BioPHYSICAL chemistry

exothermic but kinetically is extremely slow
due to the initial step of breaking the triple
bond of N 2. Despite this unfavorable step,
the overall reaction takes place readily in
nature due to facilitation of the process by the
nitrogenase enzyme system. Nitrogenase con-
sists of two essential metalloproteins, the iron
protein and the molybdenum–iron protein,
which are named after their cofactor com-
position. The three-dimensional structure of
the molybdenum–iron protein was originally
reported at a modest resolution limit of 2.8 Å
(Kim & Rees 1992). Subsequently, the quality
of the diffraction data significantly improved to
a resolution limit of 1.6 Å (Einsle et al. 2002).
The major outcome of the high-resolution
structure was the addition of a new atom in
the cofactor (Figure 15.22).
The presence of the additional atom in the
higher-resolution structure illustrates the diffi-
culty in modeling the structures of proteins
at limited resolutions. These limitations have
a significant impact on proteins with com-
plex metal clusters as the details concerning
the metal coordination are often uncertain
and difficult to model. One impact of any
resolution limit is that the lack of measur-
able diffraction past a certain angle results in
truncation errors in the Fourier analysis. To
illustrate this point, the electron density at a
point adjacent to one of the iron atoms of the
cofactor was expressed as a function of the
resolution limit, dmax:

(15.9)

where fFeis the atomic form factor for iron and s=1/dwith d being the
resolution (Einsle et al. 2002). When a finite resolution limit of 2.0 Å
is inserted, an artificial negative density, sometimes termed a ripple, is
calculated at the position where the putative nitrogen atom is located
(Figure 15.23). The effects associated with the six central iron atoms
and nine sulfur atoms of the cofactor combine to create a significant

ρπ
π
π

() ()

sin

/max

rsfs

sr

sr

s

d

= ∫ 4

2

0 2

1

2

Fe d

CHAPTER 15 X-RAY DIFFRACTION AND EXAFS 337

Cys

Fe

S

Mo

His

Homocitrate

N

Figure 15.22Model of the molybdenum–iron

cofactor showing the presence of a central atom,

tentatively identified as nitrogen, that was not

present in the original model. Modified from

Einsle et al. (2002).