Using Partial Structure R1 to Do Molecular Replacement Calculations

Xiaodong Zhang

REVIEW 4 major objections 6 minor 19 references

Using Partial Structure R1 to Do Molecular Replacement Calculations

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A crystallographic target called pR1 locates missing molecular fragments by the deepest hole of its map, completing four test structures to within 0.5 Å.

desk verdict The deepest-hole hypothesis is not borne out by the paper's own Section 10, where the lowest-R1 solution is discarded for chemical reasons; still, the pR1 baseline idea is worth a referee's time. read the letter →

arxiv 2412.14034 v1 pith:KVLHMADL submitted 2024-12-18 physics.data-an

Xiaodong Zhang This is my paper · ORCID

classification physics.data-an

keywords partialstructureR1molecularreplacementsingleatompmapcompletelydisorientedfragmentmodeltargetcrystallographysolution

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper proposes that a crystallographic target called partial structure R1 (pR1) can solve molecular replacement: the deepest hole in a pR1 map identifies the orientation and location of a missing molecular fragment. The idea generalizes the earlier single-atom R1 method by treating any known geometrical fragment as the current model, and it splits the six-dimensional search into separate orientation and location stages. The paper tests the method on four small-molecule structures, including up to 26 benzene rings, and reports that every final model matches the correct structure to within 0.5 Å. The paper argues that pR1 works where the traditional R1 target fails because it retains a baseline term for all atoms still outside the model.

What carries the argument

The central object is the pR1 map, a function that gives the R1 agreement value for each trial orientation and position of a missing fragment. It is computed from Equation (1), the core approximation: $F_c^2(hkl)$ equals the squared cosine/sine sums over atoms 1 to j (the known atoms plus the trial fragment) plus the tail $f_{j+1}^2(hkl)+\dots+f_N^2(hkl)$ of squared scattering factors for the atoms j+1 to N that are not yet placed. The load-bearing mechanism is the deepest-hole hypothesis: the orientation and location that make the pR1 map deepest are the true orientation and location of the missing fragment. To keep the calculation practical, the paper divides the search into a free-standing-fragment orientation scan, where holes in a 3-D orientation space provide candidate orientations, and a location scan in a 3-D location space, with the global minimum found by coarse grid and five-step refinement.

What would settle it

For a known structure with one fragment removed, compute the pR1 map from Equation (1) and check whether the deepest hole coincides with the missing fragment; finding a structure where the deepest hole consistently marks a different position while a shallower hole marks the true fragment would falsify the deepest-hole hypothesis.

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Extended reading notes

Core claim

The central claim is that the deepest hole of a pR1 map determines the orientation and location of a missing fragment. pR1 is defined by the same core approximation used for sR1: the expected squared structure factor is the squared sum of cosine and sine contributions from the known atoms and the trial fragment, plus a tail of squared scattering factors for the remaining unmodeled atoms. According to the paper, keeping this tail accounts for the baseline effect of the other missing atoms, and dropping it is what makes the ordinary R1 target weak; maximum-likelihood targets such as LLGI mitigate the same problem by taking a gain. With this target, the paper determines two S2O2C12 molecules, four N4C9 and four PF6 fragments in sample 2, and seven or twenty-six benzene rings in samples 3 and 4, reporting final models with all atoms within 0.5 Å of the correct coordinates.

Load-bearing premise

The whole method rests on the core approximation of Equation (1), which assumes that the modeled atoms and the unmodeled tail contribute to the squared structure factor as a squared sum plus a sum of squared scattering factors, with all cross terms between the two groups omitted.

