A Molecule in Motion from Still Images: Cryo-EM Heterogeneity and the Limits of Reconstruction Codex (AI) | Commissioned review v1 | 2026-10-22 Single-particle cryo-electron microscopy reconstructs molecular ensembles from noisy projections. A continuous latent representation can reveal structural heterogeneity, but its coordinates are not automatically time, free energy or a reaction pathway. This review connects reconstruction methods with image formation, mixture weighting and selection effects to define the evidence needed for mechanistic interpretation. Still images do not contain a clock A cryo-EM dataset samples particles frozen in different states and orientations. It can reveal structural variation, but it does not directly record the order or speed of transitions. A smooth animation through reconstructed states is a visualization of an inferred coordinate, not a movie of one molecule changing conformation. Three reconstruction approaches Scheres developed RELION's Bayesian approach to cryo-EM structure determination. Zhong and colleagues introduced cryoDRGN for heterogeneous reconstruction with neural networks. Punjani and Fleet developed three-dimensional variability analysis for continuous flexibility and discrete heterogeneity. These methods provide different representations and approximations; agreement among them is useful but does not independently establish a kinetic mechanism. References: ef-31-1, ef-31-2, ef-31-3 Orientation and conformation can trade off A change in projection can result from rotation, structural change or both. Limited angular coverage makes those alternatives harder to distinguish. A flexible model can explain noise or orientation errors through apparent conformation. Evaluation should therefore inspect orientation distributions and test whether structural variation persists under independent refinements. The contrast-transfer function has missing information Microscope conditions modulate spatial frequencies, including zeros or weakly transmitted bands. Combining particles with different conditions can restore some information, but uncertainty remains uneven across frequency and direction. A global resolution number can conceal poorly supported local features or state-specific differences. Latent distance has no automatic physical unit A neural latent coordinate can be transformed without changing the reconstructed family in a physically meaningful way. Euclidean distance in that space is therefore not inherently an energy barrier or transition time. Mechanistic interpretation requires observables that remain stable under representation changes and independent evidence connecting states to function. Occupancy depends on selection Particle picking, image quality filters and classification can retain some states more readily than others. Observed particle fractions need not equal equilibrium populations in solution. Converting them into free-energy differences requires strong assumptions about equilibrium, preparation and unbiased detection. Those assumptions should be tested rather than hidden in a familiar logarithm. Local validation is more informative than a smooth movie Held-out particle projections can test whether reconstructed changes improve prediction. Independent half-set reconstructions and alternative initializations can reveal unstable features. A biologically plausible movement that fails these tests may be a prior-driven interpolation. Structural models should preserve uncertainty where the density does not uniquely constrain an atomic interpretation. Mechanism requires another experiment Biochemical perturbations, time-resolved measurements or orthogonal structural probes can connect an ensemble to a functional cycle. The best follow-up is one for which competing structural interpretations predict different outcomes. This review's mixture examples explain representation and sampling effects; they do not claim a newly resolved molecular mechanism. A latent coordinate need not be a reaction coordinate A low-dimensional representation can organize images by conformation, orientation, ice thickness or other acquisition effects. A smooth path through that representation is therefore not automatically a molecular transition pathway. A proposed validation would compare reconstructions at fixed nuisance conditions and test whether structural changes predict independently observed contacts or distances. Repeating the analysis with alternative latent dimensions and initialization can expose fragile interpretations. The useful output is a set of conformational hypotheses with uncertainty, not a movie whose continuity alone is treated as evidence of dynamics. Free-energy interpretation requires a sampling argument Observed particle fractions reflect preparation, survival, picking, classification and reconstruction as well as molecular populations. The selection-bias calculation shows how equal true populations can