Supplementary Material

SUPPLEMENTAL MATERIAL (JBIC - - - -)

Fee, Castagnetto, Case, Noodleman, Stout, and Torres

To be made available at the url http://metallo.scripps.edu/ClusterGeom

Algebra for calculating a sphere in 3-space.

The general equation for a sphere in 3-space is

Expanding this gives

and if we make

and

we obtain a set of equations linear in a, b, c, and q having the form .

Four points not on a plane describe a sphere.

Thus, for P_i : x_i,y_i,z_i (i = 1. . .4)

which has the form

and applying Cramer's rule

where A_i is obtained by replacing the i^th column of A by B,

leading to

and

As these are just numbers, we know a, b, c, (the origin of the sphere in 3-space) and q which yields the radius as thus defining the sphere.

However, this algebraic approach is computationally unstable, and it is recommended to work with internal coordinates (http://www.ics.uci.edu/~eppstein/junkyard/circumcircle.html), i.e., transform the system using P₁ as the (0,0,0) reference point. In this c,e,z coordinate system, we use the approach described below.

Brief description of ClusterGeom4(Version 0.06).

Our program, ClusterGeom4, which is written in Java, takes the positions of 4 atoms in 3-space from either a *.pdb file or a *.cif file and calculates the parameters of the sphere, r and circumcenter position using an algorithm briefly described as follows.

For simplicity of treatment, we consider the vectors in 3-space: and where

correspond to the vertices of the tetrahedron and corresponds to the center of the circumsphere. Here a_x, a_y, a_z are the components of , is the Euclidean norm of the vector(http://mathworld.wolfram.com/L2-Norm.html), and is the cross-product of and.

Using the transformation to the c,e,z coordinate system

and

(to return to the original coordinate system). This approach is computationally stable.

For the iron clusters, GlusterGeom4 then translates all atoms along a parallel to a vector defined by the position of the Fe circumcenter (x₀,y₀,z₀ as calculated above) and the 0,0,0 defining the input data, thereby placing CC_Fe at the origin of the Cartesian system. One Fe atom is then selected to fall on the x-axis which is accomplished by a rotation of the entire molecule, and another Fe atom is chosen to lie in the xy-plane which is accomplished by rotation of the entire molecule about the x-axis. (The user chooses which atoms to align with the Cartesian frame.) Circumspheres are then calculated for the S and Sg spheres, and the positions of the S and Sg circumcenters, relative the CC_Fe = 0,0,0 are calculated.

Finally, the angular positions of the individual atoms on their respective circumspheres are calculated. These calculations are more accurate if the geocentric coordinate system is used. Hence, introducing atan2

which is sometimes called the "four quadrant inverse tangent," and, of course,

There has been much discussion of the use of atan2 in navigational literature (see http://williams.best.vwh.net/avform.htm#GCF).

Input files.

We provide the three *.pdb files used in the work:

perfect.pdb

HETATM 843 FE1 FS4 107 1.650 0.000 0.000 1.00 0.00 HETATM 844 FE2 FS4 107 -0.550 1.556 0.000 1.00 0.00 HETATM 845 FE3 FS4 107 -0.550 -0.778 -1.347 1.00 0.00 HETATM 846 FE4 FS4 107 -0.550 -0.778 1.347 1.00 0.00 HETATM 847 S1 FS4 107 0.750 1.061 -1.837 1.00 0.00 HETATM 848 S2 FS4 107 -2.250 0.000 0.000 1.00 0.00 HETATM 849 S3 FS4 107 0.750 1.061 1.837 1.00 0.00 HETATM 850 S4 FS4 107 0.750 -2.121 0.000 1.00 0.00 ATOM 306 SG1 CYS 39 3.950 0.000 0.000 1.00 0.00 ATOM 328 SG2 CYS 42 -1.317 3.724 0.000 1.00 0.00 ATOM 347 SG3 CYS 45 -1.317 -1.862 -3.225 1.00 0.00 ATOM 153 SG4 CYS 20 -1.317 -1.862 3.225 1.00 0.00

