Multiscale guidance of protein structure prediction with heterogeneous cryo-EM data
Authors: Rishwanth Raghu
Axel Levy
Gordon Wetzstein
Ellen D Zhong
Venue: NeurIPS 2025 poster ()
Keywords: Computational Biology and Bioinformatics
Generative Models
Primary area: machine_learning_for_sciences
TL;DR: We propose a diffusion guidance approach for fitting atomic models into experimental density maps using pretrained protein structure prediction models.

Abstract: Protein structure prediction models are now capable of generating accurate 3D structural hypotheses from sequence alone. However, they routinely fail to capture the conformational diversity of dynamic biomolecular complexes, often requiring heuristic MSA subsampling approaches for generating alternative states. In parallel, cryo-electron microscopy (cryo-EM) has emerged as a powerful tool for imaging near-native structural heterogeneity, but is challenged by arduous pipelines to transform raw experimental data into atomic models. Here, we bridge the gap between these modalities, combining cryo-EM density maps with the rich sequence and biophysical priors learned by protein structure prediction models. Our method, CryoBoltz, guides the sampling trajectory of a pretrained biomolecular structure prediction model using both global and local structural constraints derived from density maps, driving predictions towards conformational states consistent with the experimental data. We demonstrate that this flexible yet powerful inference-time approach allows us to build atomic models into heterogeneous cryo-EM maps across a variety of dynamic biomolecular systems including transporters and antibodies.

Multiscale guidance of protein structure prediction with heterogeneous cryo-EM data
Rishwanth Raghu Princeton University rraghu@princeton.c edu
Axel Levy Stanford University axlevy@stanford edu
Gordon Wetzstein Stanford University gordon wetzsteiin@stanford
Ellen D. Zhong
Princeton University
zhonge@princeton. edu
Abstract
Protein structure prediction models are capable of generating accurate 3D structural hypotheses from sequence alone. However, they routinely fail to capture the conformational diversity of dynamic biomolecular complexes, often requiring heuristic MSA subsampling approaches for generating alternative states. In parallel, cryo-electron microscopy (eryo-EM) has emerged as a powerful tool for imaging near-native structural heterogeneity, but is challenged by arduous pipelines to transform raw experimental data into atomic models. Here, we bridge the gap between these modalities, combining cryo-EM density maps with the rich sequence and biophysical priors learned by protein structure prediction models. Our method, CryoBoltz, guides the sampling trajectory of pretrained biomolecular structure prediction model using both global and local structural constraints derived from density maps, driving predictions towards conformational states consistent with the experimental data. We demonstrate that this flexible yet powerful inference- time approach allows to build atomic models into heterogeneous cryo-EM maps across a variety of dynamic biomolecular systems including transporters and antibodies.
Introduction
Proteins and other macromolecules in cells are constantly vibrating, deforming, and interacting with other surrounding molecules. Characterizing the variability of their atomic structures, i.c., of the relative 3-dimensional (3D) locations of their atoms, deepen understanding of the complex chemical mechanisms underlying basic biological systems. For example, understanding how driver mutation alter the probability of certain conformational states has applications ranging from drug design 25 to molecular engineering (21]
A variety of experimental methods for protein structure determination have been developed, with X-ray crystallography and cryo-electron microscopy (cryo-EM) being most widely used today. In
cryo-EM, series of breakthroughs in both hardware [80 9 24 29 and software 669
27
68 64
led to the so-called "resolution revolution" " [47). resulting in routine near-atomic resolution structure determination for well-behaved purified protein samples. Cryo-EM, in particular, also possesses the ability measure and reconstruct the conformational landscape of dynamic biomolecular com- still complex, costly, and time consuming, requiring expensive microscopes and facilities, as well as hours to days of data pro- cessing through iterative computational pipelines [49]. Notably, current reconstruction algorithms only output 3D "density maps" that approximate the electron scattering potential of the molecule.
plexes (68 64 94
10,
22 63). However, these experiments
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Atomic models.
Density maps
Atomic models.
Diflusion-generater ensemble (AF3, Boltz)
Cryo-El EM ensemble
Guided ensemble
Problem statement. Diffusion based structure prediction models 88 can sample different conformations, but the generated ensemble is generally peaked around single conformation. cryo-EM experiment probes the full conformational landscape but current reconstruction algorithms only provide density maps, atomic models. With CryoBoltz, guide the diffusion process in atomic space with experimental cryo-EM measurements to increase sample diversity and more faithfully reflect the true conformational ensemble.
Figure 1:
Fitting atomic models within these maps is a significant computational challenge for which existing methods [85
35 39) only provide partial solutions that need to manually refined.
Building on decades of data acquisition, processing, and curation 7 g machine-leaming learning based sequence-to-structtne models were developed and trained on publicly available structural data [4] [. These models, however, are still trained to map given sequence to a unique, most likely structure and are therefore bound viewing proteins as static objects. Shifting structure prediction models to dynamic paradigm constitutes one of today's 's main challenges for structural biology.
Recent exploratory lines of work have attempted address this outstanding challenge. MSA subsampling methods, for example, rely on randomly masking input sequence data to broaden the diversity of output structures [87 23
43 36). Despite results showing improved diversity specific systems, MSA subsampling methods remain an active area of research, with no clear consensus yet regarding their performance. Moreover, these methods are not well suited for complexes that can adopt many different conformational states or a continuum of conformational states. Other works, including AlphaFlow [40] and BioEmu [50), investigated incorporating physics-based molccular dynamics simulation as additional training data. These works also showed greater variability among output structures but were mainly demonstrated on small peptides, additionally requiring costly training and relying on simulations that may not capture realistic atomic motions.
Here introduce method, CryoBoltz, that leverages heterogeneous cryo-EM data to guide the sampling process of diffusion-based structure prediction algorithm (Figure II. Our implementation based on Boltz-1 88 open-source sequence-conditione diffusion model heavily inspired by the state-of-the-ane model AlphaFold3 [ Through a multiscale guidance mechanism, CryoBoltz combines the structural information learned by the pretrained diffusion model with experimentally- captured data, producing structures consistent with the cryo-EM -MyoEEM data. Importantly, our method does require additional training step, while effectively mitigating the single-structure bias of current structure prediction models. We demonstrate results on both synthetic and real cryo-EM maps of dynamic biomolecular complexes.
2 Background
2.1 Diffusion-Basel Sampling in AlphaFold3
Recent advances in protein structure prediction from sequences are exemplified by major break- throughs such as AlphaFold2 [41 and AlphaFold3 [I]. While AlphaFold2 predicts static structures with remarkable accuracy, AlphaFold3 introduces diffusion modeling head within its structure module, enabling generative sampling of different conformations, conditioned on the same sequence.

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Specifically, AlphaFold3 utilizes a diffusion model operating directly in the space of atomic coordi- nates, x E R where N represents the number of modeled atoms. Given sequence s, we call Ps(x|s) the distribution of conformations of the folded protein (or complex) at ambient temperature. We then call Pe (x|s) the marginal distribution of conformations obtained by sampling X from po(x|s) and simulating the forward diffusion process
dx f(x, l)dt + g()ddw
from 0 to i, where f(x, t) and g(t) are predefined drift and diffusion functions while dw represents a standard Wiener process in atomic coordinate space. The drift and diffusion functions are chosen such that pr(x(s) Rz (O, for some T R. One way to sample from the target distribution po (x (s) is then to sample XT from (0, I) and simulate the reverse diffusion process
dx (f(x.t) t) V log (x((s)) dt + g(t)dw
(2)
In the above equation, the score function Vx log (x(xs) is unknown and implicitly depends on the target distribution. AlphaFold3 therefore uses an approximation of the score function, called so sx(x, s, This "score model" can be obtained using finite set of samples from [x ()) and a training strategy based on denoising score matching
from T to 0 2 34
[84 76
Boltz-1 closely follows the architecture and framework of AlphaFold3 with minor modifications, achieving comparable accuracy in predicting biomolecular complex structures (88).
2.2 Likelihood-Baan -Bssee Guidance
In an "inverse problem". one aims at recovering an unknown object x from measurement y. given a known "likelihood model" p(y/x). Inverse problems are often framed as posterior sampling problems, i.e., they aim at sampling from the posterior p p(xly). Using Bayes" rule, the posterior can be decomposed as product of the likelihood, (/) and the prior distribution over x.
In this context, several works have recently shown that pretrained diffusion models can be interpreted as implicitly defined priors and therefore used to solve posterior sampling problems [38 75 | [2]
74 45 46 [86. as surveyed in (20). Effectively, these methods are able to "guide" a diffusion model using a measurement y and its corresponding likelihood model. The key insight of these works lies in noticing that the score function of the posterior can be re-written as sum: Vx log (x = vx log Pr x) Vx log p(y|x; = x). The first term is directly approximated by the pretrained score model s (x. s, t). but the challenge lies in the second term. The conditional probability p(y(x,) can be written as a conditional expectation Exxxxxxxo (x, [p(y|xo)], but approximating this expectation with Monte Carlo samples is not computationally tractable option, because sampling times from the conditional distribution p(xo ((x) requires solving n differential equations. In ScoreAL., Jalal et al. (38] first suggested to replace the latter distribution with a Dirac delta centered on x, effectively replacing ply (x:) with p(y x). Despite promising results on low-noise and linear inverse problems, ScoreALD tends to drive samples off the diffusion manifold, i.e.. in regions where (x( << 1, where the score model was only sparsely supervised and is therefore highly inaccurate. To mitigate this issue, Chung et al. [12] suggested in the DPS algorithm to center the Dirac delta distribution on Re t) = E Expxppix x
Xu]. which can be expressed as an affine function of sp(x, t) with Tweedie's 's formula [77 66 26 The guided reverse diffusion process is therefore defined as
dx
- g(t)) sx(,tt) - A(t) Vx loggplyix (x( dt + g())dw,
(3)
where 5o(y,x,t) x,,) is an additional guidance term.
In parallel to the guidance-basee approach, other works have attempted to frame the posterior sampling problem as problem of variational inference [30 [55. but remain limited by the expressivity of the
variational family (e.g., Gaussian distributions (55)) or by the necessity to repeatedly solve initial-
value problems [30]. Most recently, (CCMC-based strategies like DAPS [91] proposed to correct previous sampling methods with an equilibration step based on MCMC sampling (e.g., Langevin dynamics or Hamiltonian Monte Carlo) and showed improved performance on high-noise or highly nonlinear problems. However, owing to the simplicity and effectiveness of the DPS algorithm for our problem of interest, we basc our guiding mechanism the DPS framework.
3

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Diffusion steps
Tw Warm up (unguided diffusion)
Tg
Ti
Relaxation (unguided diffusion)
Global guidance
Local guidance
Input cryo-EM map
Point cloud
K- k-means
Figure 2: Overview of the guidance mechanism. The diffusion process starts with a "warm up" stage where the score model is only conditioned on the sequence. During "global guidance", the structure is guided to minimize its distance to point cloud representation of the input cryo-EM map. During "local guidance", guided to maximize its consistency with the original input map. Finally, the last "relaxation" steps are unguided and allow the model to correct fine-grad fine-grained details.
2.3 Forward Model for Cryo-EM Maps
Cryo-EM reconstructs a 3D electron scattering potential from many independent 2D projection images of frozen biomolecular complexes. The reconstructed density map y is usually represented Rexhxd In the forward model, a given structure's cryo-EM density is typically
as 3D array: modeled as sum of Gaussian form factors centered on each atom. Formally, the observed density map can be modeled as y = [x s)) + (22). where I' is an operator that sums isotropic Gaussians centered each heavy (non-hydrogen) atom in x. Their amplitudes and variances are tabulated [33
and typically depend on the chemical elements in x. B represents the effect of "B-factors" [44 and can be viewed spatially dependent blurring kernel modeling molecular motions and/or signal damping by the transfer function of the electron microscope. Finally, models i.i.d. Gaussian noise.
3 Methods
In this section, we describe how CryoBoltz uses an input cryo-EM map to guide a diffusion process in atomic space. Our implementation is based on the DPS algorithm (Section 2.2) [2]
3.1 Overview: Multiscale Guidance
Because the forward model turning atomic models x into density maps is highly nonlinear (Sec- tion 2.3). the likelihood function p(yix x) is multimodal w.r.t. x. making the posterior p(xly) oc p(y (x) rugged and hard to sample from with score-based methods. In order to regularize the target ensemble distribution in the early diffusion steps. CryoBoltz uses global-to-locaa guidance strategy that ignores high-resolution information until the later diffusion steps.
First, we use T.n steps of unguided reverse diffusion, only conditioning the score model on the sequence s, to bootstrap (i.e., "warm up"") the atomie model and obtain structure close to the one the diffusion model is initially biased towards (Figure I left), following Equation 2 We then use

