Chapter 3
Crystallographic studies of seven modified insulins

3.1  Introduction to modified insulins

As described in chapter 1, several features are found in every insulin structure known so far: the three disulfide bridges, the three turn a-helix of residues B9 to B19 and the two small a-helices in the A chain spanning residues A1 to A8 and A13 to A19, together with the short b-sheet structure formed in the dimer, are basic building blocks of insulin (see figure 3.1).

Figure 3.1: The insulin dimer, 4Zn native rhombohedral structure.

1. View along the local twofold axis. Disulfide bridges and dimer interface residues B23-B28 from both molecules in thick lines;
2. View perpendicular to the local twofold axis. Disulfide bridges and residues B23-B28 as before. B chain helices also highlighted in thick lines: D9-D19 (molecule 1) and B1-B19 (molecule 2).

The largest structural differences between insulin monomers in various crystal forms are found in residues B1 to B8. In 2Zn insulin all six monomers in the hexamer have B1 to B8 extended, thus exhibiting the so-called T6-state (for an explanation of the nomenclature of insulin, see chapter 4). In the 4Zn insulin hexamer, B1 to B8 in one of the two molecules becomes helical, giving rise to the T3R3-state. By analogy, it is thought possible to produce a 6Zn insulin in the R6-state. Phenol monoclinic insulin crystals can be obtained in this R6-state, but do not have the expected six off-axial zinc sites, since these are occupied by the phenol molecules.

Crystallographic studies have been carried out on several modified insulins as part of an on-going research programme into the structure of insulin in all its aspects, partly in collaboration with Novo Nordisk A/S who supplied the protein material. Modified insulins are studied structurally to understand for example the conformation of specific parts of the protein, the aggregation of insulin to dimers and hexamers, and metal binding. In the tables and text of this and the following chapters, abbreviated names will be used for the modified insulins, according to table 3.1.

Table 3.1: Abbreviations for names of the modified insulins.
HI = human insulin; des = deleted

3.1.1  B13 Glu®Gln human insulin

In 2Zn insulin, six glutamic acid residues are brought into close contact in the centre of the hexamer. Electrostatic interactions between those negatively charged residues are unfavourable and are overcome by the zinc binding of the B10 histidine residues, by hydrogen bonds and probably by other cations [Emdin et al., 1980, Hill et al., 1991]. The B13Q mutant is expected to associate specifically into hexamers, stabilised by hydrogen bonds between the glutamine residues in a twelve-membered 'ring' structure in the core as proposed by Markussen et al. (1987), shown in figure 3.2.

Figure 3.2: The proposed 'ring' structure of B13 glutamine residues in B13Q insulin.

Because Gln at position B13 favours the formation of helix at B1 to B8 [Bentley et al., 1992], this more stable hexamer is also expected to have undergone the T ® R structural transition, especially upon binding of zinc: the zinc free, 2Zn (both studied by Xiao and co-workers [Bentley et al., 1992]) and 4Zn forms of the B13Q mutant should progressively prefer the R-conformation. According to Markussen et al. (1987) B13Q has a potency relative to insulin of 0.18 in the free fat cell assay.

3.1.2  B9 Ser®Asp/B27 Thr®Glu human insulin

Introduction of negative charges at B9 in what is the core of the 2Zn native insulin hexamer will prevent hexamer and dimer formation. The B9 Ser®Asp mutation is one of the most effective in reducing dimer formation at neutral pH (Brange et al., 1988). In a dimer, two B9 residues and two B13 residues (all carboxylate groups in the mutant) would come very close together, causing strong electrostatic repulsion [Dodson et al., 1993], which can be alleviated by protonation and hydrogen bonding. In that case the B13 Glu has an elevated pK, as determined by Kaarsholm et al. (1990). At neutral pH the B13 Glu would be deprotonated, in which case hydrogen bonding can not take place and the monomers can not approach each other close enough to form dimers. Dimerisation will also be impaired by changing the interactions of B27 and B28 with the termini of the A chain. The mutant is indeed found to be monomeric at 10^-3M [Brange et al., 1988]. The structure of the monoclinic form of the mutant has been determined by J. Turkenburg (1992). In that case the mutant forms hexamers with calcium ions bound in the core which neutralise the B9 mutation.

3.1.3  A21 Asn®Gly/B9 Ser®Glu/B10 His®Glu human insulin

Addition of a negative charge at B9 introduces electrostatic repulsion and will prevent hexamer and dimer formation as discussed in section 3.1.2. In addition, abolition of the metal binding potential at B10 is expected to obliterate hexamerisation, promoting rapid absorption after subcutaneous injection. Substitution of A21 Asn by Gly is expected to decrease susceptibility to deamidation and covalent dimer formation, thus stabilising the mutant in the, often acidic, therapeutic solutions. The rate of absorption of some A21 substituted insulin mutants from the injection site appears to be virtually independent of zinc concentrations. The A21G/B9E/B10E mutant is found to be monomeric under physiological conditions [Xiao, 1990]. The relative biological activity (mouse adipocyte assay) is 58% (N. Kaarsholm, pers. comm.). This value is composed of a significantly enhanced activity afforded by the B10 Glu substitution, a decreased activity provided by the B9 Glu mutation, and a slightly decreased effect on activity from the A21 Gly substitution. In acid-base titrations to characterise ionisation patterns of mutant insulins, it is found that carboxylate groups residing close to the monomer-monomer interface have their pK values perturbed upwards [Kaarsholm et al., 1990]. Unfortunately, no data are available for an acidic side chain at B10. However, the situation will be further complicated in that case, because of the potential for this side chain to interact with the B9-B19 helix dipole (which would tend to lower pK) adding to the close proximity of the monomer-monomer interface (which would effect an increased pK as observed with carboxylates at B13 and B9) (N. Kaarsholm, pers. comm.).

3.1.4  Co²⁺ human insulin

Cobalt is very similar to zinc in size (ionic radii 0.72Å and 0.88Å respectively [Weast, 1983-1984]) and chemical behaviour, and is therefore probably able to play the same role in insulin hexamer formation. In native insulin hexamers, zinc is present either in octahedral conformation, when the insulin molecule is in the T-state, or in tetrahedral conformation, when the insulin molecule is in the R-state. According to ligand field theory, however, tetrahedral coordination is less favourable than octahedral coordination for d⁷ ions like Co²⁺. In the presence of iodide (and other halide ions), tetrahedral coordination is a possibility for Co²⁺ [Mackay and Mackay, 1981]. The addition of phenol in the crystallisation is expected to stabilise a-helix at B1-B8, favouring R- over T-conformation (Derewenda et al., 1989), which probably forces Co²⁺ into a tetrahedral environment. Whether a Co²⁺ structure has T3R3- or R6-conformation depends on the phenol concentration [Whittingham et al., 1995] and the temperature of the crystallisation [de Graaff et al., 1981].

3.1.5  B9 Ser®His human insulin

Introduction of another histidine residue into the core of the insulin hexamer is expected to add to the stability by increased zinc binding. In fact, solution studies at pH 8 have shown the B9H mutant is capable of binding around 6 zinc ions per insulin hexamer. As it turns out, this additional stability is not sufficient to provide a clinically relevant protracted profile following subcutaneous injection (N. Kaarsholm, pers. comm.). This mutant could, in rhombohedral crystal form, be an example of a 6Zn insulin in the R6-state, with six off-axial zinc binding sites. In order to promote T ® R structural transition to facilitate the formation of the R6-state, phenol was added in an attempt to obtain a different crystal form.

3.1.6  B8 Gly®Ser/B13 Glu®Gln/B30 Thr-NH₂ human insulin

Introduction of positive charges at B13 and B30, which raises the iso-electric point, is expected to create insulins more soluble in acidic therapeutic solutions. At the higher pH in the body, they would crystallise readily after injection, resulting in prolonged action. A charge-indifferent mutation at B8 is introduced to study the background of the sequence invariance at that point, which might be related to the conformation of the B8 residue in the native molecule. The hydrophobicity of the mutant is increased in comparison with native pig insulin as determined by HPLC chromatography [Markussen et al., 1987]. This is unexpected because of the hydrophilic nature of the mutation at B8 as such. For the T-conformation of the mutant Markussen proposes a distortion of the a-helix commencing at B7 (to accommodate an L-Ser residue rather than a Gly with D-amino acid Ramachandran angles as in the native molecule [Baker et al., 19988]), which might expose hydrophobic side chains. The glycine at B8 in native insulin in the R-conformation, however, has Ramachandran angles as expected for an a-helix. The introduction of serine in that position might in this conformation not have such a significant effect on the helix. Phenol should stabilise a-helix at B1-B8, like in monoclinic native insulin [Derewenda et al., 1989].

3.1.7  A4 Glu®Gln/B25 Phe®Tyr/des B30 single chain human insulin

A4 Glu is involved in protamine binding, which retards the uptake of insulin in the bloodstream and is used in some therapeutic mixtures (J. Brange, pers. comm.). Changing this residue from a negatively charged polar Glu to a neutral Gln is expected to reduce repulsion within the hexamer and generate more effective association. This mutation has a profound effect on the position of B25 [Holden, 1991] and its interaction with A19 Tyr [Xiao, 1990], which for the 2Zn native molecule is shown in figure 3.3. The interaction between B25 and A19 in T-conformation insulin is one of the few hydrogen bond interactions between the two chains, and thus naturally was thought to be important for the stability of the molecule.

Figure 3.3: The interaction of B25 with A19 in 2Zn native insulin. B25 and A19 residues from both molecules highlighted in thick lines. Distances in Å.

Des B30 insulins have biological activities very similar to full length insulins [Baker et al., 1988]. However, introduction of a peptide link, causes nearly complete abolition of activity [Derewenda et al., 1991], attributed to the rigidity of the molecule, and therefore the impossibility to achieve the conformational change probably required for binding to the receptor. B25Y(B29-A1)A4Q is a single chain precursor for an insulin analogue designed for the study of the influence of the biological activity of amino acid substitutions at position B25. The B25Y(B29-A1)A4Q mutant is found to react only very slowly with trypsin at the B29 Lys residue, while this reaction is a key step in the final preparation of the desired insulin analogue (P. Balschmidt, pers. comm.).

3.2  Crystallisation of the modified insulins

The routines for insulin crystallisation in various crystal forms had become well established by 1975 [Cutfield, 1975]. These routines were reviewed by Tolley (1987) and improved and adapted by Xiao (1990). The present standard routines for the various crystal forms of native insulin can be found in table 3.2.

