534 PART I The Immune System in Health and Disease as the scattered waves overlap, they alternately interfere with (a) and reinforce each other. An appropriately placed detector records a pattern of spots( the diffraction pattern) whose dis- tribution and intensities are determined by the structure of the diffracting crystal. This relationship between crystal structure and diffraction pattern is the basis of x-ray crystallographic analysis. Here is an overview of the procedures used OBTAIN CRYSTAIS OF THE PROTEIN OF INTEREST To those who Diffracted beams have not experienced the frustrations of crystallizing proteins, this may seem a trivial and incidental step of an otherwise Detector (e ., film) highly sophisticated process. It is not. There is great variation from protein to protein in the conditions required to produce crystals that are of a size and geometrical formation appro- priate for x-ray diffraction analysis. For example, myoglobin (b) formed crystals over the course of several days at pH 7 in a 3 M solution of ammonium sulfate. but 1.5 m ammonium sulfate at pH 4 worked well for a human IgG1. There is no set formula that can be applied, and those who are consistently successful are persistent, determined, and, like great chefs, have a knack for making just the right"sauce SELECTION AND MOUNTING. Crystal specimens must be at least 0. 1 mm in the smallest dimension and rarely exceed a few millimeters in any dimension. Once chosen, a crystal is vested into a capillary tube along with the solution from which the crystal was grown(the mother liquor"). This keeps the crys- tal from drying and maintains its solvent content, an important consideration for maintaining the internal order of the speci men. The capillary is then mounted in the diffractionapparatus GENERATING AND RECORDING A DIFFRACTION PATTERN The precisely positioned crystal is then irradiated withx-rays of a known wavelength produced by accelerating electrons against the copper target of an x-ray tube. When the x-ray beam strikes (c) the crystal, some of it goes straight through and some is scat- tered; sensitive detectors record the position and intensity of Tyr 100H the scattered beam as a pattern of spots(Figure 23-6a, b) INTERPRETING THE DIFFRACTION PATTERN. The core of diffraction analysis is the mathematical deduction of the detailed structure that would produce the diffraction pattern observed. One must calculate to what extent the waves scat tered by each atom have combined to reinforce or cancel each other to produce the net intensity observed for each spot in Asp the array. a difficulty arises in the interpretation of complex diffraction patterns because the waves differ with respect to phase, the timing of the period between maxima and min ima. Since the pattern observed is the net result of the inter action of many waves, information about phase is critical to calculating the distribution of electron densities that is re- sponsible. The solution of this"phase problem"looms as a FIGURE 23-6 X-ray crystallography.(a)Schematic diagram of an major obstacle to the derivation of a high-resolution struc- x-ray crystallographic experiment in which an x-ray beam bombards ure of any complex molecule. the crystal and diffracted rays are detected. (b) Section of x-ray dif- The problem is solved by derivatizing the protein-mod- fraction pattern of a crystal of murine IgG2a.(c) Section from the ifying it by adding heavy atoms, such as mercury, and then electron-density map of murine IgG2a. / Part (a)from L. Stryer, 1995, obtaining crystals that have the same geometry as(are iso- Biochemistry, 4th ed. parts(b)and (c) courtesy of A McPherson./as the scattered waves overlap, they alternately interfere with and reinforce each other. An appropriately placed detector records a pattern of spots (the diffraction pattern) whose dis￾tribution and intensities are determined by the structure of the diffracting crystal. This relationship between crystal structure and diffraction pattern is the basis of x-ray crystallographic analysis. Here is an overview of the procedures used: OBTAIN CRYSTALS OF THE PROTEIN OF INTEREST. To those who have not experienced the frustrations of crystallizing proteins, this may seem a trivial and incidental step of an otherwise highly sophisticated process. It is not. There is great variation from protein to protein in the conditions required to produce crystals that are of a size and geometrical formation appro￾priate for x-ray diffraction analysis. For example, myoglobin formed crystals over the course of several days at pH 7 in a 3 M solution of ammonium sulfate, but 1.5 M ammonium sulfate at pH 4 worked well for a human IgG1. There is no set formula that can be applied, and those who are consistently successful are persistent, determined, and, like great chefs, have a knack for making just the right “sauce.” SELECTION AND MOUNTING. Crystal specimens must be at least 0.1 mm in the smallest dimension and rarely exceed a few millimeters in any dimension. Once chosen, a crystal is har￾vested into a capillary tube along with the solution from which the crystal was grown (the “mother liquor”).This keeps the crys￾tal from drying and maintains its solvent content, an important consideration for maintaining the internal order of the speci￾men.The capillary is then mounted in the diffraction apparatus. GENERATING AND RECORDING A DIFFRACTION PATTERN. The precisely positioned crystal is then irradiated with x-rays of a known wavelength produced by accelerating electrons against the copper target of an x-ray tube. When the x-ray beam strikes the crystal, some of it goes straight through and some is scat￾tered; sensitive detectors record the position and intensity of the scattered beam as a pattern of spots (Figure 23-6a,b). INTERPRETING THE DIFFRACTION PAT TERN. The core of diffraction analysis is the mathematical deduction of the detailed structure that would produce the diffraction pattern observed. One must calculate to what extent the waves scat￾tered by each atom have combined to reinforce or cancel each other to produce the net intensity observed for each spot in the array. A difficulty arises in the interpretation of complex diffraction patterns because the waves differ with respect to phase, the timing of the period between maxima and min￾ima. Since the pattern observed is the net result of the inter￾action of many waves, information about phase is critical to calculating the distribution of electron densities that is re￾sponsible. The solution of this “phase problem” looms as a major obstacle to the derivation of a high-resolution struc￾ture of any complex molecule. The problem is solved by derivatizing the protein—mod￾ifying it by adding heavy atoms, such as mercury, and then obtaining crystals that have the same geometry as (are iso- 534 PART IV The Immune System in Health and Disease X-ray source X-ray beam Crystal Detector (e.g., film) Diffracted beams (a) (b) Tyr 100H Gly 97 Gly 96 Asp 101 Tyr 102 Tyr 100I Ala 100J Met 100K Trp 103 (c) FIGURE 23-6 X-ray crystallography. (a) Schematic diagram of an x-ray crystallographic experiment in which an x-ray beam bombards the crystal and diffracted rays are detected. (b) Section of x-ray dif￾fraction pattern of a crystal of murine IgG2a. (c) Section from the electron-density map of murine IgG2a. [Part (a) from L. Stryer, 1995, Biochemistry, 4th ed.; parts (b) and (c) courtesy of A. McPherson.]