Blog: Are We Capturing the Ensemble? - #87
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Add a post on how structural biology experiments preserve, blur, or lose molecular ensembles, converted from the LaTeX draft. Introduces the source distribution and "ensemble resolution", and contrasts cryo-EM particle images with reconstructed maps as inference targets. Authors: Minhuan Li, F. Emil Thomasen, Pilar Cossio Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Presentation work driven by the new ensemble post, but reusable:
- post layout: byline gains an optional `contact` front-matter field,
rendered as a muted tail on the same line as the authors instead of
as a second orphan paragraph. Guarded by `{% if %}`, so existing
posts are unchanged.
- captions: `.blog-caption` / `.blog-caption-wide` were full-size
italic body text, indistinguishable from a paragraph. Now 0.875rem,
grey, centered. Figures became blocks with a gap above the caption.
- `.blog-image-hero`: 90%-width lead figure, centered with auto
margins so the width is measured against the full column.
- `.post-lead`: opt-in drop cap on a post's first paragraph.
Also swap in the updated figure (no slide chrome), move it to the top
of the post as a lead image, and retarget the one in-text reference
that said "the figure below".
Ignore vendor/ so a local `bundle config set path vendor/bundle`
preview build cannot be committed by accident.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
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Nice work! A preview showing what the website will look like with changes due to your PR has been deployed to: https://rs-station.github.io/rs-station.github.io-preview/pr-previews/pr-87/ |
Preview builds run with --baseurl /rs-station.github.io-preview/ pr-previews/pr-N, but a root-absolute markdown image path ignores it and 404s. Route the src through relative_url so it resolves under both the preview baseurl and the empty one on the live site. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Content now follows the revised draft: the opening is reframed around two opposite intuitions (blur read as dynamics, averaging dismissed as uninformative), the Boltzmann section is replaced by a p_target vs p_src discussion, ensemble resolution gains the multi-dimensionality and reweighting material, the cryo-EM section is reframed as particles to maps, and a takeaway section, acknowledgments and a seventh reference are added. Equation numbers dropped — the revised text has no cross-references. Fixed the kernel expression, which the source renders as a stray comma. Title is now "Are We Capturing the Ensemble?", so the post and its asset directory are renamed from -seeing- to -capturing- to keep the URL consistent with the title. Done before merge, while the URL has no external references to break. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Two reusable text treatments:
- .key-term: italic in the site blue, for a term at the point it is
defined. Applied to "ensemble resolution".
- .post-ack: a closing aside, separated by a hairline and set quieter
than body copy. `em { color: inherit }` keeps the wrapping <em> from
overriding the muted color.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
minhuanli
changed the title
tjlane
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tjlane
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@minhuanli nice job, MUCH improved!
I will approve, but after you address my comment on line 29 😇
| title: Are We Capturing the Ensemble? | ||
| subtitle: What structural biology experiments preserve, blur, or discard about molecular distributions |
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You leave some "punch" on the table with the title & subtitle. Here's my suggestion:
| title: Are We Capturing the Ensemble? | |
| subtitle: What structural biology experiments preserve, blur, or discard about molecular distributions | |
| title: A Sharp Look at Fuzzy Ensembles | |
| subtitle: What structural biology experiments can reveal – and obscure – about molecular distributions |
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Or: "Sharp thinking regarding fuzzy maps"
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| To make this question precise, we first need to distinguish the distribution we want to learn from the one the experiment actually sees. | ||
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| ### What distribution enters the experiment? |
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I am not sure how you can "enter" an experiment.
| ### What distribution enters the experiment? | |
| ### What distribution does an experiment report? |
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This section is intended for a short discussion about p_src and p_target, so it is truly "what distribution enters the experiment". In the next section we then talk about how p_src was preserved or reported.