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Tg steps of a "global guidance" strategy, further described in Section 3.2 "local guidance" stage, described in Section 3.3 Finally, the last T, diftusion steps are unguided to help solve high-resolution inconsistencies (e.g., steric clashes). Figure 2 provides an overview of our multiscale guidance strategy.
followed by Ti steps of
3.2 Global Guidance
At the beginning of the global guidance stage, the density map y E Ruxxxx is transformed into 3D point cloud Y E k This conversion is done using the weighted k-means clustering algorithm with a predefined number of clusters k dependent on the number of atoms in the system and the voxel size of the map (see details in the Appendix). This point cloud, inspired by the volumetric shape constraints in Chroma [37]. provides compact and low-resolution representation of the map that can be used to efficiently guide the diffusion process towards the global shape of the protein complex. A key benefit of the point cloud representation is that the distance between and Y can be defined using standard distances derived from aptimal-transpon theory, like the Sinkhorn divergence (xx, Y), a regularized version of the Wasserstein distance (60). In the first global guidance step, the intermediate sample x is aligned with the density map prior to computing the Sinkhorn divergence (see Appendix for more details).
Following the DPS framework, we define the guided diffusion process using Equation 3 (with sequence-conditioning in the pretrained score model), where the guidance term is defined as
x, S, = V (xxxxxx,,, Y).
The schedule of the guidance strength X(t) is described in the Appendix. Note here that the global guidance term is not directly derived from a physics-based likelihood model, but rather defined heuristically in order for the atomic model x to fit the low-resolution details of the cryo-EM map.
3.3 Local Guidance
During local guidance, the original density map is used and the guidance term of Equation 3 is directly derived from the forward model described in Section 2.3 i.c.
V B[T (8o (x, (x, t))
At this stage, the guidance term includes all the structural information captured in the density map, including higher resolution details, and derives directly from physies-based assumptions on the cryo-EM forward model and noise model.
3.4
Related Work
Our work proposes to guide a pretrained diffusion model operating on atomic coordinates using experimental cryo-EM data. Equivalently, our method be seen model building method leveraging pretrained diffusion model as a regularizer.
First developed for X-ray crystallography [3]. model building methods were later adapted to operate 81 but the obtained atomic models were often incomplete and needed refinement 73 Machine-learning-biae based methods were also developed, either relying U-Net
on cryo-EM data 885
82,
architectures 72 92 61 or combining 3D transformers with Hidden Markov Models [2]] He
et al. (35 first made use of sequence information in EMBuild, and ModelAngelo (39] has recently established a new state of the art for automated de novo model building. Combining a GNN- based architecture with preprocessed sequence information [65], ModelAngelo outperforms previous approaches. However, its performance relies high-resolution maps (below 4 Å) and often yields incomplete models on blurry, low-resolution data (Figure 5 for example). As a result, manual model building remains the prevailing solution in these challenging regimes, particularly in those involving flexible or heterogeneous complexes.
The possibility of using structure prediction models regularizers for 3D reconstruction problems was only demonstrated very recently. ROCKET, Fadini et al. (8 introduced a method to use AlphaFold2 [1] prior for building atomic models that are consistent with cryo-EM, cryo-ET or X-ray crystallography data. The method regularizes the problem by transferring the optimization from atomic space to the latent space of AlphaFold2. In contrast, method leverages AlphaFold3's
5

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Table 1: Quantitative evaluation with synthetic maps (STP10 [6] and CH67 antibody [70] and ablation study. We report the Root Mean Square Deviation (RMSD) for all atoms, the Co RMSD, and the template-modeling (TM) score. For CH67, we also report the RMSD for the Co atoms in the CDR H3 loop (local RMSD). The last two columns show an ablation study on the guidance mechanism. The mean across 3 replicates is reported for the best of 25 samples (lowest all-atom RMSD). Random MSA subsampling Boltz-1 (88) (Boltz-1 + MSA sub.) run with MSA depths of 64, 128, 256, 512, and 1024, each producing 5 samples. Bold indicates best value. AF3 is AlphaFold3 M
Boltz-1
Local only
Global only
CryoBoltz
Boltz-1
AF3
Structure
Metrics
MSA sub.
RMSD (A, +)
1.057
3.815
3.768
1.263
3.860
1.287
STPI0 (inward)
Ca RMSD (Á, 4)
0.371
3,554
3,513
0.623
3.559
0.778
TM score (1)
0.998
0.863
0.865
0.994
0.862
0.990
RMSD
0.888
2.656
2.542
4.478
2.722
1.164
STPI0 (outward)
Ca RMSD
0.440
2.419
2.295
4.228
2.458
0.779
TM score
0.997
0.948
0.953
0.828
0.946
0.991
RMSD
1.048
1.961
1.954
1.887
1.443
1.281
Ca RMSD
0.637
1.469
1,522
1.453
0.945
0,880
CH67 antibody
Local RMSD
1.269
3.120
3,270
3.191
1.718
1.899
TM score
0.994
0.972
0,969
0.971
0.990
0.988
diffusion-based structure module for efficient optimization directly in atomic space. Other works investigated the possibility to guide diffusion-based models using experimental data [54] 53 but were only used to process X-ray crystallography data. In this modality, each measurement provides an average of the contribution of each conformation in the crystal, which inherently limits the extent to which structural variability can be analyzed. Finally, ADP-3D 48 demonstrated diffusion-based model refinement using cryo-EM measurements, but the method requires an initial model (provided, for example, by ModelAngelo 33 and was not compared existing structure prediction methods.
4 Results
4.1 Experimental Setup
We evaluate our method six biomolecular systems. For two of them, we guide CryoBoltz with synthetic density maps (STP10 6 and CH67 antibody (70) and use real, experimental maps for the other four systems (P-glycoprotein [14] Pmal, CYP102A1, and YbbAP (56)). We chose these four systems because (1) they have two or more density maps corresponding different conformational states; (2) the corresponding atomic models were deposited after the Boltz-1 (8) training cutoff; (3) they are composed
Datasets and metrics.
two or fewer unique chains, so that an accurate unguided Boltz-1 prediction can be obtained; and (4) the sequence is shorter than 2,200 residues, which we found to be the max sequence length that could fit in Boltz-1. For three of these systems (P-glycoprotein, CYP102A1, and YbbAP), at least
map is of lower resolution (>4 Å). To assess the quality of generated structure, align it to the deposited (reference) structure pairing a-carbons, then compute Ca root mean square deviation (RMSD), all-atom RSMD, and template-modeling (TM) score [93]. We sample 25 structures for each of three model replicates. We additionally report map-model fit metrics in Supplementary Table B2
Baselines. We compare CryoBoltz against the diffusion- structure prediction models Boltz- 1 88 and AlphaFold3 M. We additionally evaluate Boltz-1 with MSA subsampling, producing 5 samples each for 64, 128, 256, 512, and 1024 randomly drawn MSA sequences. On the experi- mental datasets, we also compare our results to those obtained with the model building algorithm ModelAngelo [39].

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CryoBoltz
b)
Boltz-1
AlphaFold3
Outward state PDB:7AAQ
Inward state PDB:7AAR
Figure Results on STP10 a) CryoBoltz can predict both the outward and inward states, when guided with the respective cryo-EM density map. Best sample (lowest all-atom RMSD across all model replicates) is shown. b, e) Current structure prediction models are biased towards one of these states. Boltz-1 [8]] only predicts the outward state (b) while AiphaFold3 []] only predicts the inward state (c). Five best samples relative to the outward and inward PDB structures, respectively, are shown.
4.2 Synthetic datasets
We demonstrate our method on the sugar transporter protein STPIO, a plant protein that switches between inward-facing and outward-facing facinn conformations shuttles substrates across
STP10.
cell membrane 66. From the deposited atomic models of these structures (PDB: : 7AAQ. 7AAR) 4
5 we
generate synthetic density maps at resolution of 2 Á using the molmap function in ChimeraX 59 In Figure 3 we show that density-guided diffusion allows for accurate modeling of both conformational states. W Wile unguided Boltz-1 only samples the outward conformation, CryoBoltz guidance drives the rearrangement of helices to sample the inward conformation. MSA subsampling slightly improves the accuracy of Boltz-1 I but still only samples the outward conformation. AlphafFold3, in contrast, only samples the inward conformation. As seen in Table CryoBoltz not only models both conformations, but also improves the accuracy of the predictions over their unguided counterparts, achieving an all-atom RMSD below Á for the outward state.
CH67 antibody. CH67 is antibody whose Fab domain binds the influenza hemagglutinin receptor during the human immune response (70). Responsible for this interaction is the complimentarity- determining region (CDR) H3, short loop that is highly variable across antibody fam- ilies and thus is modeled poorly by pro- tein structure prediction methods. To as- sess the ability of our method to cope with the lower resolutions typically obtained for antibody cryo-EM maps, we simulate 4 Å density map of the CH67 Fab domain 4HKX) (71). In Figure 4 we show that CryoBoltz accurately models the CDR H3 loop, correctly placing the backbone and most of the side chains. With some samples achieving a local RMSD below 1 Á on this region (Supplementary Fig- ure B2 our method improves over Boltz-1 and AlphaFold3 (Table T.. due to both better global modeling of the full Fab structure as well as local modeling the H3 loop itself (Supplementary
CDR H3
PDB:4HKX
CryoBoltz
Boltz-1
AlphaFold3
Figure 4: Results on CH67 antibody [70]. CryoBoltz fits the CDR H3 loop more accurately than Boltz-1 (8 and AlphaFold3 [ Three best samples (lowest all- atom RMSD across all model replicates) are shown on the right.
Figure B1

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Table 2: Quantitative evaluation using real cryo-EM density maps of four biomolecular systems.
We report the mean all-atom RMSD (A), Ca RMSD (Å) and TM score for the best of 25 samples (lowest all-atom RMSD) across 3 model replicates. We indicate the resolution of the input map (res.) as well as the completeness (comp.) of the model built by Angelo (MA) [3] (percentage of
modeled over deposited residues). Pgp is P-glycoprotein 14 and CYP is CYP102AI. Bold indicates best value.
CryoBoltz RMSD
Boltz-1 RMSD
AlphaFold3 RMSD
ModelAngelo
Res.
RMSD
TM
RMSD
TM
RMSD all
TM
Comp. (%)
TM
Structure
(A)
all
Co
Score
all
Co
score
Co
score
score
Pgp (apo)
4.3
1.382
1.208
0.989
6,994
7.194
0.767
3.827
3.865
0,904
40.3
0.361
Pgp (inward)
4.4
1.348
1.187
0.989
5.630
5.692
0.828
2.692
2.663
0.947
18.3
0.134
Pgp (occluded)
4.1
1.727
1.677
0.979
2.929
2,904
0.942
3,440
3,420
0,921
2.3
0.010
Pgp (collapaed)
4.4
1.309
1.261
0.988
3.425
3.412
0.917
4.568
4.554
0.864
2.5
0.010
Pmal (active)
3,25
2.046
1.776
0.973
2,987
2.752
0.935
6.628
6,389
0.769
91.5
0.889
Pmal (inhibired)
3,52
1.999
1,590
0.979
6,140
5.829
0.794
8.017
7,776
0.723
72.8
0.721
CYP (open)
6.5
4.167
3,946
0.957
8.532
8.439
0.788
6,490
6.361
0.890
0.0
0.000
CYP (clmsed)
4.4
2.004
1.552
8.667
0.743
3.585
3.391
0.946
0.102
YbbAP (bound)
3.66
1.320
0.678
0.997
3.623
3.339
0.928
3.749
3.480
0.922
81.7
0.801
YbbAP (unbound)
4.05
2.454
2.039
0.974
7.842
7.654
0.776
4.022
3.744
0.913
55.4
0.548
4.3 Experimental datasets
P-glycoprotein. P-glycoprotein is a membrane transporter that conducts cellular export of toxic com- pounds including chemotherapy drugs, making it an important therapeutic target for inhibition (14). We test our method on experimental density maps corresponding to four states in the transport cycle: the apo state, inward state, occluded state, and collapsed state (EMD-40226, 40259, 40258, 40227). We mask the maps around their corresponding deposited atomic models (PDB: 8GMG, 8SA1, 8SA0, 8GMJ) [IS] [8 17 [6] in order to remove non-protein detergent density, which is a byproduct of sample preparation for transmembrane proteins. As shown in Figure [ and Table P CryoBoltz samples the full set of conformations, outperforming baselines all metrics across all four states. We additionally find that Angelo predictions are highly incomplete, with only between 2.3% and 40.3% of residues modeled. We provide ModelAngelo with the original maps as they lead to marginally higher performance.
Pmal. We use two experimental maps of a Pmal monomer 14MD- 64136), corresponding to the active and inhibited states (PDB: 9UGB, 9UGC) [89 90 of this ATPase. Unguided Boltz only samples the active state, whereas guidance also samples the inhibited state with an all-atom RMSD of 2.00 A and Ca RMSD of 1.59 Á (Table Figure 6b. AlphaFold3 predictions are not accurate with respect to either state.
CYP10ZAI. We use two experimental maps of CYP102A1 (EMD-27534, 27536), of resolutions 4.4 A and 6.5 Å, corresponding to the open and closed states : 8DMG) [78] 79 of this oxygenase. Guidance improves the all-atom RMSD of the closed state from 8.78 Á to 2.00 Á over unguided Boltz-1, whereas for the lower resolution open state map, a more modest improvement from 8.53 Å to 4.17 Å is observed. ModelAngelo only models 18.9% of the 4.4 À map and none of the 6.5 Ä map.
YbbAP, We use two experimental maps of the YbbAP transporter [56] (EMD 51DD-51292 51291), corre- sponding states in which ATP is bound unbound (PDB 9GE6) 58 57. Unguided Boltz only samples the bound state, which guidance further improves to an all-atom RMSD of 1.32 Á. The unbound state is additionally obtained through guidance. We observe that MSA subsampling also allows Boltz-1 to sample the unbound sample in some model replicates (Supplementary Table B1
4.4 Ablations
To validate our multiscale approach, we ablate the model by exclusively running the global guidance phase or local guidance phase. As shown in Table [] while global guidance alone often improves metrics over baselines, local guidance further boosts accuracy by fitting higher-resolution details.
8

