Unlocking hidden biomolecular conformational landscapes in diffusion models at inference time
Authors: Daniel D. Richman
Jessica Karaguesian
Carl-Mikael Suomivuori
Ron O. Dror
Venue: NeurIPS 2025 spotlight ()
Keywords: protein conformations
biomolecular systems
enhanced sampling
diffusion
importance sampling
protein flexibility
Primary area: machine_learning_for_sciences
TL;DR: ConforMix, a new enhanced sampling method applied to biomolecular diffusion models, improves conformational sampling

Abstract: The function of biomolecules such as proteins depends on their ability to interconvert between a wide range of structures or conformations. Researchers have endeavored for decades to develop computational methods to predict the distribution of conformations, which is far harder to determine experimentally than a static folded structure. We present ConforMix, an inference-time algorithm that enhances sampling of conformational distributions using a combination of classifier guidance, filtering, and free energy estimation. Our approach upgrades diffusion models---whether trained for static structure prediction or conformational generation---to enable more efficient discovery of conformational variability without requiring prior knowledge of major degrees of freedom. ConforMix is orthogonal to improvements in model pretraining and would benefit even a hypothetical model that perfectly reproduced the Boltzmann distribution. Remarkably, when applied to a diffusion model trained for static structure prediction, ConforMix captures structural changes including domain motion, cryptic pocket flexibility, and transporter cycling, while avoiding unphysical states. Case studies of biologically critical proteins demonstrate the scalability, accuracy, and utility of this method.

Unlocking hidden biomolecular conformational landscapes in diffusion models at inference time
Daniel D. Richman" Stanford University
Jessica Karaguesian" Stanford University jkara@stanford edu
ddri cawiichammaaorreeeo wwd.. edu
Carl-Mikael Suomivuori'
Ron O. Dror Stanford University rondrorêcs. stanford. edu
Stanford University
cotummivuorii www.rrrrrrrllleeeeee. edu
Abstract
The function of biomolecules such as proteins depends on their ability to inter- convert between wide range of structures "conformations." Researchers have endeavored for decades to develop computational methods to predict the distri- bution of conformations, which is far harder to determine experimentally than a static folded structure. We present ConforMix, an inference-time algorithm that enhances sampling of conformational distributions using a combination of classifier guidance, filtering, and free energy estimation. Our approach upgrades diffusion models- whether trained for static structure prediction conforma- tional generation-to enable more efficient discovery of conformational variability without requiring prior knowledge of major degrees of freedom. ConforMix is orthogonal to improvements in model pretraining and would benefit even a hypo- thetical model that perfectly reproduced the Boltzmann distribution. Remarkably, when applied to diffusion model trained for static structure prediction, ConforMix captures structural changes including domain motion, cryptic pocket flexibility, and transporter cycling, while avoiding unphysical states. Case studies of biologically critical proteins demonstrate the scalability, accuracy, and utility of this method.
models-whether
Introduction
Biology depends on molecular flexibility. Proteins, RNA, DNA, and other components biological systems adopt dynamic 3D conformations, which are key function 8). Understanding and mod- eling these dynamics informs both basic biology research and applications to medicine, agriculture, and other areas, and is therefore major aim of both experimental and computational scientists. The statistical distribution of the atomic configurations of a molecular system in equilibrium at given temperature determined by their potential energies. Specifically. state with lower potential energy is exponentially more probable than a higher potential energy state, as determined by the Boltzmann distribution (31). To sample this distribution, scientists have invested decades of effort in creating methods such as Monte Carlo samplers and molecular dynamics simulations (MD), but these methods are typically extremely slow and suffer from accuracy problems (25 31 32).
More recently, machine learning models have revolutionized biomolecular structure prediction, and efforts are underway extend these advances to train models that do not merely predict static structures but generate diverse conformations from the true Boltzmann distribution
17
Equall contribution.
Present affiliation: Yale School of Medicine.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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35]. As the field evolves, new questions arise about how best to take advantage of these models, access the information they contain, and target opportunities for further improvement. We ask the following question: Given pretrained generative structure model, what strategy should be deployed at inference time to efficiently and accurately sample its conformational landscupe?
In this work, we present an enhanced sampling algorithm, ConforMix, that can be applied to diffusion-based biomolecular structure prediction models such as the AlphaFold 3 family. ConforMix reveals hidden conformations and estimates free energies more efficiently than the default sampling from diffusion models. Our approach is based on the hypothesis that the probability distribution of generative models contains more information than is efficiently sampled. Importantly, even a generative model that perfectly sampled the true Boltzmann distribution major long-term goal in machine learning for biology-would for many uses, still require enhanced sampling algorithms to fruitfully explore For instance, correct sampling of the hightbbinding proteins barnase and barstar at standard state would generate an unbound structure with probability approximately 10-14 (33). Directly drawing samples from the distribution would be an extremely inefficient way to estimate this probability, determine transition states along the binding pathway, or understand the effects of environmental factors in modulating this affinity 30 39
Contributions
We introduce, implement, and benchmark ConforMix. Our contributions include:
A novel algorithm combining twisted sequential Monte Carlo, which performs asymptoti- cally exact sampling of conditional distributions, with an automated procedure for exploring the diffusion landscape, using conditional sampling subroutine. Optionally, statisti- cally optimal sample reweighting algorithm, applied to diffusion models for the first time, can be used to reconstruct the unconditional distribution from the conditional samples.
Dramatically improved inference-time sampling in structure prediction models. We imple- ment ConforMix in Boltz-1, an AlphaFold 3-like diffusion model that typically predicts only one distinct conformation for given input. ConforMix-Bolle generates realistic and diverse conformations for a variety of proteins, without prior knowledge of important degrees of freedom. In prior work, conditional sampling on biomolecular diffusion models has required additional input information, such as experimentally measured pairwise distances.
Efficient free energy estimation. We also implement ConforMix in BioEmu. diffusion- based model for conformational sampling, and compare free energy estimates from BioEmu with and without ConforMix. Using ConforMix boosts the speed of free energy estimation.
2 Related Work
Computational methods have been used to sample molecular conformations for decades. The well- known Metropolis-Hastimm algorithm (23 for Monte Carlo sampling was first used to simulate the statistical mechanics of particles in box. Elastic network models represent a protein as low-resolution
beads connected by springs and recover the principal motions that would occur in this representation,
which often are representative of motions of the actual system [20). More sophisticated methods, such as coarse-grand -ranined or all-atom molecular dynamics simulation, model the physical interactions with progressively more detail and have been used to generate detailed probabilistic distributions for a number of proteins
More recently, machine learning models such as AlphaFold 3 (1] have revolutionized the problem of static protein structure prediction. AlphaFold 3 is the most prominent example of class of diffusion-based structure prediction methods that excel at generating the single most likely protein structure for a given amino acid sequence. While AlphaFold generates five samples per run, for well-ordered proteins these samples are often almost identical and are better understood as very similar predictions of the same static structure rather than a representation of conformational variety.
Using such models to model the distribution of conformations, however, is task still in its infancy. The most well-studied approaches involve subsampling or otherwise perturbing the multiple sequence alignment (MSA) input [13 15 27 35) or templates input 2 4 9 to AlphaFold and related models. These inputs specify, respectively, y, sequence co-evolutionary information and related 3D structures. Emphasizing different sequence or structural features in the input has empirically produced significant conformational diversity. Subsampling methods, however, suffer from fundamental limitations. First, subsampling necessarily involves reducing the information available to the model, which often