geometry_optimized.pdb

HETATM    2 FE1 FS4   100      -1.585   0.000 -0.597 0.00 0.00
HETATM    4 FE2 FS4   100       0.768 -1.403 -0.545 0.00 0.00
HETATM    6 FE3 FS4   100       0.041   0.000   1.693 0.00 0.00
HETATM    8 FE4 FS4   100      0.768   1.403 -0.545 0.00 0.00
HETATM    3 S1   FS4   100     -0.058   0.000 -2.214 0.00 0.00
HETATM   10 S2   FS4   100     -1.009   1.839   0.716 0.00 0.00
HETATM   11 S3   FS4   100     -1.009 -1.839   0.716 0.00 0.00
HETATM   12 S4   FS4   100       2.071   0.000   0.785 0.00 0.00
ATOM      1 SG1 CYS   1        -3.816   0.000 -1.162 0.00 0.00
ATOM      5 SG2 CYS   2         1.991 -3.150 -1.413 0.00 0.00
ATOM      7 SG3 CYS   3        -0.159   0.000   3.986 0.00 0.00
ATOM      9 SG4 CYS   4         1.991   3.150 -1.413 0.00 0.00

Here is the *.pdb file for cluster I of C. acidurici ferredoxin extracted from 2FDN.pdb.

ca_clusterI.pdb

HETATM 728 FE1 FS4    61      -0.383 14.097 73.478 1.00 6.17          FE
HETATM 729 FE2 FS4    61      -0.472 14.212 76.235 1.00 6.22          FE
HETATM 730 FE3 FS4    61       0.411 16.375 74.732 1.00 5.87          FE
HETATM 731 FE4 FS4    61       1.898 14.148 74.918 1.00 5.87          FE
HETATM 732 S1   FS4    61       0.312 12.505 74.972 1.00 6.65           S
HETATM 733 S2   FS4    61      -1.696 15.449 74.720 1.00 6.53           S
HETATM 734 S3   FS4    61       1.497 15.333 73.029 1.00 6.00           S
HETATM 735 S4   FS4    61       1.375 15.546 76.617 1.00 6.02           S
ATOM    118 SG1 CYS     8      -1.541 13.335 71.688 1.00 6.39           S
ATOM    156 SG2 CYS    11      -1.126 13.800 78.370 1.00 7.60           S
ATOM    183 SG3 CYS    14       0.347 18.607 74.751 1.00 7.02           S
ATOM    612 SG4 CYS    47       3.897 13.134 75.135 1.00 6.03           S

The *.cif file in the format used by ClusterGeom4 follows, as edited from the *.cif file provided by Zbigniew Dauter.

ca_clusterI.cif

_cell_length_a 33.95(2)

_cell_length_b 33.95(2)

_cell_length_c 74.82(4)

_cell_angle_alpha 90.00

_cell_angle_beta 90.00

_cell_angle_gamma 90.00

Fe1_61 Fe -0.01128(4) 0.41522(4) 0.982070(15)

Fe2_61 Fe -0.01391(4) 0.41861(4) 1.018910(15)

Fe3_61 Fe 0.01211(4) 0.48234(4) 0.998820(14)

Fe4_61 Fe 0.05592(4) 0.41672(4) 1.001310(14)

S1_61 S 0.04050(7) 0.45790(7) 1.02402(2)

S2_61 S 0.04409(7) 0.45165(7) 0.97606(3)

S3_61 S 0.00920(8) 0.36833(7) 1.00203(3)

S4_61 S -0.04995(7) 0.45506(8) 0.99866(3)

Fe1_62 Fe 0.18647(4) 0.72137(4) 0.938180(14)

Fe2_62 Fe 0.21797(4) 0.73013(4) 0.971520(14)

Fe3_62 Fe 0.17264(4) 0.66534(4) 0.963440(14)

Fe4_62 Fe 0.13942(4) 0.73790(4) 0.966120(14)

S1_62 S 0.16791(8) 0.70173(7) 0.98835(3)

S2_62 S 0.12655(7) 0.69368(7) 0.94468(2)

S3_62 S 0.18801(7) 0.77721(7) 0.95428(3)

S4_62 S 0.23296(7) 0.68188(7) 0.95149(3)

Output files.