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Apo state PDB:8GMG
Inward state PDB:8SA1
Occluded state PDB:8SA0
Collapsed state II PDB:8GMJ
CryoBoltz
ModelAngelo
Figure 5: Results on P-glycoprotein [14. CryoBoltz recovers distinct states of the protein using four experimental cryo-EM EM maps. ModelAngelo 39 produces highly incomplete models.
Local guidance alone also improves performance unguided Boltz-1, but is ultimately insufficient in driving large conformational changes. We report ablations for real density maps in Supplementary Table B1 The combination of local and global guidance leads better accuracy than either one alone for most of the maps.
5 Discussion
This work introduces guidance mechanism that increases the capability of current diffusion- based structure prediction models. The guiding information, derived from experimental cryo-EM measurements, biases sampling towards atomic models consistent with the observed data. Our method does not require any retraining or finetuning and can be used on top of any available model, thereby making it possible to benefit from their continuous improvement. Through experiments on both synthetic and experimental data, we show that CryoBoltz can increase the diversity of sampled conformations revealing states that are missed by existing diffusion models and predict more accurately the structure of regions that are key to function, like CDR loops in antibodies. On experimental data, we show that state-of-the the-ttt-rrt model building methods can fail and CryoBoltz, leveraging knowledge acquired from large-scale datasets of protein structures, can fit atomic models within minutes, saving hours of manual refinement. With the increasing availability of predicted structures priors for cryo-EM model building, the principled validation of the resulting atomic models, especially those derived from lower resolution maps, remains an open question.
An important limitation of CryoBoltz is the limited stability of optimization, due to the multimodality of the likelihood (x). This instability mitigated by sampling several structures simultaneously and selecting the best fit posteriori, but this comes at the cost of increased memory and time consumption. Importantly, CryoBoltz also relies on the base (unguided) model being able provide good initialization during the "warm-up" stage, which we found not to be the case several systems (e.g., DSLI/SNARE complex [19) full IgG antibody [67 Future directions
this work therefore include exploring ways to stabilize guidance, mitigating the drift towards "off-manifold" regions (where the diffusion model highly inaccurate), or getting rid of heuristic choices like the specific duration of each guidance stage. Finally, when having access to N cryo-EM maps, associated with

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Pma1
CYP102A1
YbbAP
CryoBoltz
Active state PDB:SUGB
Open state PDB:BDME
Bound state PDB:3GE7
Inhibited state PDB:9UGO
Clased state PD8:8DMG
Unbound state
PDB:SGE6
Figure 6: Results on Pmal, CYP102A1, and YbbAP [56] Cryoboltz guides the atomic model into two distinct conformations per complex based on experimental density maps.
similar conformations, exploring the possibility to optimize unique deformation model instead of N independent models constitutes an interesting avenue for future work.
Conclusion. In this study, we demonstrate the possibility of increasing the sample diversity of state-of-the-arr generative models using experimental cryo-EM data. Doing so, we hope to contribute to the ongoing community effort towards efficiently exploring the conformational landscape of macromolccules with machine learning models.
Acknowledgements
The authors acknowledge the use of computing resources at Princeton Research Computing, consortium of groups led by the Princeton Institute for Computational Science and Engineering (PICSciF) and Office of Information Technology's Research Computing. The Zhong lab is grateful for support from the Princeton Catalysis Initiative, Princeton School of Engineering and Applied Sciences, Chan Zuckerberg Imaging Institute, Janssen Pharmaceuticals, and Generate Biomedicines. The funders had no role study design, data collection and analysis, decision to publish or preparation of the manuscript.
References
[1] Josh Abramson, Jonas Adler, Jack Dunger, Richard Evans, Tim Green, Alexander Pritzel, Olaf Ronneberger, Lindsay Willmore, Andrew Ballard, Joshua Bambrick, et al. Accurate structure prediction of biomolecular interactions with alphafold 3. Nature, 630(8016):493-5555 5000,,5005500 2024.
[2] Brian DO Anderson. Reverse-time diffusion equation models. Stochastic Processes and their Applications, 12(3):313-326, 1982.
10

---

[3] Minkyung Baek, Frank DiMaio, Ivan Anishchenko, Justas Dauparas, Sergey Ovchinnikov, Gyu Rie Lee, Jue Wang. Qian Cong. Lisa N Kinch, Dustin Schaeffer, al. Accurate prediction of protein structures and interactions using three-track neural network. Science, 373(6557):871 (11165557)871887777 -876, 2021.
[4] I.. Bavnhojj P.A. Paulsen, J.C. Flores-Canales, B. Schiott, and B.P. Pedersen. Sugar/h+ symporter stp10 in outward occluded conformation, 2021.
[5] L.. Bavnhoj, P.A. Paulsen, J.C. Flores-Canales B. Schiott, and B.P. Pedersen. Sugar/h+ symporter stp10 in inward open conformation, 2021.
[6] Laust Bavnhøj, Peter Aasted Paulsen, Jose C. Mlores-Canales Birgit Schiøtt, and Bjøm Panyella Pedersen. Molecular mechanism of sugar transport in plants unveiled by structures of glucose/h+ symporter stp10. Nature plants, (10):1409-1499, 2021.
[7] Helen Berman, Kim Henrick, and Haruki Nakamura. Announcing the worldwide protein data bank. Nature struciural & molecular biology, 10(12):980-980, 2003.
[8] Helen Berman, Kim Henrick, Haruki Nakamura, and John Markley. The worldwide protein data bank (wwpdb): ensuring single, uniform archive of pdb data. Nucleic acids research, 35 (suppl_!::D311->
2007.
[9] Peter Brüggeller and Erwin Mayer. Complete vitrification in pure liquid water and dilute aqueous solutions. Nature, 288(5791):5699-557 1980.
[10] Muyuan Chen and Steven J Ludtke. Deep learning-basc mixed-dimensional gaussian mixture model for characterizing variability in cryo-em. Nature methods, 18(8):930-936, 2021.
[11] Jooyoung Choi, Sungwon Kim, Yonghyun Jeong, Youngjune Gwon, and Sungroh Yoon. Ilvr: Conditioning method for denoising diffusion probabilistic models. arXiv preprint 1xXiv:2108.029338 2021.
[12] Hyungjin Chung, Jeongsol Kim, Michael T Mccann, Mare L Klasky, and Jong Chul Ye. Diffu- sion posterior sampling for general noisy inverse problems. arXiv preprint arXiv:2209. 14687, 2022.
[13] Kevin Cowtan. The buccaneer software for automated model building. 1. tracing protein chains. Acta crystallographica section D: biological crystallography, 62(9):1002-100 1011, 2006.
[14] A.T. Culbertson and M. Liao. Cryo-em of human p-glycoprotein reveals an intermediate occluded conformation during active drug transport. Nature Communications, 16:3619, 2025. doi: 1677388541467-025-555
[15] A.T. Culbertson and M. Liao. Cryoem structure of p-glycoprotein in apo state, 2025.
[16] A.T. Culbertson and M. Liao. Cryoem structure of p-glycoprotein in collapsed closed state under continuous turnover conditions with verapamil, 2025.
[17] A.T. Culbertson and M. Liao. Cryoem structure of p-glycoprotein in occluded closed state under continuous turnover conditions with verapamil, 2025.
[18] A.T. Culbertson and M. Liao. Cryoem structure of p p-glycoprotein in inward facing 2 state under continuous turnover conditions with verapamil, 2025.
[19] Kevin A DAmico, Abigail E Stanton, Jaden D Shirkey, Sophie M Travis, Philip D Jeffrey, and Frederick M Hughson. Structure of a membrane tethering complex incorporating multiple snares. Nature structural & molecular biology, 31(2):246-2544 2024.
[20] Giannis Daras, Hyungjin Chung, Chieh-Hsin Lai, Yuki Mitsufuji, Jong Chul Ye, Peyman Milanfar, Alexandros Dimakis, and Mauricio Delbracio. survey on diffusion models for inverse problems. arXiv preprint 2100002410 2024.

---

[21] Fatima A Aavila-Hernande Biao Jin, Harley Pyles, Shuai Zhang, Zheming Wang, Timothy F Huddy, Asim K Bera, Alex Kang, Chun-Long Chen, James J De Yoreo, et al. Directing polymorph specific calcium carbonate formation with de novo protein templates. Nature Communications, 14(1):8191, 2023.
[22] Marc De Graef. Introduction to conventional transmission electron microscopy. Cambridge university press, 2003.
[23] Diego Del Alamo, Davide Sala, Hassane S Mchaourab, and Jens Meiler. Sampling alternative conformational states of transporters and receptors with alphafold2. Elife, 11:e75551, 2022.
[24] J Dubochet and AW McDowall. Vitrification of pure water for electron microscopy. Journal of microscopy, 124(3)3 4, 1981.
[25] Sasha B Ebrahimi and Devleena Samanta. Engineering protein-based therapeutics through structural and chemical design. Nature Communications, 14(1):2411, 2023.
[26] Bradley Efron. Tweedie's s formula and selection bias. Journal of the American Statistical Association, (1664966:1602-1611 2011.
[27] Dominika Elmlund and Hans Elmlund. Simple: Software for ab initio reconstruction of heterogeneous single-particles. Journal of structural biology, 180(3):420-444 42000-27720020 2012.
[28] Alisia Fadini, Minhuan Li, Airlie J McCoy, Thomas Terrwilliger, Randy J Read, Doeke Hekstra, and Mohammed AlQuraishi. Alphafold as a prior: Experimental structure determination conditioned on pretrained neural network. bioRxiv, pages 2025-02, 2025.
[29] AR Faruqi and R Henderson. Electronic detectors for electron microscopy. Current opinion in structural biology. (((5::54-555,, 2007.
[30] Berthy T Feng, Jamie Smith, Michael Rubinstein, Huiwen Chang, Katherine L Bouman, and William T Freeman. Score-based diffusion models as principled priors for inverse imaging. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 10520- 10531, 2023.
[31] Jean Feydy, Pierre Roussillon, Alain Trouvé, and Pietro Gori. Fast and scalable optimal transport for brain tractograms. In Medical Image Computing and Computer Assisted Intervention MICCAI 2019: 22nd International Conference, Shenzhen. China, October 13-17, 2019, Proceedings, Part III, page 030-32247-2. doi: 10. (000/978-3-000-3333
Berlin, Heidelberg, 2019. Springer-
ISBN 978-3-
[32] Nabin Giri and Jianlin Cheng. De novo atomic protein structure modeling for cryoem density maps using 3d transformer and hmm. Nature Communications, 15(1):5511, 20244
[33] Theo Hahn, Uri Shmueli, and JC Wilson Arthur. International tables for crystallography, volume 1. Reidel Dordrecht, 1983.
[34] Ulrich G Haussmann and Etienne Pardoux. Time reversal of diffusions. The Annals of Probability, pages 1188-1205, 1986.
[35] Jiahua He, Peicong Lin, Ji Chen, Hong Cao, and Sheng- You Huang. Model building of protein complexes from intermeddiaterresouttion cryo-em maps with deep learning-guidat automatic assembly. Nature Communications, 13(1):0066, 2022.
[36] Lim Heo and Michael Feig. Multi-state modeling of g-protein coupled receptors at experimental accuracy. Proteins: Structure, Function, and Bioinformatics, 90(1 1): 2022.
[37] John B. Ingraham, Max Baranov, Zak Costello, Karl W. Barber, Wujie Wang. Ahmed Ismail, Vincent Frappier, Dana M. Lord, Christopher Ng- Te-hhhoi--ig Erik R. Van Vlack, Shan Tie, Vincent Xue. Sarah C. Cowles, Alan Leung, João V. Rodrigues, Claudio L. Morales-Perez, Alex M. Ayoub, Robin Green, Katherine Puentes, Frank Oplinger, Nishant Obermeyer, Adam R. Root, Andrew I. Beam, Frank J. Poelwijk, and Gevorg Grigoryan. Illuminating protein space with a programmable generative model. Nature, 623(7789):0070- 1078, Nov 2023. ISSN 1476-4687. doi: 10. 10.10388-1158--22-007222
Panwar, Fritz
12