Editorial extensions

If this is right

pR1 can be used as a molecular-replacement target for small-molecule crystals: in all four test structures, the final model is within 0.5 Å of the correct structure.
Retaining the tail term in Equation (1) is the paper's explanation for why pR1 succeeds where the traditional R1 target fails.
A completely disoriented, spherically averaged fragment model can predict the locations of missing fragments, shortening the search enough to handle structures with many fragments such as 26 benzene rings.
Errors in molecular replacement can be found and fixed by deleting fragments that bond incorrectly and resuming the calculation, as done for samples 3 and 4.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the deepest-hole hypothesis is general, pR1 maps could also serve as an incomplete-model diagnostic: the deepest hole should point at whatever part of the structure is missing, not only in molecular replacement.
The paper's comparison with maximum-likelihood targets is left qualitative, so a natural testable extension is a head-to-head pR1 versus LLGI search on the same data to see where the baseline term most changes the ranking.
The complete-disorientation model's failure for S2O2C12 and N4C9 at n=1 and its recovery at n=1000 suggests an unexplored tuning rule for this predictor; understanding when large n is needed could extend the method to more rigid fragments.
Because the method is demonstrated only on four small structures, macromolecular application is open; the orientation-equivalence test that ignores atom types would likely need type awareness for proteins.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is an honest, clearly written proof-of-concept for a partial-structure R1 target in molecular replacement, but the paper's central claim — that the deepest hole of a pR1 map selects the correct orientation and location — is contradicted by its own Section 10. For ring 25 in sample 4, orientation 16 gives R1 = 0.5827 and a chemically meaningless placement; the correct orientation 2 has R1 = 0.5836 and is adopted only because the chemist sees it makes a proper bond. That is a 0.0009 R1 difference, so the target is nearly flat near the correct answer. Similarly, sample 3 required deleting and re-discovering ring 0 after visual inspection, so the 'complete success' of the strict calculation is not fully automatic.

What the paper does well: the idea of retaining the unmodeled-atom baseline term (the tail fj+1^2+...+fN^2) in an R1 target is conceptually interesting and clearly explained in Section 12. The two-step search (orientation from a free-standing fragment, then location from a pR1 map) is a sensible decomposition and is described with enough detail to reimplement. All four final models match the known structures to 0.5 Å, which is a real result, albeit on small molecules.

The soft spots are not minor. The n=1000 scaling in the disoriented-fragment model is ad hoc and unexplained; a spherical-average scattering factor times 1000 has no physical basis as stated. The manual first placements at (0.3,0.3,0.3) and the lucky guesses about which orientation labels correspond to which fragments in samples 1 and 2 mean the method's success on those samples is partly handcrafted. And Equation (1), the core approximation, drops cross terms between the modeled fragment and the tail; this is inherited from the earlier sR1 paper without sensitivity analysis here.

The honest reading is that pR1 produces candidate placements that, after chemical filtering, can lead to a correct structure. That is a weaker claim than the abstract's, and it is the claim the evidence actually supports. The paper would be improved by an automatic decision rule that reproduces the successes without human judgment.

This is a paper for crystallographers who think about MR targets, not for users looking for a turnkey tool. It deserves a serious referee: the concept is new, the writing is clear, and the counterexample is instructive rather than hidden. I would send it to review with a request to soften the claim and to address the manual steps explicitly.

Referee Report

4 major / 6 minor

Summary. Zhang presents pR1 as a generalization of sR1, hypothesizing that the deepest hole of a pR1 map determines the orientation and location of a missing fragment. The paper describes a two-step protocol: first detect candidate orientations from holes in the pR1 map of a free-standing fragment in 3D rotation space; then, for each trial orientation, locate the fragment by the deepest hole (or global minimum) of a pR1 map in translation space, ranking orientation-location candidates by R1. The approach is demonstrated on four small-molecule crystal structures, and final models match the known structures within 0.5 Å. A spherical 'completely disoriented fragment' model is introduced to predict possible locations and speed up the search. The central claim is that pR1 is a successful MR target.