When acting on a *.pdb file the ClusterGeom4 output file, *.log contains the following.

ca_clusterI.log

ClusterGeom version 0.05j ($Date: 2002/04/16 01:11:15 $ [UTC])
==============================================================

[Xatom = FE1, XYatom = FE3]

Number of atoms parsed: 15
Cluster type: fe4s4

#Iron atoms (xyz):
FE1              1.670      -0.000         0.000
FE2           -0.613      -0.890      -1.272
FE3           -0.544         1.578         0.000
FE4           -0.510      -0.693         1.431
iron circumcenter :    0.000         0.000         0.000 ; r =    1.670

#SulfurAtoms (xyz):
S1               0.726      -2.085         0.107
S2               0.704         0.923      -1.819
S3               0.785         1.132         1.789
S4            -2.207         0.032         0.123
all sulfurs circumcenter :    0.001         0.001         0.061 ; r =    2.209
dist(SCC, FeCC) =    0.061 Angstroms

#Cys Sulfur atoms (xyz):
SG               3.923         0.056      -0.215
SG            -1.947      -1.989      -2.745
SG            -1.355         3.645      -0.239
SG            -1.167      -1.899         3.215
SG(Cys) circumcenter :    0.017   -0.011      -0.000 ; r =    3.912
dist(SCysCC, FeCC) =    0.020 Angstroms

*****
Relative GeomSpherical coords (longitude, latitude, r):

Number of atoms parsed: 15
Cluster type: fe4s4

#Iron atoms (geospherical):
FE1           -0.000         0.000         1.670
FE2           -124.558      -49.644         1.670
FE3           109.030         0.000         1.670
FE4           -126.390      58.976         1.670

#SulfurAtoms (geospherical):
S1            -70.837         1.215         2.209
S2            52.677      -58.327         2.209
S3            55.270      51.480         2.209
S4            179.190         1.609         2.209

#Cys Sulfur atoms (geospherical):
SG               0.978      -3.147         3.912
SG            -134.797      -44.562         3.912
SG            110.574      -3.494         3.912
SG            -122.087      55.264         3.912

*****
Hammer coords (xH, yH):

Number of atoms parsed: 15
Cluster type: fe4s4

#Iron atoms (hammer):
   0.613         0.000      FE1
-1.065      -0.892      FE2
   2.355         0.000      FE3
-0.892         1.039      FE4

#SulfurAtoms (hammer):
-0.619      -0.006      S1
   0.860      -1.038      S2
   1.062         0.907      S3
-2.373         0.001      S4

#Cys Sulfur atoms (hammer):
   0.632      -0.056      SG
-1.279      -0.821      SG
   2.375      -0.076      SG
-0.937         0.978      SG

*****
Generating output files
Modified PDB file 2fdn_cluster_1.pdb.mod saved succesfully
XYZ and GeomSpherical coordinate files saved succesfully
> 2fdn_cluster_1.pdb.xyz and 2fdn_cluster_1.pdb.spher created

See below for output when a *.cif file is used as input.

Hammer-Aitoff projection.

Hammer-Aitoff projections (xy) on a unitary sphere; 35.25^o are first added to all longitudes in order to center the cluster on the projection. The Hammer-Aitoff projection in 2D is given by longitude (q) = 2 * arctan ((z * x) / (4 * z² - 2)) and latitude (f) = arcsin (y * z) where z = (1 – (0.25 * x)² – (0.5 * y)²)^1/2. The graticule for the desired ranges of q, f values was calculated from the inverse of the above expressions, x = 2 * t * cos(f) * sin(q/2) and y = t * sin(f) where t = (2 / (1 + cos(f) * cos(q/2))^1/2. Short scripts are available to generate the q,f graticules as well as the xy projections.

Equations of error propagation.

Taylor (1) provides an excellent exposition on error propagation, and a useful website, developed at the National Institute of Standards and Technology, is found at: http://www.itl.nist.gov/div898/handbook/mpc/section5/mpc55.htm.

Analysis of error in the derived circumspherical parameters begins with the unit cell parameters: a, b, c and a, b, g and the fractional coordinates of each atom (f_xi, f_yi, f_zi) along with the estimated error in the latter (df_xi, df_yi, df_zi). For the case of SHELX refinement, these are found in the *.cif file that is written when ACTA is included in the *.ins file during the final least squares refinement (2).

Depending on the space group (cf. Chap. 18 of (3)), atom positions with associated errors are calculated. For the ferredoxin of C. acidurici, the space group is P4₃2₁2, a = 33.95 Å, b = 33.95 Å, c = 74.82 Å and a = b = g = 90 deg,

allowing the simple conversions:

and

We ignore the error associated with a, b, c which are very small (see below).

