The System with Ligands

The grand PF of one polymer can be written directly by inspection of the various states of the polymer as depicted in Fig. 3.15. To save some writing, we use the shorthand notation 

Each term in (3.5.12) corresponds to one row in Fig. 3.15. The first term is simply (0), for the empty system. The second term corresponds to all of the 24 states with one ligand. There are eight configurations of the subunits, and for each of these we can place a ligand on three different sites. Similarly, we have 24 terms for the polymer with two ligands and eight terms for the fully occupied polymer. Altogether there are 64 terms. 

In this representation each term in the sum corresponds to one column in Fig. 3.15. 

In the following we shall use the shorthand notation for a polymer in a specific state of occupancy, regardless of the conformational states of the subunit  

Note that (1 0 0) refers to the state in which the first site is occupied (say the upper subunit in Fig. 3.15), the second subunit empty (say the left-hand subunit) and the third subunit also empty. In general, 2(1 0 0) would be different from 2(0 1 0) and from 2(0 0 1), but in our model the subunits are identical. Therefore we shall use only one of these to represent single occupancy. Similarly, for double occupancy we write 2(1 1 0). The PF in (3.5.12) is now written in a more compact form as 

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We shall first examine some aspects of the behavior of the empty system and then proceed to the study of the system with ligands. 

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