Significance. If the central claim held, the paper would challenge the longstanding view that R1-type targets are unsuitable for molecular replacement, and it would offer a conceptually simple alternative to maximum-likelihood targets. The strengths are the clear falsifiable formulation and the use of externally known crystal structures as ground truth for validation. However, the evidence is limited to four small-molecule examples, and the paper explicitly reports manual interventions and an ad hoc n=1000 scaling. The deepest-hole criterion is contradicted in Section 10 for ring 25. The demonstrated pipeline is therefore not yet an automatic MR method, but it provides candidate solutions that, after chemical filtering, complete the tested structures. The significance is moderate and conditional: the results are promising enough to warrant revision, but the present claims outrun the evidence.

major comments (4)

[Abstract, Section 3, Section 10] The central hypothesis that the deepest hole (lowest R1) determines the missing fragment is contradicted by the paper's own sample 4 result. Section 10 reports that for ring 25, orientation 16 yields R1=0.5827 and an isolated ring, while orientation 2, with R1=0.5836, is correct and is adopted manually. Thus the lowest-R1 selector fails in one of four test cases; the claim must be weakened to 'pR1 generates candidate placements that may require chemical filtering,' and an automatic decision rule must be supplied.
[Sections 6, 7, 8, 9, 10] The reported successes rely on human judgment at several steps: ring 0 is placed at (0.3,0.3,0.3) by hand in Section 9 (and similarly molecule 0 in Section 6 and the first Cu atom in Section 7), and Section 9 states that benzene ring 0 'is deleted and re-discovered' after visual inspection, contradicting the 'complete success' claimed in Section 8 for the strict calculation. Section 10 likewise requires visual identification and deletion of 12 suspected bad rings. Since no automated decision rule is provided for these steps, the method as demonstrated is not a complete MR algorithm, and the 0.5 Å validation applies to the final manually adjusted model.
[Section 2, Eq. (1)] The core approximation in Eq. (1) drops all cross terms between the known atoms/current fragment (groups 1 and 2) and the tail of other missing atoms (group 3). This approximation is inherited from Zhang & Donahue (2024) and is not rederived or tested here. Because every pR1 hole and every placement in Sections 6-10 is computed under this approximation, its adequacy is load-bearing: if the omitted cross terms are substantial, the deepest hole need not coincide with the true fragment position. The authors should at least provide a numerical test of the approximation, e.g., comparing Eq. (1) with exact |F|² for the known structures.
[Section 8, Eqs. (2)-(3)] The 'completely disoriented fragment' model introduces a parameter n that is first defined as n≡1 (Eq. 3) and later arbitrarily set to 1000 for two of the fragment types 'to resume prediction power.' This is a free parameter tuned to the examples, with no physical or statistical justification. The claim that the model 'can predict the locations' of missing fragments is accordingly not robust; the authors should either derive n from first principles or abandon the disoriented-model prediction as evidence.

minor comments (6)

[Section 2] The symbol R1 is used without a formal definition; the reader is not told how R1 is computed from Fc² (e.g., R1 = Σ||Fo|-|Fc||/Σ|Fo|, or a variant). Please define R1 and pR1 explicitly.
[Sections 6-10] The procedure for identifying 'holes' in a pR1 map (e.g., local minima, threshold criteria) is not specified; the reported counts (14340, 780, 4176, 432 holes) cannot be reproduced without this information.
[Section 8] The relationship between Eq. (2), Eq. (3) and the nomenclature 'completely disoriented model' is not fully explained; in particular, the derivation of the sinc term G(4πsr_i) should be sketched or referenced.
[Section 3] The 'clustering ghost atoms' and 'triangular bonding' rules are referenced only to the previous paper; a brief summary is needed for the present paper to be self-contained.
[Supporting information S3/S4] The rotation and coordinate-conversion matrices would benefit from a worked example and from verification of the sign conventions; the current presentation is hard to check.
[Section 1] 'General MR calculations' is overstated given the small-molecule scope; please qualify the claim to the demonstrated regime.

Circularity Check

2 steps flagged · score 4.0 of 10

pR1 is tested against external structures, so the core derivation is not circular; however, two validation steps are partially circular: the n=1000 disoriented-model parameter is tuned to the test cases, and the lowest-R1 rule is manually overridden in sample 4 using chemical knowledge of the correct answer.

fitted input called prediction [Section 8, equations (2)-(3)]
"By strict definition of a completely disoriented fragment, the parameter n in equation (3) equals 1. ... Interestingly, in these cases, if n is increased to 1000, the prediction power resumes."