Table 3.2: Standard routines for crystallisation of insulin in various crystal forms. Adapted from Tolley (1987) and Xiao (1990).
¤ from Xiao (1990); ª from Tolley (1987) with adaptations by Xiao (1990); ^¶ from Tolley(1987); ^§ NaCl, NaBr, NaI or NaSCN

Table 3.3: Crystallisation protocols of the batch crystallisation of five modified insulins, one of which in two different crystal forms.
ª resulting crystal form: rh=rhombohedral; or=orthorhombic; mc=monoclinic

Most of the insulins described in this thesis have been crystallised by batch method by various people. The actual conditions employed in the crystallisation of the insulins by batch method can be found in table 3.3. Two mutants have been crystallised by vapour diffusion with the following protocols (both by J. Clarkson):

1. B9D/B27E:

• Add 10 mg insulin to 200 ml 0.02 M HCl and 8 ml 0.5 M NaOH. The mixture precipitates. Store in refrigerator for 72 hours;

• Add 100 ml 0.02 M HCl to partly dissolve the protein. Centrifuge and use supernatant for crystallisation by vapour diffusion in hanging drop. Store surplus supernatant in refrigerator for 24 hours;

• Supernatant precipitates. Warm up (45 ^oC) to partly dissolve the protein. Centrifuge and use supernatant for crystallisation by vapour diffusion in hanging drop. The reservoir solution contained 1 ml 0.02 M citrate/phosphate buffer pH6. The drop solution contained 4 ml of buffer/protein solution in a 40:60 ratio. This protocol resulted in orthorhombic crystals suitable for diffraction experiments.

2. B25Y(B29-A1)A4Q: The reservoir solution was made up of 995 ml 0.02 M citrate/phosphate buffer pH6 and 5 ml saturated ammonium sulphate. The drops contained 5ml of a solution of 9.9 mg insulin in 200 ml 0.02 M HCl. This protocol resulted in cubic crystals under a brown skin, due to the impurities in the insulin preparation. However, crystallisation attempts after purification failed. Careful analysis of the original insulin preparation by Novo Nordisk A/S revealed the presence of 0.25 zinc ion per monomer insulin (P. Balschmidt, pers. comm.), which would have been removed by the purification steps. Zinc was obviously a necessity in the successful crystallisation of the mutant.

Further crystallisation experiments include:

• The batch crystallisation of B8S/B13Q/B30amide in cubic crystal form in order to study the conformation of B8 without the constraints of metal binding and hexamerisation. The crystals obtained were unsuitable for diffraction experiments;

• The batch crystallisation of B9H in rhombohedral crystal form in the presence of glycerol instead of ethanol. This would facilitate cryocrystallographic experiments. Crystals of rhombohedral B9H grown under the standard conditions (see table 3.3) deteriorated quickly upon addition of the cryoprotectant. Crystallisation experiments under the new conditions were unsuccessful. Brange and others (see Brange, 1987) have observed that the addition of glycerol to a neutral solution of insulin impairs the chemical stability of insulin. Glycerol is, however, also used as an isotonic agent in some pharmaceutical insulin preparations;

• In a separate attempt to obtain B9H crystals suitable for cryocrystallographic experiments, a cryoprotectant solution was made with all the constituents of the standard mother liquor apart from insulin, and 1,2-ethanediol instead of ethanol to function as cryoprotectant. 346 ml aliquots of a standard solution containing 1250 ml 0.2M Na₃Cit, 8.3 mg ZnAc₂, 304.5 mg NaCl, 85 ml 1M NaOH, 35ml 1M HCl and 280 ml 0.2M HCl, mimicking the original crystallisation solution, were subsequently diluted with varying amounts of ethanediol and water in order to obtain a suitable cryoprotectant solution. Crystals from the original rhombohedral crystallisation were submerged in a solution with 30% cryoprotectant, to check their viability in solutions with ethanediol. The crystals did not change noticeably over a period of 24 hours. The 30% cryoprotectant solution was tested separately for glassy appearance upon flash-freezing, and was found to be unsuitable. However, a 40% ethanediol solution froze satisfactorily. The crystals in the 30% solution were taken to the synchrotron at Daresbury (UK), where the solution was replaced with the 40% solution, after which the crystals proved suitable for data collection.

J. Clarkson has attempted to obtain fresh crystals of A21G/B9E/B27E and B25Y(B29-A1)A4Q for data collection at cryogenic temperatures, without success.

3.3  Data collection and processing

Data were collected by various people on various sources and detectors, according to availability of apparatus and requirements of individual projects. The information pertaining to data collection protocols is shown in table 3.4. Statistics of the data used for refinement, are given in table 3.5.

Table 3.4: Data collection information.
¤ rot.an. = rotating anode; DL = Daresbury Laboratory
ª Xen = Xentronics Area Detector; Raxis = R-AXIS IIC Imaging Plate;
Rigaku = Rigaku AFC5 Diffractometer; Mar = MarResearch Imaging Plate
^¶ RT = room temperature; cryo = cryogenic temperature, 120K
^§ RDPS = R-AXIS IIC Data Processing Software for VAX workstations.

Table 3.5: Data statistics for the data sets used in the refinements.

3.4  Structure Determination

The first structure of the insulin molecule has been known since 1969 (Adams et al., 1969). Isomorphous replacement studies of modified insulin are, therefore, normally unnecessary. For modified insulins which seem isomorphous with 2Zn insulin or one of the other forms of insulin determined so far, structure determination and refinement starts with the calculation of Fourier maps with the phases of the isomorph. Regarding structures described in this thesis, this was possible in most cases, namely B13Q, B9D/B27E, B8S/B13Q/B30amide, CoI, and both crystal forms of B9H. Cell constants, space group and isomorphous R are given in table 3.6 for the modified insulins studied, with the appropriate information for native structures for comparison.

Table 3.6: Crystallographic information of native and modified insulins.
^* rhRT = rhombohedral form, room temperature data collection; rhF = rhombohedral form, data collection at 120K; mc = monoclinic form;
¤ a, b and c in Å ; a, b and g in ^o;
ª Z' is the number of molecules in the asymmetric unit;
^§ isomorphous R-factor based on orthorhombic native pig insulin structure;
^¶ B25Y(B29-A1)A4Q is presumably isomorphous with rat insulin II and insulin from the snake Zaocys dhumnades dhumnades Cantor which have been reported to crystallise in P4₂32 with similar cell constants (Wood et al., 1978, and Liang et al., 1984, respectively), but no coordinates are available for insulin in this space group.

The remaining structures, namely A21G/B9E/B10E and B25Y(B29-A1)A4Q, required complete molecular replacement studies to produce a starting model for refinement. In order to study the symmetry of the aggregation of all eight different structures, self-rotation functions were calculated.

3.4.1  Molecular replacement

  B9 Ser®Asp/B27 Thr®Glu human insulin

The molecular replacement studies of B9D/B27E only served to establish the isomorphism of the mutant with orthorhombic native pig insulin. At first, the data were indexed in a cell with a=37.99Å, b=51.54Å, c=57.90Å. A rotational search in AMoRe with an orthorhombic native dimer (b_max=90^o) resulted in a set of 15 peaks with a correlation coefficient larger than half of that of the first peak. The first four peaks are given in table 3.7.

Table 3.7: Rotation function solutions for B9D/B27E. cc = correlation coefficient; a,b,g are Eulerian angles within the AMoRe conventions.

Table 3.8: Translation function solutions for B9D/B27E. t_x,t_y,t_z are fractional translations; R = R-factor. Note that the translations for peak 1-1 and 3-1 are the same, apart from whole and half unit cell translations.

The translation search revealed the true nature of these four peaks, shown in table 3.8, each along with their second best translations. The rigid-body refinement clarified them even further, after which the three best solutions, transformed so as to act on the input coordinates, are as follows:

The first solution indicates identity with just a rotation of 90^o around the y-axis, which would put the x-axis along -z and the z-axis along +x. This effect can also be achieved by reindexing (h,k,l to l,-k,h), which at the same time transforms the unit cell constants in such a way that they resemble closely the orthorhombic native pig insulin cell constants (see table 3.6). AMoRe confirms the validity of reindexing, changing solution 1 to

When b=0, only the sum of a+g is relevant, giving the total rotational component of the transformation of the model molecule into the unknown cell (this is a well-known property of Euler angles). Hence in this case identity is achieved by rotating 360^o (337.41 + 21.88) around the z-axis. Thus after reindexing the B9D/B27E mutant is isomorphous, judged from the cell constants and the molecular replacement, although the R_iso is 0.452. Upon careful comparison of the mutant data with the orthorhombic native data, the relatively high value of R_iso can be traced back to a small percentage of the data. According to SCALEIT [CCP4 suite, 1994], only 17 out of the 4548 reflections from the mutant data set have a large difference as compared with those in the native data set, which incidentally was collected on the same instrument.

The direction cosines of the non-crystallographic twofold axis of the refined dimer as determined by overlapping the two monomers, correspond to angles of around (30,90,120), i.e. this axis lies in the xz-plane, 30^o away from the positive x-axis and 120^o away from the positive z-axis. The self-rotation function for the B9D/B27E mutant shows peaks at 37.9% of the maximum height with polar angles (w,f,k)=(119.5,0,180), which correspond to the same direction cosines as mentioned before: 0.8703, 0.0000, -0.4925.

  A21 Asn®Gly/B9 Ser®Glu/B10 His®Glu human insulin

For mutant A21G/B9E/B10E, the cell constants do not resemble those of any known insulin structure, indicating non-isomorphism. In addition, the R_iso is 0.581, against the data of the first choice of isomorph, namely native orthorhombic insulin. The cell volume of the mutant is 6.5% smaller than that of orthorhombic native insulin, indicating the same protein content in slightly closer packing. Molecular replacement studies were done with molecule 2 (chains A and B) from the orthorhombic native dimer as a search model. One peak in the rotation function stood out with a correlation coefficient (cc) of 23.2, where subsequent peaks are 20.9, 19.7, 19.4 etc. The highest 50 peaks of the rotation function were then used in a translation search. The highest peak was very clear, with cc=24.4 and R=51.7, with its second best translation also the second highest peak overall (cc=14.8 and R=54.5). The highest peak was fixed in a translation search for a second monomer, using the next 17 highest peaks from the first translation function (with their translations reset to zero). A second peak was found with a high correlation coefficient (47.1, whereas no other peak was higher than 25.1), with a translation of roughly (½,½,½) compared to the first monomer:

Rigid body fitting of these two peaks improved the solution considerably: cc=70.4 and R=38.1 for the two monomers together, and rotations and translations were as follows (internal AMoRe format):

These monomers are clearly related by a translation of (½,½,½) and a small rotation, and thus can not form a dimer directly. The possibility of a symmetry equivalent of one of the monomers complementing the other monomer in dimer formation was investigated. This would necessitate the non-crystallographic twofold axis of the dimer to be parallel to one of the 2₁ screw axes of the space group symmetry. In order to double-check this interpretation, the molecular replacement calculations were repeated with a full orthorhombic dimer as a model. The correlation coefficient of the first peak in the rotation function is distinctly higher than any of the others: 30.2 with the subsequent peaks at 20.9, 20.8, 20.8, 19.3 etc. After the translation function the result is unambiguous: cc=46.0, R=52.0 for the first peak, with cc=14.6, R=54.9 for the second best peak. The highest peak refines to (shifted solution)

Investigation of the non-crystallographic symmetry of the refined dimer by overlapping one monomer on the other, produces direction cosines (0.99932, -0.00497, 0.03672), corresponding to angles of almost (0,90,90). This means the non- crystallographic twofold axis is indeed parallel to the x-axis and thus to a 2₁ screw axis. The self-rotation confirms the presence of twofold axes (20.7% of the height of the origin peak) almost along the cell axes, with direction cosines (0.9890, 0.1478, 0.0000).