---

[38] Ajil Jalal, Marius Arvinte, Giannis Daras, Eric Price, Alexandros G Dimakis, and Jon Tamir. Robust compressed sensing mri with deep generative priors. Advances in Neural Information Processing Systems, 34: 14938-14954 2021.
[39] Kiarash Jamali, Lukas Käll, Rui Zhang, Alan Brown, Dari Kimanius, and Sjors HW Scheres. Automated model building and protein identification in cryo-em maps. Nature, pages 1-2, 2024.
[40] Bowen Jing, Bonnie Berger, and Tommi Jaakkola. Alphafold meets flow matching for generating protein ensembles. arXiv preprint (iXii::2402.048445, 2024.
[41] John Jumper, Richard Evans, Alexander Pritzel, Tim Green, Michael Figurnov, Olaf Ron- neberger, Kathryn Tunyasuvunakool, Russ Bates, Augustin Židek, Anna Potapenko, et al. Highly accurate protein structure prediction with alphafold. nature, 596(7873):5833555) 2021.
[42] W. Kabsch. A solution for the best rotation to relate two sets of vectors. Acta Crystallographica Section A, 32(5):922-923, 1976. doi: https://doi.org// /tgp//0..17///5567774770000 873.
[43] Yogesh Kalakoti and Bjöm Wallner. Afsample2 predicts multiple conformations and ensembles with alphafold2. Communications Biology, 8(1):373, 2025.
[44] Satinder Kaur, Josue Gomez-Blanco, Ahmad AZ Khalifa, Swathi Adinarayanan, Ruben Sanchez- Garcia, Daniel Wrapp, Jason S McLellan, Khanh Huy Bui, and Javier Vargas. Local com- putational methods to improve the interpretability and analysis of cryo-em maps. Nature communications, 12(1):1240, 2021.
[45] Bahjat Kawar, Gregory Vaksman, and Michael Elad. Snips: Solving noisy inverse problems stochastically, Advances in Neural Information Processing Systems, 34:21757-21769, 2021.
[46] Bahjat Kawar, Michael Elad, Stefano Ermon, and Jiaming Song. Denoising diffusion restoration models. Advances in Neural Information Processing Systems, 35:23593-23606, 2022.
[47] Werner Kühhbrandt.. The resolution revolution. Science, 343(6118))14443-1444 2014.
[48] Axel Levy, Eric R Chan, Sara Fridovich-Kan Keil, Frédéric Poitevin, Ellen D Zhong, and Gordon Wetzstein. Solving inverse problems in protein space using diffusion-based priors. arXiv preprint arXiv:2406.04223, 2024.
[49] Axel Levy, Rishwanth Raghu, J Ryan Feathers, Michal Grzadkowski, Frédéric Poitevin, Jake D Johnston, Francesca Vallese, Oliver Biggs Clarke, Gordon Wetzstein, and Ellen D Zhong. End-to-end neural ab initio reconstruction of challenging cryo-em and cryo-et datasets. bioRxiv, pages 2024-05 2024.
[50] Sarah Lewis, Tim Hempel, José Jiménez-Luna, Michael Gastegger, Yu Xie, Andrew YK Foong, Victor García Satorras, Osama Abdin, Bastiaan S Veeling, Iryna Zaporozhets, et al. Scalable emulation of protein equilibrium ensembles with generative deep learning. bioRxiv, pages 2024-12, 2024.
[51] Dorothee Liebschner, Pavel Afonine, Matthew L Baker, Gábor Bunkóczi, Vincent B Chen, Tristan I Croll, Bradley Hintze, L-W Hung, Swati Jain, Airlie McCoy, et al. Macromolecular structure determination using x-rays, neutrons and electrons: recent developments in phenix. Acta Crystallographica Section D: Structural Biology, 75(10))861-877, 2019.
[52] Zeming Lin, Halil Akin, Roshan Rao, Brian Hic, Zhongkai Zhu, Wenting Lu, Nikita Smetanin, Robert Verkuil, Ori Kabeli, Yaniv Shmueli, et al. Evolutionary-scale prediction of atomic-level protein structure with a language model. Science, 379 2023.
[53] Advaith Maddipatla, Nadav Bojan Sellam, Meital Bojan, Sanketh Vedula, Paul Schanda, Ailie Marx, and Alex M Bronstein. Inverse problems with experiment-guided alphafold. arXiv preprint arXiv:2502.09377. 2025.
[54] Sai Advaith Maddipatla, Nadav Bojan Sellam, Sanketh Vedula, Ailie Marx, and Alex Bronstein. Generative modeling of protein ensembles guided by erystallographic electron densities. arXiv preprint 21Xiv:2412.13223. 2024.
13

---

[55] Morteza Mardani, Jiaming Song, Jan Kautz, and Arash Vahdat. A variational perspective on solving inverse problems with diffusion models. arXiv preprint arXiv:2305.04.39, 2023.
[56] Martin B.L. McAndrew, Jonathan Cook, Amy Gill, Kavya Sahoo, Clare Thomas, Phillip J. Stansfeld, and Allister Crow. Structure of ybbap-tesa: a type vii abe transporter-lipid hydrolase complex. bioRxiv, 2025. doi: (0.1101/2025.06 15.16.6526..6.44.
[57] M.B. McAndrew, J. Cook, A. Gill, K. Sahoo, C. Thomas, P.J. Stansfeld, and A. Crow. Structure of e. coli ybbap, 2025.
[58] M.B. McAndrew, J. Cook. A. Gill, K. Sahoo, C. Thomas, P.J. Stansfeld, and A. Crow. Structure of e. coli ybbap with bound atp analogue, 2025.
[59] Elaine C. Meng, Thomas D. Goddard, Eric F. Pettersen, Greg S. Couch, Zach J. Pearson, John H. Morris, and Thomas E. Ferrin. Ucsf chimerax: Tools for structure building and analysis. Protein Science, 32(1 1):44992, 2023, doi: https://ooi.org/10 1..///..10000 10.0000//roo
[60] Gabriel Peyré, Marco Cuturi, et al. Computational optimal transport: With applications to data science. Foundations and Trends@ in Machine Learning, 11(5-6)3355-077, 2019.
[61] Jonas Pfab, Nhut Minh Phan, and Dong Si. Deeptracer for fast de novo cryo-em protein structure modeling and special studies on cov-related complexes. Proceedings of the National Academy of Sciences, 218())=2017525111
2021.
[62] Ali Punjani and David J Fleet. 3d variability analysis: Resolving continuous flexibility and discrete heterogeneity from single particle cryo-em. Journal of structural biology, 213(2): 107702, 2021.
[63] Ali Punjani and David Fleet. 3dflex: determining structure and motion of flexible proteins from cryo-em. Nature Methods, 20(6):860-870, 2023.
[64] Ali Punjani, John L. Rubinstein, David J Fleet, and Marcus A Brubaker. cryospare: algorithms for rapid unsupervised cryo-em structure determination. Nature methods, 14(3):290-295) 2017.
[65] Alexander Rives, Joshua Meier, Tom Sercu, Siddharth Goyal, Zeming Lin, Jason Liu, Demi Guo, Myle Ott, C Lawrence Zitnick, Jerry Ma, et al. Biological structure and function emerge from scaling unsupervised learning 250 million protein sequences. Proceedings of the National Academy of Sciences, 1 (18(15):220663311 2021.
[66] Herbert E Robbins. An empirical bayes approach to statistics. Breakthroughs in Statisties: Foundations and basic theory, pages 388-394, Springer, 1992.
[67] Erica Ollmann Saphire, Paul WHI Parren, Ralph Pantophlet, Michael B Zwick, Garrett M Morris, Pauline M Rudd, Raymond A Dwek, Robyn I. Stanfield, Dennis R Burton, and Ian A Wilson. Crystal structure of a neutralizing human igg against hiv-1: a template for vaccine design. science, 293(5532):1155 115-51111115-115:: 2001.
[68] Sjors HW Scheres. Relion: implementation of bayesian approach to cryo-em structure determination. Journal of structural biology, 180(3)5519553) 530, 2012.
[69] Sjors HW Scheres, Haixiao Gao, Mikel Valle, Gabor T Herman, Paul PB Eggermont, Joachim Frank, and Jose-Maria Carazo. Disentangling conformational states of macromolecules in 3d-em through likelihood optimization. Nature methods, 4(1):27-29, 2007.
[70] Aaron G. Schmidt, Huafeng Xu, Amir R. Khan, Timothy O' O'Donnell, Surender Khurana, Lisa R. King, Jody Manischewitz, Hana Golding, Pirada Suphaphiphat, Andrea Carfi, Ethan C. Settembre, Philip R. Dormitzer, Thomas B. Kepler, Ruijun Zhang, M. Anthony Moody, Barton F. Haynes, Hua-Xina Xin Liao, David E. Shaw, and Stephen C. Harrison. Preconfiguration of site during affinity maturation of broadly neutralizing influenza virus antibody. Proceedings of the National Academy of Sciences, (1(())264-266) 2013. doi: 10. 1073/pnas.
12 122266109.
14

---

[71] A.G. Schmidt, H. Xu, A.R. Khan, T. O'Donnell, S. Khurana, L.R. King, J. Manischewitz, H. Golding, Suphaphiphat, A. Carfi, E.C. Settembre, P.R. Dormitzer, T.B. Kepler, R. Zhang. M.A. Moody, B.F. Haynes, H.X. Liao, D.E. Shaw, and S.C. Harrison. Influenza hemagglutinin complex with ch67 fab, 2012.
[72] Dong Si, Spencer A Moritz, Jonas Pfab, Jie Hou, Renzhi Cao, Liguo Wang, Tianqi Wu, and Jianlin Cheng. Deep learning to predict protein backbone structure from high-resolution cryo-em density maps. Scientific reports, (0(1):4282, 2020.
[73] Abhishek Singharoy, Ivan Teo, Ryan McGreevy, John E Stone, Jianhua Zhao, and Klaus Schulten. Molecular dynamics-based refinement and validation for sub-5 å cryo-electron microscopy maps. Elife, 5:e16105, 2016.
[74] Jiaming Song, Arash Vahdat, Morteza Mardani, and Jan Kautz. Pseudoinverse-guidee diffusion models for inverse problems. In International Conference Learning Representations, 2023.
[75] Yang Song, Jascha Sohl-Dickstein. Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:201 13456, 2020.
[76] Yang Song, Conor Durkan, lain Murray, and Stefano Ermon. Maximum likelihood training of score-based diffusion models. Advances neural information processing systems, 34: 1415-1428, 2021.
[77] Charles M Stein. Estimation of the mean of multivariate normal distribution. The annals of Statistics, pages 1135-1151, 1981.
[78] M. Su and H. Xu. Cyp102al in open conformation, 2023.
[79] M. Su and H. Xu. Cyp102al in closed conformation, 2023.
[80] Kenneth A Taylor and Robert M Glaeser. Electron diffraction of frozen, hydrated protein crystals. Science, 16(4416): 1974.
[81] Genki Terashi and Daisuke Kihara. novo main-chain modeling for em maps using mainmast. Nature communications, (1):1611, 2018.
[82] Thomas Terwilliger, Paul D Adams, Pavel V Afonine, and Oleg V Sobolev. A fully automatic method yielding initial models from high-resolution cryo-clectron microscopy maps. Nature methods, 15995)995-9008 2018
[83] Ian J. Tickle. Statistical quality indicators for clectron-density maps Acta Crystallographica Section D) 68(4):454 467, Apr 2012. doi: 10.10075500074449110033
[84] Pascal Vincent. connection between score matching and denoising autoencoders. Neural computation, 23(7): 1661))66611774 2011.
[85] Ray Yu-Ruei Wang. Mikhail Kudryashev, Xueming Li, Edward Egelman, Marek Basler, Yifan Cheng. David Baker, and Frank DiMaio. De novo protein structure determination from manr-ttomi-resllttionn cryo-em maps. Nature methods, 12(4)3335-338 2015.
[86] Yinhuai Wang, Jiwen Yu, and Jian Zhang. Zero-shot image restoration using denoising diffusion null-space model. arXiv preprint arXiv:22 22. 2022.
[87] Hannah K Wayment- Steele, Adedolapo Ojoawo, Renee Otten, Julia M Apitz, Warintra Pit- sawong, Mare Hömberger, Sergey Ovchinnikov, Lucy Colwell. and Dorothee Kern. Predicting multiple conformations via sequence clustering and alphafold2. Nature, 625(7996)832-883, 2024.
[88] Jeremy Wohlwend, Gabriele Corso, Saro Passaro, Noah Getz, Mateo Reveiz, Ken Leidal, Wojtek Swiderski, Liam Atkinson, Tally Portnoi, Itamar Chinn, Jacob Silterra, Tommi Jaakkola, and Regina Barzilay. Boltz-1: Democratizing biomolecular interaction modeling. bioRxiv, 2024. doi: 10.120///02..1111 12.4167777.
15