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produces poor-quality outputs. Second, molecular conformations are continuous, while subsampling of sequences or templates discrete operation. Third, the structure distribution accessed by subsampling methods is not well defined, and despite years of study there is no clear means of reconstructing actual probabilistie ensembles.
Beyond soput-perturbation methods, other efforts have involved building new models to predict con- formations II [7 Strategies include leveraging molecular dynamics simulations or experimental data, either during training or at runtime [3 T6 21 34]. While these approaches have shown promise, they do not yet accurately reproduce the thermodynamic ensembles of arbitrary proteins.
Based on the successes of MSA subsampling and template perturbation methods, we hypothesized that diffusion models have learned richer energy landscapes than generally recovered and that these landscapes can be accessed via more sophisticated sampling approach. As improvements in model training lead more accurate learned landscapes, it will become increasingly valuable only access the most dominant configurations from the model but also extract rich information about transition mechanisms and probabilities. We aim open the door this type insight.
3 Methods
Given a biomolecular structure diffusion model p(z(s), where is the input biological system provided to the model (for instance, the amino acid sequence of protein and its multiple sequence alignment) and x E R2x3 specifies the predicted atomic coordinates, our objective is to efficiently explore and characterize the distribution p.
A) ConforMix uncovers alternate conformations
ConforMix samples
latent space of structure diffusion model
default samples
Overview ConforMixRMSD workflow
default inputs
structure diffusion model predictions
identify rigid elements
sequence
default sampling
semple deniity
MSA
deviation from defouit
apply series of bias potentials
ConforMix predictions
pobaabiity
P(A) P(C
conditional
reweight
P(B)
sampling
samples
deviation from defsult
Figure I: (A) ConforMix adds conditioning to diffusion-based structure prediction models, enabling deeper and more efficient exploration. (B) ConforMix uses series of bias potentials to target new states. CoDD an instantiation that biases sampling away from default predictions to sample conformational transitions without requiring any intervention. Sample reweighting can be applied to recover the ground state distribution.
3.1 ConforMix
Diffusion models learn probability distributions, and the standard sampling procedures, which we refer to as default sampling, are designed to draw i.i.d. samples from this distribution. To explore further and more efficiently than possible with default sampling, we employ conditional sampling, which is widely used with diffusion models to guide sampling toward particular regions of the learned

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probability distribution [5] 10]. As we will see, conditional sampling offers clear benefits even without specialized prior knowledge about the protein of interest. While time-dependent classifier guidance and classifier- free guidance are commonly used in other diffusion contexts, these methods are not well suited to our needs because they require either additional training or special architectural choices, which are impractical for our needs.
Instead, to devise a purely inference-time method, we turn Twisted Diffusion Sampling [37] form of sequential Monte Carlo (SMC), to guide conditional generation. SMC has advantages over more typical guidance methods, including (a) requiring only a -iee-indeenndent guidance function, which enables us to easily describe conditions as function of the fully denoised state of the system, and (b) providing an asymptotic guarantee of sampling the true target conditional distribution in the limit of many particles. Twisted diffusion sampling works in conjunction with an underlying diffusion model that learns to sample a target data distribution ( 8). Diffusion models define a forward noising process, operating over sequence of T steps, that constructs an extended distribution (<Tr:l = (1)))(=T,) ... {<11 Ir (r))g(r))))) The diffusion model po t|s) can then be trained to approximate the score function V log qr (z]]s,, which is used to simulate the noising process in reverse. We emphasize that ConforMix itself does not involve additional model training.
Instead, twisted diffusion operates as a particle filter. The sampling algorithm is instantiated with series of guidance functions y (z) = exp( exp(-U)(z))), where U, is a potential. For example, many motions can be described in terms of the distance between two groups of atoms A and B, so we might select a potential
(,(1) = (1)ã ااll X,)²
where a is strength parameter, AA μB are the centroids of the atom groups, and by E [mmnn Amaxl is a target distance. The corresponding score function
V (o) = a (Ilma - Aall - X,) V= - Hell
(2)
easy to compute. During inference, at each denoising timestep t, we construct an inexpensive estimate of the fully denoised state f.. which we plug into yj to approximate the potential of the current state. We then compute V.. Vy = (Ja, 2o)"'va Vaa3y Ba and use this signal to guide Ia towards p(zly), s). By simultaneously denoising several such particles 2, and periodically resampling them to maintain correct sampling, we can obtain approximate samples from the desired conditional distribution. For more details, we refer the reader to Algorithm SI in the Supplement and to Algorithm in (37), which provides an asymptotic guarantee that the sampling approaches the true conditional distribution as the number of particles becomes large.
In our general framework, ConforMix, twisted diffusion sampling can be used to sample from nearly arbitrary conditional distributions. To select suitable conditioning, we are motivated by two biological use cases: (I) automated exploration of the conformational landscape, where a user provides only an input system (i.e. amino acid sequence, and optionally MSA and/or templates), and (2) user-defined exploration of conformational states, where a user wishes to examine a specific hypothesized motion be customized to scan targeted degrees of freedom.
or state. In the rest of this paper, we focus primarily on the first case, but we note that ConforMix can
3.2 ConDorMixRMSD
Our approach to the automated exploration problem, which we call ConforMiXRMSD, is described in Algorithm [
Here we assume that a user wishes to perform undirected exploration of the protein conformational distribution learned by the underlying model. The idea of ConforMixRMSD is to simply generate the most probable samples that are sufficiently different from the default prediction Fy. AlphaFold 3-family generative models often have probability distributions p(z|s) that are highly concentrated around one conformation. After generating an initial conformation za with default sampling, we construct a series of guidance potentials that steer the probability distribution away from Ia using root mean square deviation (RMSD) metric: U, = 2 (RM f= where RMSD = min Natoms Ed || - (Rxges + t)ll2, and E SO(3) and E R respectively rotate and translate x to best align to / RMSD is differentiable and computable in closed form via the Kabsch algorithm. The fastest motions of a protein, which are easier to predict are often fluctuations of disordered loop regions. To avoid exclusively sampling these motions, we apply