  A4 Glu®Gln, B25 Phe®Tyr, des B30 single chain human insulin

Two insulins have been crystallised in space group P4₂32, like mutant B25Y(B29-A1)A4Q, namely rat insulin II and insulin from an Asian snake. Both have cell constants very similar to those of the mutant. Atomic coordinates, however, are not available. The relatively high solvent content of the rat insulin crystals rendered them unsuitable for data collection [Wood et al., 1978]. The study of the snake insulin in China was stopped because the supply of the protein was insufficient (Liang D.C., pers. comm.). The sequences of the three insulins are compared in table 3.9. The snake insulin has two significant changes: B2 is proline instead of valine, which puts some restrictions on the conformation of the chain N-terminus, and B5 is arginine instead of histidine, which will prevent alternative zinc binding.

Table 3.9: Sequence differences between three insulins in space group P4₂32.
¹ insulin mutant B25Y(B29-A1)A4Q;
² insulin type II from rat;
³ insulin from the Asian snake Zaocys dhumnades dhumnades Cantor;
⁴ from Derewenda (1990)

Molecular replacement studies were done with a variety of models: monomers from various crystal forms (2Zn rhombohedral, 4Zn rhombohedral, cubic), dimers and hexamers, either complete or trimmed to the most rigid core by removing chain termini. The most successful model is a 2Zn rhombohedral dimer, with B1-7 removed from both B chains. Hexameric models were mainly used to check the solution and the packing. The rotation function does not show many features. The highest peak has a correlation coefficient of 34.3, and 20 other peaks have a correlation coefficient higher than half that. In the translation function the 20th rotation function peak (which had a cc of 22.1) is clearly the highest with cc=46.2 and R=46.1:

The mutant has one molecule in the asymmetric unit and from packing studies of the dimer solution it was clear that molecule 1 was nearest to the correct solution for the mutant structure. Rigid body fitting was performed on both of the monomers separately. The refined solutions are

The second solution was then applied to a complete molecule 1 from the 2Zn native insulin dimer in the correct cell. The space group symmetry (see figure 3.4) causes six monomers to come together in a T6 hexamer of 32 symmetry.

Figure 3.4: Symmetry of space group P4₂32. Reproduced from the International Tables Volume C [Wilson, 1992].

3.4.2  More self-rotations

  B13 Glu®Gln human insulin

The self-rotation function of the B13Q mutant (space group R3) shows 60^o repeats of two sets of non-crystallographic twofold axes (see figure 3.5). The most prominent set has peaks of 26.4% of the height of the origin peak, at (w,f)=(90,(12+n.60)) with n=0,1,...,5. The second set has slightly lower height (22.7%) at (w,f)=(90,(44+n.60)). These twofold axes confirm the approximate 32 symmetry of the hexamer. The hexamer is built up of three exact dimers around the threefold axis of the space group, which is along the z-axis. The dimers' non-crystallographic twofold axes are perpendicular to the crystallographic threefold axis, and thus lie in the xy-plane.

Figure 3.5: Self-rotation function of mutant B13Q; section k=180^o.
w runs from 0 to 90^o from the centre to the perimeter, f runs from 0 to 360^o around the perimeter.

  Zn²⁺®Co²⁺ human insulin

The the self-rotation functions of the isomorphous CoI and B13Q insulins, both rhombohedral structures in T3R3-conformation, are very similar, as expected. The only significant differences are the order and peak height of the peaks for the twofold symmetry. In CoI insulin the most prominent set of twofold peaks (see previous section) has a height of 23.5% and f-angles of (44+n.60)^o with n=0,1,...,5, while the second set has a height of 22.5% and f-angles of (12+n.60)^o.

  B9 Ser®His human insulin, rhombohedral form

The B9H mutant in the rhombohedral form is isomorphous with both CoI and B13Q insulin, and therefore has similar self-rotation patterns. The set of twofold peaks with f-angles of (44+n.60)^o has a peak height of 35.5%, the set with f=(12+n.60)^o has a peak height of 33.5%.

  B9 Ser®His human insulin, monoclinic form

Figure 3.6: Self-rotation function of mutant B9H in monoclinic form; section k=180^o. For w and f see legend of figure 3.5. Arrow indicates the direction of the threefold axis perpendicular to one set of twofold axes.
a) orthogonalisation such that the monoclinic axis b is along z, perpendicularly out of the plane of the paper, with a and c^* in the plane of the paper, as indicated;
b) orthogonalisation such that c^* is perpendicularly out of the plane of the paper, with a and b along x and y, respectively, as indicated.

The asymmetric unit of the B9H mutant in the monoclinic form contains a full R6 hexamer, for which the non-crystallographic twofold and threefold symmetry is expected to show clearly in a self-rotation. The non-crystallographic twofold symmetry is quite strong (figure 3.6a and b). The highest non-crystallographic peak on section k=180^o has a height of 49.7% of the origin peak, with (w,f)=(90,110.4) in figure a and (90,0) in figure b. This peak indicates a twofold axis along the crystal a-axis, and shows the monoclinic angle of 110.4^o(figure 3.6a). This axis is one of the non-crystallographic dimer axes, or rather its symmetry-equivalent, which is along the reciprocal c-axis. The other two dimer axes are in more general positions in the self-rotation (see figure 3.6b). The heights of the peaks are indicated.

Figure 3.7: Self-rotation function of mutant B9H in monoclinic form; section k=120^o. For w and f see legend of figure 3.5. For further information see legend of figure 3.6.

The non-crystallographic threefold symmetry of the hexamer is shown in figure 3.7a and b. The full symmetry of the insulin hexamer is 32, as revealed by the combination of three twofold axes roughly perpendicular to a threefold axis in the direction indicated by arrows in figures 3.6b and 3.7b. In the present mutant, like in native monoclinic insulin, this local threefold axis is perpendicular to the reciprocal c-axis. There is a peak for rotation of dimer 1 onto dimer 2, and one for dimer 1 onto dimer 3, and two more peaks because of the space group symmetry.

Additional threefold symmetry is featuring on the section k=120^o, with additional roughly appropriately spaced twofold axes on section k=180^oat roughly 90^oto the threefold axes, indicated by dashed lines in figure 3.6b. The thick dashed line combines with the higher peak (36.2% of the origin peak) on the left on the 0-180 meridian in figure 3.7b, revealing additional 32 symmetry; the actual k-angle of this peak is 121.4^o. The thin dashed line combines with the lower peak (35.7%) on the right; the actual k-angle of this peak is 110.9^o. This 32 symmetry is slightly artificial, since it involves translational symmetry from the space group 2₁ screw axis, and is therefore difficult to confirm with packing diagrams. A dimer from one hexamer will be rotated onto another dimer in another hexamer. The angles between the twofold and threefold axes are shown in tables 3.10 and 3.11.

Table 3.10: Angles between twofold axes in B9H monoclinic insulin

Table 3.11: Angles between twofold axes and threefold axes in B9H monoclinic insulin. Only combinations of 32 symmetry tabulated.

  B8 Gly®Ser, B13 Glu®Gln, B30 Thr-NH₂ human insulin

Since the B9H and B8S/B13Q/B30amide mutants in the monoclinic crystal form are isomorphous, the self-rotation functions are very similar. Section k=180^oshows the monoclinic angle of 110.5, sufficiently different from the monoclinic angle of B9H insulin to be distinguishable in the peak list of the self-rotation function. The peak height for this non-crystallographic symmetry element is 43.5%. The non-crystallographic threefold axis lies perpendicular to the z-axis and has a peak height of 32.6%.

3.5  Refinement

3.5.1  B13 Glu®Gln human insulin

Refinement of B13Q started with the calculation of (2F_obs-F_calc) and (F_obs-F_calc) maps with the magnitudes from the mutant and the phases from the 4Zn native rhombohedral insulin structure. When more highly refined coordinates became available for the native structure, the refinement of the mutant was re-initiated, using some of the knowledge acquired in the previous attempt. An overview of the refinement of B13Q is shown in figure 3.8.

Figure 3.8: Overview of R-factor during refinement of B13Q insulin (1.9Å).
*: manual rebuild, including water; then PROLSQ refinement of coordinates when the R-factor is >0.25, refinement of coordinates and temperature factors at lower R-factors;
#: adapting the matrix value for X-ray relative to geometry contribution between cycles of PROLSQ refinement;
= : resetting temperature factors prior to PROLSQ refinement (see *);
B1: first indication of the need for swapping the positions of B1/B2 main chain (molecule 2) and B3 side chain;
B2: B1-B3 (molecule 2) satisfactorily refined to new positions;
!: changing the appropriate waters to chloride ligands for the zinc ions;
P: PROCHECK used to aid rebuilding for the first time;
R: changing from using resolution limits 10-1.9Å to 10-2.3Å in PROLSQ refinement;
+: ARP refinement of water structure, incorporating PROLSQ;
D: investigating disorder at B13 (molecule 1).

The preliminary refinement attempt indicated that the zinc ion on the axis in molecule 2 is absent and should be removed at the beginning of refinement. Residue B13 was changed from Glu to Gln. The first refinement, starting from an R-factor of 0.264, consisted of an X-PLOR protocol with full heat stage, and resetting of temperature factors for the main chain between 10 and 25Ų, and for the side chains between 10 and 30Ų. The maps then confirmed the absence of the axial zinc in molecule 2. Spikes upwards in figure 3.8 are commonly caused by manual rebuilding of the structure with FRODO, after which least-squares refinement was performed using PROLSQ. In the initial stages, at R-factors higher than around 0.25, only atomic coordinates were refined, while at lower R-factors temperature factors were allowed to refine isotropically. Temperature factors were reset at various stages to free the refinement from local minima. The restraints on geometry were adjusted by adapting the relative weight of the contribution of the X-ray data.

