E43 · Single-particle reconstruction

Single-particle Cryo-EM: From Movies to a Map

Acquire independent particle movies, align calibrated frame motion, match a broad reference and reconstruct a map from the stored projections.

Selected window status $\text{—}$

Stored particle movies $\text{—}$

Recorded electron events $\text{—}$

Stored movie dose $\text{—}$

Selected particle, one-based $\text{—}$

Accepted particle windows $\text{—}$

Inferred viewing directions $\text{—}$

Viewing-normal eigenvalue ratio $\text{—}$

Selected reference correlation $\text{—}$

Final / initial objective $\text{—}$

Half-map agreement, shell four $\text{—}$

Experiment target $\text{—}$

Predict · acquire · reconstruct

Fill the missing views

Reconstructed slice index, each object axis

8

Total dose per particle movie

D

40\,e^{-}/\mathring A^2

Illustrative ice thickness

t

60\,nm

Independent particle copies

N

96

Copies forced into one viewing direction

0\,\%

Preserved particle fraction

100\,\%

Frame drift scale, integer shifts

1\,\mathrm{pixel}

Calibrated underfocus

\Delta f

1.5\,\mu m

Assigned second-lobe amplitude

1

Counts: 0 expectation, 1 seeded statistics

1

Selected recorded particle

j

50\,\%

Display contrast only

G

1

Target: at least sixty-four accepted windows, ten viewing directions and balanced coverage; thin ice, preserved particles and a moderate dose. A high half-map agreement alone cannot pass the target.

Controls plan the next movie collection. Acquire, then process the stored counts. Presets load completed examples. Particle selection and gain only change presentation.

Four frames per independent copy. Predefined picking windows and drift calibration are supplied. Orientation matching uses a fixed broader reference, which is shown separately; map density starts from zero and is solved from the recorded images.

Grid pitch: 0.8 nanometres; no atomic-resolution claim. The selected map slice is a processing result outside the instrument. Apparatus and particle sizes use different schematic magnifications.

Synthetic weak-phase teaching model: four-lobe phantom, sixteen-voxel grid, twelve viewing directions and two in-plane angles. Picking windows, integer drift, defocus and count calibration are supplied; this is reference-assisted matching, not ab initio reconstruction or CTF estimation. Glass preparation, ice attenuation and dose damage are illustrative. Half-map agreement shares a reference and calibration, so it is not a gold-standard resolution certificate. No atomic interpretation, multiple scattering, detector MTF, continuous orientation search or conformational classification.

Start with the essentials

Focus question: Can more copies repair a missing viewing direction?
One-sentence intuition: Independent copies reduce noise; diverse directions constrain the third dimension.

Core mathematical model

Weak-phase count formation

\begin{aligned}\mathbb E[C_{jf}]&=b\,[1+a(H*P_{R_j}\rho)_f]\\H(q)&=-\sqrt{1-A^2}\sin\chi-A\cos\chi\end{aligned}

The recorded frames are shifted copies of a CTF-filtered projection; the background, contrast and transfer function are calibrated.

Electron-optical phase

\chi(q)=\pi\lambda\Delta f\,q^2-\frac{\pi}{2}C_s\lambda^3q^4

Underfocus is positive; frequencies are cycles per nanometre. The damage envelope is an assigned illustrative attenuation.

Count-derived reconstruction

\begin{aligned}\widehat\rho&=\arg\min_{\rho\geq0}\sum_j\|HP_{\widehat R_j}\rho-y_j\|^2\\&\quad+\alpha\|\rho\|^2\end{aligned}

Nonnegative projected gradient uses the same discrete projector and its exact transpose. The reference supplies orientations, never map density.

Conditional half-map agreement

F_s=\frac{\operatorname{Re}\sum_{k\in s}V_1(k)\overline{V_2(k)}}{\sqrt{\sum_{k\in s}|V_1(k)|^2\sum_{k\in s}|V_2(k)|^2}}

Independent copies are assigned to halves before matching. Both halves share a broad reference and calibration; agreement does not prove direction coverage or absolute resolution.

Common difficulties

Scientific boundary

Typical misconceptionA reconstructed map is an atomistic protein structure.

Better mental modelSynthetic weak-phase teaching model: four-lobe phantom, sixteen-voxel grid, twelve viewing directions and two in-plane angles. Picking windows, integer drift, defocus and count calibration are supplied; this is reference-assisted matching, not ab initio reconstruction or CTF estimation. Glass preparation, ice attenuation and dose damage are illustrative. Half-map agreement shares a reference and calibration, so it is not a gold-standard resolution certificate. No atomic interpretation, multiple scattering, detector MTF, continuous orientation search or conformational classification.

Reference and agreement

Typical misconceptionA high shell correlation guarantees a correct map in every direction.

Better mental modelBoth halves share an assumed low-resolution reference and calibrated transfer. No joint refinement or gold-standard independence is claimed. Rejected particles and all assigned viewing directions are reported; no FSC-derived resolution is presented.

Run the experiment

01
Collect a movie
Start from reset, acquire movies, and move the selected particle through the stored collection.
What to observe: Four noisy frames retain their count values when acquisition settings change.
02
Correct and classify
Process the stored movies and compare the raw sum, motion-corrected image and supplied reference.
What to observe: Matching infers one of twenty-four discrete orientations; rejected windows remain visible.
03
Solve a volume
Inspect the three orthogonal reconstruction slices and the falling data objective.
What to observe: Every voxel comes from recorded contrast and the projection operator; no ideal map is relabelled as a reconstruction.
04
Challenge the agreement
Compare diverse views with twice as many copies in one direction, then try thick ice and failed preparation.
What to observe: Two half-maps can agree strongly while all accepted copies look along one direction.