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rigid-element mask: we only compute RMSD on amino acids that are part of secondary structure elements, helices or sheets. All amino acids still remain free to move during sampling.
Because the realistic range of motion varies per protein and is not known a priori, we seek to discover the flexibility of each protein by generating structure predictions spanning the range 0 to 20 Á RMSD to za- After samples are generated, we filter those that are physically implausible. Specifically, reject samples where any 10-residue sliding window has an average pLDDT value of more than 20% below that of the default prediction, as well structures with clashes. The sliding window approach detects local non-physical perturbations from sampling beyond the protein's 's flexibility range; indeed, the amount of filtering increases as we bias to larger RMSID Fa (Figure S6).
Algorithm 1 ConforMixRMSD for exploration of conformational landscapes
Input: Biomolecular structure prediction model p. input system s, target RMSD values R, constraint strength number of samples per RMSD Nsamples Output: Samples {. for all R and i
1: Fd < p(x: 8)
# Predict a structure using default sampling # &ddentffy atoms within secondary structure elements
2: mask < RIGIDELLEMENTSSANE
3: ( |1) + exp -a (RMSD(z, Tai maskk - -))²)
# Define conditioning potential
4: for R. do
5: for :ori=1 11=1, 1,.... . samppes do
6:
Fr.i f- CONFORMIX(E:
7: end for
8: end for
return { Naompier for all r E R
9:
3.3 Sample reweighting and free energy estimation
While some scientific problems require only qualitative information about accessible conformational states and flexibility, others require estimates of statistical quantities such as free energy differences. For this reason, we wish to recover the free energy landscape of structure prediction models.
Samples generated from ConforMix are sampled from series of conditional probability distributions p(zly, s). To form a clear picture of this latent distribution, we wish to reweight our mixture of conditional samples to the unconditional distribution. Combining samples from multiple conditional distributions requires estimating the partition functions P(U;). An unbiased estimator of this quantity available directly from twisted diffusion sampling, but in practice these estimates are noisy, particularly for rare samples, and therefore convergence is slow.
To solve the challenge of estimating the partition functions p(y;). turn statistical tool that to the best of our knowledge has not previously been applied in the context of diffusion models. The multistate Bennett acceptance ratio (MBAR) free energy estimation algorithm combines sample information from multiple conditional distributions to jointly estimate the probabilities (p(1))}, up to (negligible) constant factor [28] 29). In practice, this means that given sufficiently accurate samples from a series of overlapping distributions, such as the conditional distributions of ConforMix, we can reconstruct the unbiased model landscape in those areas. We discuss free energy estimation further in Section 4.4. The mathematical details of MBAR are deferred to the appendix.
Results
We evaluate ConforMix in multiple settings to explore the following questions:
Q1. How do conformational samples generated via inference-time guidance with fixed inputs (sequence, MSA, etc.) compare in quality and coverage to samples generated via methods that require altering the input MSA?
Q2. Can relevant degrees of freedom be extracted from the energy landscape of model trained for single structure prediction?
Q3. As future generative models improve accuracy in predicting the true Boltzmann distribution, can enhanced sampling algorithms like ConforMix provide rapid quantitative information?
5

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4.1 ConforMixRRMSD recovers experimentally observed conformations
We first implement ConforMix in Boltz-1 [36], an open-source diffusion-basee structure prediction model similar to AlphaFold 3. Importantly, Boltz was trained on the Protein Data Bank (PDB), and not with any other dynamics information. While the default Boltz sampling can generate multiple samples, they are generally highly concentrated and are more usefully thought of as multiple approximations of the same static structure than as samples from the true conformational distribution of the protein. To address QI, we collect samples using ConforMixRMSD with Boltz (ConforMixRMSD--Bol) as the underlying structure prediction model.
We examine performance of ConforMixRMSD-Boltz on proteins that exhibit different types of conformational changes: (a) domain motion, (b) transporter eycling, (c) cryptic pocket formation, and (d) fold switching. The set of 38 proteins that exhibit domain motions are the combination of proteins curated by Lewis et al. (17) and in OC23 by Kalakoti al. [T3.. The set of 15 membrane transporters that exhibit inward-oper open and outvard-open conformations were curated in TP16 by Xie
Huang (8). The set of 31 proteins that exhibit cryptic pocket formation were curated by Lewis et al. 17 The set of 15 fold switchers proteins are a subset of those curated by Porter et al. (26).
On these sets, Boltz alone typically recovers only single conformation. Sampling from Boltz with ConforMiXRMSD, however, reveals that the hidden energy landscape contains degrees of freedom that transition to alternative conformations seen in experiment and deposited in the PDB (Figure 2). As comparators, we implement three MSA-modification protocols in Boltz: AFCluster [35), AFSample2 [33, and CF-random [15] (see details in Supplement). We also compare to default Boltz sampling with 1, 000 samples. On the domain motion, transport, and cryptic pocket sets, ConforMixRMSD recovers more alternate conformations than all baselines as measured by RMSD and TM-scores to PDB structures (Tables [T] S3 and Figures 2
[S] S4 S7|ST0] demoontratnnn its power explore conformational space novel manner. MSA-based methods show stronger performance on fold switchers, suggesting such rearrangements are be better captured discrete input modulation, whereas ConforMiXRMSDD better suited continuous (e.g. domain, transporter, pocket) transitions.
A) Biotin carboxylase
B) Lipid II flippase MurJ
ouboward
referance structures
reference structures
ConfortSiRMMED
alosed
ConforNi-MM00
samplig
debult
RMMSD IDV1
RMSD to DNCS
BNCC
25 onward open
sampled structure open
nearest sampled structure to: outward open conformation
dosed conformation
inward open conformation
DV
conformation
SNCC
10
RMSD to 1DV2
ConfonMARMSD
RMSD to 6NC7
19
outrrard openingldesng PC2 (28%g)
1DV2
10V1
PC2 (29%)
1DV2
to 10V1
24A
default
default sammplig
PC1 (96%)
PCI %g
Interdomain opentnglclosing
0.46 to IDV2
3.6 to 1DV1
Inward opening/ccaing
Figure 2: ConFOrMiXRMSD uncovers conformational states that are not sampled by default. Confor- mational sampling of (A) a domain motion protein and (B) membrane transporter. For each system, Top Left: density of sampling relative to reference experimental structures. Bottom Left: projection of the ConforMiXRMSDD sampled structures (orange) onto the first two principal components com- puted from their internal atomic distances. Experimentaly determined reference structures (grey) are projected onto the same space. Right: reference structures and the closest structure generated by each sampling approach (lowest RMSD).
We also find that recovery of experimentally observed states from ConforMiXRMSDD-R sampling is competitive with BioEmu [7 (Figure S2 model trained to generate conformational ensembles,

