it is essential that errors in copying are duly
avoided. There is a limit,however, to the fidelity of the copying process due to the thermal
motion of the molecules. Therefore there wil be a corresponding limit in the maximal length
of the molecule that can be duplicated essentially free of errors. For molecules longer than this
limit,the probability for the occurrence of copying errors wil be overwhelming. In order to
calculate this critical length we repeat the considerations of the previous section. The vacancy
in a crystal corresponds here to a copying error. Since no hydrogen bonds wil be formed in this
case, an energy increase E wil result. Energy and entropy again fight for the privilege to minimize
the free energy. If the RNA-molecule consists of N = 2" bases, we obtain for the free energy
of a copy containing zero or one error:
The critical length of the molecule is given by F1 = 0, i.e. by E = 0.7 y1 k T. The corresponding
length of the molecule is thus
N= 2" = 2 (elO.7 kT).
(Eq. 18)
Since the energy of a hydrogen bond is roughly 0.1 eV, we have E 0.2 eV or 0.3 eV. From
this we obtain N x 214 lo4. Since the critical length depends exponentially on E an exact
estimate is rather difficult.
Our result shows that the transfer-RNA which contains about seventy base pairs and is likely
to be one of the oldest information carrying molecules, could reduplicate without difficulty in
an error-free way during the initial phases of the evolution. In contrast to this, the DNA-molecules
of microbes, containing 1 O6 base pairs each, can reduplicate in an accurate manner only with the
help of enzymes.
CONCLUSION
The preceding examples have shown that numerous interesting properties of thermodynamic
systems can be described without the help of complicated mathematical methods by using the
information theory approach to thermodynamics outlined above. All examples considered here
are based on a single equation which is used in various versions and interpretations, i.e. the free
energy of a system consisting of 2" pieces. Without difficulty, the number of examples considered
here can be increased and problems such as adiabatic demagnetization, the entropy of thermal
radiation etc. can be considered. In many of these problems, a quantitative calculation will not
be needed and a qualitative insight into the behaviour of the system, based on the information
theory approach to thermodynamics, can be of great pedagogical value.
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