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@minhuanli my comment purely concerned English usage (the content: understood). I think you need a different verb, as a subject cannot "enter" an experiment.
| Two ways in which an experiment can encode a conformational ensemble. Ensemble-averaged measurements combine contributions from many molecules into each observable. In single-particle or single-molecule measurements, each observation arises from an individual molecule, and the ensemble is represented statistically across many observations. | ||
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| Structural biology is increasingly being asked to answer questions about ensembles rather than single structures. But two opposite intuitions can lead us astray. In cryo-electron microscopy (cryo-EM), a fuzzy or weak region of a reconstructed map is sometimes treated as if it were direct evidence of an ensemble: blur becomes dynamics. In the other direction, an experiment such as X-ray diffraction may be dismissed as incapable of constraining an ensemble because its measurements average over many molecules. |
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I'd spice this up just a bit by adding a sentence that highlights some of the opportunity presented by ensembles:
"This exciting frontier might let us finally understand allostery, how entropy contributes to structure, and how proteins change their shape when they recognize binding partners."
Or something like that.
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| ### What distribution enters the experiment? | ||
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| Before asking what information the measurement preserves, we should first be clear about what distribution is being measured. Let $$p_{\mathrm{target}}(x)$$ denote the molecular distribution relevant to the scientific question, and $$p_{\mathrm{src}}(x)$$ the distribution actually present in the prepared sample when the measurement is made. Often we hope that $$p_{\mathrm{src}}$$ faithfully represents $$p_{\mathrm{target}}$$, but the two need not be identical. |
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| Before asking what information the measurement preserves, we should first be clear about what distribution is being measured. Let $$p_{\mathrm{target}}(x)$$ denote the molecular distribution relevant to the scientific question, and $$p_{\mathrm{src}}(x)$$ the distribution actually present in the prepared sample when the measurement is made. Often we hope that $$p_{\mathrm{src}}$$ faithfully represents $$p_{\mathrm{target}}$$, but the two need not be identical. | |
| Before asking what information the measurement preserves, we should first be clear about what distribution is being measured. Let $$p_{\mathrm{target}}(x)$$ denote a molecular distribution relevant to the scientific question, and $$p_{\mathrm{src}}(x)$$ the distribution actually present in the prepared sample when the measurement is made. Often we hope that $$p_{\mathrm{src}}$$ faithfully represents $$p_{\mathrm{target}}$$, but the two need not be identical. |
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Not sure why this change is required?
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Change the definite "the molecular distribution relevant to the scientific question" to indefinite: "a molecular distribution".
I am doubtful you can logically argue that there is a single distribution "per question" (if that even makes sense). Feel free to go for it and prove me wrong.
I actually might quibble with the implication here that there is some Platonic "ideal distribution" one seeks at all. That idea sounds imprecise. But that is a broader debate I don't think we need to have.
| p_{\mathrm{src}}\longrightarrow\text{measurements}\longrightarrow\text{processed data}. | ||
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| Which distinctions within $$p_{\mathrm{src}}$$ survive this chain? |
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| Which distinctions within $$p_{\mathrm{src}}$$ survive this chain? | |
| What happens to $$p_{\mathrm{src}}$$ as it is transformed by these steps? |
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this suggestion is not quite right. p_src remains unchanged, and since it is the quantity we want to recover, it is not transformed by these steps. What changes through these steps is our ability to determine p_src.
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point taken, but: then say that!
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| where $$m(x)$$ is the forward model for the observable and $$\varepsilon$$ represents measurement uncertainty. The experiment does not reveal the conformation of any individual molecule. Instead, it reports an expectation of the observable over the source distribution. | ||
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| Importantly, averaging in **observable space** is not the same as averaging in **conformational space**. Suppose two conformations, $$x_A$$ and $$x_B$$, occur with probabilities $$p_A$$ and $$p_B$$. The measured signal is $$p_A m(x_A)+p_B m(x_B)$$ not, in general, $$m\left(p_A x_A+p_B x_B\right)$$. This distinction matters. If the observable responds differently to the two conformations, their contributions can remain separately constrained even though the measurement averages over many molecules. An X-ray scattering pattern, for example, need not correspond to a fictitious structure halfway between two populated conformations. Spatially distinct states can leave distinct contributions to the measured density. "Averaged" therefore does not mean "only informative about an average structure." |
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I do think the example of altconfs is a familiar and powerful one that could be added here.