At stage B1 (see figure 3.8) it became clear that the N-terminus of the B chain of molecule 2 was poorly defined, after which many omit maps were calculated (by setting the occupancy of appropriate atoms to zero and performing a few cycles of refinement with the reciprocal space refinement program used at the time) and rebuilding was attempted. The introduction of information from PROCHECK during the rebuilding stages made the spikes upwards smaller on the whole, indicating more geometrically acceptable changes so that less refinement of the geometry was required by PROLSQ. The highest resolution data were not as good and complete as originally assumed, leading to the change in resolution limits at point R. Refinement of the water structure was made easier and more successful when the automatic refinement program ARP [Lamzin and Wilson, 1992] became available. Refinement of the disorder at B13 (molecule 1) was approached in separate concurrent refinement runs: in run A one conformation of the side chain was included with water in the remaining electron density, in run B vice versa.

The final R-factor for all data between 25.65 and 2.3Å resolution is 0.182. For restraint and geometry information, see table 3.13 at the end of this section.

3.5.2  Zn²⁺®Co²⁺ human insulin

The starting model for refinement of CoI insulin was the native rhombohedral zinc insulin molecule in T3R3-conformation. Preliminary investigations of the modified molecule indicated the presence of two metal ions on the threefold rhombohedral axis, and a phenol molecule in the position resembling that found in monoclinic structures in the R6-state [Derewenda et al.,1989], which in the native rhombohedral T3R3-structure is roughly where the off-axial zinc is situated. An overview of the refinement procedure is shown in figure 3.9.

Figure 3.9: Overview of R-factor during refinement of CoI insulin (1.9Å).
*: manual rebuild, including water; then PROLSQ refinement of coordinates only in the first stages, refinement of both coordinates and temperature factors after point B;
B: changing from coordinates-only to coordinates-and-temperature-factor refinement;
+: ARP refinement, incorporating PROLSQ.
S: swapping the side chain of B3 with the main chain of B1/B2;
w: revising the water structure;
L: second phenol molecule included with hydrogen bonds to B10 and B13;
P: PROCHECK information aiding rebuilding for the first time;
D: sorting out disorder of residue D21 (molecule 1);
= : resetting temperature factors prior to PROLSQ refinement;
o: residues B1-B3 omitted;
i: residues B1-B3 included again;
A: probing of the density around position (0,0,15) (orthogonal Å) with various cations and anions present in the crystallisation solution.

The first step consisted of rigid body refinement of the protein component of the molecule in X-PLOR, where the dimer model was refined as a whole rigid body first, after which it was split up into monomers. Figure 3.9 starts with the R-factors for the first reciprocal space refinement cycle, in which the metal ions (zinc, in the initial stages) and phenol molecule were included. The R-factor for all data to 1.9Å was 0.2982 at this stage. The C-termini of both B chains and the N-terminus of the B chain of molecule 2 were excluded from refinement because of the obvious need for rebuilding.

At point C (see figure 3.9) the metal ions were changed from zinc to cobalt, and the axial ligand of the metal ion in molecule 2 was changed from water to iodide. PROLSQ refinement followed, first without keeping a special distance between the metals and ligands, and then a few cycles with a special distance imposed between cobalt and iodide. The distances between cobalt and histidine were allowed to refine freely.

At point S the density for the N-terminus of the B chain of molecule 2 became interpretable. The side chain of residue B3 was swapped with the main chain of residues B1/B2, changing the last turn of the a-helix to an extended conformation. At point L a second phenol molecule was included, which has hydrogen bonds with B10 His Nd₁ and B13 Glu Oe₁. The total number of phenol molecules in this T3R3 hexamer is therefore six. From point R the data between 1.9 and 1.95Å were excluded from refinement because of problems caused by the incompleteness of that resolution shell of data.

At point G all but the three most obvious waters, one of which is liganded to the cobalt ion in molecule 1, were deleted, after which the water structure was rebuilt in five runs of ARP. R-factor data were only recorded for the last run: down from 0.1920 to 0.1783. Refinement cycle 250 to 350 were taken up with refinement of the water structure by detailed rebuilding and reciprocal space refinement. From point A onwards it was tried to model a threefold degenerate acetate ion on the threefold axis on the surface of the hexamer, in the shallow depression which is lined by the three B chain helices in the R-conformation half of the hexamer. The density around (0,0,15) (orthogonal Å) was probed with cobalt and sodium cations, and acetate, citrate, iodide and chloride anions. None of the combinations of cat- and anions gave a totally satisfactory result judged by the electron density after refinement, also reflected by very similar R-factors for every conformation investigated. The density most resembles an acetate ion, probably coordinated to sodium. The final R-factor for CoI insulin is 0.1933 for all data between 33.33 and 1.95Å. For restraint and geometry information, see table 3.13 at the end of this section.

3.5.3  B8 Gly®Ser, B13 Glu®Gln, B30 Thr-NH₂ human insulin

With the advent of new techniques and ideas in protein crystallography, and better model coordinates being made available, it seemed necessary to re-initiate refinement of the B8S/B13Q/B30amide a few times. Some of the experience gained in preliminary stages, was used explicitly at the beginning of the final refinement procedure.

The hexameric starting model for the refinement was built up from three native monoclinic dimers from a molecular replacement search with AMoRe. The packing within the hexamer should resemble the mutant hexamer more closely than the original hexameric native monoclinic model. The R-factor for this model was 0.4014, while the free R-factor for the 10% of data to be excluded from the refinement, was 0.3953. An overview of the full refinement procedure is shown in figure 3.10.

Figure 3.10: Overview of R-factors during refinement of B8S/B13Q/B30amide insulin, conventional R-factor in thick line, free R-factor in thin line (2.1Å).
*: manual rebuild, including water; then, unless otherwise indicated, PROLSQ refinement of coordinates only in the first stages, refinement of both coordinates and temperature factors after point B;
= : resetting temperature factors prior to PROLSQ refinement (see *);
B: changing from coordinates-only refinement to coordinates-and-temperature factor refinement;
X: X-PLOR refinement followed by PROLSQ coordinate refinement;
+: ARP refinement, incorporating PROLSQ. Water molecules suggested by ARP were rejected;
w: developing the water structure with X-SOLVATE, followed by reciprocal space refinement with PROLSQ;
O: rebuilding on the basis of overlaps of all the A and B chains on each other to keep check of the pseudo-symmetry;
D1: deleting all waters with temperature factor higher than 70Ų2;
D2: deleting all waters with temperature factor higher than 90Ų2;
R: reciprocal space refinement of coordinates and temperature factors performed with REFMAC for the first time. Four cycles of refinement in every stage, only first and last R-factors indicated.

The first step in the refinement consisted of real space refinement of all the main chain peptide bonds and all the side chains with X-AUTOFIT [Oldfield, 1996]. Previously determined coordinates for the zinc ions, chlorides and phenol molecules were included at this point. The C-terminal residues of all six B chains, the N-terminal residues of chains H and L, the atoms of E1 and I1 and the side chains of residues A14, D1 and I14 were excluded from the subsequent first round of reciprocal space refinement with PROLSQ. Refinement stage X (see figure 3.10) was an extensive X-PLOR protocol, with full occupancy for all available atoms. The protocol consisted of rigid body refinement of the hexamer as a whole, then of the dimers separately, followed by the monomers. The subsequent simulated annealing run was of the 'slowcool' type, without full equilibration at high temperatures. This was immediately followed by PROLSQ coordinate refinement. Stages of manual rebuilding were aided by information from PROCHECK. The water structure was built up with X-SOLVATE in QUANTA. After point R (see figure 3.10) reciprocal space refinement was performed with REFMAC, using the maximum likehood residual for structure factors. The R-factor for the last point in figure 3.10 is 0.194 (free R-factor 0.280), calculated for the data between 11.0 and 2.1Å. The final R-factor for all data between 43.44 and 2.1Å is 0.215, the free R-factor 0.306. For restraint and geometry information, see table 3.14 at the end of this section.

3.5.4  B9 Ser®His human insulin

  Monoclinic crystal form

Figure 3.11: Overview of R-factors during refinement of B9H insulin, monoclinic form, conventional R-factor in thick lines, free R-factor in thin lines (2.1Å).
*: manual rebuild, including water; then, unless otherwise indicated, PROLSQ refinement of coordinates only in the first stages, refinement of both coordinates and temperature factors after point B;
= : resetting temperature factors prior to PROLSQ refinement (see *);
B: changing from coordinates-only refinement to coordinates-and-temperature factor refinement;
X1: X-PLOR minimisation (coordinates and temperature factors), no molecular dynamics involved;
C: changing the fourth ligands for both zinc ions to chloride;
+: ARP refinement, incorporating PROLSQ;
A: ARP refinement, after which the water molecules suggested are removed from the structure;
w: developing the water structure with X-SOLVATE, followed by reciprocal space refinement with PROLSQ;
G: reducing the restraints on the geometry slowly over 35 cycles of refinement;
O: rebuilding on the basis of overlaps of all the A and B chains on each other to keep check of the pseudo-symmetry;
P: using PROCHECK to aid manual rebuilding for the first time;
M: reciprocal space refinement of coordinates and temperature factors performed with REFMAC for the first time. Four cycles of refinement in every stage, only first and last R-factors indicated.

The starting model for refinement of B9H insulin in monoclinic form was constructed from three native monoclinic dimers, positioned in the mutant unit cell with AMoRe. This model should resemble the mutant structure more closely than the native hexamer model positioned in the mutant unit cell. The R-factor of this model (which contains no ligands of any kind) is 0.4007, while the R-factor for the 10% of reflections to be excluded from refinement, is 0.4424. An overview of the refinement procedure is given in figure 3.11.

The first maps gave clear indications for the positions of the B9 mutations, the presence of two zinc ions and their fourth ligands on the non-crystallographic threefold axis, the presence of phenol molecules very similar to the native structure, and some of the terminal residues that had been omitted from the starting model. This information was included in the first reciprocal space refinement, the starting point of figure 3.11. In the first stages, only coordinates were refined. Point X1 represents two cycles of minimisation in X-PLOR. The water structure was investigated both with ARP and X-SOLVATE. After point A ARP was only used for refinement, while any water molecules suggested by ARP were not included in the structure.

From point M reciprocal space refinement was performed with REFMAC, using the maximum likelihood residual for structure factors. At that stage it became clear that some of the electron density peaks in the core of the hexamer represented zinc ions rather than water molecules. The R-factors of the final model are 0.2156 (conventional R-factor) and 0.3167 (free R-factor), for all data between 57.74 and 2.1Å. The refinement was performed with all data between 13.0 and 2.1Å. For restraint and geometry information, see table 3.14 at the end of this section.