The paper defines the completely disoriented spherical model with n=1. When n=1 fails for S2O2C12 and N4C9, n is increased to 1000 to make the same examples regain 'prediction power.' This is a free parameter fitted to the target data with no derivation or out-of-sample test; the claimed predictive ability of the disoriented model for those fragments is therefore a consequence of tuning n, not an independent prediction.
other [Section 10, sample 4]
"When determining benzene ring 25, orientation 16 gives the lowest R1 of 0.5827, however, its resulting benzene ring is isolated. Upon investigation, the second-best orientation is orientation 2, which has the second lowest R1 of 0.5836. This orientation is initially rejected because it has a slightly higher R1. Because this orientation yields chemically correct benzene ring, the result of this orientation should be adopted."

The central rule is that the lowest-R1 candidate determines orientation and location. In sample 4 the lowest-R1 candidate is explicitly rejected and the second-lowest is adopted because chemical knowledge says the ring is correct. The reported correct placement of ring 25 is therefore not the output of the pR1 decision rule; it is a post-hoc selection consistent with the known correct structure. The success of sample 4 is thus not independent evidence for the deepest-hole hypothesis.

full rationale

The paper's main derivation chain is not self-definitional: pR1 maps are computed from Eq. (1) using the known partial model and the trial fragment, and the resulting holes are compared against four externally known crystal structures, so the central claim is not constructed from the conclusion by definition. The heavy reliance on the author's prior sR1 paper for Eq. (1), the ghost/triangular-bond filters, and the deepest-hole hypothesis is self-citation, but the present work provides independent demonstrations on external structures, so I do not count those citations themselves as circular. Two steps do undercut the independence of the validation. First, the completely disoriented model is defined with n=1 and then n is arbitrarily raised to 1000 when the model fails on S2O2C12 and N4C9, which is fitting a parameter to the test set. Second, Section 10 explicitly overrides the lowest-R1 choice for ring 25 on chemical grounds, and Section 9 concedes that ring 0 in sample 3 had to be deleted and rediscovered after visual inspection, so the reported successes are not fully produced by the stated pR1 decision rule. These are partial circularities in the validation rather than a closed derivation loop, so the overall score is moderate.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central claim rests on an unproved squared-structure-factor approximation, a spherical average model with a fitted scale factor, and several hand-chosen search parameters and starting placements. No new physical entities are introduced.

free parameters (6)

n (disoriented-model scale factor) = 1 or 1000
Section 8 introduces n in Eq. (3) as the strict value 1, then states that for S2O2C12 and N4C9 prediction fails with n=1 and "if n is increased to 1000, the prediction power resumes". This is a hand-fitted multiplier. For benzene predictions n=1 is used.
Number of pR1 holes retained = 1000
Sections 6, 7 and 9 select the 1000 deepest holes of each free-standing pR1 map to generate candidate orientations; no sensitivity analysis is given.
Initial placement of first fragment or atom = (0.3,0.3,0.3) fractional
Sections 6, 7 and 9 start by placing molecule 0, a Cu atom, or benzene ring 0 at (0.3,0.3,0.3) by hand; the algorithm does not search for the first fragment.
Atom-match equivalence threshold = 0.5 Å
Section 3 declares two orientation representations equivalent if atom positions match within 0.5 Å, which filters candidate orientations.
Translation and rotation coarse grid = 0.4 Å and 5 degrees
Section 3 uses these step sizes for the coarse search and refines by local step halving; chosen without error analysis.
Local refinement steps = 5 halvings
Section 3 refines holes and global minima by halving the step size locally five times; an arbitrary precision setting.

