Structural Biology from Zero · 1: Why You Can't See a Protein

An optical microscope cannot resolve the atomic structure of a protein. Proteins are much smaller than the wavelength of visible light, so their atoms and bonds lie below the diffraction limit of conventional optical imaging.

The limitation follows from wave optics. Structural biology uses measurements with finer spatial information, including X-ray scattering, electron microscopy, and nuclear magnetic resonance, to infer molecular structure. Starting with this physical constraint gives the experimental methods that follow a common rationale.

The resolution problem

A microscope cannot resolve two points that are closer together than roughly half the wavelength of the light it uses. Ernst Abbe wrote down in 1873 that the minimal distance $d$ resolvable by a microscope using light of wavelength $\lambda$ is

$d = \frac{\lambda}{2\,\text{NA}}$

where $\lambda$ is the wavelength and $\text{NA}$ is the numerical aperture of the lens. Numerical aperture measures how wide a cone of light the lens gathers and reaches about $1.4$ for the best oil-immersion objectives. Green light sits near $\lambda = 550\ \text{nm}$ , so the finest detail an optical microscope can resolve is about

$d = \frac{550\ \text{nm}}{2 \times 1.4} \approx 196\ \text{nm}.$

Let's put a protein next to that number. A small protein is about $2\text{–}4\ \text{nm}$ across. A ribosome, one of the largest molecular machines in the cell, is around $25\ \text{nm}$ . A carbon–carbon bond in the protein backbone is $0.154\ \text{nm}$ , usually written as $1.54$ Angstrom or $1.54\ \text{Å}$ .

The best conventional optical microscope is therefore about a thousand times too coarse to resolve a bond, and roughly a hundred times too coarse to resolve the shape of a small protein. The limitation concerns spatial resolution: the instrument cannot distinguish the molecular features needed for an atomic model.

Super-resolution fluorescence microscopy, recognized by the 2014 Nobel Prize, uses techniques such as controlled fluorophore blinking to reach a few tens of nanometres. It can localize labeled features below the conventional diffraction limit, but it does not resolve individual atoms.

Probes shorter than a bond

If your ruler's smallest division is one metre, you cannot measure a coin. The fix is obvious: get a finer ruler. In wave terms, the "division size" is the wavelength, so to resolve atoms separated by $\sim 1.5\ \text{Å}$ we need a probe that has a comparable wavelength. Visible lights have wavelengths on the order of $5{,}500\ \text{Å}$ and are hopeless. Instead, the following probes are possible alternatives:

X-rays. Copper $K\alpha$ X-rays have $\lambda = 1.54\ \text{Å}$ , almost exactly the length of the bond we want to resolve. Synchrotrons tune X-rays from roughly $0.5$ to $2\ \text{Å}$ . This wavelength range allowed X-ray crystallography to produce the first protein structures in the 1950s.

Electrons. A moving electron is also a wave, with de Broglie wavelength $\lambda = h/p$ . Accelerate it through a few hundred kilovolts allows it to become very short in wavelength and (because it's now near the speed of light) relativistic:

$\lambda = \frac{h}{\sqrt{2 m_e eV\left(1 + \dfrac{eV}{2 m_e c^2}\right)}}.$

At $300\ \text{kV}$ — a standard cryo-EM microscope — this comes out to about $0.0197\ \text{Å}$ , roughly a hundredth of an ångström, finer than any atom. Therefore, the wavelength is not the bottleneck for electron microscopy; the real bottleneck is keeping a fragile, frozen biological sample from being destroyed by the beam, which is a story for later in the series.

# A 300 kV electron's wavelength (relativistic de Broglie)
V = 300e3
m, e, h, c0 = c.m_e, c.e, c.h, c.c
lam = h / np.sqrt(2*m*e*V * (1 + e*V/(2*m*c0**2)))
print(f"300 kV electron: {lam*1e10:.4f} Å")   # ~0.0197 Å — finer than an atom

Nuclear spins. Nuclear magnetic resonance does not form an image from a short-wavelength probe. It measures the magnetic environments of atomic nuclei and interactions between them, then reconstructs structures from many experimental restraints. Neutron and small-angle scattering provide additional kinds of structural information.

These methods organize much of the experimental toolkit. X-rays and electrons provide short-wavelength probes, while NMR converts local magnetic measurements into structural restraints. Neutron and small-angle scattering add information at other spatial scales. Most of this series develops the physical basis and practical limits of these complementary measurements.

Why structure is worth this much trouble

Atomic structure is valuable because it constrains molecular mechanism. The arrangement of atoms identifies binding sites, catalytic groups, steric contacts, and conformational changes that can explain function when combined with biochemical evidence.