  Rhombohedral crystal form

B9H rhombohedral insulin is isomorphous with native 4Zn insulin. A starting model for refinement was derived from a molecular replacement search with AMoRe, which confirmed isomorphism. The advent of new techniques and ideas has had a great impact on the process of refinement of the B9H mutant. Refinement of the mutant against data collected at room temperature was not followed through when cryocrystallographic techniques were introduced. However, the success of the first attempt at collecting data at 120K was limited. The crystal was not very stable in the cryoprotectant solution, and upon freezing only diffracted to around 2.5Å. These data were complete and reliable to 2.6Å resolution. A later attempt at data collection was more successful, when more experience had been gained with chosing a cryoprotectant and the techniques of flash-freezing. Crystals were submerged in a solution with 1,2-ethanediol instead of glycerol which had been the earlier choice, and one of these diffracted well to 1.9Å resolution. Data sets could not be merged because of non-isomorphism due to temperature effects upon freezing (see table 3.12).

Refinement of the mutant with REFMAC was started with a model including zinc ions on the rhombohedral axis, and indications for chloride ions and other zinc ions in the form of water molecules. Unfortunately, REFMAC is as yet incapable of dealing effectively with restraining special distances when atoms in special positions and atoms from symmetry-related molecules are involved. The refinement of the rhombohedral B9H mutant has therefore stagnated at R-factors of 0.2338 (for the working set, data between 17.08 and 1.92Å) and 0.3097 (for the 10% of reflections kept 'free'). Refinement with X-PLOR was only effective in the earliest stages of refinement, not for the detailed refinement of water structure and the intricate zinc ion structure of the mutant. For restraint and geometry information, see table 3.13 at the end of this section.

Table 3.12: Unit cell parameter change upon freezing B9H rhombohedral insulin

3.5.5  B9 Ser®Asp, B27 Thr®Glu human insulin

The starting model for B9D/B27E insulin was produced with AMoRe, although the mutant is isomorphous with native orthorhombic insulin. The refinement is described below, with an overview shown in figure 3.12.

Figure 3.12: Overview of R-factors during refinement of B9D/B27E insulin, conventional R-factor in thick lines, free R-factor in thin lines (2.3Å).
*: manual rebuild, including water; then, unless otherwise indicated, REFMAC refinement of coordinates and temperature factors;
w: developing the water structure with X-SOLVATE, followed by reciprocal space refinement with REFMAC;
= : resetting temperature factors prior to REFMAC refinement (see *);
X1,X3,X4,X5,X6,X7: X-PLOR full refinement protocol (slowcool), immediately followed by REFMAC;
X2: X-PLOR full refinement protocol (slowcool) with all non-water atoms included with occupancy 1.0;
X8: X-PLOR full refinement protocol (slowcool), followed by 4 cycles of REFMAC; no waters included, experimental standard deviations not used;
b: temperature factors of water molecules reset to average temperature factor of protein.

The conventional crystallographic R-factor for the starting model was 0.5119 for all data to 2.3Å. Ten percent of the reflections were excluded from the refinement procedure, reserved for calculations of the free R-factor. Reciprocal space refinement was performed with REFMAC and X-PLOR. In the second cycle of X-PLOR refinement all atoms present in the coordinate set (apart from water molecules) were refined, without omitting uncertain ones. After X-PLOR step 8 it was discovered that the low resolution reflections produced erratic statistics. Some trials were done where experimental standard deviations were not used in the scaling of reflections, different resolution limits were used, and ultimately the idea of using the free R-factor was given up. The refinement of 829 atoms (at the last point of figure 3.12) with 3632 reflections, keeping 384 reflections separate for free R-factor calculations, is not warranted. It seemed justified to use the test reflections for scaling purposes in REFMAC until the number of parameters became too large.

The unpredictable behaviour of both R-factors is probably due to the fact that the structure factors calculated from the model are all systematically lower (in the range used for refinement) than the observed structure factors (see figure 3.13), which is caused by the significant differences of just a few low resolution reflections. This must be due to incorrect measurements or a systematic error.

Figure 3.13: Indication of problems with a small subset of reflections. In the resolution range used for refinement, all reflections have F_obs higher than F_calc, which can not be corrected with a scale factor because of the low resolution reflections. Structure factors on arbitrary scale.

The conventional R-factor at the end of the refinement procedure for B9D/B27E insulin for all data between 13.0 and 2.3Å is 0.2286. The R-factor is 0.3265 for all data between 29 and 2.3Å, further illustrating the problem at low resolution. For restraint and geometry information, see table 3.14 at the end of this section.

3.5.6  A21 Asn®Gly, B9 Ser®Glu, B10 His®Glu human insulin

The molecular replacement study of A21G/B9E/B10E insulin revealed a new packing of insulin dimers. The data collected at room temperature extended to 2.8Å resolution, which made detailed refinement impossible. The data collected at 120K were incomplete and of insufficient quality. These data could not be merged with the data collected at room temperature because of non-isomorphism.

Figure 3.14: Overview of R-factors during refinement of A21G/B9E/B10E insulin.
Xr: X-PLOR rigid body refinement of dimers, monomers, and B chain C-termini;
Xm: X-PLOR minimisation (including temperature factors);
R1: REFMAC refinement of coordinates and temperature factors, followed by manual rebuilding;
R2: REFMAC refinement of coordinates and temperature factors, preceded by resetting of temperature factors;
R3: REFMAC refinement of coordinates and temperature factors, preceded by manual rebuilding of protein and developing water structure with X-SOLVATE;
R4: REFMAC refinement of coordinates and temperature factors using all observed reflections, preceded by manual rebuilding of protein and developing water structure with X-SOLVATE;
R5: REFMAC refinement of coordinates and temperature factors.

Although the results of refinement of a protein structure at 2.8Å resolution have to be interpreted with extreme care, the process can usually be done very rapidly. An attempt was made with the A21G/B9E/B10E mutant, when the maps after molecular replacement, and rigid body refinement and minimisation in X-PLOR proved easily interpretable. The mutant aggregates in dimer form very closely resembling that of the native orthorhombic molecule, but in different packing. This puts the C-termini of the B chains in close contact with symmetry-related molecules. The maps, however, clearly showed the possibilities for change. Also, the mutations could be modelled in these maps. The first stage of reciprocal space refinement brought the R-factors down to 0.286 and 0.370. After rebuilding the protein molecules and modelling some of the solvent structure, the 10% 'free' reflections were included in the refinement to increase the number of reflections for every parameter refined. Within four steps of six minicycles of REFMAC refinement, the R-factor had dropped to 0.182. An overview of the limited refinement of the mutant is shown in figure 3.14. For restraint and geometry information, see table 3.14 at the end of this section.

3.5.7  A4 Glu®Gln, B25 Phe®Tyr, des B30 single chain human insulin

The B25Y(B29-A1)A4Q mutant crystallised in a space group for which no detailed structure has been published. Unfortunately the mutant did not diffract well enough to warrant detailed refinement. The R-factor of the molecular replacement model was 0.5767 for all data to 2.8Å. Since there were only 1386 reflections, no free R-factor was used in the refinement.

The mutations from Phe to Tyr and from Glu to Gln could not be interpreted unambiguously at this resolution. However, the modifications at the C-terminus of the B chain were clearly defined in maps. Residue B30 was deleted, after which a peptide bond was created between residues B29 and A1, the density for which was clear and continuous. Also, some strong (F_obs-F_calc) density was interpretable as a zinc ion close to B10 histidine, with the space group symmetry such that three histidines coordinate to this zinc ion. The coordinates were refined with X-PLOR and PROLSQ, but refinement was unstable and unreliable at 2.8Å resolution. The refinement was stopped at an R-factor of 0.3728 for all observed data, which lie between 11.6 and 2.8Å.

Table 3.13: Geometry restraints of the rhombohedral modified insulin structures. Root mean square deviations, with target values in brackets.

Table 3.14: Geometry restraints of four non-rhombohedral structures. Root mean square deviations, with target values in brackets.

3.6  Description of the structure models

The main features of the three-dimensional structure of insulin are seen in all of the modified insulins described in this thesis. The insulin monomer is held together by three disulfide linkages at A6-A11, A7-B7 and A20-B19. The a-helix running from residues B9 to B19 is largely undisturbed by modifications in its sequence. Where aggregation takes place, the dimer interface contains the small antiparallel b-sheet structure of residues B23-B28, and the hexameric structures have metal ions in the cores. N- and C-termini are often disordered, as was already described by Adams et al. (1969). The main differences of the modified insulin structures will be described below.

3.6.1  B13 Glu®Gln human insulin

The mutation of Glu to Gln at position B13 is expected to produce a more stable hexamer because of the reduction in charge repulsion in the core, possibly with an elaborate hydrogen bonding 'ring' structure of the six glutamine residues as described by Markussen et al. (1987). The mutant readily crystallised in rhombohedral form (space group R3) in T3R3-conformation. The positions of the mutated residues were not completely clear immediately at the beginning of refinement (see figure 3.15), so the sites were excluded from initial refinement. An omit map calculated (as described in section 3.5.1) after completion of refinement confirms the refined positions (see figure 3.16). Residue B13 (molecule 1) is disordered, and the simple twelve-membered 'ring' structure of the six glutamines is not observed. Moreover, the two glutamines in a dimer are within hydrogen bonding distance of each other, but not of neighbouring symmetry-related B13 glutamines. Contacts in the core of the hexamer are mediated through water molecules.

Figure 3.15: Indications for mutated residues in B13Q insulin at the start of refinement.
Stereo view of both B13 residues and F_obs-F_calc density at +3s.

Figure 3.16: Omit maps for mutated residues in B13Q insulin in fully refined positions.
Stereo view of both B13 residues and F_obs-F_calc density at +3s, in the same orientation as figure 3.15.

The zinc binding of the mutant only became clear after repeated trials with all zinc ions omitted and various combinations of zinc ions included in early refinement and map calculations. The disorder of the B10 histidine (molecule 2) as seen in native 4Zn insulin, is not present in the B13Q mutant. Instead, the histidine is solely pointing towards the off-axial zinc site. The B13Q mutant is therefore a true 'four zinc' insulin, in contrast with the native structure which actually contains five metal binding sites. The binding of zinc in the axial site in molecule 1, octahedrally coordinated by three symmetry-related B10 histidines and three symmetry-related water molecules, is shown in figure 3.17. The tetrahedral coordination of zinc by B10 histidine, a symmetry-related B5 histidine and two chloride ions is shown in figure 3.18.

Figure 3.17: Stereo view of zinc in molecule 1 of B13Q insulin, octahedrally coordinated on the threefold axis.

Figure 3.18: Stereo view of zinc in molecule 2 of B13Q insulin, tetrahedrally coordinated.