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Table 1: Coverage of experimenally-determinne reference conformations by method and dataset
Domain motion (n=38)
Membrane transporters
Cryptic pockets
Fold switching
(n=15)
(n=31)
(n=15)
Worst-matched reference
Default Boltz sampling
0.33 (#0.14)
0.13 (#0.17)
0.15 (=0.12)
0.13 (#0.17)
AFCluster-Bolee
0,46 (+0.15)
0.19 (+0.19)
0.35 (=0.18)
0.27 (++0.23
CF-random- Boltz
0.51 (a0.17)
0.20 (a0.20)
0.39 (#0.16)
0.20 (a0.20)
conformation
AF'smplee2Bolle
0.44 (+0.15)
0.20 (+0.200
0.33 (=0.17)
0.10 (+0.15)
(harder task)
ConforMiiRMSD-Bote
0.69 (+0.15)
0.33 (+0.23)
0.45 (=0.18)
0.13 (40.17)
Default Boltz Sampling
0.94 (#0.07)
0.59 (+0.23)
0.94 (=0.08)
0.60 (+0.27)
Best-matched
AFCluster Boltz
0.92 (+0.009)
0.61) (+0.277
0.97 05)
0.600 (+0.27)
reference
CF-random--Bole Boltzz
0.87 (+0.12)
0.60 (+0.23)
0.97 (=0.05)
0.60 (#:0.7)
conformation
(casier task)
AFsumple2-Boltz
0.90 (=0.08)
0.67 (#0.23)
0,93 (=0.08)
0.70 (+0.30)
ConforMixRMSDD-oltz
0.97 (+0.04)
0.79 (#0.19)
0.94 (=0.08)
0.67 (10.23)
Coverage at X% measures the fraction of proteins with samples matching a reference conformation within X% of the RMSD between reference structures. Displayed are values of coverage evaluated at 50% of the eeference-to-rffeeeme RMSD. We evaluate coverage separately for best-matched and alternate (worst-matched) states, Error bars are 95% confidence intervals over 1,000 bootstraps.
although we note that many of the evaluated proteins were held out of training for BioEmu but were likely present in the Boltz training set.
4.1.1 Runtime performance
Due to the additional cost of the guidance and resampling steps in Twisted Diffusion Sampling, sampling with ConforMix takes ~ 3x the wall clock time compared to default sampling. However, individual ConforMix samples are much more informative than default samples. ConforMiXRMSDD can scan large motions of a protein within the space of few dozen samples, which takes just few minutes for a moderately sized protein. For many such proteins, default sampling would not reveal such motions even after thousands of samples. Timing statistics are provided in Table ST
4.2 ConforMixRMSS) samples conformational transitions of domain motion proteins
It is important for any structural sampling method distinguish meaningful conformational fluctua- tions from random perturbations. Consider a protein that exhibits an open-to-closed domain motion. Consider two sampling approaches: (A) generates structures that map the domain transition from open-to-closed totoooooed-iieeeeeeeeeee -iisedl with lower energy wells at observed dominant conformations while (B) generates structure variation in many directions. While both methods may sample the reference open and closed states of this protein at the same RMSD, approach A is clearly more useful as identifies the biologically significant motions. Approach B is difficult to use practice, as reference conformations are not typically known and thus identifying relevant conformations from the collection of heterogeneous variation is not tractable.
To evaluate whether sampling methods explore biologically relevant conformational landscapes versus generating diffuse structural noise, we analyze the variance of generated ensembles using prin- cipal component analysis on pairwise structural distances. We project experimental PDB reference structures onto the principal components assess whether the major axes of structural variation in the samples correspond to observed conformational transitions. Focusing the domain motion set, where proteins are known to exhibit a predominant motion between states, we find that Con- forMixRMSD tends to produce more organized sampling that highlights the transitions between known conformations, while MSA-basce methods typically yield dess-interpretable diffuse sampling (Figures)
S3 S
As discussed in the previous section, Boltz sampling generates limited structural diversity, typically clustering near one experimental state. However, we find that the limited variance that does exist between samples often corresponds to the direction of motion needed to reach the alternative confor- mational state- state-buttl lacks the magnitude to actually traverse the transition. This suggests the model recognizes the relevant degrees of freedom but undersamples them. MSA-based approaches present the opposite problem: they generate abundant structural diversity and can more frequently recover both reference structures, but sampling often doesn't 't map to relevant motion. MSA-based methods show lower values for both the degree of sample variance explained by top principal components and
7

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A) Dipeptide binding protein dppA
default sampling
ConForMixRMSD
AFCluster
open
conformation
IDPE
closed
PC 1999
dooed
open
PC2
closed
dosed conformation
open
closed
1DFP
PC1 (81%)
PC1 (94%)
PC1 (20%)
B) Set of domain motion proteins
default sampling
ConforMixAMSD
AFCluster
exper mental structure differences
% experimental difference
100
sample variation aligns
significant off-path variation
motion collinsar with
aligned with +C1
experimental difference
motion
sampling
diverges experiment
samples exhibit
100
50
0
100
dominant motions
sample variance explained by PC1+PC2
Figure 3: ConforMiXRMSD samples domain motion, revealing transitions consistent with experiment while avoiding noisy paths. (A) Principal component analysis pairwise Ca distances of samples generated for domain motion protein, dppA. Default sampling extends toward but does reach the open conformation, while ConforMixRMSSD traces an opening/closing path. While AFCluster generates open and closed states, its sampling of many other large fluctuations makes it harder to identify the relevant motion. (B) Analysis of variance of samples generated by default sampling, ConforMiXRMSD, and AFCluster, all used with Boltz. Each point describes results for one protein. Default sampling and ConforMixRMSD tend to exhibit concentrated variance between samples that align with the direction of domain motion between reference structures. Note that this metric captures alignment of the sampling direction with experimental conformational differences, but not the extent of sampling along that direction- a method may align well without sampling both experimental conformations. AFCluster often produces samples whose structural differences do not match the direction of domain motion between references, or lack dominant directions of variance-indication off-path sampling. Black-outlined points denote dppA.
the principal component alignment with experimental transitions. These methods generate predictions diffusely across structure space, sometimes matching reference states, but without concentrating sampling along pathways likely to exist between observed states.
ConforMiXRMSDD by contrast, often generates substantial conformational diversity while concentrat- ing that diversity along experimentally relevant transitions. For the dipeptide binding protein dppA (Figure 3)) for instance, 96% of the variance in ConforMixRMSD samples explained by single principal component that directly corresponds to the domain hinging motion between experimental states. More generally for domain motion proteins (Figure 3). the top two principal components of each ConforMixRMSII ensemble generally explain both high fraction of the sample variance (indicating the method generates focused diversity) and a high fraction the variance between exper- imental reference structures (indicating this diversity aligns with known conformational changes). When this is the case, conformational ensembles are readily interpretable: their major modes of structural variation correspond to biologically meaningful motions. PCA plots for all proteins in the domain motion set are provided in Figure S11
As an alternate metric, the "fill ratio" introduced by [13 measures how continuously samples cover the conformational path between reference states based on TM-scores. ConforMixRMSD sampling results in higher fill ratios than the other evaluated methods (Figure (5). We also compute geometric quality metrics on ConforMix-generatee compared to default sampling, but most samples appear reasonable (Table S2)
samples and observe slightly elevated rates of outliers