According to error propagation theory, the general expression for the error in a derived parameter, e.g.,

is given by

which is the general expression for the propagated error in q. The values of the partial derivatives of q taken at yz, xz, and xy are the coefficients for the propagation of error in x, y, and z, respectively.

Error in the circumspherical parameters.

Radii of the spheres. For a sphere centered on 0,0,0

and our derivatives are

for the individual atoms. The error in r_i is then given by

which from the data of Dauter et al. (4) for cluster I of the C. acidurici ferredoxin, we calculate

dr(Fe1) = 0.00113

dr(Fe2) = 0.00113

dr(Fe3) = 0.00106

dr(Fe4) = 0.00106

the average being 0.00109 Å.

Thus, for this set of data, the radius of the Fe circumsphere and its standard error is

Å.

Similarly for the S and Sg circumspheres, we calculate

as used in Table 1 of the manuscript.

Longitude and latitude. Turning to the error in the latitude and longitude of the position of each atom on its respective circumsphere, i.e., with the circumsphere centered on 0,0,0, we start with

and recalling generally that

we obtain

and

The standard deviation in q is then obtained from

Using the ferredoxin data, this varies from 0.000998 to 0.00107 degrees for the Fe atoms, 0.00179 to 0.00202 for the S atoms, and from 0.001762 to 0.00218 degrees for the Sg atoms.

Turning to angles of latitude, generally

which, because we are using geocentric coordinates, is replaced by the identity

(see http://www.geom.umn.edu/docs/reference/CRC-formulas/node42.html. Hence,

from which we obtain the derivatives

and the error in f is then given by

The latitudinal errors in the Fe atom positions range from 0.000998 to 0.00103 degrees, from 0.00172 to 0.00202 degrees for the S atoms, and from 0.00176 to 0.00218 degrees for the Sg atoms. These are the values used in Table 1 of the manuscript.

The above cited error values were obtained when ClusterGeom4 operated on a *.cif file containing the error in fractional coordinates. In addition to that found in the *.log file (see above), the output contains the following information

Fe1_61 Fe -0.382956(0.001358) 14.096719(0.001358) 73.4784774(0.0011223)

Fe2_61 Fe -0.4722445(0.001358) 14.2118095(0.001358) 76.2348462(0.0011223)

Fe3_61 Fe 0.4111345(0.001358) 16.375443(0.001358) 74.7317124(0.00104748)

Fe4_61 Fe 1.898484(0.001358) 14.147644(0.001358) 74.9180142(0.00104748)

S1_61 S 1.374975(0.0023765) 15.545705(0.0023765) 76.6171764(0.0014964)

S2_61 S 1.4968555(0.0023765) 15.3335175(0.0023765) 73.0288092(0.0022446)

S3_61 S 0.31234(0.002716) 12.5048035(0.0023765) 74.9718846(0.0022446)

S4_61 S -1.6958025(0.0023765) 15.449287(0.002716) 74.7197412(0.0022446)

SG_8 S -1.54133(0.0023765) 13.334881(0.0023765) 71.6880348(0.0022446)

SG_11 S -1.1261215(0.0030555) 13.8003355(0.0030555) 78.370209(0.0022446)

SG_14 S 0.3466295(0.002716) 18.607316(0.0023765) 74.7511656(0.0022446)

SG_47 S 3.89746(0.0023765) 13.1342365(0.0023765) 75.1349922(0.0014964)

Error estimates for r:

Fe1_61 0.0011315145265711

Fe2_61 0.0011310228531794

Fe3_61 0.0010636994486845

Fe4_61 0.0010598967750216

S1_61 0.0015411042407426

S2_61 0.0022503778474609

S3_61 0.0022482807473861

S4_61 0.0022659113447766

SG_8 0.0022491947188299

SG_11 0.0022733949322062

SG_14 0.0022525185751999

SG_47 0.0015326108367592

STATS

Fe atoms

Array

(

[min] => 0.0010598967750216

[max] => 0.0011315145265711

[sum] => 0.0043861336034566

[sum2] => 4.8143755090884E-06

[count] => 4

[mean] => 0.0010965334008641

[stdev] => 4.0139391481851E-05

[variance] => 1.6111707485333E-09

)

S atoms

Array

(

[min] => 0.0015411042407426

[max] => 0.0022659113447766

[sum] => 0.0083056741803662

[sum2] => 1.7628323278632E-05

[count] => 4

[mean] => 0.0020764185450916

[stdev] => 0.00035696282767794

[variance] => 1.2742246034383E-07

)