The termini of the four chains in the asymmetric dimer may be described as follows:

• The A chain N-terminus (molecule 2) is clearly in electron density but has slightly raised temperature factors compared to the average of 33.1Ų for the main chain of A. The A chain C-terminus is very clear with temperature factors lower than the average for the residues up to and including A20;

• The B chain N-terminus (molecule 2) has become helical, thus forming an R-conformation, but not completely to residue B1. The side chain of residue B3 takes up the position of what would be the main chain positions of B2 and B1 were the helix to stretch to B1. Residues B1 and B2 exhibit an extended conformation (see figure 4.2). Although the temperature factors of these residues are high at >50 whereas the average of the main chain of B is 30.9Ų, the electron density gives an indication for the validity of the extended conformation as compared to the full helical conformation (see figure 3.19).

  
  Figure 3.19: Stereo view of the comparison of electron density for two conformations of the N-terminus of molecule 2 in B13Q insulin.
  2F_obs-F_calc maps and refined coordinates; orange: map at start of refinement, B1-B3 included in map calculations; light blue: map corresponding to coordinates after rearrangement of the N-terminus to extended conformation, B1-B2 not included in map calculations (coordinates not fully refined).

  The Ramachandran plot of the model in the early stages of refinement indicated that residues B2 and B3 were in unacceptable regions (see figure 3.20) whereas the Ramachandran angles of these residues in the final model are within the most favoured regions. The B chain C-terminal residues are clear in the electron density, although they have high temperature factors (53.1-73.5Ų for the main chains of the last four residues);

  
  Figure 3.20: Ramachandran plot for the starting model of B13Q insulin.
  Darkest grey represents the most favoured regions (A,B,L); medium grey represents additional allowed regions (a,b,l,p); lightest grey represents generously allowed regions (~a,~b,~l,~p); white regions are disallowed.

• The C chain termini (molecule 1) have barely elevated temperature factors (average for the main chain of C is 33.0) and are very clear in the electron density;

• The D chain N-terminus (molecule 1) clearly exhibits an extended T-conformation. The temperature factors of the terminus are elevated gradually towards the end of the chain to a value of 37.5Ų for the main chain. The C-terminus has high temperature factors, rapidly increasing to 63.6Ų for the main chain of the last residue, but is clear in electron density maps.

Temperature factor plots for main chain and side chain atoms are shown in figures 3.21 a to d.

Figure 3.21: Temperature factor plots for the B13Q mutant.
a) Chain A. Average for main chain is 33.1Ų, for side chain 34.1Ų.
b) Chain B. Average for main chain is 30.9Ų, for side chain 34.9Ų.
c) Chain C. Average for main chain is 33.0Ų, for side chain 35.2Ų.
d) Chain D. Average for main chain is 26.2Ų, for side chain 27.7Ų.

3.6.2  B9 Ser®His human insulin

  Monoclinic crystal form

The mutation of serine to histidine in position B9 allows for extra zinc binding in the core of the insulin hexamer, which it was anticipated should result in increased stability. In order to study zinc binding in the case of all-R-conformation B chains, the B9H mutant was crystallised in monoclinic form, the most stable hexamer (space group P2₁). The hexameric model for the mutant was put together from molecular replacement studies in AMoRe, with an R2 dimer from native monoclinic insulin as a search model. A model built up from smaller units could help to avoid model bias, since the aggregation of the mutant could be slightly different. The molecular replacement solutions were very clear and produced a recognisable hexamer instantly. Indications of the positions for the new histidine side chains were present in the first electron density maps (see for example figure 3.22), and became clearer as refinement progressed.

Figure 3.22: First indication of the mutation sites of B9H insulin, monoclinic form.
Stereo view of one of the B9 residues with F_obs-F_calc map at +3s.

Omit maps calculated (as described in section 3.5.1) at the end of refinement confirm the final positions of the mutated residues (see figure 3.23). The six B9 histidines point towards the centre of the hexamer, as shown in figure 3.24.

Figure 3.23: Omit maps for the mutation sites of B9H monoclinic insulin after refinement.
Stereo view of the same B9 residue with F_obs-F_calc map at +3s in the same orientation as figure 3.22.

Figure 3.24: Stereo view of the core of B9H monoclinic insulin

During the course of refinement it became clear that apart from the two traditional zinc ions situated on the non-crystallographic threefold axis (ZN1 and ZN2), tetrahedrally coordinated by three B10 histidines and a chloride ion, more zinc was present in the structure. There is potential for zinc in the centre of the hexamer, coordinated by the Ne2 atoms of the B9 histidines, and by the other nitrogen atom (Nd1) of the B9 histidines, also coordinated by Nd1 of a B10 histidine of another monomer within the hexamer. Zinc was included in places where the electron density clearly indicated an atomic position, less than ~2.5Å away from a histidine nitrogen atom. This resulted in the addition of ten zinc ions, all with half occupancy. The zinc ions coordinated by two Nd1 atoms from a B9 and a B10 histidine residue, were refined with two half occupied chloride ions as third and fourth ligands. The environments of all 12 zinc ions are tabulated in table 3.15. The zinc ions are included in figure 3.24, along with the B10 histidines and the B13 glutamic acids. The picture shows the conformation of the B13 residues, all pointing towards the centre of the hexamer. This would have been highly unlikely without the zinc cations to counterbalance the negative charges of the glutamic acids.

Table 3.15: Environments of the zinc ions in monoclinic B9H insulin.
Distances between zinc and histidine nitrogens were restrained to 2.1Å. Distances between zinc and chloride were not restrained.
¹tf = temperature factor.

There is no indication of zinc at B9Nd1 or F9Nd1. As may be seen from table 3.15, not all zinc positions are equally well-defined. However, the environments are unsuitable for water molecules. The exact amount of zinc in the crystals can not be determined unambiguously by crystallographic means at this resolution.

The structural biology of zinc in relation to histidine has been reviewed by Christianson (1991). Although the zinc ions on the non-crystallographic threefold axis were refined with occupancy 1.0, full occupancy of any of the zinc ions is not warranted by the temperature factors, the electron density and the chemistry of zinc and histidines at the pH of the crystal (which is 7.27). The temperature factors of the 'axial' zinc ions is within the same region as those of the nitrogens coordinated to them (14.6-26.5Ų), leading to the conclusion that the occupancy of those zinc ions must be very close to unity. The occupancies of the other ten zinc ions vary, but judged by their refined temperature factors and those of their ligands, these zinc ions have occupancies 0.5 or less.

In order for histidine to coordinate to two metal ions at the same time, it will have to lose both its protons. The pK_a of the second proton in histidine is 14.0-14.5, while this pK_a may be lowered around two pH units by coordination to a metal ion. In protein structures, this has been seen in copper-zinc superoxide dismutase [Tainer et al., 1982]. The pH of the present mutant crystallisation is much lower than the 12.0 seen as viable for binding of two metal ions to one histidine residue, so the local environment of these histidines has an exceptionally high effective pH. The locality of the zinc binding potential can also be derived from the geometry around the metal positions. The geometry of Zn²⁺ interactions with sp² nitrogen-containing heterocycles (as in histidine) has been examined by Vedani and Huhta (1990). The metal ion prefers a head-on and in-plane approach to the lone electron pair of the nitrogen atom. From their study of the small molecule structures containing zinc-imidazole centres in the Cambridge Structural Database [Allen et al., 1979], Vedani and Huhta have deduced that the zinc ion normally lies well within 30^o from the C-N-C bisector (see figure 3.25). The geometry of some of the zinc ions in the monoclinic B9H mutant, however, deviates significantly from their findings (see table 3.16). The four zinc ions tetrahedrally coordinated by two histidines (B9 and B10, both by nitrogen Nd1) and two chlorides are significantly out-of-plane. In an ideal zinc-histidine pair, the plane deviation would be zero and the angles would both be 126^o. In the case of deviations from the histidine plane, 'head-on' only manifests itself in very similar CC and CN angles (for a definition of these angles, see the legend of table 3.16), decreasing with increased plane deviation. Therefore, the ZN1-L10Ne2 and ZN9-H9Nd1 pairs are outliers.

Figure 3.25: Preferred binding of zinc to histidine: the clustering of 'head-on' (left part of the figure) and 'in-plane' (right part of the figure) preference of zinc in histidine-environment in the Cambridge Structural Database indicates a maximum deviation of 30^o in both cases. The figure shows a top and side view of a histidine ring, and a cone with a 30^o opening angle in dashed lines. The zinc ions in the Cambridge Structural Database are all found in the area indicated by a black ellipse.

Table 3.16: Geometry of the zinc ions in monoclinic B9H. Plane deviations and angles in ^o.
¤ angle CC = angle ZN-Ne2-Cd2 or angle ZN-Nd1-Cg;
ª angle CN = angle ZN-Ne2-Ce1 or angle ZN-Nd1-Ce1.

Phenol molecules could be identified in positions described by Derewenda et al. (1989) with hydrogen bonds to main chain oxygen and nitrogen in A6/A11, C6/C11, E6/E11, G6/G11, I6/I11 and K6/K11 all between 2.5 and 3.1Å. The refined positions of the phenol molecules are confirmed by omit maps (as described in section 3.5.1) at the end of refinement (see figure 3.26).

Figure 3.26: Omit maps for the phenol molecules in B9H monoclinic insulin after refinement.
The spatial separation of the molecules in the figure does not reflect that in the model.

Although the first two residues of chains D, H and L are not clearly visible in electron density maps, it can be determined without doubt that the B9H mutant in monoclinic form is an example of an R6 hexamer. The temperature factors for the first two residues of chains D and H are relatively high (see figure 3.29), reflecting their ambiguity in electron density maps. The comparatively low temperature factor of residue L1 is due to the fact that it was reset but not refined (the residue was excluded from further refinement). The N-termini of the B chains are all essentially helical, as can be seen in figure 3.27, with in some cases a small distortion at the end resulting in an extended conformation for the first residue.

Figure 3.27: Ribbon diagram of B9H monoclinic insulin.
All twelve chains in the hexamer in different colours.

The C-termini of the B chains are disordered in all six monomers, resulting in high temperature factors (see figure 3.29). Parts of these C-termini were excluded from refinement. The electron density for the A chains was easily interpretable and the temperature factors were fluctuating within the range also seen in other insulin structures (see figure 3.28).

Figure 3.28: Average temperature factors per residue for the A chains of B9H insulin, monoclinic form

Figure 3.29: Average temperature factors per residue for the B chains of B9H insulin, monoclinic form

  Rhombohedral crystal form

The B9H mutant crystallised readily in rhombohedral form (space group R3) in T3R3-conformation. Cryocrystallographic data collection was successful with a non-standard cryoprotectant (1,2-ethanediol), after which structure determination and refinement proceeded smoothly until problems were encountered with the restraint of special distances involving atoms at special positions and atoms from symmetry-related molecules. The mutant is isomorphous with native 4Zn insulin, and has zinc ions on the threefold axis, both in the T-conformation and in the R-conformation trimer (see figure 3.30). Both zinc ions are tetrahedrally coordinated by three B10 His Ne2 and a chloride anion.

