ISIC-8 Relationship between Host Framework Isomerization and Packing Coefficient in Bile Acid Inclusion Crystals K. Kato, K. Sada and M. Miyata Department of Material and Life Science, Graduate School of Engineering, Osaka University 2-1 Yamadaoka, Suita, 565-0871 Osaka, Japan

    Bile acids are known to form inclusion crystals with various organic compounds. Their crystal structures indicate that the acid molecules arrange in various ways to yield guest-dependent frameworks. These isomerizations enable bile acids to serve as host compounds which is applicable to a wide variety of guest in shape and size. Thus, most of bile acids show quite complicated polymorphisms. In order to understand the polymorphisms, recently we proposed one useful parameter: Packing coefficient of the host cavity (PCcavity)[1], which is the volume ratio of the guest compound to the host cavity. PCcavity is a good parameter to estimate the isomerization of host framework. Moreover, we indicated that PCcavity is not dependent on the host compounds and the host frameworks. Here we show the applications of PCcavity in several bile acids.
    Cholic acid, one of the most famous bile acid, forms inclusion crystals with various guests in size. We already determined many inclusion crystal structures with aromatic compounds. Cholic acid forms the four host frameworks as shown in Figure 1. The volumes of aromatic guests relate to the isomerizations of host frameworks. Figure 2 shows the relationships between the guest volume and PCcavity. It can be seen that the values of PCcavity are statistically distributed in the range of 55-70%. The small guests tend to be included in the a-gauche framework while the larger one be included in the b-trans framework. When the volume of guest reaches 120Å3 and the PCcavity up to 70%, host framework change from a-gauche to b-trans. Moreover, when the volume of guest reaches 140Å3, host-guest ratio change from 1:1 to 2:1 with the isomerization of host framework from b-trans to a-trans. As mentioned above, each host frameworks of cholic acid isomerize when the PCcavitygoes up to over upper limit (70%). These predictable isomerizations are based on PCcavity.
    Another bile acids follow the isomerization rule. Norcholic acid, which have one methylene group shorter side chain than cholic acid, also form various host frameworks. Similarly the other norbile acids show guest-dependent polymorphisms. We illustrate here the most complicated polymorphism of norbile acid. Nordeoxycholic acid (NDCA) form seven guest-dependent host frameworks (H, M1, M2, T1,T2, B1 and B2) (Figure 3). The guest-dependent polymorphism of NDCA is seemingly incomprehensible phenomenone. However, these host frameworks are classified by hydrogen bonding modes and guest volumes.
    Four hydrogen bonding modes, H, M, T and B type, are observed in seven host frameworks. H type is observed only with methanol, because the cavity of H framework is very small. M type hydrogen bonding is formed by all the oxygene of NDCA and the guests. Alcohols have hydrogen donor and acceptor in hydroxyl group together to be included in M framework. In T type hydrogen bonding, oxygen at 12th position of NDCA captures the oxygen of guest. So, ketones and nitriles are include in T type framework. On the other hand, B type hydrogen bonding is formed by oxygens of only NDCA. Because of no limitation of functional group of guest, various compounds, aromatics, ethers, esters etc., are included.
    Moreover, M, T and B types form two host frameworks in each case (M1and M2, T1and T2, B1 and B2). These two different frameworks are used properly according to the volume of guests. Figure 4 shows the relationships between the guest volume and PCcavity. M1, T1and B1 frameworks include relatively small guests. When these values of PCcavity reach over the upper limit, these frameworks isomerize to M2, T2and B2 frameworks, respectively. Isomerizations of NDCA host frameworks also occur near the PCcavity upper limit.
    As described above, host framework isomerizations are observed when PCcavity reach the upper limit, regardless of host molecles and frameworks. PCcavity should be one of the most useful parameters for designing inclusion crystals and predicting isomerizations of host frameworks.

[1] K. Nakano, K. Sada, Y. Kurozumi and M. Miyata, Chem. Eur. J. 2001, 1, 209