Subcellular Systems - Molecular Theory of the Living Cell - page 333

In view of the importance of the concept of the conformon in interpreting
single-molecule data of Lu et al. (1998) to be presented in Sect. 11.3.3 , the step-
by-step derivation of the conformon equation , Eq. 11.19 , is thought to be important
enough to be reproduced below from Ji (1990, pp. 197-200) (replacing the original
figure numbers with the corresponding ones from this chapter and adding a
new table):
To estimate the information content of conformons, it is necessary to postulate a commu-
nication system that links the source of message to the receiver through a channel (Pierce
1980). The communication system of our interest is schematically shown Fig. 11.22 , and
the various components of the systems are identified in Table 11.8 .
To calculate the Hartely information content of any message, it is necessary to know the
number of all possible messages (W 0 ) and the number of messages actually selected (W).
Then the average information content (I) of a message is given by

I ¼ log 2 ð W 0 = W) ð 1 Þ

Equation ( 1 ) can be derived from Shannon's formula (Pierce 1980) by assuming that all
messages have equal probability of selection. I is maximum when W ¼ 1;

I ¼ log 2 W 0 ð 2 Þ

Applying Eq. ( 2 ) to Step 1 in Fig. 11.22 , it is clear that the maximum information
content of the primary message (I p )is

log 2 m n I p ¼ ð 3 Þ

where m the number of amino acid residues

constituting an enzyme. We assume that all of the information contained in the primary message,
I p , is transduced into the information content of conformons, each conformon consisting of an
alignment of x amino acid residues (out of n) into a transient (i.e., kinetically labile and metastable)
structure at the active site of an enzyme (see Step 2). The maximum information content of one
conformon can then be estimated on the basis of two further assumptions: (1) all conformons are
unique (i.e., no degeneracy) and (2) the maximum number of conformons consisting of x amino
acid residues out of a polypeptide chain of n amino acid residues can be calculated as

¼ the number of different amino acids and n ¼

W 0 ¼ n != n ð Þ!

ð 4 Þ

Inserting Eq. ( 4 ) into Eq. ( 2 ) leads to the maximum information content of one
conformon:

I conformon ¼ log 2 n ½ != ð Þ! n x ð 5 Þ

If all the primary information is transduced into p conformons, we have

I p ¼ p I conformon
¼ p log 2 n ½ !=ð n x Þ! ð 6 Þ

From Eqs. ( 3 ) and ( 6 ), one obtains

p

m n

½ n != ð Þ! n x ¼ ð 7 Þ