Figure 3.30: Axial zinc ions in B9H rhombohedral insulin.
Stereo views of both axial zinc ions; top: situation in molecule 1, T-conformation; bottom: situation in molecule 2, R-conformation. Residues B10 from both molecules shown in thick lines, with symmetry-related B10 residues in thinner lines. The spatial separation of the zinc ions in the figure does not reflect that in the model.

During the course of refinement, the presence of two more zinc ions was firmly established. A third zinc ion is tetrahedrally coordinated by B5 His Ne2 and B9 His Ne2 (both from molecule 2) and two water molecules (see figure 3.31). The temperature factor of this zinc ion is slightly higher than those of its ligand atoms: 45Ų for the zinc ion and 31 to 39Ų for the ligand atoms. A fourth zinc ion is tetrahedrally coordinated by B10 His Nd1 from molecule 1, B9 His Nd1 from a symmetry-related molecule 1, and two water molecules (see figure 3.32). The geometry of the B9 histidine in relation to the zinc ion, is imperfect, but can not be restrained in this particular refinement program because it is a symmetry-related residue. This histidine residue may be disordered, which would explain the presence of B13 Glu from molecule 2 within hydrogen bonding distance if the histidine ring is in a slightly different orientation. The occupancy of the zinc ion was set at 2/3, after which the temperature factor refined to 34Ų. The ligands for this zinc ion have temperature factors between 28 and 42Ų. If the occupancy of this zinc ion is assumed to be correctly assigned a value of 2/3, the stoichiometry of zinc to B10 histidine (molecule 1) is 1:1. This means that all histidines in the structure lose only one proton, which is the more appropriate at the pH of the crystallisation (which is 7.43).

Figure 3.31: Extra zinc in molecule 2 in B9H rhombohedral insulin.
Stereo view of the tetrahedral coordination by B5, B9 and two water molecules, with 2F_obs-F_calc electron density at +1s.

Figure 3.32: Extra zinc in molecule 1 in B9H rhombohedral insulin.
Stereo view of the tetrahedral coordination by B10, a symmetry-related B9 and two water molecules, with 2F_obs-F_calc electron density at +1s.

The geometry of the zinc ions in rhombohedral B9H insulin with respect to the histidine rings is reasonable compared to the averages found by Vedani and Huhta (1990), for the axial zinc ions and the zinc ion coordinated by histidines B5 and B9 from molecule 2 (see table 3.17). The fourth zinc ion, however, is distinctly out-of-plane, because the position of the B10 histidine of molecule 1 is fixed by the axial zinc ion on the other nitrogen. The geometry of the tetrahedral coordination of the fourth zinc ion is, therefore, distorted, while that of the other extra zinc ion (ZN3) is regular, as shown in table 3.18.

Table 3.17: Geometry of the zinc ions in rhombohedral B9H. Plane deviations and angles in ^o.
¤ angle CC = angle ZN-Ne2-Cd2 or angle ZN-Nd1-Cg;
ª angle CN = angle ZN-Ne2-Ce1 or angle ZN-Nd1-Ce1.

Table 3.18: Tetrahedral environment for the extra zinc in rhombohedral B9H insulin.

The conformation of the N-terminus of the B chain of molecule 2, although considered to be in the R-state, is not entirely helical. Like in the B13Q mutant, the side chain of residue B3 occupies the position of the main chain of residues B1 and B2 if the helix would have extended to B1, and vice versa. This part of the structure is shown in figure 4.2. The temperature factors for the B9H rhombohedral insulin mutant are shown in tables 3.19 and 3.20. The temperature factors for the residues in the A chains do not deviate much from the average for the whole chain. Both B chains show similar patterns: low temperature factors for the helical residues and residues 24-26 of the b-sheet, higher temperature factors for the loop at 20-23 and towards the N-terminus, and high temperature factors for the C-termini indicating disorder.

Table 3.19: Average temperature factor per residue of A chain of B9H insulin, rhombohedral form

Table 3.20: Average temperature factor per residue of B chain of B9H insulin, rhombohedral form

3.6.3  B8 Gly®Ser, B13 Glu®Gln, B30 Thr-NH₂ human insulin

At the neutral pH of the crystallisation, the B8S/B13Q/B30amide mutant forms stable hexamers, in R6-state because of the addition of phenol. Although the presence of a hydrophilic serine residue in place of glycine at position B8 causes unexpectedly increased hydrophobicity (characterised by a high capacity factor relative to pig insulin in elution from the HPLC column [Markussen et al.,1987]), the conformation of residues B1-B19 is entirely helical without much distortion (see figure 3.33). All six B8 mutation sites are clear in electron density, and the serines make hydrogen bonds mainly with B26 tyrosine Oh and B4 main chain oxygen of the same chain. The increased hydrophobicity of the mutant can not be explained from the present crystal structure. The presence of an intricate hydrogen bonding network of the B13 glutamine residues in the mutant was investigated. However, five out of six of the glutamine side chains bend away from the centre of the molecule, and hydrogen bond to B9O and B9Og of the other monomer in the same dimer. Only F13 points straight towards a central water molecule, hydrogen bonding to it. L13 bends away from the centre, but not quite towards J9, hydrogen bonding to two water molecules instead. There are no hydrogen bonds between the glutamine residues. Thus, the 'ring' structure of six glutamines as proposed by Markussen et al. (1987), is not observed.

Figure 3.33: Stereo view of the overlap of the a-helix at B1-B19 in B8S/B13Q/B30amide and native monoclinic insulin.
Mutant structure in thick lines, native structure in thin lines.

Two zinc ions are clearly identifiable on the non-crystallographic threefold axis of the hexamer. ZN1 is tetrahedrally coordinated by Ne2 of histidines D10, F10 and J10 in the present structure, with chloride as a fourth ligand. ZN2 is tetrahedrally coordinated by Ne2 of histidines B10, H10 and L10, and a chloride ion. Phenol molecules are observed in positions as described by Derewenda et al. (1989), hydrogen bonded to A6O and A11N of every A chain in the hexamer. The refined positions of the phenol molecules are confirmed through omit maps (calculated as described in section 3.5.1) at the end of refinement (see figures 3.34 a to f).

Figure 3.34: Omit maps for the phenol molecules of B8S/B13Q/B30amide insulin after refinement.
The spatial separation of the molecules in the figure does not reflect that in the model.

The chain termini of the B8S/B13Q/B30amide mutant are as follows:

• Both A chain termini are clear in electron density maps;

• The B chain N-terminus is helical to B1 and clearly identifiable in electron density maps. The C-terminus is disordered beyond B28;

• Both C chain termini are clear;

• The D chain N-terminus is poorly defined but the geometry of the final model is good. The C-terminus is disordered beyond D28;

• The E chain N-terminus is unclear and its geometry is unfavourable. Repeated omit maps do not indicate better positions. The C-terminus is very clear. There is a salt bridge between one of the C-terminal oxygens of E21 and F22 Arg Nh₂;

• The F chain N-terminus is helical to F1 and clear in electron density. The C-terminal residues beyond F28 were not included in the refinement since there is no indication of their positions;

• The G chain N-terminus is well-defined. The last peptide bond in the C-terminal region has poor electron density;

• The H chain N-terminus is unclear, resulting in residue H1 being excluded from refinement. The C-terminus is well-defined apart from the side chain of H29; this residue has therefore been refined with zero occupancy for its side chain;

• Both I chain termini are clear in electron density;

• The J chain N-terminus is not completely clear in the electron density maps, but the geometry of the refined positions is good. The C-terminus is interpretable to the end, apart from the lysine side chain of J29, which is excluded from refinement;

• Both K chain termini are clear in the electron density maps;

• The L chain N-terminus has poor electron density, and seems to come into contact with the equally poorly defined N-terminus of the H chain. The C-terminal residues beyond L28 were excluded from refinement.

Figure 3.35: Average temperature factors per residue for the main chains of B8S/B13Q/B30amide insulin

Because the C-termini of the B chains are especially flexible, from the crystal structure of the B8S/B13Q/B30amide insulin no information is gained about the amide group of residue B30. More indications of the quality of the chain termini can be derived from the temperature factor plots, figures 3.35 a to l.

3.6.4  Zn²⁺®Co²⁺ human insulin

The concentration of Co²⁺ ions in blood plasma is ten times lower than that of Zn²⁺ ions (0.002 mM and 0.02 mM, respectively [Glusker, 1991]). Although cobalt is not naturally found in insulin, the ions are similar in size and are expected to be able to take up the same role in insulin hexamerisation.

The crystallisation solution contained two reagents which have a drastic and almost antagonistic effect on the process of potential cobalt binding to insulin. On the one hand phenol promotes R-conformation. This might force Co²⁺ into a tetrahedral environment, which is unfavourable for d⁷ ions like Co²⁺. On the other hand halide ions are added, which allows Co²⁺ in tetrahedral coordination, as seen in some small molecule structures in the Cambridge Structural Database [Allen et al., 1979]. Co²⁺ insulin turned out to crystallise in rhombohedral space group R3, in T3R3-conformation. The disorder of B10 histidine (molecule 2) is clearly absent in Co²⁺ insulin, resulting in only two well-defined metal positions on the rhombohedral threefold axis. In molecule 2, the R-conformation trimer, Co²⁺ is tetrahedrally coordinated by three symmetry-related B10 His Ne2 and an iodide anion (see figure 3.36). In molecule 1 Co²⁺ is octahedrally coordinated by the other three symmetry-related B10 His Ne2 in the hexamer, and three symmetry-related water molecules (see figure 3.37).

Figure 3.36: Cobalt ion in molecule 2 in CoI insulin.
Stereo view of the tetrahedral coordination by B10 His (thick lines), two symmetry-related B10 His residues (thinner lines) and an iodide ion.

Figure 3.37: Cobalt ion in molecule 1 in CoI insulin.
Stereo view of the octahedral coordination by B10 His (thick lines), two symmetry-related B10 His residues (thinner lines) and three symmetry-related water molecules.

A phenol molecule is present in the phenol pocket in the R3 trimer of Co²⁺ insulin, similar to that seen in monoclinic insulin, hydrogen bonded to A6O and A11N in molecule 2, confirmed by omit maps (as described in section 3.5.1) at the end of refinement. This is the region of the off-axial zinc site in the R3 trimer in 4Zn native rhombohedral insulin, with which Co²⁺ insulin is isomorphous. A second phenol molecule is found in the same region of the molecule, with hydrogen bonds to B10 Nd1 and B13 Oe1. The phenol molecules prevent disorder of B10 His, stabilising it in coordination with cobalt on the threefold axis (see figure 3.38).