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A) SemiSWEET sugar transporter
inward open confomation
oocluded conformation
oulward open conformation
Inward open
Inward openinglctog
alssed
PC2 (15 (15.7%)
outward open
occluded
PC1 (74,8%)
open
outward opening/closing
0,9 t 4XSN AB
0,9 A 4QNG, AB
1.2 to 4XSN CD
B) Hammerhead ribozyme
default prediction
ConForMlxAMSD sampling MD-observed states
Figure 4: Exploration of biological macromolecules of interest. (A) ConforMixRMMSD-BOO recovers all three experimentally determined conformations of the SemiSWEET transporter. Default Boltz sampling recovers only the occluded state. PCA demonstrates how the samples capture the major motions as the transporter opens to the inward (intracellular) or outward (extracellular) sides. (B) Preliminary application of ConforMixRMMD--oole RNA structure shows it can recapitulate MD) observed transitions.
4.3
ConforMixRMSSD recovers heterogeneous states in multi-chain and RNA systems
We further evaluate ConForMixRMSD on select biomolecular systems known to exhibit interesting heterogeneity. First, consider multi-chain transporter protein, the SemiSWEET sugar transporter, which cycles through three distinct states to transport substrate across a membrane (Figure A (14). The inward- and outward-open states enable substrate uptake and release, while occluded state that is closed to both sides allows the substrate to pass through the transporter. Thus far, ML-based conformational sampling approaches have primarily been effective on single-chain proteins. Boltz by default predicts only the occluded state for this system. With ConforMixRMSSD sampling, however, Boltz recovers all three states. PCA analysis and visual inspection of sampled structures reveal intermediate states between each known conformation, forming a conformational "trajectory".
While most of our testing focuses proteins, ConforMix be applied to any biomolecular system as long as it is supported by the underlying model. We demonstrate sampling of the hammerhead ribozyme (Figure BB). small catalytic RNA molecule that adopts multiple conformations. These conformations have not been deposited in the PDB, so instead we take molecular dynamics simulations from [2 reference data (the grey structures Figure represent MD frames). ConforMiXRMSDD Boltz visually recapitulates key aspects of the unzipping transition observed in the MD simulations. The sampled structures qualitatively capture the conformational trajectory, suggesting that ConforMix can extract meaningful conformational heterogeneity from RNA systems, though comprehensive evaluation across RNA systems would be needed fully characterize performance.
We conclude that (1) Boltz's learned conformational landscape is rich enough to be of practical utility many protein systems of interest, and (2) ConforMixRMSD enables inference-time access to this landscape without the disadvantages associated with ASA-modification methods.
4.4 Rapid free energy estimation with BioEmu
To illustrate the ability of ConforMix to improve sampling in variety of situations, we implement it BioEmu [17 as well. Unlike Boltz, BioEmu produces broad distributions of conformations with default sampling. However, default sampling is an inefficient way to observe rare events or estimate quantities such as free energy differences, so we assess the ability of ConforMix to rapidly estimate free energies from BioEmu.

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ConforMix speeds free energy estimation, trp-cage-helix
Estimated AG
Default sampling
ConforMix
10
10a
Number of samples
Figure 5: ConforMix sampling in BioEmu enables faster convergence of free energy estimates than default sampling. Using series guidance potentials based on RMSD the native state enables systematic collection of samples that, in turn, enable more rapid free energy estimation. The free energy difference estimated is between the lowest free energy RMSD value (3A to the reference state) and more extended conformation at 7. 7.5A. 90% confidence interval from 50 bootstraps is shown.
While ConforMix can be used to study states that are not seen at all in unbiased sampling, for purposes of comparison consider set of transitions that also be observed without enhanced sampling. Specifically, we evaluate ConforMix on local unfolding proteins from BioEmu, which contain structural motifs that undergo transitions between ordered and disordered states. Because BioEmu does not produce a single consensus structure from default sampling, here we instead use RMSD the folded reference structure the basis for defining series of guidance potentials (see Supplement). We compare the rate convergence of i.i.d. probabilities from ConforMix estimates with MBAR reweighting unbiased sampling in BioEmu (Figure(5). Specifically, we estimate the free energy difference between the lowest free energy RMSD value and a specific less folded state. We observe that ConforMix produces estimates close to the true unbiased estimates and converges significantly more quickly.
Discussion
Predicting biomolecular dynamics represents major frontier for machine learning. By enhancing inference-time sampling in diffusion models, ConforMix rapidly reveals hidden states and continuous motions without prior knowledge from the user. It also enables characterization of the underlying free energy landscape of the models, which we anticipate will assist in future training and evaluation. The broader impact of tools like this is initially in improved understanding of basic biology and then in applications to medicine and other areas.
The primary limitation of ConforMix, like other enhanced sampling methods, is that it depends the robustness and utility of the underlying energy landscape it samples. While Boltz has learned a useful landscape for many proteins, its default sampling typically does not adequately explore the landscape. ConforMix sampling enables us to identify major missing states: known experimental conformations that do not exist with realistic probabilities in the Boltz probability distribution. Other limitations include potential systematic errors due to the inexact sampling of twisted diffusion in the non-asymptotic regime and the statistical uncertainty associated with MBAR. We note that ConforMix has more general uses beyond the specific instantiation of ConforMixRMSDD For instance, users can supply more informative biasing potentials, perhaps based on experimental evidence. If desired, ConforMix can be used in combination with input-modification approaches such as MSA subsampling, although we leave that exploration future work.
ConforMix is fundamentally flexible. multiple molecules. It is able to operate in both all-atom and backbone-one diffusion methods. It is orthogonal to model training. We anticipate that as models mature and energy landscapes approximate the true Boltzmann distribution more closely, inference-time sampling methods such ConforMix will only become more valuable, both for direct study of protein systems and for model development.
not restricted to proteins, and it can handle complexes of
The code for this project is available at
10

