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              Protein Structure                                                                           217

              protein stability, the overall stability of multimeric assem-  the protein subunits that serve to alter the position of the
              bliesisproportionaltothehydrophobicsurfaceareaburied  polypeptide chains or cofactors within the regions respon-
              within the interface.                             sible  for  ligand  binding  or  catalytic  activity.  Allosteric
                A large number of enzymes exist as symmetric macro-  effectors serve to either inhibit or enhance these confor-
              molecular assemblies where they commonly exhibit C and  mational changes. Thus in all cases the active site residues
              D point group symmetries and contain two-, three-, four-,  are influenced either directly or indirectly by the protein–
              and six-fold axes of symmetry. In the simplest cases this  protein interactions between subunits. Typically a rotation
                                                                               ◦
              feature provides additional thermodynamic stability for  of subunits of 5–15 is sufficient to accomplish allosteric
              a protein that would otherwise be rather small. In more  control.
              complex arrangements the protein–protein interfaces form
              the active site such that the oligomerization is required
                                                                B.  Viruses
              for function. Finally, in the most highly evolved enzymes
              there is communication between the active sites that re-  Viruses  represent  particularly  evolved  forms  of  macro-
              side on symmetrically related subunits. This provides the  molecular assemblies. Mature virions are encoded by a
              foundation for enzyme regulation as observed in most al-  protective coat that is formed in part by virally encoded
              losteric enzymes.                                 proteins. Viruses come in many shapes and sizes, but they
                                                                all  share  the  property  of  using  multiple  copies  of  coat
                                                                proteins to protect their genomic material. In many cases
              A.  Allosteric Enzymes
                                                                the proteins assemble to form a symmetric shell, where
              The simplest model for allosteric control was set forward  the symmetries are either helical as found in tobacco mo-
              by Monod, Changeux, and Jacob in 1963 and provided  saic virus or icosahedral as seen in the spherical viruses.
              the basis for understanding feedback inhibition and co-  The  use  of  multiple  copies  of  a  protein  to  form  a  vi-
              operative binding of ligands by proteins. In their model  ral coat is enormously efficient from a genomic point of
              it was assumed that an allosteric enzyme (or protein) ex-  view; however, it introduces several interesting structural
              ists in equilibrium between two symmetric states; inactive  problems.
              and active (T and R states). The transition between these  Allsimplesphericalvirusesexhibiticosahedralsymme-
              states was assumed to be concerted, that is the symme-  try. This implies that the surface contains 60 equivalent po-
              try of the macromolecular assembly is conserved. Fur-  sitions or that the shell is built from 60 equivalent protein
              thermore the active state has a greater affinity for sub-  subunits. Although this is observed for a few very small
              strate than the inactive state. From these considerations  virus particles, most contain many more than 60 subunits.
              the activity of the enzyme depends on the position of the  For example the viral shell of most small plant viruses con-
              equilibrium between the inactive and active states. Thus  tains 180 identical protein subunits. This poses a problem
              increasing the substrate concentration drives the equilib-  of how to arrange 180 subunits on the surface of an icosa-
              rium to the active form and gives rise to a sigmoidal re-  hedral  shell  since  the  subunits  cannot  experience  sym-
              lationship between the initial velocity of the reaction and  metrically equivalent environments. Fifty years ago it was
              the substrate concentration. As importantly the position  proposed by Caspar and Klug that viral subunits would be
              of the equilibrium can be altered by allosteric effectors  arranged on a hexagonal surface lattice with quasiequiva-
              that  preferentially  bind  to  either  the  inactive  or  active  lent symmetry where the contacts between subunits would
              state.  This  is  the  basis  of  feedback  inhibition  whereby  be organized to minimize their differences in assembly.
              the  product  of  a  biosynthetic  pathway  inhibits  the  en-  That is, if a virus contains 180 subunits on its surface,
              zyme that catalyzes the first committed step. This sim-  these would be grouped into three sets of 60 subunits
              ple model explains many of the properties of allosteric  where each group would experience similar interactions
              enzymes; however, a more complex model based on se-  compared to the other groups. At first sight this hypoth-
              quential binding of substrates to yield multiple conforma-  esis accounts for the structure of simple viruses where it
              tion states is required to explain the finer details of many  has been shown that most of the interactions between the
              enzymes.                                          protomers on the surface are essentially identical; how-
                The structural basis of allostery has been well devel-  ever, closer examination of the virus structures that have
              oped through the study of enzymes such as aspartate tran-  been determined reveals that in all cases the groups of
              scarbamoylase and phosphofructokinase. In all enzymes  protomers behave as though they are different proteins by
              studied  thus  far  several  common  themes  have  evolved.  utilizing their domains in different ways to accommodate
              First the overall symmetry of the inactive and active states  their structurally unique environments (Fig. 18). Thus, it
              appear  to  be  conserved.  Second  the  transition  between  would appear that the main requirement for a virus coat
              these states involves a change in the relationship between  protein is to have a shape and conformational flexibility to
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