Figure 3.38: Phenol helps stabilise cobalt coordination in molecule 2 of Co²⁺ insulin.
Stereo view of the two phenol molecules, hydrogen bonding to residues A6, B10 and B13; F_obs-F_calc electron density at +3s. The phenol molecules were omitted from these map calculations.

The N-terminus of the B chain in molecule 2, supposedly in R-conformation, is not entirely helical to residue B1. As seen with the B13Q and the B9H mutants, the first two residues of the B chain exhibit an extended conformation, in which not the main chain of residues B1 and B2 forms the start of the helix, but the side chain of residue B3. Although the temperature factors for the first residues of the B chain are rather high (see figure 3.39), the Ramachandran angles are much better in this conformation, and the electron density is convincing (see figure 4.2). The C-termini of both B chains have high temperature factors, reflecting their flexibility.

Figure 3.39: Average temperature factors per residue for CoI insulin.
Main chains in thick lines, side chains in thin lines.

3.6.5  B9 Ser®Asp, B27 Thr®Glu human insulin

The B9D/B27E mutant is monomeric in solution [Brange et al., 1988]. The mutations in B9D/B27E insulin prevent its aggregation into hexamers because of the charge repulsion in the region where dimers would pack together into a hexamer. Without any added ions to balance the charges, the mutant does, however, crystallise as dimers isomorphously with orthorhombic native insulin. Although the pH of the crystallisation is unclear, it should be close to 6 since that is the pH of the buffer used. If the carboxylic acids at B9 and B13 have hydrogen bonds with each other, the pH must have been lower in order to allow partial protonation.

The non-crystallographic axis of the dimer is in the xz-plane, making a 30^o angle with the x-axis. The packing of the mutant is shown in figure 3.40, with the direction of the dimer axis indicated.

Figure 3.40: Packing of B9D/B27E insulin.
Stereo view of the xz-plane, with the direction of the dimer axis indicated by a thick line. Cell edges also indicated.

Because the data for the B9D/B27E mutant were not optimal (see section 3.5.5), the maps were not convincing at every stage of the refinement. In the first maps, with the side chains at the mutation sites omitted (calculated as described in section 3.5.1), the electron density for the mutations at positions B9 was reasonably clear (see figure 3.41). For residue B27 of molecule 2, however, there was no indication as to where the side chain might be, while for the same site in molecule 1 there were problems with the positioning of the side chain with respect to residues B25 from both molecules (see figure 3.42). After a few refinement cycles with REFMAC the situation at the B27 site in molecule 1 became much clearer. Omit maps for the final positions of the mutated residues B27 are shown in figure 3.43. From figure 3.44 it can be seen that the B25 Phe side chains are aligned, and the B27 side chain of molecule 2 is involved in hydrogen bonding with four water molecules and a long contact (3.4Å) with the N-terminal nitrogen of the A chain of molecule 1 of a symmetry-related dimer. The B27 side chain of molecule 1 is apparently not solvated, and has one hydrogen bond with the B29 main chain oxygen of the same chain.

Figure 3.41: Omit map of B9 in both molecules of B9D/B27E insulin before refinement.
F_obs-F_calc electron density at +3s.

Figure 3.42: Omit map of B27 in both molecules of B9D/B27E insulin before refinement.
F_obs-F_calc electron density at +3s.

Figure 3.43: Omit map of B27 in both molecules of B9D/B27E insulin after refinement.
F_obs-F_calc electron density at +3s.

Figure 3.44: The situation around B25 and B27 in both molecules of B9D/B27E insulin.
Stereo view including all atoms within 3.5Å of B25 and B27 residues.

The situation around the four carboxylic acid residues B9 and B13 is unclear. In an omit map of the final coordinates, the difference density for the aspartate and glutamate side chains is limited (see figure 3.45). Two conformations were modelled for the side chain of B13 in molecule 2, both with half occupancy. The five carboxylic groups as they were modelled all have hydrogen bonds, to each other and to water molecules. This indicates that the acid groups must have been at least partially protonated.

Figure 3.45: Omit map for residues B9 and B13 in both molecules of B9D/B27E insulin after refinement.
Stereo view including two nearby water molecules; F_obs-F_calc electron density at +3s.

The temperature factors for the main and side chains of B9D/B27E insulin are shown in figure 3.46. Those of the first three residues of the D chain (molecule 1) have been reset to 20Ų and then not refined. The C-termini of the B chains are very flexible and thus have high temperature factors, but could be identified in electron density maps, apart from the side chains of both B29 lysines. The helical regions of the B chains have lower values, while the loops at B20 to B23 have slightly raised temperature factors, as expected.

Figure 3.46: Average temperature factors per residues for B9D/B27E insulin.
Main chains in thick lines, side chains in thin lines.

3.6.6  A21 Asn®Gly, B9 Ser®Glu, B10 His®Glu human insulin

Aggregation of A21G/B9E/B10E insulin is hampered by charges at the surface where dimers would make contact to form a hexamer, and by removal of the zinc binding site. The mutant does, however form dimers in the usual way. The mutant crystallised in space group P2₁2₁2₁, with a packing different from that of native orthorhombic insulin. The non-crystallographic twofold axis of the mutant dimer is parallel to the x-axis. The packing of the mutant, indicating the screw axes of the space group and the direction of the non-crystallographic axis of the dimer, is shown in figure 3.47.

Figure 3.47: Packing of A21G/B9E/B10E insulin.
Stereo view of the xz-plane, with the 2₁ screw axes indicated in thin lines, and the direction of the dimer axis as a thick line, almost parallel to one set of screw axes. Cell edges also indicated.

The most significant changes in the mutant with respect to the native dimer involve the packing of the C-terminus of the B chain of molecule 1 and the B20-B23 loop of molecule 2 with respect to each other, and with respect to the C-terminus of the B chain of molecule 2 in a symmetry-related dimer. In the starting model, these regions were in too close contact, but the first maps indicated improved positions, especially for the main chain of B27-B30 of molecule 1 (see figure 3.48). The refined positions of B27-B30 of molecule 1, B20-B23 of molecule 2 and B27-B30 of the appropriate symmetry-related molecule 2 are shown in figure 3.49, together with the starting positions for comparison.

Figure 3.48: Indications for improved positions for the C-termini of the B chains of A21G/B9E/B10E insulin.
Stereo view of the 2F_obs-F_calc map at +1s indicating a better position for residues B27 and B28 of molecule 1, to avoid clash with B29 from a symmetry-related molecule 2. Symmetry-related atoms in thinner lines.

Figure 3.49: Final positions for the C-termini of the B chains of A21G/B9E/B10E insulin.
Stereo view in the same orientation as figure 3.48, with 2F_obs-F_calc map at +1s. Starting model (indicated by suffix 's' in molecule indicator) in thin lines, final model (indicated by suffix 'f' in molecule indicator) in thick lines. Symmetry-related atoms from both starting (dashed lines) and final (thin lines) models in bottom right-hand corner.

On the dimer surface where hexamerisation usually takes place, the mutant has six glutamic acid groups. At the pH of the crystallisation, which is 6.57, these are probably fully ionised and can not hydrogen bond with each other. Since the resolution of the data is only 2.8Å, the final omit maps (calculated as described in section 3.5.1) are somewhat poor (see figure 3.50). However, the indications for the positions of the refined side chains are present. Only two of the six glutamates make hydrogen bonds with protein: B10 (molecule 2) comes into close contact with A14 Tyr Oh of a symmetry-related molecule 1, and B13 (molecule 2) makes a hydrogen bond with the N-terminal nitrogen of a symmetry-related B chain (molecule 1). Two glutamates, namely B9 (molecule 2) and B13 (molecule 1), seem to make no contacts at all, while the other two only make contacts with solvent.

Figure 3.50: Final positions for the six central glutamic acids in A21G/B9E/B10E insulin; stereo view with F_obs-F_calc electron density at +3s.
Symmetry-related atoms in thin lines.

At the resolution of the data (2.8Å), refinement is not totally reliable, and the temperature factors are essentially meaningless.

3.6.7  A4 Glu®Gln, B25 Phe®Tyr, des B30 single chain human insulin

B25Y(B29-A1)A4Q insulin crystallised in space group P4₂32 with one insulin molecule in the asymmetric unit, and six insulin monomers grouped around the special positions with 32 symmetry to form four hexamers in the unit cell. The packing of the mutant (see figure 3.51) is equivalent to that seen for rat insulin II and insulin from the snake Zaocys dhumnades dhumnades Cantor, which has been reported by Wood et al.(1978) and Liang et al.(1984), respectively.

Figure 3.51: The packing of mutant B25Y(B29-A1)A4Q in the xz-plane.
Stereo view of the C_a-atoms of 20 hexamers; cell edges also indicated.

Although the structure was not fully refined, some of the modifications were clearly interpretable from the electron density. The cross-link between residues B29 and A1, and the deletion of residue B30, is shown in figure 3.52. The conformation of residue B29 is such that after the b-sheet of residues B23 to B28 the chain immediately turns into the a-helix of what was the beginning of the A chain. Thus this a-helix is slightly longer in the mutant than in native insulin.

Figure 3.52: The peptide bond between B29 and A1 in B25Y(B29-A1)A4Q insulin.
Stereo view with 2F_obs-F_calc electron density at +1s showing the elongated stretch of helix.

The conformation of the side chain of residue B25 from the native model was inappropriate for the mutant, clashing with the same residue from the twofold related monomer. A new position for this side chain was obvious from omit maps (calculated as described in section 3.5.1), even at limited resolution. Although the mutation from Phe to Tyr could not realistically be modelled, the new positions for the B25 residues result in convincing stacking of the aromatic rings (see figure 3.53). The amide group of the A4 Gln is poorly defined in the map. Although the change in charge must have some effect on the environment around this residue, the low resolution of the maps (2.8Å) prevented interpretation.

Figure 3.53: Aromatic stacking of twofold related B25 residues in B25Y(B29-A1)A4Q insulin.
Stereo view with 2F_obs-F_calc electron density at +1s.

The validity of the molecular replacement result was confirmed by the presence of convincing electron density for a zinc ion on the threefold axis at the point where three B10 histidine residues come together, as shown in figure 3.54.

Figure 3.54: Electron density for zinc in B25Y(B29-A1)A4Q insulin.
Stereo view of residue B10 (thick lines) and two symmetry-related B10 residues (thinner lines) with 2F_obs-F_calc electron density at +1s. Position for zinc and a fourth ligand indicated by crosses.

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