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Acknowledgments
We thank the anonymous reviewers for their valuable suggestions and feedback on the manuscript. We thank Karl Krauth, EJ Fine, Ayush Pandit, Shawn Costello, Masha Karelina, Brian Trippe, Hunter Nisonoff, and Bowen Jing for scientific discussions.
This work was supported by NIH grant R35GM158122 122 D.D.R. acknowledges support from the National Science Foundation Graduate Research Fellowship Program. J.K. acknowledges support from the Knight- Scholars program and the Natural Sciences and Engineering Research Council of Canada Graduate Research Scholarship.
References
[1] Josh Abramson et al. "Accurate structure prediction of biomolecular interactions with Al- phaFold 3", en. In: Nature 630.8016 (June 2024). Publisher: Nature Publishing Group, pp. 493 500. ISSN: 1476-4687. DOr:
URL: htt::https://eee http::///ww.ntttrr nature
ccmm//rtticcLee/s45588--22---
(visited 05/16/2025).
[2] Diego del Alamo et "Sampling alternative conformational states transporters and recep- tors with AlphaFold2". In: eLife 11 (Mar. 2022). Ed. by Janice L Robertson, Kenton J Swartz, and Janice L Robertson. Publisher: eLife Sciences Publications, Ltd, e75751. ISSN: 2050-084X. URL: htttps://de org/10. /554/eLife 75751 (visited
DOI: 10. 7554/ 7554/eLife. eliff. 75751 on 10/24/2025).
[3] Benjamin P. Brown et al. "Approximating Projections of Conformational Boltzmann Distribu- tions with AlphaFold2 Predictions: Opportunities and Limitations". In: Journal of Chemical
Theory and Computation 20.3 (Feb. 2024). Number: 3 Publisher: American Chemical Soci-
ety, pp. 1434-1447. ISSN: 1549-9618. DOI: 10. 1021/ acs actc.3001188
URL: https
//doi.org/11 10. 10/1/ acc/ jctc cc00081 (visited on 02/17/2025).
[4] Luca Chiesa, Dina Khasanova, and Esther Kellenberger. "Modeling Active-State Conforma- tions of Cooupee Receptors Using AlphaFold2 via Template Bias and Explicit
Protein Constrains". In: Journal of Chemical Information and Modeling 65. 12 (June 2025). Publisher: American Chemical Society, pp. 6298-6309,
ISSN: 1549-9596.
DOL: [0. 1021/
5c00489
URL: https::/doi.. org 10. 1021 20221/ccs... jcim 5c00489 (visited on
T0/24/2025).
[5] Prafulla Dhariwal and Alexander Nichol. "Diffusion Models Beat GANs on Image Synthesis". In: Advances in Neural Information Processing Systems. Vol. 34. Curran Associates, Inc., 2021, pp. 8780-8794, URL: :ttttp::/ppoceeeiingg newrips........ cc/ htt///apppr////// 2021 /0002//aahh///// / ala
(visited 10/22/2025). [6] Jiahao Fan al. " "Accurate Conformation Sampling via Protein Structural Diffusion". In: Journal of Chemical Information and Modeling 64.22 (Nov. 2024). Publisher: American
Chemical Society, pp. 8414 8426. ISSN: 95966 DOI: 10. 1021/ acs. jeim. 4c00928
URL: https: //do:::///oi... o 10. 1021 jcim 4c00928 (visited on 05/12/2025).
[7] Hashim M. Al-Hashimi and Nils G. Walter. "RNA dynamics: It is about time". In: Current
opinion in structural biology 18.3 (June 2008), pp. 321-329. ISSN: 0959-440X. DOE: 10
1016 j sbi 2008 04 004 URL.: hhttps pmc ncbi nlm nih gov articles/
PMC2580758/ (visited on 10/22/2025).
[8] Katherine Henzler- Wildman and Dorothee Kern. "Dynamic personalities of proteins". en.
In: Nature 450. 172 (Dec. 2007). Publisher: Nature Publishing Group, pp. 972. ISSN:
1476-4687 DOT: 10. 1038/ nature06522 URI.: httph::t///// www. nature. com/ artiiiesic
nature06522 (visited on 10/22/2025).
[9] Lim Heo and Michael Feig. "Multi-state modeling of G-protein coupled receptors at exper- imental accuracy"'. In: Proteins: Structure, Function, and Bioinformatics 90.11 (2022). _eprint: https///niiillllrnggyviii.oooool
1097-0134. DOL: 10. 1002 prott 26382 URL: 10021100t...2333383300 pp. 1873-1885. ISSN: doi/abs/ haa.b///...00//po/00 1002/prot. 26382 (visited on 10/24/2025).
wwwp::wwwl...................e.. com/
[10] Jonathan Ho and Tim Salimans. Classifier Diffusion Guidance. arwi::220.ii::011100002 [es].
July 2022. DOI: 48550/ arXiv. 2207 12598
URL: /ttt:://at/ate orwxiiivorr///.o abs/ ab2/2207 2207
12598 (visited on 10/22/2025).