The canonical case is DNA. When Watson and Crick proposed the double helix in 1953, drawing on Rosalind Franklin's X-ray diffraction work and other evidence, complementary base pairing immediately suggested a copying mechanism. Separating the two strands leaves each as a template for rebuilding its partner.

Proteins tell the same story with more drama. Max Perutz and John Kendrew spent over two decades solving the first protein structures — myoglobin and hemoglobin — and were rewarded with the 1962 Nobel. Hemoglobin turned out to change shape as it binds oxygen, and that motion explains how your blood loads oxygen efficiently in the lungs and dumps it in tissues. And the molecular basis of sickle-cell anemia is a single amino-acid change — a glutamate swapped for a valine on the surface of the β-chain — that exposes a sticky hydrophobic patch, causing hemoglobin molecules to polymerize into fibers that deform the red cell. This illustrates how one atom's worth of chemistry causes one disease via structure deformation.

This is why resolving the structure is crucial to understanding protein functions. An enzyme's active site tells you what reaction it catalyzes and what might inhibit it; A receptor's binding pocket is where half the drugs in your medicine cabinet act. You cannot reason about any of it from the sequence alone — although, remarkably, the sequence is enough to determine the structure, as Christian Anfinsen showed by unfolding and refolding ribonuclease in a test tube (1972 Nobel). The chain finds its own shape. The information is all there in the order of amino acids, but the structure is how that information becomes function.

A field defined by its data

Structural biology has an unusually concrete foundation: the Protein Data Bank, founded in 1971 with seven structures. Today, it holds more than 200,000 experimentally determined structures, each one a hard-won set of 3D coordinates that anyone can download for free. It is one of science's great open archives, and we will utilize it for much of this series.

An important word of honesty before we get attached to these models: A structure in the PDB is not a photograph. It is a model — a set of atomic coordinates — built to be consistent with experimental measurements, whether that's an X-ray diffraction pattern, a cryo-EM density map, or a set of NMR restraints. Every structure carries an estimate of how trustworthy it is (the resolution, in Angstroms) and a per-atom record of uncertainty. Part of becoming a structural biologist, rather than just a consumer of pretty pictures, is learning to read a structure critically: to know which parts are nailed down and which are an educated guess.

Recent developments in deep learning added a further layer of complexity to the picture. In 2021, DeepMind's AlphaFold2 began predicting protein structures from sequence accurately enough to be useful, and the AlphaFold database now holds over 200 million predicted models — a thousand times more than every experiment in history combined. It is important to note, however, that a predicted structure is a hypothesis with its own, different failure modes, and you cannot judge it without understanding how the experimental structures it learned from were made. The AI era makes the fundamentals more important, not less.

Your first look at a molecule

Let's pull a real structure out of the PDB and measure it ourselves. We'll use deoxyhemoglobin (PDB ID 4HHB, one of Perutz's own depositions) and ask how big it actually is.

from Bio.PDB import PDBList, PDBParser
import numpy as np

# Fetch the coordinates straight from the Protein Data Bank
PDBList().retrieve_pdb_file("4HHB", file_format="pdb", pdir=".")
structure = PDBParser(QUIET=True).get_structure("hb", "pdb4hhb.ent")

coords = np.array([atom.coord for atom in structure.get_atoms()])
extent = coords.max(0) - coords.min(0)        # bounding box, in ångströms
print(f"{len(coords):,} atoms")               # ~4,700
print(f"spanning {extent[0]:.0f} × {extent[1]:.0f} × {extent[2]:.0f} Å")

Around 4,700 atoms packed into a box roughly $70\ \text{Å}$ on a side — about $7\ \text{nm}$ , comfortably below the $196\ \text{nm}$ floor we computed earlier.

The interactive viewer below renders deposited coordinates directly. It includes hemoglobin, myoglobin, lysozyme, insulin, and a DNA fragment, with cartoon, stick, sphere, and molecular-surface representations.

Interactive. Compare several structures and switch representations to examine their overall folds, atomic packing, and molecular surfaces. Opens full-screen in a new tab.

In hemoglobin, the four flat heme groups mark the oxygen-binding sites. The sphere representation shows how tightly atoms pack in a folded protein. These coordinates are an experimentally constrained model reconstructed from X-ray diffraction data. In the next article, we will take a closer look at the building blocks for hemoglobin as well as almost any relevant protein you can find on Earth - the 20 amino acids.

The resolution problem

Probes shorter than a bond

Why structure is worth this much trouble

A field defined by its data

Your first look at a molecule

Further reading