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MAD PHASING  119

        followed by soaking in HoC1 3 . Although MAD  such as argon and krypton have been utilized for this
        phasing was not used in this particular structure  purpose (Cohen et al., 2001; Quillin and Matthews,
        determination, it illustrates the potential for incor-  2003). For larger proteins, clusters of heavy atoms
        poration of atomic species which can provide larger  have been successfully used (Rudenko et al., 2003).
        anomalous signals (Urs, 1999). Other types of spe-  Bijvoet (S Bij−Calc ) and dispersive (S Dis−Calc ) signal
        cialized techniques include labelled substrates or  levels expected from the incorporated anomalously
        inhibitors that carry atoms or groups that scatter  scattering species can be estimated through use of
        anomalously.                                 the following formulae:
          The most broadly used, general technique is
                                                                   1/2       1/2    f
        the replacement of methionines in proteins by  S Bij−Calc  =  1  N A    Peak  and
        selenomethionines. The technique, initially intro-       2     N P      Z eff
        ducedbyHendricksonandcoworkers(Hendrickson                  1/2       1/2    |f     − f
                                                                 1      N A      Edge  Remote |
        et al., 1990), has been widely used. Essentially,  S Dis−Calc  =
        it involves expression of the cloned protein of          2      N P          Z eff
        interest in a methionine auxotrophic strain with
                                                     where
        exogenously provided selenomethionine as the sole
        source of this amino acid. Several reviews that  N A = number of anomalous scatterers
        describe the technology and the problems involved  N P = number of non-hydrogen atoms in the macro-
        (Hendrickson, 1998), including methods for replac-  molecule
        ing both methionine and cysteine residues by their  Z eff  = effective scattering factor of an atom (6.7 for
        seleno analogs (Strub et al., 2003), and replace-  protein atoms).
        ment of other residues by methionines to generate
        sites for selenium atoms (Gassner and Matthews,  8.3.2 Choice of wavelengths
        1999), are available. Although achieving incorpo-
        ration of selenomethionines into proteins expressed  Generally, data at three wavelengths is preferred for
        in non-bacterial cell cultures is still in many cases a  determination of both Bijvoet and dispersive differ-
        challenge, it has been accomplished in some cases  ences, in case of a single anomalous species in the
        (Lustbader et al., 1995; Wu et al., 1994). Techniques  unit cell. Although in principle, the remote wave-
        for introduction of selenium into nucleic acids and  length can double as the peak wavelength, as long
        oligonucleotides have also been described (Teplova  as it is on the short wavelength side of the absorp-
        et al., 2002).                               tion edge (Peterson et al., 1996), use of an additional
          A second set of general methods is the classical  wavelength improves accuracy and precision of the
        approach used for derivatization of crystals in MIR  determined phases (Hendrickson, 1991). In particu-
        phasing (Garman and Murray, 2003). One of the  lar for methods that use least squares calculations in
        advantages of MAD methods over MIR is that iso-  estimation or refinement of parameters, it provides
        morphism is not a requirement. The structure of a  valuable additional observations. Bijvoet differences
        derivatized protein that is non-isomorphous with  are determined by measurements of either Bijvoet
        the native can be determined directly from MAD  or Friedel mates at the wavelength corresponding to
        data, and the native structure subsequently deter-  the absorption peak, or on its short wavelength side.
        mined through molecular replacement, if necessary.  Dispersive differences require the measurement of
        Among the more recent developments in techniques  intensities at two different wavelengths, one at a
        of anomalous scatterer incorporation are those that  wavelength close to the inflexion point of the absorp-
        involve binding of anomalous scatterers to macro-  tion spectrum (Fig. 8.1), and a second one far enough
        molecular surfaces using short soaks. Compounds  away to enable as a large a signal as practicable. It is
        that can be used include both negative ions such  important, in many cases, to measure the absorp-
        as bromide (Dauter, 2000, 2002) as well as positive  tionspectrumfromthecrystalsunderstudysincethe
        ions such as rubidium (Korolev et al., 2001). In addi-  environment of the anomalous scatterer might sig-
        tion, binding cavities in proteins for inert gas atoms  nificantly change the position of the infection point
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