yield an apparent energy gap. To interpret fractions thermodynamically, one would need evidence that the relevant states are sampled near equilibrium and that detection probabilities are known or sufficiently similar. A proposed perturbation could change a physical control variable and test the predicted redistribution, while keeping image-processing choices fixed. Agreement would strengthen the model but would still need to account for preparation effects. A visually plausible structural ensemble cannot supply the missing sampling assumptions. A model that can be challenged The four equations below are a compact analytical model, not a joint fit to all the cited papers. Their interpretation is as follows. Particle image yi is a contrast-transfer-modulated projection of conformation-dependent volume V, with orientation Ri and noise. State-dependent selection s changes observed particle occupancy even if the underlying ensemble is fixed. An equilibrium population ratio gives a free-energy difference only with appropriate state definitions and unbiased equilibrium sampling. Fourier-shell correlation compares independent reconstructions within a frequency shell; masking and shared information can affect its interpretation. The observational target is structural variation that predicts independent particle images. The model deliberately isolates a tractable mechanism; its purpose is to reveal which measurements would distinguish that mechanism from an alternative. Parameter values in the figures are declared illustrative inputs. A curve produced by those values is a mathematical consequence, not an estimate of an unmeasured biological or physical quantity. A discriminating validation design The primary comparison should test state differences surviving independent reconstruction and projection tests. The unit of independent replication is independent particle set and preparation; repeated readings from the same unit improve precision but do not create independent replication. A strong validation would hold out new preparations and orthogonal functional measurements before choosing thresholds or fitting nuisance corrections. In particular, orientation ambiguity and state-dependent particle selection must be measured, constrained or varied in a sensitivity analysis. Report both the principal estimate and how it changes when that assumption is relaxed. A model that succeeds only after choosing the most favorable exclusion rule has answered a different question from one evaluated with a locked rule. Worked numerical analysis If two true states are equally populated but selection retains one with probability one and the other with probability 0.5, observed fractions become two thirds and one third. Naively applying the equilibrium formula would infer an apparent difference of kBT times ln(2), despite equal true populations. The figures show selection-distorted occupancy and its apparent energy consequence; they are not molecular free-energy measurements. These calculations can be reconstructed from the companion Python file and its parameter table. Axis labels retain the model's units, and the caption distinguishes the quantities varied from those held fixed. The numerical examples were selected to expose a dependency, not to reproduce the appearance of a published figure. A useful independent check is to evaluate a limiting case and then recompute an intermediate point without the plotting code. Agreement validates the arithmetic within the declared model; it does not establish that nature follows that model. Evidence, transfer and next steps The scope of the conclusion is limited by orientation ambiguity and state-dependent particle selection. Transfer to new preparations and orthogonal functional measurements requires evidence beyond fitting the original observations. A future replication should preserve raw measurements, calibration records, exclusions and a machine-readable link between each result and the corresponding analysis. The evidence table below identifies what each selected primary study contributes. The comparison is a focused narrative synthesis, not a systematic review or a claim that all subsequent evidence has been surveyed. The proposed study has not been performed here. Its value is that a negative result would constrain an explicit explanation rather than merely lower a benchmark score. Equations (1) y_i=C_iP_{R_i}V(z_i)+\epsilon_i Particle image yi is a contrast-transfer-modulated projection of conformation-dependent volume V, with orientation Ri and noise. (2) p_{obs}(z)\propto p_{true}(z)s(z) State-dependent selection s changes observed particle occupancy even if the underlying ensemble is fixed. (3) \Delta F=-k_BT\ln(p_2/p_1) An equilibrium population ratio gives a free-energy difference only with appropriate state definitions and unbiased equilibrium sampling. (4) \mathrm{FSC}(k)=\frac{\sum F_1F_2^*}{\sqrt{\sum|F_1|^2\sum|F_2|^2}} Fourier-shell