SG atoms

Array

(

[min] => 0.0015326108367592

[max] => 0.0022733949322062

[sum] => 0.0083077190629952

[sum2] => 1.7649937309565E-05

[count] => 4

[mean] => 0.0020769297657488

[stdev] => 0.00036303732689263

[variance] => 1.3179610071735E-07

)

Error estimates for longitude [atom degrees (radians)]:

Fe1_61 0.0055175231257885 (9.6298945099938E-05)

Fe2_61 0.0054718400045935 (9.5501624222498E-05)

Fe3_61 0.0047499879628258 (8.2902929381407E-05)

Fe4_61 0.0054508327848007 (9.5134979070423E-05)

S1_61 0.008724848890333 (0.00015227733987529)

S2_61 0.0088381042945433 (0.00015425401957443)

S3_61 0.012439655704741 (0.00021711294986222)

S4_61 0.0087769025956324 (0.00015318584842062)

SG_8 0.010143536234106 (0.00017703810508049)

SG_11 0.012643698883794 (0.00022067417515294)

SG_14 0.0083613358056401 (0.00014593283967331)

SG_47 0.0099387143505446 (0.00017346328883221)

Error estimates for latitude [atom degrees (radians)]:

Fe1_61 0.0010340668437313 (1.8047871108816E-05)

Fe2_61 0.0009979658294837 (1.7417789546887E-05)

Fe3_61 0.0010075291115097 (1.7584700305538E-05)

Fe4_61 0.0010129535448015 (1.7679374526534E-05)

S1_61 0.0017203701367661 (3.0026123239554E-05)

S2_61 0.0018201618028012 (3.1767816377917E-05)

S3_61 0.0017889764772086 (3.1223529768019E-05)

S4_61 0.0020228165202092 (3.5304808441384E-05)

SG_8 0.0018635243044386 (3.2524634803391E-05)

SG_11 0.0021844001768871 (3.8124975267827E-05)

SG_14 0.0017621103856293 (3.0754628012819E-05)

SG_47 0.0017654569097542 (3.0813035877295E-05)

Other useful scripts

convert

A utility script for quick conversion between xyz, spherical, geospherical, and cylindrical coordinate systems. If used as "convert", 3 parameters need to be passed, the type of conversion and the input and output files (.pdb format).

$ convert xyz2spher inputfile outputfile

if we create symbolic links to "convert," only two parameters (input file and output file) are needed

$ ln –s convert xyz2spher

$ xyz2spher inputfile outputfile

For helpwith usage and parameters do $ convert without I/O files.

hammer

Uses q, f information to calculate x,y projections on the Hammer-Aitoff graticule.

graticule

Uses inverse Hammer-Aitoff equations to generate the graticule for 2D visualization of spherical information

greatcircle

Calculates intermediate points of a great circle (http://williams.best.vwh.net/avform.htm#GCF).

Obtaining the ClusterGeom package.

Programs may be downloaded from http://metallo.scripps.edu/ClusterGeom.

Identification of structures used in the manuscript.

DAKVIU
Tetrabutylammonium tetrakis((2,4,6-tris(isopropyl)phenylthio)-(mu!2$-sulfido)-ir
      on)
C60 H92 Fe4 S8 1-,C16 H36 N1 1+
T.O'Sullivan,M.M.Millar
J.Am.Chem.Soc., 107, 4096,1985

BZMSFE
bis(Tetraethylammonium) tetrakis(benzylthio-(mu!3$-sulfido)-iron)
C28 H28 Fe4 S8 2-,2(C8 H20 N1 1+)
B.A.Averill,T.Herskovitz,R.H.Holm,J.A.Ibers
J.Am.Chem.Soc., 95, 3523,1973

FESTPH
bis(Tetramethylammonium) tetrakis(thiophenolato-iron sulfide)
C24 H20 Fe4 S8 2-,2(C4 H12 N1 1+)
L.Que Junior,M.A.Bobrik,J.A.Ibers,R.H.Holm
J.Am.Chem.Soc., 96, 4168,1974

FESBAS10
Tetra-n-butylammonium pentasodium tetrakis((mu!3$-sulfido)-(beta-mercaptopropion
      ate-S)-iron) N-methylpyrrolidone solvate
C12 H16 Fe4 O8 S8 6-,C16 H36 N1 1+,5(Na1 1+),5(C5 H9 N1 O1)
H.L.Carrell,J.P.Glusker,R.Job,T.C.Bruice
J.Am.Chem.Soc., 99, 3683,1977