---

[89] Z.L. You and L. Bai. Cryo-em structure of the pmal with ordered n-terminal extension in the activated state, 2025.
[90] Z.L. You and L. Bai. Cryo-em structure of the pmal with ordered n-terminal extension in autoinhibited state, 2025.
[91] Bingliang Zhang, Wenda Chu, Julius Berner, Chenlin Meng, Anima Anandkumar, and Yang Song. Improving diffusion inverse problem solving with decoupled noise annealing. arXiv preprint arXiv:2407.01521, 2024.
[92] Xi Zhang, Biao Zhang, Peter L Freddolino, and Yang Zhang. Cr-i-tasser: assemble protein structures from cryo-em density maps using deep convolutional neural networks. Nature methods, 19(2):155204, 2022.
[93] Yang Zhang and Jeffrey Skolnick. Tm-align: a protein structure alignment algorithm based on the tm-score. Nucleic Acids Research, 33(7):2302-2300 01 2005. ISSN 1305-1048. doi:
10. 4
[94] Ellen D Zhong, Tristan Bepler, Bonnie Berger, and Joseph Davis. Cryodrgn: reconstruction of heterogeneous cryo-em structures using neural networks. Nature methods, 18(2):176-185, 2021.
16

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Appendix
A Supplemental Methods
A.1 Point cloud construction
For global guidance, the input density map is converted to point cloud by performing weighted k-means clustering on the voxel coordinates, where the weights are given by the map intensity values. k is set [N/(4r)), where N is the number of atoms in the system and is the voxel size of the map in Å. Prior to clustering, density values below threshold may be set and connected density components below size threshold may be removed ("dusted"). See Experimental Details for dataset-dependent values, where applicable.
A.2 Simulated map construction
For local guidance, a density map is simulated from the sample using single Gaussian per atom whose amplitude is given by atomic number, as implemented in the default molmap function of ChimeraX [9]. The map is simulated to match the voxel size and nominal resolution of the input map.
A.3 Alignment to density map
For efficient optimization of the point cloud guidance term, the intermediate sample must be aligned to the input density map. We obtain unguided sample and dock it into the map using the ChimeraX fitmap function [59]. Prior the first step of guidance, the intermediate sample aligned the
unguided sample via the Kabsch algorithm [42]
A.4 Sinkhorn divergence
For two point clouds X Nx3 and Y Rx3 the entropy-regullrizze optimal transport distance is given by
N M
N
M
OT, YX,Y = min ΣΣ
Ci.
>
Σ
Yi log Yij
YER NXM
where y is transport plan whose rows each sum to 1/N and columns each sum to 1/M. The first term is the Wasserstein distance between the point clouds, where the cost Ciş between two points is the squared Euclidean distance || 12 The second term is the entropy of y, which allows for tractable and differentiable optimization and is controlled by the regularization strength As the entropy term introduces an approximation error to the true Wasserstein distance, the Sinkhorn divergence corrects for this and is defined
D Y) OT, (X,) (x.,,,))))__,xx))))))))) - -
I
We use the GeomLoss library for efficient optimization of the objective D with respect to the sample coordinates (31] The reach parameter set to 10 while all others are set to their defaults.
A.5 Guidance schedule
For the synthetic datasets, the numbers of steps in the guidance phases are Tú = 125. T, = 25, T: 25, and T,- 25. For the experimental datasets, the numbers of steps are T., 100. T, 50, T: 25, and T,- 25. During the global guidance phase (for all datasets), the guidance strength is annealed along a cosine schedule from 0.25 0.05, i.e., X(t) 0.05 + 1 (0.25 0.05) + cos( )). During the local guidance phase, the guidance strength is made constant at A(t) = 0.5.
A.6 Experimental Details
STP10. Deposited structures of the inward and outward conformations (PDB: 7AAQ. 7AAR) 4 were stripped of non-protein entities. Synthetic density maps of 2 Á resolution and Á voxel size were
17

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generated using the ChimeraX molmap function [59]. then padded to dimension w = h = d = 100. The wild-type protein sequence corresponding PDB: 7AAQ was given input.
CH67 Antibody. The deposited structure of the antibody Fab (PDB: 4HKXX) was stripped of non- protein entities and the bound hemagglutinin receptor. A synthetic density map of Å resolution and Á voxel size was generated and padded to dimension w = h = d = 100. For CryoBoltz and Boltz-1 [88), the step_seee scale parameter, which controls the temperature of the sampling distribution, is set at 3.0 to increase CDR H3 loop accuracy.
P-glycoprotein. The experimental maps of four conformational states (EMD- 40259, 40258, 40227) were masked around their corresponding deposited models (PDB: 8GMG, 8SA1, 8SAO, 80MJ) IS to remove micelle density, using the ChimeraX volume zone function [59] A padding of voxels was then added each side.
Pmal. The experimental maps of two conformational states (EMD-64135, 64136) were cropped to a tight box at density threshold of 0.35 then padded by 10 voxels on each side. This removed empty background regions for computational efficiency. During the global guidance phase of the method, the maps were thresholded at value of 0.35.
CYP102A1. The experimental maps of two conformational states (EMD-27534, 27536) were cropped tight box at density threshold of 1. 1.25 then padded by 10 voxels each side. During the global guidance phase of the method, the maps were thresholded at a value of 1.25.
YbbAP. The experimental maps of two conformational states JEMD-51292 51291) were cropped to a tight box at a density threshold 0.005 then padded by 10 voxels on each side. During the global guidance phase of the method, the maps were thresholded at value of 0.005, and dusted with size threshold 100.
A.7 Computational resources
All experiments were performed single Nvidia A100 GPU with 80 GB VRAM.
B
Supplemental Results
B.1 Map-model fit and statistical significance
In Table B2 report evaluation metrics and confidence bounds the best generated sample as assessed by map-model fit. Three replicates of each method are run to produce 25 samples per replicate. Samples ranked according to the real-space correlation coefficient (RSCC), which is the Pearson correlation between the input density map and a map simulated from the sample [83]. For the unguided baselines, we first align each sample to the deposited model via the Kabsch algorithm [42] CryoBoltz demonstrates statistically significant improvement over baselines across a majority of maps and metrics.
B.2 Spread of sample quality
In Figures B2 and B3 we visualize the full distribution of RMSD values over all samples produced by CryoBoltz, Boltz-1 and AlphaFold3. For nearly all maps, majority of CryoBoltz samples are more accurate than those produced by the basclines.
18

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Table B1: Additional baselines and ablations for experimental cryo-EM density maps. Extending
Table 2 we report accuracy metrics for MSA subsampling of Boltz-1, as well as ablations of the local and global guidance phases. We report the mean all-atom RMSD (A), Ca RMSD (A) and TM score for the best of 25 samples (lowest all- all-atom RMSD) across 3 model replicates, Random MSA subsampling of Boltz-1 (Boltz-1 + MSA sub.) run with MSA depths of 64, 128, 256, 512, and 1024, each producing 5 samples. Pgp is P-glycoprotein and CYP is CYP20IAL. Bold indicates best
value(s).
CryoBoltz RMSD
Boltz-1
+ MSA subsampling
Local only RMSD
Global only
RMSD
TM
RMSD
RMSD
TM
RMSD
TM
RMSD
RMSD
TM
Structure
all
Ca
score
all
Co:
score
score
500re
Pgp (apo)
1,382
1,208
0.989
6.902
7.099
0.770
5.897
6.026
0.810
1,501
1,335
0.986
Pgp (inward)
1.348
1.187
0.989
5.541
5.601
0.831
4,416
4.438
0.878
1.369
1.252
0.988
Pyp (occluded)
1.727
1.677
0.979
2.875
2.847
0.945
1.916
1.882
0.974
1.714
1,673
0.979
Pgp (collapsed)
1.309
1.261
0
3,497
3,482
0.914
1.781
1.754
0.977
1.453
1.424
0.984
Pmal (active)
2.046
1.776
0.973
3,204
2,935
0.927
3.228
2.938
0.930
2.164
1,907
0.967
Pmal (inhihited)
1.999
1.590
0.979
7.444
7.156
0.745
7.299
6.974
0.751
2,223
1,829
0.971
CYP (open)
4.167
3,946
0.957
11,971
11,868
0.635
8.342
8.242
0.804
3,918
3.720
0.989
CYP (closed)
2.004
1.552
0.990
13.395
13.262
0.594
6.132
5.986
0.857
2,089
1.763
0.987
YbЫAP (bound)
1.320
0.678
0.997
3,586
3,273
0.931
3.625
3.360
0.926
1.695
1.161
0.991
YbbAP (unbound)
2.454
2.039
0.974
5.254
4.992
0.865
7.069
6.825
0.823
2.762
2,400
0.964
Table B2: Evaluation of samples chosen by map-model fit. We report the Root Mean Square Deviation (RMSD) for all atoms, the Ca RMSD, the template-modeling (TM) score, and the real- space correlation coefficient (RSCC). For CH67, we also report the RMSD for the Ca atoms in the CDR H3 loop (local RMSD). The mean and 95% confidence interval across 3 replicates are reported for the best of 25 samples as assessed by map fit (highest RSCC). Bold indicates (statistically significant) best value(s).
Structure
Metrics
CryoBoltz
Boltz-1
AlphaFold3
RMSD (A, L)
1.1756 = 0.0859
3.8313 + 0.0810
1.3250 + 0.0216
STP10 (inward)
Ca RMSD (Á, L)
0.4776
0.0262
3.5838 4 0.0913
0.6543
0.0248
TM score (1)
0.9969
0.0002
0.8620 = 0.0043
0.9939
0.0003
RSCC (t)
0.8525 = 0.0043
0.2402 = 0.0031
0.7343
0.0029
RMSD
0.9090
2.6596 + 0.0039
4.4777
0.0244
STP10
Ca RMSD
0.4670
0.0613
2.4203 + 0.0102
4.2283
0.0369
(outward)
TM score
0.9971
0.0006
0.9485
+ 0.0004
0.8276
+: 0.0022
RSCC
0.8862
0.0064
0.5098 + 0.0015
0.1946
0.0011
RMSD
1.2957
0.2995
1.9940
0.0810
1.9719
0.1210
Ca RMSD
0.8739
0.2010
1.4970 = 0.0418
1.4935
0.0902
CH67 antibody
Local RMSD
1.3326
- 1.0667
3.5518 - 0.1133
3.9562 + 0.417
TM score
0.9917
0.0027
0.9713 1 0.0029
0.9708 1 0.0035
RSCC
0.9521
0.0041
0.8452 + 0.0155
0.8466 + 0.0117
RMSD
1.4931
0.0803
7.0928
0.1115
3,8272
1.444
P-glycoprotein
Ca RMSD
1.3377
0.1124
7.3054 - 0.1164
3.8652 1.5225
(apo)
TM score
0.9876
= 0.0004
0.7650
+ 0.0054
0.9036 + 0.0611
RSCC
0.8157
0.0007
0.4261 + 0.0033
0.5797 + 0.0982
RMSD
1.4311
+L 0.0346
5.6799
+ 0.75
2.6923 +: 1.1995
P-glycoprotein
Ca RMSD
1.2828
0.0407
5.7454
+ 0.1302
2.6634
1,2533
(inward)
TM score
0.9876
0.0007
0.8293
- 0.0056
0.9475
0.0440
RSCC
0.8165
0.0011
0.5109
+ D.0069
0.6927
0.0884
19