correlation compares independent reconstructions within a frequency shell; masking and shared information can affect its interpretation. Analytical figures Figure 1. Selection changes the apparent state population Two conformations have equal true populations. Only their relative selection probability changes, illustrating a bias from picking or reconstruction. figures/cryoem-conformational-inference-01.csv Figure 2. A population bias becomes an apparent energy gap Applying an equilibrium Boltzmann relation to selected fractions creates an apparent gap -ln(r). This does not justify equilibrium free-energy inference from non-equilibrium or selected particles. figures/cryoem-conformational-inference-02.csv Comparison Evidence or design choice | What it identifies | What remains unresolved Source 1 | RELION formalized Bayesian single-particle structure inference. | Image formation and prior assumptions remain relevant. Source 2 | cryoDRGN represented heterogeneous structures with neural networks. | Latent coordinates are not automatically kinetic or thermodynamic coordinates. Source 3 | 3D variability analysis modeled continuous and discrete heterogeneity. | Linearized representations and particle selection constrain interpretation. Primary observable | structural variation that predicts independent particle images | orientation ambiguity and state-dependent particle selection Independent test | state differences surviving independent reconstruction and projection tests | Requires new measurements Transfer set | new preparations and orthogonal functional measurements | Not validated by the constructed numerical example Proposed validation protocol 1. Specify structural variation that predicts independent particle images before fitting. 2. Retain independent identifiers for each independent particle set and preparation. 3. Separate new preparations and orthogonal functional measurements from model development. 4. Measure or bound orientation ambiguity and state-dependent particle selection. 5. Record units, calibration and the observation operator. 6. Compare the primary model with a named rival explanation. 7. Prespecify the test: state differences surviving independent reconstruction and projection tests. 8. Archive raw data, exclusions, parameter files and executable analysis. Limitations 1. Image formation and prior assumptions remain relevant. 2. Latent coordinates are not automatically kinetic or thermodynamic coordinates. 3. Linearized representations and particle selection constrain interpretation. 4. Companion figures are constructed analytical examples, not new experimental results. 5. Transfer to new preparations and orthogonal functional measurements has not been demonstrated by this review. Research questions 1. Which conformational features survive changes of latent representation? 2. How can state-dependent particle selection be calibrated? 3. What orthogonal measurement connects structural occupancy to function? Source evidence ef-31-1: RELION formalized Bayesian single-particle structure inference. Boundary: Image formation and prior assumptions remain relevant. Locator: Abstract / selected primary-source sections; see linked bibliographic record. ef-31-2: cryoDRGN represented heterogeneous structures with neural networks. Boundary: Latent coordinates are not automatically kinetic or thermodynamic coordinates. Locator: Abstract / selected primary-source sections; see linked bibliographic record. ef-31-3: 3D variability analysis modeled continuous and discrete heterogeneity. Boundary: Linearized representations and particle selection constrain interpretation. Locator: Abstract / selected primary-source sections; see linked bibliographic record. References ef-31-1. Sjors H.W. Scheres. RELION: Implementation of a Bayesian approach to cryo-EM structure determination. Journal of Structural Biology (2012). https://doi.org/10.1016/j.jsb.2012.09.006 ef-31-2. Ellen D. Zhong, Tristan Bepler, Bonnie Berger, Joseph H. Davis. CryoDRGN: reconstruction of heterogeneous cryo-EM structures using neural networks. Nature Methods (2021). https://doi.org/10.1038/s41592-020-01049-4 ef-31-3. Ali Punjani, David J. Fleet. 3D variability analysis: Resolving continuous flexibility and discrete heterogeneity from single particle cryo-EM. Journal of Structural Biology (2021). https://doi.org/10.1016/j.jsb.2021.107702 Provenance A focused narrative analysis of the named primary studies, not a systematic literature search or a claim to comprehensive coverage through 2026. Source-based research review and original mathematical analysis written by Codex (AI). Cited experiments belong to the cited research teams. Concept cover created with the built-in ImageGen tool. Quantitative figures are explicit constructed analyses, with code and numerical data; they are not measurements from the cited papers. This local draft has no independent peer-review or journal-acceptance record.