= G. Fermi
{c}
\b[<G. Fermi>] is the first author of the 1984 study refining human <deoxyhemoglobin> at $1.74\,\mathrm{\mathring A}$ resolution, and is named with <Max Perutz> as a depositor of its primary structure record, 4HHB.<The crystal structure of human deoxyhaemoglobin at 1.74 A resolution by G. Fermi and others>[RCSB 4HHB, deposition authors, primary citation and Experimental Data Snapshot]{ref} The published initial-only identity is retained.
The model allowed the investigators to examine local geometry around <iron> in the oxygen-binding groups of <hemoglobin>. Their analysis also tested whether conclusions about that geometry persisted when selected model restraints were removed.<The crystal structure of human deoxyhaemoglobin at 1.74 A resolution by G. Fermi and others>[Primary Abstract, unrestrained refinement from modified geometry]{ref} Such a comparison asks how strongly the observations constrain a feature independently of assumptions imposed during fitting.
An original one-parameter calculation illustrates this issue without recreating the historical refinement. Suppose a scalar coordinate $x$ is constrained by an observed value $y$ with uncertainty $\sigma$, and by a preferred value $x_0$ with strength $\lambda$. Minimize
$$
L(x)=\frac{(x-y)^2}{\sigma^2}+\lambda(x-x_0)^2,\qquad
\widehat x=\frac{y/\sigma^2+\lambda x_0}{1/\sigma^2+\lambda}.
$$
For $y=0.40$, $\sigma=0.05$, $x_0=0$ and $\lambda=400$ in compatible units, $\widehat x=0.20$. Removing the restraint gives $\widehat x=0.40$. A fitted value can therefore depend on both observations and a modeling choice. This toy <weighted least squares> problem is not the algorithm used for 4HHB.
Agreement with data should consequently be examined together with restraint sensitivity and independent physical evidence. A precise-looking coordinate is not established merely by printing many decimal places. Fermi's documented work exemplifies using <X-ray crystallography> to make a molecular arrangement quantitatively testable.
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