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RMSD
1.8070
0.0094
2.9844 + 0.1159
3,4641
+ 0,0747
P-glycoprotein
Ca RMSD
1.7505
2.9566
3.4429
0.0738
(occluded)
TM score
0.9778
0.0004
0.9402 # 0.0011
0.9209
0,0021
RSCC
0.7662
= 0,0006
0.6191 = 0.0072
0.5857
= 0.0001
RMSD
1.3881
0.0349
3,4253 + 0.2934
4.5681 + 0.1824
P-glycoprotein
Ca RMSD
1.3397
0.0363
3.4117 1: 0.2929
4.5538 1. 0.1798
(collapsed)
TM score
0.9860
0.0007
0.9174 + 0.0128
0.8642
0.0084
RSCC
0.7884
0.5746
0,0330
0.4904 0.0108
RMSD
2.1745
= 3,0098
6.6283 1.0733
Pmal
Ca RMSD
1.9144
0.3517
2.7817 = 0.2590
6,3890 + 1.0764
(active)
TM score
0.9706
0.0082
0,9352 = 0.0114
0.7691 + 0.0523
RSCC
0.5633
0,0113
0.3540 + 0.0234
0.2054
0.0102
RMSD
2.0499
0.1296
6.1404 + 0.7005
8.2569 0.5666
Pmal
Ca RMSD
1.6640
1: 5.8287
8.0042 0.5289
(inhibited)
TM score
0.9774
0.0026
0.7943 + 0.0339
0.7167
0,0202
RSCC
0.5276
0.0012
0.2439
= 0.0246
0.2166 + 0.0027
RMSD
4,3939 0.0988
8.5324 1. 0.1545
6.5074 1. 0.0836
CYP201A1
Ca RMSD
4.1473 0.0923
8.4389
0.1539
6.3770
0.0791
(open)
TM score
0.9535
0.7878
1 0.0110
0.8912
0.0036
RSCC
0.7693
0.0013
0.5074 + 0.0059
0.6220 0.0043
RMSD
2.8636
0.6566
8.7837 = 0.3684
3.5848
0.5770
CYP201A1
Ca RMSD
2.4669 = 0.7572
8.6674 + 0.3758
3,3910 + 0.6050
(closed)
TM score
0.9868
0.0022
0.7435 = 0.0151
0,9459 0.0186
RSCC
0.8062
0.0002
01.4977
0.0059
0.6830
0.0338
RMSD
1.3842
3.6264 1: 0.2116
3.7488
YbbAP
Ca RMSD
0.7578
0.0892
3.3550
+: 0.2512
3.4802
0.1897
(bound)
TM score
0.9961
0.0006
0.9283 + 0.0092
0.9219
0.0079
RSCC
0.7046
0.0005
0.5074 + 0.0116
0.4966
0.0083
RMSD
3.8623
0.6404
8.2798 +: 0.2012
4.0646 1: 0.4578
YbbAР
Ca RMSD
3.5271
0.7067
8.0973
0.2010
3.7913
0.4791
(unbound)
TM score
0.9607
0.7751 1:
0.9114 0.0184
RSCC
0.7098
0.0011
0.4944 + 0.0111
0.5594 + 0.0178
20

---

CryoBoltz
Boltz-1
AlphaFold3
PDB:4HKX
Figure B1: Full CH67 antibody [70] structures generated by all methods. Top 5 samples from each method, as ranked by all-atom RMSD
STP10 (inward)
STP10 (outward)
60
30-
CryoBoltz
Boltz-1
AlphaFold3
Samples
20
20
5.0
40
RMSD
RMSD
CH67 (full)
CH67 (CDR H3)
20-
20-
Samples
1.0
20
50
84 10.0 11.0
12
20
40
5.0
80
50
10.0
11.0
RMSD
RMSD
Figure B2: Distribution of RMSD values for synthetic maps. All-atom RMSD values for all samples over all replicates are visualized as histograms with bins.
21

---

P-glycoprotein (apo)
70
P-glycoprotein (inward)
CryoBoltz
10-
10-
Samples
Boltz-1
AlphaFold3
20-
1.0
20
30
5.0
5.
90
RMSD
RMSD
P-glycoprotein (occluded)
P-glycoprotein (collapsed)
60-
30
Samples
10-
RMSD
RMSD
Pma1 (active)
70-
Pma1 (inhibited)
30-
50-
Samples
30-
21-
10-
17. 20.0
15.0
25.0
RMSD
RMSD
CYP102A1 (open)
70-
CYP102A1 (closed)
Samples
42
20
70-
1.0
5.0
10.0
15.0
264
25. RMSD
200
26.
400
25.
5.0
10.6
15.0
25.0
26.6
20.0
36.0
43.0
46.0
RMSD
YbbAP (bound)
YbbAP (unbound)
60-
50-
Samples
30-
10
13.0
30
17.0
RMSD
RMSD
Figure B3: Distribution of RMSD values for experimental maps. All-atom RMSD values for all samples over all replicates are visualized as histograms with 50 bins.
22