assumptions (4)

domain assumption Equation (1) approximates the squared structure factor by adding the squared cosine and sine sums of known atoms and the missing fragment to the sum of squared scattering factors of all remaining atoms, omitting all cross terms between the modeled block and the tail.
Section 2 calls this "the core approximation"; it is inherited from Zhang and Donahue (2024) and is used to compute every pR1 value, but its validity is not justified in this report.
domain assumption A completely disoriented fragment can be represented by a spherically symmetric scattering factor fp(s) = [sum_i f_i(s) G(4π s r_i)] × n centered at the fragment origin.
Section 8, Eqs. (2) and (3). This averaging model underlies the fast location prediction for all missing fragments, and the n factor must be changed from 1 to 1000 for some fragments to restore prediction.
ad hoc to paper Candidate orientations of missing fragments are those that produce the deepest holes of a free-standing fragment pR1 map in orientation space.
Sections 3 and 6-10 use this heuristic to prune the orientation search; it is the method's working assumption rather than a theorem, and its success is assessed only on the four examples.
domain assumption Placements causing clustering ghost atoms or triangular bonding are chemically implausible and are rejected.
Sections 3 and 4 apply these rules inherited from sR1 work; the rules are used to filter candidate locations and can reject true solutions, as illustrated by the manual re-determination of benzene rings.

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Cite this review

Pith. "Pith review of Using Partial Structure R1 to Do Molecular Replacement Calculations." pith.science (2026). https://pith.science/paper/KVLHMADL

@misc{pith2026241214034,
  author       = {Pith},
  title        = {Pith review of: Using Partial Structure R1 to Do Molecular Replacement Calculations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KVLHMADL}},
  note         = {Machine review of arXiv:2412.14034}
}

read the original abstract

The concept of partial structure R1 (pR1) is a generalization of the concept of single atom R1 (sR1) (Zhang & Donahue, 2024). The hypothesis is that the deepest hole of a pR1 map determines the orientation and location of a missing fragment. In current implementation, the calculation is divided into two steps. The first step is to detect possible orientations of all missing fragments by the holes of a pR1 map of a free-standing fragment in a 3-dimensional orientation space. The second step is to determine the orientation and location of a missing fragment. To this end, if done strictly, all the candidate orientations are tried. With each candidate orientation, the best choice of location of the missing fragment is determined by the deepest hole of a pR1 map in a 3-dimensional location space. This best choice is combined with the trial orientation to form one candidate orientation-location. After trying all candidate orientations, a list of candidate orientation-locations are formed, from which, the one with the lowest R1 determines the orientation and location of a missing fragment. Then a newer pR1 is defined by including the atoms of this newly determined fragment into the known atoms. This newer pR1 is used to determine the next missing fragment in the same way. To shorten the calculation time, the possible locations of all missing fragments can be predicted by the holes of a pR1 map of a completely disoriented model of a fragment. All these ideas of using pR1 to do molecular replacement calculations have been demonstrated by four example data sets.

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Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages

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2024

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

& Sarma, R

Bott, R. & Sarma, R. (1976). J. Mol. Biol. 106, 1037-1046

work page 1976

[2] [2]

Bricogne, G. (1992). Proceedings of the CCP4 Study Weekend. Molecular Replacement, edited by W

work page 1992

[3] [3]

C., Carrozzini, B., Cascarano, G

Burla, M. C., Carrozzini, B., Cascarano, G. L., Giacovazzo, C. & Polidori, G. (2020). Acta Cryst. D76, 9-18

work page 2020

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L., Giacovazzo, C., Mazzone, A

Caliandro, R., Carrozzini, B., Cascarano, G. L., Giacovazzo, C., Mazzone, A. & Siliqi, D. (2009). Acta Cryst. A65, 512-527

work page 2009

[5] [5]

Crowther, R. A. (1972). In The Molecular Replacement Method, Ed. M. G. Rossmann, Gorden &

work page 1972

[6] [6]

Eventoff, W., Hackert, M. L. & Rossmann, M. G. (1975). J. Mol. Biol. 98, 249-258

work page 1975

[7] [7]

& Read, R

Fujinaga, M. & Read, R. J. (1987). J. Appl. Cryst. 20, 517-521

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& Jolles, P

Harada, Y., Lifchitz, A., Berthou, J. & Jolles, P. (1981). Acta Cryst. A37, 398-406

work page 1981