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You might not believe most junior cryoEM people don't know what is "altconf" and occupancy.
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Hmm I do find that surprising! But maybe expected in 3.5 Å land. This comment you can resolve if you like, I will not die on this hill.
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| The important point is therefore not that one class of experiment "measures ensembles" while the other does not. Both impose constraints on $$p_{\mathrm{src}}$$, but they preserve different distinctions within it. The next question is the one that matters for ensemble inference: **which differences between two possible source distributions would these measurements actually allow us to resolve?** | ||
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| ### The question of ensemble resolution |
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| ### The question of ensemble resolution | |
| ### Can we measure an "ensemble" resolution? |
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The subtitles also underperform -- think about making some declarative statements. The skimming reader will only see those!
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The ensemble resolution is still an open question in my mind. I’m trying to raise the question here rather than propose a solution. If we ask, “Can we measure an ‘ensemble’ resolution?”, would readers assume that we’re going to answer “yes” in what follows, or does it still come across as an open question?
Also, for this blog, I don’t think I’m really trying to cater to skimming readers. I’m a bit tired of optimizing for that—those readers already have plenty to skim through on Twitter every day....
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@minhuanli I would just push to say: for any reader, the sub-titles right now don't carry too much information. If you can make them stronger, do so. Having small "headlines" that drive home the points you want to make really helps communicate: both for the distracted audience and the deep reader.
Content follows the revised draft. Structural change: a new section, "How processing can wash out the source distribution", and the old "Cryo-EM: from particles to maps" section is dissolved into it and into "The question of ensemble resolution", which now also carries the fuzzy-density argument. The framing becomes explicit two-stage information loss — measurement, then processing. Line edits throughout: blur becomes heterogeneity rather than dynamics; p_src is named the ensemble distribution; single-particle rather than single-molecule experiments; the measurement process is named K; the figure caption follows suit. Two slips in the source are not carried over: Clark et al. was cited twice in one sentence, and "An X-ray diffraction intensities" had a stray article. Key term is bold italic in the site blue. Date moved to Aug 31, so the post file, its asset directory and the URL are renamed to match. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
2 participants
New blog post by Minhuan Li, F. Emil Thomasen and Pilar Cossio.
Are We Capturing the Ensemble? — What structural biology experiments preserve, blur, or discard about molecular distributions.
The post opens from two opposite intuitions: that a fuzzy region of a cryo-EM map is direct evidence of an ensemble, and that an averaging experiment such as X-ray diffraction cannot constrain an ensemble at all. Both judge an experiment by the appearance of its final representation rather than by how the data were generated and processed.
Structure
The flow is distribution → measurement → processing → resolution → takeaway.
p_target, the distribution the scientific question is about, fromp_src, the ensemble distribution actually present in the prepared sample. Vitrification in cryo-EM is the concrete example of the two coming apart.Files:
_posts/2026-08-31-are-we-capturing-the-ensemble.mdassets/posts/2026-08-31-are-we-capturing-the-ensemble/measurement_types.png— lead figureSeven references under Further reading. Image paths go through
relative_urlso they resolve under the preview baseurl as well as at the site root.Site changes
Driven by this post, but reusable, so worth a look:
_layouts/post.html— the byline gains an optionalcontactfront-matter field, rendered as a muted tail after the author names. Guarded by{% if page.contact %}, so the existing posts render as before.assets/css/styles.css.blog-caption,.blog-caption-wide) were full-size italic body text, indistinguishable from a paragraph. They are now smaller, grey and centered, with a gap between figure and caption. This restyles captions in the existing posts too..blog-image-hero— 90%-width lead figure, centered withautomargins. The existing percentage-margin classes compound with.blog-caption'spadding: 0 15%, because the markdown pattern nests the<img>inside the caption paragraph; auto margins avoid that..post-lead— opt-in drop cap on a post's first paragraph..key-term— bold italic in the site blue, for a term at the point it is defined..post-ack— acknowledgments set off by a hairline and set smaller than body copy..gitignore— ignorevendor/, so a localbundle config set path vendor/bundlepreview build cannot be committed by accident.