---

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16. Declaration of LLM usage
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Question: Does the paper describe the usage of LLMs if it is important, original, or non-standard component of the core methods this research? Note that if the LLM used only for writing, editing, or formatting purposes and does not impact the core methodology. scientific rigorousness, or originality the research, declaration is not required.
Answer: [NA]
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Reviews:
[{"review_id": "fLY5ODVu4S", "reviewer": "Reviewer_SWNS", "summary": "CryoBoltz is an inference-time framework that enhances diffusion-based protein structure predictors by integrating information form heterogeneous cryo-electron. It adds data-driven guidance to a pretrained score model without retraining. Using a multiscale strategy over four stages it drives models toward conformations consistent with experimental data. The stages include initial unguided sampling, coarse global alignment to a point-cloud representation of the density map, fine local fitting against the full map, and final unguided relaxation. CryoBoltz works atop any diffusion-based predictor namely Boltz-1, and overcomes their static bias. Evaluations on synthetic maps for a transporter and an antibody and on real cryo-EM maps of P-glycoprotein demonstrate its ability to recover diverse states with high accuracy. This approach bridges sequence-based models with experimental observables.", "questions": "•\tCould the authors provide more quantitative comparisons to alternative methods, namely ADP-3D? \n\n•\tI appreciate the synthetic dataset generation for th STP10 and CH67 antibodies. Could you show for one of them how the \naccuracy of your model changes with the resolution of your synthetic density maps. It would be interesting to see a line plot of resolution vs rmsd for all the compared methods. It would be nice to understand on a single molecule where the method works best and potential where it fails with respect to the other methods?\n\n•\tCould the authors test the method on a new pdb structure that is not included in the Boltz-1 training dataset? Is this an area where your inference-time methods shine even more? \n\n•\tCould the authors compare their approach on a larger experimental dataset. Its currently hard to judge whether the 4 proteins (section 4.4) are cherry picked or whether the outperformance generalises. \n\n•\tLow priority: Does using Boltz-2 further improve your method?", "limitations": "A more detailed experimental section would help in understanding the true limitations of the method.", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "-\tThe authors clearly outline their proposed method.\n-\tThe figures are instructive, clear and of high quality. \n-\tThe authors show their multi step guidance is required through various ablations\n-\tThe authors illustrate a failure of the models to reproduce cryo-EM data without any guidance\n-\tOverall, the complexity of the approach is minimal. Comparison to other approaches and other guidance methods could be extended.\n-\tThe approach of generating synthetic data is interesting but could be leveraged more to investigate the performance as a function of resolution in greater detail.\n-\tThe experimental comparisons are valuable, but the authors only compare on a single protein (P-glycoprotein) with 4 different structures. Could the authors use a larger benchmark dataset to compare their method to show the results aren’t cherry picked? \n- Overall the a larger benchmark dataset would be helpful to asses the trust worthiness of the method. If its very hard to obtain cryo-em data you could extend your synthetic generation approach to a relevant subset of the pdb? Or all new PDB structures post Boltz-1 training? \n-\tThe reviewer does not have the domain expertise to judge the significance of this work for the broader bio community.", "was_revised": true, "final_justification": "The authors have included three substantial new experiments in the rebuttal phase, including ablations with respect to resolution in their synthetic datasets and further comparison to experiments. These have significantly strengthened the evaluation of their approach and I am therefore increasing my score to accept. The experimental comparisons in particular demonstrate the potential impact of the work presented in the paper. However, as the authors compare against only four experimental structures, I retain some concerns regarding the general applicability of the method. Additionally, the paper is focused on a very specific sub-area of AI. Due to these two points I have not raised my score further.", "rebuttal": "We thank the reviewer for their thoughtful comments on our work. We are glad the reviewer appreciates the clarity of the writing and the value of the synthetic experiments. As the first method to leverage the state-of-the-art AlphaFold3 as a prior for cryo-EM model building, we believe our method will broaden the structural interpretation of experimental data, and hope to showcase its applicability through the additional experiments we detail in our response below.\n\n**Additional Validation on Experimental Data.**\nWe thank the reviewer for the suggestion to further evaluate our approach on experimental data. We assessed our method on 3 additional protein systems associated with real cryo-EM density maps, and whose deposited models are not part of the Boltz-1 training set. For each experimental map, we obtain 25 samples from each method, choose the best sample as assessed by map-model fit (real-space correlation coefficient), and report its all-atom RMSD and TM-score with respect to the deposited model. For ModelAngelo, we obtain its single prediction and report model completeness and TM-score. We additionally expand our set of baselines to include ADP-3D, and describe these evaluations further in the **ADP-3D Baseline** section below. Metrics are presented in the table below, and we summarize the results here:\n- *Pma1*: We use two experimental maps of this ATPase [EMD-64135, 64136], corresponding to its active and inhibited states [PDB: 9UGB, 9UGC]. Unguided Boltz only samples the active state, whereas guidance also samples the inhibited state with an RMSD of 2.01 Å. AlphaFold3 predictions are not accurate with respect to either state. \n- *CYP102A1*: We use two experimental maps of this oxygenase [EMD-27534, 27536], of resolutions 4.4 Å and 6.5 Å, corresponding to its open and closed states [PDB: 8DME, 8DMG]. Guidance improves the RMSD of the closed state from 7.89 Å to 2.39 Å over unguided Boltz-1, whereas for the lower resolution open state map, a more modest improvement from 7.93 Å to 4.33 Å is observed. ModelAngelo only models 19% of the 4.4 Å map and none of the 6.5 Å map.\n- *YbbAP*: We use two experimental maps of this transporter [EMD-51292, 51291], corresponding to states in which ATP is bound or unbound [PDB: 9GE7, 9GE6]. Unguided Boltz only samples the bound state, which guidance additionally improves to an RMSD of 1.31 Å. The unbound state is also obtained through guidance. Since the unbound state map is of medium resolution at 4.05 Å, ModelAngelo only models 55% of the structure.\n\nOur results on these systems, along with the P-glycoprotein example in the manuscript (Figure 5), demonstrate our method’s ability to recover diverse conformations from real experimental maps, especially at resolutions where other methods fail. We will include these results, including visualizations, in our revised manuscript.\n\n|*Method*   |*Metrics*|Pma1 (active)|Pma1 (inhibited)|CYP (open)|CYP (closed)|YbbAP (bound)|YbbAP (unbound)|\n|---------  |---------|:-----------:|:--------------:|:--------:|:----------:|:-----------:|:-----------:|\n|           |Res. (Å) |3.25         |3.52            |6.50       |4.40         |3.66         |4.05         |\n|CryoBoltz  |RMSD     |**1.869**    |**2.010**       |**4.326** |**2.387**   |**1.312**    |**3.087**    |\n|           |TM       |**0.979**    |**0.978**       |**0.956** |**0.988**   |**0.996**    |**0.965**    |\n|Boltz-1    |RMSD     |2.627        |7.559           |7.934     |7.888       |3.547        |8.819        |\n|           |TM       |0.953        |0.740           |0.823     |0.780       |0.930        |0.761        |\n|AlphaFold3 |RMSD     |7.177        |8.493           |6.447     |3.147       |3.613        |3.882        |\n|           |TM       |0.744        |0.711           |0.889     |0.960       |0.927        |0.919        |\n|ModelAngelo|Comp.    |91.47        |72.81           |0.00      |18.91       |81.69        |55.41        |\n|           |TM       |0.889        |0.721           |0.000     |0.102       |0.801        |0.548        |\n|ADP-3D     |RMSD     |9.906        |12.119          |-         |-           |34.409       |52.125      |\n|           |TM       |0.934        |0.888           |-         |-           |0.286        |0.091       |\n\n**ADP-3D Baseline.**\nWe thank the reviewer for the suggestion to compare ADP-3D, which we evaluate on P-glycoprotein (Figure 5), Pma1, and YbbAP. CYP102A1 produced errors due to its large size. For each cryo-EM map, we provide ADP-3D with the ModelAngelo prediction as the required initial structure, and choose the best of 5 samples by map-model fit. For Pma1 and YbbAP metrics, please see the table in the **Additional Validation on Experimental Data** section above. For P-glycoprotein, we reproduce Table 2 of the manuscript below for the reviewer’s convenience. We find that ADP-3D improves TM-score over ModelAngelo for Pma1 and P-glycoprotein maps, due to some additional modeling of the incomplete initial structure. However, we also observe very poor RMSD scores, especially for YbbAP and P-glycoprotein, where completely incorrect predictions are made for large portions of the structure.\n\n|*Method*   |*Metrics*|Glycoprotein (apo)|Glycoprotein (inward)|Glycoprotein (occluded)|Glycoprotein (collapsed)|\n|---------  |---------|:-----------:|:--------------:|:--------:|:----------:|\n|           |Res. (Å) |4.3    |4.4   |4.1|4.4|\n|CryoBoltz  |RMSD     |**1.381**|**1.329**|**1.745**|**1.340**|\n|           |TM       |**0.989**|**0.989**|**0.979**|**0.986**|\n|Boltz-1    |RMSD     |6.994|5.630|2.929|3.425|\n|           |TM       |0.767|0.828|0.942|0.917|\n|AlphaFold3 |RMSD     |3.827|2.692|3.440|4.568|\n|           |TM       |0.904|0.947|0.921|0.864|\n|ModelAngelo|Comp.    |40.33    |18.25  |2.26|2.53|\n|           |TM       |0.361   |0.134|0.010|0.010|\n|ADP-3D     |RMSD     |27.367|41.998|58.630|62.491|\n|           |TM       |0.583|0.333|0.092|0.073|\n\n\n**Accuracy vs Resolution.**\nWe appreciate the reviewer’s suggestion to analyze all-atom RMSD as a function of map resolution. In the table below, we report the mean and standard deviation of 10 samples guided to the inward state of the STP10 system (Figure 3), across varying resolutions of the synthetic map. We find that performance is best at resolutions better than 6 Å. We additionally observe that RMSD slightly increases going from a 2 Å to a 5 Å map, likely due to smoother gradients in the local guidance phase, suggesting that our method may be improved by adopting a frequency marching schedule. \n\n||||||||||\n|----------------|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n|**Res (Å)**     |2.0  |3.0  |4.0  |5.0  |6.0  |8.0  |10.0 |15.0 |\n|**RMSD Mean**   |1.181|1.116|1.064|1.061|1.095|1.276|1.411|1.680|\n|**RMSD Std.**   |0.034|0.048|0.108|0.104|0.102|0.058|0.058|0.058|\n\n**Extending to Boltz-2.**\nWe agree with the reviewer that extending our approach to Boltz-2 represents an important area of future work. Since Boltz-2 introduces significant code changes and was released after the NeurIPS deadline, we have not yet integrated our guidance method. The improved predictive capabilities of Boltz-2 may indeed broaden the applicability of our guidance approach."}, {"review_id": "ZwGGzyhkEo", "reviewer": "Reviewer_Cxm9", "summary": "The paper propose a method for guiding generative models for protein stuctures (from sequence data) based on observed experimental densities. The guiding is done using two approaches: local (density based) and global (geometry/structure based, derived form the densities). The method builds on the idea of posterior sampling, where the AF3 type models act as priors and the observed densities define the likelihoods. The paper shows that this approach leads to more accurate structures than the unconditional/unguided sampling methodds (AF3 and Boltz-1)", "questions": "The validation was done on one structure for which there was real experimental data. To what extend can we believe the method will generalize to other structures? \n\nTo what extend are the reduction in RMSD important? The structures obtained by guidance are naturally going to be closer to \"ground truth\" resolved structures, which are probably resolved using cryoEM data? But the unguided structures may very well be accurate too, it's just that they have not been observed in such states in cryoEM. Now, I may be talking nonsense here as I don't know the field too well, but my point is, I expect a bias of some sort but can't quite put my finger on it. Perhaps the authors could either alleviate my concern, or transparently lay down the limitations of this validation.", "limitations": "Overall limitations and impact have been adequately addressed. The scientific impact could be more deeply discussed though (cf the questions field)", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "# Strengths\n\n1.\tThe paper is very well written\n2.\tThe formulation of the problem (posterior inference) is elegant and the derivation is sound.\n3.\tThe results are good.\n\n# Weaknesses\n\n1.\tThe validation seems a bit biased by design since Table 1 is made using synthetic maps. This means that the maps are rendered from a know structure, so we know the to-be-recovered structure is indeed contained in this rendered density maps. Wouldn’t the guidance necessarily lead to the optimal structures? What kind of noise is used in the rendering and how realistic is it? Should this table then be considered more as a sanity check? I do appreciate that this table at confirms the benefit of including observational data in the generative process.\n2.\tThe validation seems limited considering 2/3 are based on synthetic density maps. The 3rd problem is on experimental density maps. Although the it confirms the applicability on experimental data, the validation may be too limited to draw general conclusions. \n\n# Minor\n1.\tThe paper is applied and no new general principles are presented that generalize outside of the domain of structure prediction. The new guiding term (global) seems a bit ad-hoc but effective. The general principles used are known in the broader context of inverse modeling. However, within the specific application domain the paper seems relevant.\n2.\tThe paper explains the contribution as “multi-scale”. However I do not see why one is called global and the other local. The local is based on pixel-wise errors and in that sense can be considered local. However, all pixels are used, and the signal is in that sense global. The named global term is based on based distances between point clouds.  Wouldn’t a more informative naming be density vs geometry guidance or something? The main difference is imo not local vs global, but the fact that the “global” term directly gives a supervisory signal on the actual geometry. E.g. a small shift of the structure could lead to a big change in density error, whereas a small shift remains a small distance in the geometric loss. Since the problem is geometric, the “global” terms seems to be the most suitable guiding term, and I don’t understand why we would need the local term at all. In fact, the experiments show that global term is the superior one.", "was_revised": true, "final_justification": "Based on the response I moved my score upwards from borderline reject to borderline accept. I think the additional clarifications are useful and validated the significance of the paper. Since this is not my primary field of interest (structural biology) I'm not particularly impressed by the approach taken or its novelty, however, the paper is sound and seems a valuable contribution to DL-based structure prediction. And can be impactful as such.", "rebuttal": "We thank the reviewer for their thoughtful comments on our work. We are glad the reviewer appreciates the clarity of the writing and the strength of the results. Our primary motivation is to fit atomic structures into cryo-EM maps of dynamic complexes, which often requires time-consuming manual effort especially on lower resolution maps where current automated methods tend to fail. By leveraging the powerful generative prior of AlphaFold3, our method provides a new framework for cryo-EM model building that aims to overcome these limitations. We present several additional experiments on real data to further showcase the general applicability of our approach.\n\n**Additional Validation on Experimental Data.**\nWe thank the reviewer for the suggestion to further evaluate our approach on experimental data. We assess our method on 3 additional protein systems associated with real cryo-EM density maps, and whose deposited models are not part of the Boltz-1 training set. For each experimental map, we obtain 25 samples from each method, choose the best sample as assessed by map-model fit (real-space correlation coefficient), and report its all-atom RMSD and TM-score with respect to the deposited model. For ModelAngelo, we obtain its single prediction and report model completeness and TM-score. Metrics are presented in the table below, and we summarize the results here:\n- *Pma1*: We use two experimental maps of this ATPase [EMD-64135, 64136], corresponding to its active and inhibited states [PDB: 9UGB, 9UGC]. Unguided Boltz only samples the active state, whereas guidance also samples the inhibited state with an RMSD of 2.01 Å. AlphaFold3 predictions are not accurate with respect to either state. \n- *CYP102A1*: We use two experimental maps of this oxygenase [EMD-27534, 27536], of resolutions 4.4 Å and 6.5 Å, corresponding to its open and closed states [PDB: 8DME, 8DMG]. Guidance improves the RMSD of the closed state from 7.89 Å to 2.39 Å over unguided Boltz-1, whereas for the lower resolution open state map, a more modest improvement from 7.93 Å to 4.33 Å is observed. ModelAngelo only models 19% of the 4.4 Å map and none of the 6.5 Å map.\n- *YbbAP*: We use two experimental maps of this transporter [EMD-51292, 51291], corresponding to states in which ATP is bound or unbound [PDB: 9GE7, 9GE6]. Unguided Boltz only samples the bound state, which guidance additionally improves to an RMSD of 1.31 Å. The unbound state is also obtained through guidance. Since the unbound state map is of medium resolution at 4.05 Å, ModelAngelo only models 55% of the structure.