In X-ray diffraction, X-rays passing through a regularly ordered crystal interfere with one another, creating a spot pattern on a detector. By analyzing that pattern, scientists can calculate where the atoms sit and reveal the 3-D structure of the molecule. Hodgkin digitized these complex patterns with high-precision cameras, laborious hand calculations, and one of the earliest electronic computers. She tackled very large biomolecules such as vitamin B12 and insulin, determining their atomic arrangements for the first time. Her results accelerated research in nutrition and diabetes therapy. X-ray crystallography later expanded to DNA and many enzymes, laying the foundation of modern structural biology. It shows how physical techniques and medicine can work together for society’s benefit.

The theory of X-ray crystallography relies on Bragg’s law (nλ = 2d sin θ) and on measuring reflection intensities I(hkl) to obtain the magnitudes of structure factors F(hkl). The missing phase information—the phase problem—must be solved; Hodgkin employed heavy-atom and isomorphous replacement methods to do so. After determining penicillin, she exploited cobalt in vitamin B12 as an intrinsic heavy scatterer. She computed electron density maps via inverse Fourier transforms on an EDSAC computer, building atomic models with ~0.05 nm resolution. For insulin, molecular symmetry and two Zn2+ heavy atoms helped her solve the orthorhombic lattice. These achievements opened the door to enzymatic mechanism studies and rational drug design, integrating structural biology with pharmacology and nutrition science. Her data-processing strategies anticipated later fast Fourier transform algorithms and the use of synchrotron radiation.

Hodgkin systematized multiple isomorphous replacement analysis with effective molecular replacement, combining anisotropic scattering correction and heavy-atom enrichment to attack the macromolecular phase problem. Vitamin B12 (C63H88CoN14O14P) involved 937 parameters and was then the largest single-crystal structure solved; heavy-atom difference patterns yielded non-centrosymmetry and fixed the space group as P212121. For insulin she reduced the R-factor to the 13 % range, pinpointing disulfide bridge conformations and tetrahedral Zn coordination sites. Her workflow coupled sequential Patterson refinement with Fourier difference density fitting, conceptually foreshadowing synchrotron MAD phasing. She also established experimental protocols that simultaneously applied Lorentz-polarization corrections and initial B-factor estimates during structure-factor scaling, effectively defining high-resolution data-collection standards for large biomolecules.