1IR0

JRNL        AUTH   K.FUKUYAMA,T.OKADA,Y.KAKUTA,Y.TAKAHASHI
JRNL        TITL   ATOMIC RESOLUTION STRUCTURES OF OXIDIZED [4FE-4S]
JRNL        TITL 2 FERREDOXIN FROM BACILLUS THERMOPROTEOLYTICUS IN
JRNL        TITL 3 TWO CRYSTAL FORMS: SYSTEMATIC DISTORTION OF
JRNL        TITL 4 [4FE-4S] CLUSTER IN THE PROTEIN
JRNL        REF    J.MOL.BIOL.                   V. 315 1155 2002

1IQZ

JRNL        AUTH   K.FUKUYAMA,T.OKADA,Y.KAKUTA,Y.TAKAHASHI
JRNL        TITL   ATOMIC RESOLUTION STRUCTURES OF OXIDIZED [4FE-4S]
JRNL        TITL 2 FERREDOXIN FROM BACILLUS THERMOPROTEOLYTICUS IN
JRNL        TITL 3 TWO CRYSTAL FORMS: SYSTEMATIC DISTORTION OF
JRNL        TITL 4 [4FE-4S] CLUSTER IN THE PROTEIN
JRNL        REF    J.MOL.BIOL.                   V. 315 1155 2002

2FDN I & II

JRNL        AUTH   Z.DAUTER,K.S.WILSON,L.C.SIEKER,J.MEYER,J.M.MOULIS
JRNL        TITL   ATOMIC RESOLUTION (0.94 A) STRUCTURE OF CLOSTRIDIUM
JRNL        TITL 2 ACIDURICI FERREDOXIN. DETAILED GEOMETRY OF [4FE-4S]
JRNL        TITL 3 CLUSTERS IN A PROTEIN
JRNL        REF    BIOCHEMISTRY                  V. 36 16065 1997

1B0Y

JRNL        AUTH   E.PARISINI,F.CAPOZZI,P.LUBINI,V.LAMZIN,C.LUCHINAT,
JRNL        AUTH 2 G.M.SHELDRICK
JRNL        TITL   AB INITIO SOLUTION AND REFINEMENT OF TWO
JRNL        TITL 2 HIGH-POTENTIAL IRON PROTEIN STRUCTURES AT ATOMIC
JRNL        TITL 3 RESOLUTION
JRNL        REF    ACTA CRYSTALLOGR., SECT.D     V. 55 1773 1999

1IUA

JRNL        AUTH   L.LIU,T.NOGI,M.KOBAYASHI,T.NOZAWA,K.MIKI
JRNL        TITL   ULTRAHIGH-RESOLUTION STRUCTURE OF HIGH-POTENTIAL
JRNL        TITL 2 IRON-SULFUR PROTEIN FROM THERMOCHROMATIUM TEPIDUM
JRNL        REF    TO BE PUBLISHED

BZTFEA
tris(Tetraethylammonium) tetrakis((benzylthiolato-S)-(mu!3$-sulfido)-iron)
C28 H28 Fe4 S8 3-,3(C8 H20 N1 1+)
J.M.Berg,K.O.Hodgson,R.H.Holm
J.Am.Chem.Soc., 101, 4586,1979

BUTFAX
tris(Tetraethylammonium) tetrakis((mu!3$-sulfido)-(p-bromophenyl-thio)-iron)
C24 H16 Br4 Fe4 S8 3-,3(C8 H20 N1 1+)
D.W.Stephan,G.C.Papaefthymiou,R.B.Frankel,R.H.Holm
Inorg.Chem., 22, 1550,1983

References

1. Taylor, J. R. (1982) An Introduction to Error Analysis (University Science Books, Mill Valley, California).

2. Sheldrick, G. M. & Schneider, T. R. (1997) Methods Enzymol. 277, 319 - 343.

3. Stout, G. H. & Jensen, L. H. (1968) X-ray structure determination: A practical guide (Collier-Macmillan, London).

4. Dauter, Z., Wilson, K. S., Sieker, L. C., Meyer, J. & Moulis, J. M. (1997) Biochemistry 36, 16065 - 16073.