\n\nOur results on these systems, along with the P-glycoprotein example in the manuscript (Figure 5), demonstrate our method’s ability to recover diverse conformations from real experimental maps, especially at resolutions where other methods fail. We will include these results, including visualizations, in our revised manuscript.\n\n|*Method*   |*Metrics*|Pma1 (active)|Pma1 (inhibited)|CYP (open)|CYP (closed)|YbbAP (bound)|YbbAP (unbound)|\n|---------  |---------|:-----------:|:--------------:|:--------:|:----------:|:-----------:|:-----------:|\n|           |Res. (Å) |3.25         |3.52            |6.50       |4.40         |3.66         |4.05         |\n|CryoBoltz  |RMSD     |**1.869**    |**2.010**       |**4.326** |**2.387**   |**1.312**    |**3.087**    |\n|           |TM       |**0.979**    |**0.978**       |**0.956** |**0.988**   |**0.996**    |**0.965**    |\n|Boltz-1    |RMSD     |2.627        |7.559           |7.934     |7.888       |3.547        |8.819        |\n|           |TM       |0.953        |0.740           |0.823     |0.780       |0.930        |0.761        |\n|AlphaFold3 |RMSD     |7.177        |8.493           |6.447     |3.147       |3.613        |3.882        |\n|           |TM       |0.744        |0.711           |0.889     |0.960       |0.927        |0.919        |\n|ModelAngelo|Comp.    |91.47        |72.81           |0.00      |18.91       |81.69        |55.41        |\n|           |TM       |0.889        |0.721           |0.000     |0.102       |0.801        |0.548        |\n\n**Validation by RMSD.**\nWe agree with the reviewer that samples from the unguided model may also correspond to valid states of a protein. However, our goal is to specifically obtain atomic structures that are consistent with cryo-EM data. Our motivation in baseline comparisons against unguided Boltz-1 and AlphaFold3 is not to suggest that these structures are necessarily incorrect, just that they do not correspond to the target cryo-EM state in the absence of guidance. Guidance provides a mechanism through which the powerful predictive capabilities of these pretrained models can be directed towards the states a cryo-EM practitioner desires from their data.\n\n**Validation on Synthetic Data.**\nWhile a noiseless synthetic map does correspond perfectly to its target structure, it is not certain a priori that Boltz-1 will be able to sample this structure. Indeed, Boltz-1 never samples the inward conformation of the STP10 system (Section 4.2). As the reviewer suggests, our synthetic experiments can thus be seen as validation that our proposed guidance strategy is effective at driving the sampling process toward a structure consistent with a map.\n\n**Multiscale Guidance.**\nWe apologize for the lack of clarity surrounding nomenclature of the multiscale guidance strategy. The terms “global” and “local” are meant to describe the scale of the conformational changes driven by these two guidance phases. The global phase is most effective at guiding coarser domains of the structure, since the Wasserstein distance metric permits a strong gradient even between a sample atom and map point that are far apart.  However, since the point cloud is only a rough approximation of the map, the density errors applied during the local phase are more adept at guiding loops and secondary structure elements into the right locations. While the global guidance phase is indeed responsible for the majority of reduction in RMSD, we find that the local guidance phase remains important for accurate model fitting. Conducting an ablation on the inhibited state of Pma1, global guidance alone reduces RMSD from 7.6 Å to 3.0 Å, while the addition of local guidance further improves accuracy to 2.0 Å. We will include ablations on real data in our revised manuscript.\n\n**Novelty.**\nWe agree with the reviewer that the novelty of the method primarily lies within this application domain. That said, we believe our multiscale guidance strategy may have broader relevance and hope that it will inspire other diffusion guidance approaches in 3D small molecule generation or computer vision."}, {"review_id": "smkEQczXaZ", "reviewer": "Reviewer_XC5a", "summary": "This paper presents CryoBoltz, a method that bridges protein structure prediction models like AlphaFold3 with cryo-EM data via multiscale guidance, driving sampling towards conformational states consistent with experimental observations. By integrating global and local structural constraints from density maps, CryoBoltz overcomes the single-structure bias of existing models, enabling accurate atomic modeling of heterogeneous cryo-EM maps for dynamic systems like transporters and antibodies.", "questions": "- What if AlphaFold3 fails to accurately predict the protein structure? I suppose that if the AF-predicted structures can fit the density up to some rotation and translation of some part of the structure, the error can be corrected. But if there are some larger errors, can the density correct the AF-3 structures?\n- Is it possible to incorporate the cryo-EM data into the training process, like CryoSTAR? Maybe adding a learable pair representation at the template module to finetune the Boltz-1 is enough.\n- I think incorporating some validation metrics (to avoid the prior from AF3)  will potentially boost the effectiveness of this study.", "limitations": "NA", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n- Utilizes AlphaFold3 as a prior to enhance the accuracy of heterogeneous analysis, effectively integrating rich sequence and biophysical priors with cryo-EM data to drive predictions toward experimental consistency.  \n- Implements a smart design of global and local guidance mechanisms: global guidance targets large-scale conformational adjustments using low-resolution point cloud representations, while local guidance refines high-resolution details based on physics-based forward models. \n\n\n\nWeaknesses\n\n- There is a vulnerability in relying on AlphaFold3 as a prior. If AlphaFold3 fails to accurately predict the protein structure, the entire heterogeniety analysis accuracy relying on it may be severely compromised, potentially leading to incorrect interpretations of the data.\n- The potential biases introduced by AlphaFold3 pose an issue. For instance, if it mispredicts a loop region as a helix while getting the global structure correct, it's unclear whether the cryo - EM data can effectively correct such local mispredictions. There is also a lack of clarity on how to detect such biases and whether there are failure cases presented to alert users and prevent them from being misled by the model.", "was_revised": true, "final_justification": "The authors answered my questions and I have no further concerns. I think this paper bridge the gap between cryoem and protein structure prediciton with a smart approach.", "rebuttal": "We thank the reviewer for their thoughtful comments on our work. We are glad the reviewer appreciates the use of AlphaFold3 as a strong biophysical prior for atomic modeling into cryo-EM maps, as well as the novelty of the proposed multiscale guidance strategy. While we show through our experiments that our approach broadens the scope of cryo-EM model building, we also hope that our flexible inference-time method will benefit from the parallel advances in biomolecular structure prediction. We elaborate on these aspects below.\n\n**Robustness of the Prior.**\nThe reviewer is correct that our method inherits both the strengths and limitations of the underlying structure prediction model. We aim to take advantage of the strong biophysical priors learned by AlphaFold3/Boltz-1, which is beneficial especially when fitting atomic models to lower resolution maps (Figure 5). Conversely, for complexes that are badly mispredicted by the base model, including full antibody complexes and DSL1 which we note in the Discussion section, guidance is unable to overcome this bias. However, a key strength of our inference-time approach is that it can be applied to any structure prediction model with a diffusion-based sampler. We thus envision that the continuous developments in structure prediction will further boost the ability of our guidance strategy to model highly dynamic complexes.\n\n**Validation Metrics.**\nWe thank the reviewer for the suggestion to expand the validation metrics. Map-model fit, as assessed by real-space correlation coefficient as in Supplementary Table B1, is one approach to model validation and selection. Additional measures of model quality such as MolProbity score or Q score would indeed serve as important validation, and we will include these in our revised manuscript. We will additionally conduct analyses of Boltz-1 confidence scores, which may serve as another mechanism for a user to detect failure cases.\n\n**Training with Cryo-EM Maps.**\nWhile the flexibility of inference-time guidance is a strength of our approach, fine-tuning Boltz with map conditioning, potentially incorporating our guidance algorithm, represents an interesting avenue for future work. We thank the reviewer for this suggestion."}, {"review_id": "PyvjEYZiFy", "reviewer": "Reviewer_jQC6", "summary": "This paper proposes a guided diffusion procedure for sampling from AlphaFold3 while conditioning on density maps obtained from Cryo-EM experiments. The authors propose a two-stage, global-to-local sampling scheme. In the global stage, the diffusion model is guided towards the course structure of the protein conditioning on sequence alone, and in the local stage, Cryo-EM information is incorporated through the likelihood of the forward model. Since the required guidance term is intractable, a previously proposed approximation to it is used.\n\nThe authors evaluate their method on several protein structures, including some simulated and some experimental Cryo-EM maps.", "questions": "-\tHave the authors considered the possibility of test set contamination? I.e., to what extent are the experimental results attributable to model generalization vs. memorization of structures in the train set? One standard way to measure this would be to measure the sequence (or structure) similarity of each of the test proteins to the nearest sequence/structures in the AF3 train set.\n-\tCould the authors explain why ModelAngelo performs so poorly in Figure 5? Is it simply because it cannot handle proteins with multiple states well?", "limitations": "-\tThe number of proteins demonstrated is very small – only three. It is hard to avoid the possibility of cherry-picking or a lucky selection. In that sense I think the experimental section is lacking and not statistically significant.\n-\tAs mentioned above, I do not see any effort to measure the possibility of test-set contamination.\n-\tTwo of the three systems involve synthetic rather than experimental Cryo-EM maps. I would like to see more actual Cryo-EM maps used. Actual maps are noisy and potentially pose a much more difficult problem.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Quality\n\nThe quality of the paper is good. It is well written and figures are well-presented.\n\nClarity\n\nThe clarity of the exposition is above average, and I enjoyed reading the paper.\n\nSignificance\n\nI would judge the significance of this work as moderate-to-high. The field being tackled is extremely active, and many researchers in structural biology are targeting this problem. As time goes on, Cryo-EM microscopy will become more and more common. A lack of multi-conformational accuracy is one of the few remaining gaps in AF3’s performance, and this model appears to do a decent job of addressing that. \n\nOriginality\n\nOriginality seems moderate. I do believe that this idea was “in the air” somewhat, in that I expect other groups to publish similar work. Guidance of diffusion models for proteins is not new, and it’s only a matter of time before it was successfully applied to Cryo-EM. However, the exact implementation, going from global to local, seems like an original advance, and appears to be very important for getting the method to work well in practice.", "was_revised": true, "final_justification": "As I still have concerns about the degree of evidence the authors have presented that their method will generalize, I hold my score.", "rebuttal": "We thank the reviewer for their thoughtful comments on our work. We are glad the reviewer appreciates the impact of this work in multi-conformation structure analysis, the strength of the multi-scale guidance strategy, and the clarity of the writing. As the reviewer highlights, atomic model building into cryo-EM maps is an active research area which stands to benefit from the recent advances in biomolecular structure prediction, especially to overcome the limitations of manual model building and low resolution maps. Through several additional experiments on real data, as described below, we hope to showcase the applicability of our approach for broadening the scope of cryo-EM map interpretation.\n\n**Additional Validation on Experimental Data.**\nWe thank the reviewer for the suggestion to further evaluate our approach on experimental data. We assess our method on 3 additional protein systems associated with real cryo-EM density maps, and whose deposited models are not part of the Boltz-1 training set. For each experimental map, we obtain 25 samples from each method, choose the best sample as assessed by map-model fit (real-space correlation coefficient), and report its all-atom RMSD and TM-score with respect to the deposited model. For ModelAngelo, we obtain its single prediction and report model completeness and TM-score. Metrics are presented in the table below, and we summarize the results here:\n- *Pma1*: We use two experimental maps of this ATPase [EMD-64135, 64136], corresponding to its active and inhibited states [PDB: 9UGB, 9UGC]. Unguided Boltz only samples the active state, whereas guidance also samples the inhibited state with an RMSD of 2.01 Å. AlphaFold3 predictions are not accurate with respect to either state. \n- *CYP102A1*: We use two experimental maps of this oxygenase [EMD-27534, 27536], of resolutions 4.4 Å and 6.5 Å, corresponding to its open and closed states [PDB: 8DME, 8DMG]. Guidance improves the RMSD of the closed state from 7.89 Å to 2.39 Å over unguided Boltz-1, whereas for the lower resolution open state map, a more modest improvement from 7.93 Å to 4.33 Å is observed. ModelAngelo only models 19% of the 4.4 Å map and none of the 6.5 Å map.\n- *YbbAP*: We use two experimental maps of this transporter [EMD-51292, 51291], corresponding to states in which ATP is bound or unbound [PDB: 9GE7, 9GE6]. Unguided Boltz only samples the bound state, which guidance additionally improves to an RMSD of 1.31 Å. The unbound state is also obtained through guidance. Since the unbound state map is of medium resolution at 4.05 Å, ModelAngelo only models 55% of the structure.\n\nOur results on these systems, along with the P-glycoprotein example in the manuscript (Figure 5), demonstrate our method’s ability to recover diverse conformations from real experimental maps. We will include these new results, including visualizations, in our revised manuscript.\n\n|*Method*   |*Metrics*|Pma1 (active)|Pma1 (inhibited)|CYP (open)|CYP (closed)|YbbAP (bound)|YbbAP (unbound)|\n|---------  |---------|:-----------:|:--------------:|:--------:|:----------:|:-----------:|:-----------:|\n|           |Res. (Å) |3.25         |3.52            |6.50       |4.40         |3.66         |4.05         |\n|CryoBoltz  |RMSD     |**1.869**    |**2.010**       |**4.326** |**2.387**   |**1.312**    |**3.087**    |\n|           |TM       |**0.979**    |**0.978**       |**0.956** |**0.988**   |**0.996**    |**0.965**    |\n|Boltz-1    |RMSD     |2.627        |7.559           |7.934     |7.888       |3.547        |8.819        |\n|           |TM       |0.953        |0.740           |0.823     |0.780       |0.930        |0.761        |\n|AlphaFold3 |RMSD     |7.177        |8.493           |6.447     |3.147       |3.613        |3.882        |\n|           |TM       |0.744        |0.711           |0.889     |0.960       |0.927        |0.919        |\n|ModelAngelo|Comp.    |91.47        |72.81           |0.00      |18.91       |81.69        |55.41        |\n|           |TM       |0.889        |0.721           |0.000     |0.102       |0.801        |0.548        |\n\n**ModelAngelo Performance.**\nModelAngelo is trained solely on cryo-EM maps of resolution 4 Å or better. This accounts for its poor performance on lower resolution maps, especially those of P-glycoprotein and CYP102A1. In contrast, our method’s use of a powerful generative prior aids in fitting atomic structure into lower resolution density.\n\n**Memorization vs Generalization.**\nWe thank the reviewer for suggesting checks of test set contamination. We compute the highest structure match score between the tested deposited models and PDB entries contained in the Boltz-1 training set. The structures of the CYP102A1 and YbbAP systems have no matching entries. One state of Pma1 has a match score of 20%, while the other has no matching entries. Finally, the match scores of 3 of the 4 P-Glycoprotein states (Figure 5) are between 40% and 48%, while the last state has no matching entries. Therefore, most structures have little to no overlap with the training dataset, validating that the generalization capabilities of structure prediction models extend to the case of inference-time guidance. We further emphasize that even in cases of structural overlap, as in P-glycoprotein, unguided Boltz-1 fails to sample multiple states, making guidance a useful intervention."}]

Author rebuttal:

Meta-review: This paper presents an approach to combing the predictive power of structure prediction models like AlphaFold3 with experimental data from cryoEM in the form of a 3D density.  The approach works by using the density map to guide the structure prediction given the sequence.  The method is demonstrated on three structures, two based on synthetic data and one based on experimental data.  In all cases the result is compared against a ground truth structure and shows significant improvement in predictive accuracy vs baseline methods.

During the rebuttal and discussion phase the authors reported several new experiments on real data, showing further gains and allaying some reviewer concerns.  The final consensus among all reviewers was positive and the AC agrees.  However, the AC strongly suggests the following changes:
 - describe and incorporate the newly reported experimental results
 - incorporate all other feedback from the reviews and discussion
 - modify the title to not explicitly reference AlphaFold3.  The proposed method could, in principle, be used with AlphaFold3 but is never actually demonstrated on it.  An acceptable title could be: "Multiscale guidance of protein structure prediction with heterogeneous cryo-EM data" but I leave the specifics at the authors discretion.
Decision: Accept (poster)