---

[1]] Bowen Jing, Bonnie Berger, and Tommi Jaakkola. "AlphaFold Meets Flow Matching for Generating Protein Ensembles (NeurIPS)". en. In: Oct. 2023. URL: httppt//p///oeereeiirr
net/ wwwforrmmiidyyyceeeeeee-ee (visited on 02/12/2024).
[12] John Jumper et al. "Highly accurate protein structure prediction with AlphaFoldd en. In: Nature 596.7873 (Aug. 2021), pp. 589. ISSN: 0028-0836, 1476-4687, 10158
021 03819 2 URL: https: www nature. com http:/atiiilsseeem s4wpss//s555--e-- 021 03819 (visited on 12/12/2022).
[13] Yogesh Kalakoti and Björ Wallner. "AFsample2 predicts multiple conformations and ensem- bles with AlphaFold2". en. In: Communications Biology 8.1 (Mar. 2025). Publisher: Nature
Publishing Group, p. 373. ISSN: 2399-36443 DOI: 10. 1038/ s42003 -000--00---77777--177 URL:
https://wwa wwwurat.reee..o com/ wtt.aaaaiiclssseeee --2003- 025 07791- (visited on 10015///000000000000000 10/15/2025).
[14] Naomi R. Latorraca et al. "Mechanism of Substrate Translocation in an Alternating Access
Transporter". English. In: Cell 169.1 (Mar. 2017). Publisher: Elsevier, 96-107.c12. ISSN:
0092-8674, 1092-4172 DOL: 10. 1016/j cell. 2017. 03. 010 URL: httL::htts:///we
honn///l//abbtrrac///0002222 (10///0000000047777))00) 30289 (visited on 10/24/2025).
[15] Mycongsang Lee al. "Large-scale predictions of alternative protein conformations by AlphaFold2-based sequence association". en. In: Nature Communications 16.1 (July 2025). Publisher: Nature Publishing Group, p. 5622. ISSN: 2041-1723, DOL: 10. 1038 941667444277702 60759- 5 URL: https: ://p:://www nature. com htl//ariicls s4146744477777 025 60759-5 (visited on 10/15/2025).
[16] Axel Levy et al. Solving Inverse Problems in Protein Space Using Diffusion- Based Priors.
Ttl:22406.023333 [cs]. Apr. 2025, DOI: 10. 48550 arXiv 2406 04239
URL: http
//arxiv... org/ /a////bs//2....////// 04239 (visited on 10/24/2025).
[17] Sarah Lewis et al. Scalable emulation of protein equilibrium ensembles with generative deep learning. en. Pages: 2024. 12.05. 626885 Section: New Results. Feb. 2025. DOI: 10 1101/
2024. 12. 05. 626885 URL: https: //www/ biorxiv. org/ content/ 1101/2024 12 05. 65.662885v2 (visited on 05/09/2025).
[18]
Kresten Lindorff-Larsen al. "How Fast-Folding Proteins Fold". In: Science 334.6055 (Oct. 2011). Publisher: American Association for the Advancement of Science, pp. 517-520. DOI:
10 10.1126/science / 1208351
URL: https / /wwww/wwwww////////////w scc-scciiiii wwwenceeeeeeccccccccc org. stanford. idm oclc
org 112.1:.1122sscciiee
1208351 (visited on 05/16/2025)
[19] Yikai Liu al. ExEnDiff: An Experiment- guided Diffusion model for protein conformational Ensemble generation. en. Pages: 2024, 10.........5..... Section: New Results. Nov. 2024. DOI:
10. 22.1102/2224.0 10. 04 616517 URL: httth:///vv/ wwwrxii..iiv..............iii..b ottp:/oorooooooooeeooo crgg/oontet///o/ 1101/
2024. 10. 04. 616517v2 (visited on 02/04/2025).
[20]
López-Blanco Blanco and Pablo Chacón. "New generation of clastic network models". In: Current Opinion in Structural Biology. Theory and simulation Macromolcular machines
José Ramón López-
37 (Apr. 2016), pp. 46-53. ISSN: 0959-440X. DOL: 10. 1016/ sbi 2015 11 013 URL:
https: : / www sciencedirect. com sec//ccienceeeee article pttppppipppp/// 000999904444010007755 (visited on 05/16/2025).
[21] Jiarui Lu al. Str2Str: Score-based Framework for Zero-shot Protein Conformation Sam- pling. Issuc: arXiv:2306.03 21117/22221X1120001110111 bio. Mar. 2024. Do1: 10. 10..44850////0 arxiiv
2306. 03117
URL: http:://axiii.tii ats/////////// 03117 (visited on 01/29/2025).
[22] Man Lu et al. A hammerhead ribozyme selects mechanically stable conformations for catalysis against viral RNA". In: Communications Biology 8.1 (2025), p. 165.
[23] Nicholas Metropolis al. "Equation of State Calculations by Fast Computing Machines".
In: The Journal of Chemical Physics 21.6 (June 1953), pp. 1087-1092, ISSN: 0021-9606. DO1: 10. 1063/1 1699114 05/12/2025).
URL: https: //doi org/ 1063/ 1699114 (visited on
[24] Antonio Mirarchi, Toni Giorgino, and Gianni De Fabritiis. "mdCATH: A Large-Scale MD) Dataset for Data-Driven Computational Biophysics". en. In: Scientific Data 11.1 (Nov. 2024). Publisher: Nature Publishing Group. p. 1299. ISSN: 2052-4463, DoL: 10. 0000038//4197022
04140- URL: hhtpp:: : www nature..
wwature.co//eee com / /415l///////////////
(visited
on 05/1 05/16/2025..
12

