Isomorphous dimensions Replacement

As to the B/branched a-olefin copolymers, the degree of cocrystallization falls progressively with the size of the comonomer units. Apart from the B/3MB system, already discussed, in the B/4-methyl-pentene-l copolymers partial isomorphous replacement of monomer units in the two homopolymer crystal phases is observed, with lattice dimensions changes (Table 1). With 4,4 -dimethyl-pentene-l both homopolymer phases occur, physically separated, without lattice dimension changes. In each case, for high butene contents, the PB II phase is observed, i.e. the phase with larger CSA, which indicates that at least some degree of cocrystallization is always present. 

Isomorphous replacement in isotactic polyaldehydes was shown by A. Tanake, Y. Hozumi, K. Hatada, S. Endo, and R. Fujishige (42). These authors studied the binary polymer systems formed by acetaldehyde, propionaldehyde, n-butyraldehyde, iso-butyraldehyde and w-heptanal. All the copolymers are crystalline over the whole range of compositions. In the case of binary copolymers of acetaldehyde, propionaldehyde and K-butyraldehyde the unit cells have the same tetragonal space group UJa, with the same chain axis (4.8 A), while the dimensions of the a axis change continuously as a function of the copolymer composition. In the case of copolymers of isobutyraldehyde with other aldehydes, the continuous variation of the lattice constants a and c were observed. 

In 1954, Perutz introduced the isomorphous replacement method for determining phases. In this procedure a heavy metal, such as mercury or platinum, is introduced at one or more locations in the protein molecule. A favorite procedure is to use mercury derivatives that combine with SH groups. The resulting heavy metal-containing crystals must be isomorphous with the native, i.e., the molecules must be packed the same and the dimensions of the crystal lattice must be the same. However, the presence of the heavy metal alters the intensities of the spots in the diffraction pattern and from these changes in intensity the phases can be determined. Besides the solution to the phase problem, another development that was absolutely essential was the construction of large and fast computers. It would have been impossible for Perutz to determine the structure of hemoglobin in 1937, even if he had already known how to use heavy metals to determine phases. 

Several diffraction criteria define a promising heavy-atom derivative. First, the derivative crystals must be isomorphic with native crystals. At the molecular level, this means that the heavy atom must not disturb crystal packing or the conformation of the protein. Unit-cell dimensions are quite sensitive to such disturbances, so heavy-atom derivatives whose unit-cell dimensions are the same as native crystals are probably isomorphous. The term isomorphous replacement comes from this criterion. 

Crystals are isomorphous if they have the same space group and unit-cell dimensions, and the types and the positions of atoms in each crystal are the same except for a replacement of one or more atoms in one structure with different types of atoms in the other. Isostructural crystals have the same structure, but not necessarily the same cell dimensions nor the same chemical composition, and have a comparable variability in the coordinates of the atoms to that of the cell dimensions and chemical composition. For more information on crystallographic terms see the International Union of Crystallography (IUCr) online dictionary http //reference.iucr.org/dictionary. 

Sometimes different compounds give apparently identical crystals. Isomorphism is the similarity of crystal shape, unit cell dimensions, and structure between substances of nearly, but not completely, identical chemical composition. It is derived from the Greek words - isos meaning equal and morphe for form or shape. The arrangements of atoms in the isomorphous crystals are identical, but the identity of one or more atoms in this arrangement has been changed. For example, sulfur in a sulfate may often be replaced by selenium, to give an isomorphous selenate. Ideally, isomorphous compounds are so closely similar in composition that... 

The method of isomorphous replacement is rarely used for small molecules, in part because small unit cells are seldom exactly isomorphous, the change in the identity of one atom causing a significant change in unit-cell dimensions. The use of this method from small molecules, however, illustrates the steps in the procedure. 

In (a) and (c) there would be no great difference between the characters of the A-S and B—S bonds in a particular compound, while in (b) the B and S atoms form a covalent complex which may be finite or infinite in one, two, or three dimensions. By analogy with oxides we should describe (a) and (c) as complex sulphides and (b) as thio-salts. Compounds of type (c) are not found in oxy-compounds, and moreover the criterion for isomorphous replacement is different from that applicable to complex oxides because of the more ionic character of the bonding in the latter. In ionic compounds the possibility of isomorphous replacement depends largely on ionic radius, and the chemical properties of a particular ion are of minor importance. So we find the following ions replacing one another in oxide structures Fe, Mg , Mn , Zn, in positions of octahedral coordination, while Na" " more often replaces Ca (which has approximately the same size) than K , to which it is more closely related chemically. In sulphides, on the other hand, the criterion is the formation of the same number of directed bonds, and we find atoms such as Cu, Fe, Mo, Sn, Ag, and Hg replacing Zn in zinc-blende and closely related structures. 

The first step is to introduce heavy atoms into the protein crystal. This is usually done by soaking the crystals in a solution containing 0.1—10 mmol 1 1 of the heavy atom compound (Hg, Pt, Au, U compounds are often used) but sometimes the macromolecule is also co-crystallized with the heavy atom compound. As discussed in Section 9.03.4, protein crystals contain large solvent channels, which allow the diffusion of small molecules within the crystal. An important caveat is that the binding of the heavy atom compound must not distort the crystal appreciably neither the overall unit cell dimensions nor the conformation of the macromolecule. If it does, the underlying assumption that we can subtract away the protein component is false. In other words, the native (no heavy atom) and derivative (with heavy atom) must be isomorphous, and the techniques are called in general isomorphous replacement. 

Aprotein crystal absorption is virtually eliminated for a typical crystal <1 mm in dimension. Sometimes it is not possible to make heavy atom derivatives owing to the chemical nature of a specific protein or the particular crystal form. Many proteins contain an essential metal atom or alternatively selenium can be incorporated into a protein. Similarly bromine can be incorporated into a nucleotide. In all these cases data can be collected at multiple wavelengths using SR and this allows phases to be determined. Protein structures have now been solved by several variants of these methods. This is an important technical capability because it either reduces the number of heavy atom derivatives that need to be found for isomorphous replacement or allows phase determination from a single crystal. 

We can then replace F by a D-isomorphic boimded-above quasi-coherent complex—see (3.9.6)(a)—which by [H, p. 42, 4.6.1)] (dualized) may be assumed flat. Since F has flnite tor-dimension, an application of [I, p. 131, 5.1.1] to a suitable D-isomorphic trimcation of F allows one to assume further that F is bounded. Then an induction on the number of nonvanishing components of F (using the triangle [H, p. 70, (1)]) reduces the problem to where F is a single flat quasi-coherent Oy-module. 

The phenomenon by which various monomer units can replace each other in the lattice is termed isomorphism. Isomorphism is possible in copolymers if the corresponding unipolymers show analogous crystal modifications, similar lattice constants, and the same helix type. For example, according to Table 5-5, the y form of it-poly(propylene) and modification 1 of it-poly (butene-1) possess triclinic crystal form, similar lattice constants for the c dimension, and the same helix type. The copolymers of propylene and butene-1 therefore show isomorphism. Isomorphism occurs particularly readily in helix-forming macromolecules, since the helix conformations lead to channels in the crystal lattice, which can easily accommodate different substituents. 

Preliminary diffraction data to 3.2A reveal that the enzyme crystallizes in the orthorhombic system and the cell dimensions are a =59.6 A, b = 142.1 A and c = 214.2 A. The molecular structure is not known and to our knowledge, neither is that of any protein of homologous sequence. Therefore, the structure will have to be solved by application of the multiple isomorphous replacement method. Currently, we are in the process of screening for appropriate heavy atom derivatives. 

---