---

[25] Franco Ormeño and Ignacio J. General. "Convergence and equilibrium in molecular dynamics
simulations". en. In: Communications Chemistry 7.1 (Feb. 2024). Publisher: Nature Publishing
Group, p. 26. ISSN: 2399-3669. Dot: 10 1038/ / #42004 024 01114 11455 5 URI.: https
//www.nature wwwm waa.m/aticclesse 042004 024 - 1 (visited on 10/24/2025).
[26] Lauren L. Porter and Loren L. Looger. "Extant switchngg proteins are widespread". In:
Proceedings of the National Academy of Sciences 115.23 (June 2018). Publisher: Proceedings
of the National Academy of Sciences, pp. 5968-5973. DOL: 10. 1073
10t.1/0a7.......m pnas 1800168115
URI.: https://wwwwt http://ww...aa.....//o///ooos/// wtt.:ogg//ooooooe wttp:////..1.1......a.eea. 1073/p0a3...... http://maaa..001111111111 180011811115551 (visited on 10/23/2025).
[27] James P. Roney and Sergey Ovchinnikov. "State-of-the-AAr Estimation of Protein Model Accuracy Using AlphaFold". In: Physical Review Letters 129.23 (Nov. 2022). Publisher:
American Physical Society, p. 238101. DOL: 10. 1103/PhysRevLett. 129. 238101 URL:
https //link. aps org/ doi / 10. 1103 PhysRevLett. 129 238101 (visited on 05/10/2025).
[28] Michael R. Shirts. Reweighting from the mixture distribution as a better way to describe the Multistate Bennett Acceptance Ratio. 1XXiv:1704008891 [cond-mat]. Dec. 2017. DOI:
10. 40..4850/aaa arr.0//rxiv.... 1704. 00891
URL: http:://arxis http://wwwvvvrro../////// abs/ abs/1704.00897 (visited on
05/12/2025).
[29] Michael Shirts and John D. Chodera. "Statisticallyy optimal analysis of samples from multiple equilibrium states". In: The Journal of Chemical Physics 129.12 (Sept. 2008), p. 124105. ISSN:
0021-9606. DOI: 10. 1063/10 2978177 (visited on 05/12/2025).
URL: https: //doi org/ 10. 1063/1 1. 2978177
[30] Benjamin Trendelkamp Schroer and Frank Noé. "Efficient Estimation of
Kinetics".
In: Physical Review X 6.1 (Jan. 2016). Publisher: American Physical Society, p. 010009.
DOL: 10. 1103/ Pwtr///yyseee.... 6. 011009. URL: https: / /innk..... aps org/ bfrg//oii/nn /oo///.11111//////// 10. 1103/ PhysRevX. 6. 011009 (visited on 10/22/2025).
[31] Mark E Tuckerman. Statistical mechanics: theory and molecular simulation. Oxford university press, 2023.
[32] Wilfred F. Van Gunsteren and Chris Oostenbrink. "Methods for Classical-Mechanical Molec- ular Simulation in Chemistry: Achievements, Limitations, Perspectives". en. In: Journal of Chemical Information and Modeling 64. 16 (Aug. 2024), pp. 6304- ISSN: 1549-9596. 1549-960X. DO1: 10. 1021/ acs joim. 4c00823 URL: https: hwwp://puusssuue acs org/ org/ doi/10 1021/acs. juimm 4c00823 (visited on 10/24/2025).
[33] Ting Wang et al. "How Optimal Are the Binding Energetics of Barasee and Barstar?" en. In: BBoohyssical Journal 87.3 (Sept. 2004), pp. 1618-1630. ISSN: 00063495, DOI: 10. 1529/ biophysj. 104, 040964, URL: https: //1inkinguugnn elsevier com com/retrivee/ppiiii.....
50006349504736437 (visited on 05/10/2025).
[34] Yan Wang et al. Protein Conformation Generation via Force-Guided SE(3) Diffusion Models. Issue: arXiv:2403. 1408 110.::222433.1088 [iib Sept. 2024. DOI: 10. 48550/ arxiv
2403. 14088 URL: http:: org/ wtwg/b///////ooeee/o.///eeee/e/e 2403. 14088 (visited on 01/31/2025).
[35] Hannah K. Wayment-Steele et al. "Predicting multiple conformations via sequence clustering and AlphaFold2". en. In: Nature 625.7996
(Jan. 2024). Number: 7996 Publisher: Nature
Publishing Group. pp. 832-839 ISSN: 1476-4687. DoL: 10. 1038 /41586 -
023 06832
9 URL: https: // //w////www. www. nature. com / articles s41586 023 06832 9 (visited on 03/25/2024).
[36] Jeremy Wohlwend et al. "Boltz-1 Democratizing Biomolecular Interaction Modeling". In bioRxiv (May 2025), p. 1.1.6111.....4166. ISSN: 2692-8205. DOL:
624167 URL: https:://ppttt ncbi nlm. mih. wtt.g//arrtticeeee///111111----- (visited on 10/15/2025).
[37] Luhuan Wu et al. Practical and Asymptotically Exact Conditional Sampling in Diffusiio Models. Issue: arXiv:2306. 17775 arXiv:2306. [stat]. Nov. 2024. DOI: 10.
htrg/abs/2306 17775 (visited on 01/20/2025). [38] Tengyu Xie and Jing Huang. "Can Protein Structure Prediction Methods Capture Alterna- tive Conformations of Membrane Transporters?" In: Journal of Chemical Information and Modeling 64.8 (Apr. 2024). Publisher: American Chemical Society, pp. 3524-3536. ISSN: 1549-9596. DOI: 10. 2.001//acs acim.3c00993
2306. 17775 URL: httt:://aatttt/
URL: AuL:https::/ //doi org/ 10. 1021/aca
jcim 3c01936
(visited on 02/03/2026).
13

---

[39] Huan- Xiang Zhou and Paul A Bates. "Modeling protein association mechanisms and kinet- ics". In: Current Opinion in Structural Biology. Catalysis and regulation / Protein-protein interactions 23.6 (Dec. 2013), pp. 887-893. ISSN: 0959-440X. DOT: 10 1 sbi
2013 06 014 URL: https: // www scie encedireee com / science / artiileeiiilppppee 509594400133001176 (visited on 10/22/2025).
14

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Reviews:
[{"review_id": "QrUcmqRo3k", "reviewer": "Reviewer_YdFU", "summary": "The paper proposes the algorithm ConforMix for sampling from a distribution of conformations. ConforMix requires a pretrained generative model as its backbone and aims to improve the prediction of conformations produced by this model. ConforMix combines three separate algortihmic components:\n- To reweight samples, the partition function of the imposed condition is estimated via the multistate Bennett acceptance ratio. \n- Twisted Diffusion is applied to condition the sampling process on any differentiable feature.\n- The generated samples of ConforMix are rejected if any 10-residue sliding window exhibits an average pLDDT value more than 20% lower than that of the default prediction.\n\nConforMix is implemented in Boltz to generate diverse conformations rather than a single conformation for a given input, and in BioEmu to improve free energy estimation. The authors commit to releasing these implementations upon publication, and code snippets are already provided in the supplementary material.", "questions": "- What is the computational cost of ConforMix? How long is the sampling time of ConforMix+Boltz compared to sampling with Boltz only? How long is the sampling time of ConforMix+BioEmu compared to BioEmu only?\n- Is it necessary to estimate the normalizing constants  $Z_{1},...,Z_{J}$ appearing in line 173, as well as in Eq. (3) and Eq. (4), in order to solve the linear system described in lines 178–181? If so, how do the authors estimate these normalizing constants? \n- How large is $J$ in the experiments of the paper? Is it clear that the system of $J+1$ unknowns admits a (unique) solution?\n\n### Minor comments:\n- To open up the content of the paper to people with a computer science background only, it would help to add references to the first paragraph of the introduction. The second paragraph of the introduction is missing in the reviewers opinion some references as well.\n- there are also no references in the second paragraph of the introduction\n- (Line 83): internal comment \n- (line 92): broken reference\n- (line 151): bracket and period are interchanged.\n- (Line 157): internal comment \n- (line 235): is \"MDLu et al.\" correct?\n- (line 292): \"the\" instead of \"hte\"", "limitations": "The authors have sufficiently addressed the limitations of their work.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "### Strengths\n- ConforMix is implemented in the open-source tools Boltz (an open-source, diffusion-based structure prediction model) and BioEmu (a diffusion-based model for conformational sampling). The authors commit to releasing these implementations upon publication, enabling future research to easily test ConforMix and integrate it with their own conformation-generating models.\n- ConforMix empirically broadens the accessible states of proteins, as demonstrated in four protein studies using Boltz. When combined with BioEmu, ConforMix can generate ensembles that extend beyond those sampled with BioEmu alone. In addition, applying ConforMix to RNA structures shows that it can recapitulate transitions observed in molecular dynamics simulations.\n- The advantage of integrating ConforMix is demonstrated for both a static conformation-generating model (Boltz) and a dynamic one (BioEmu).\n\n### Weaknesses\n- The paper does not introduce new methodologies but rather combines existing methods into an ensemble tailored to improve the prediction of conformations generated by a given model, whether static or dynamic. Nonetheless, the reviewer acknowledges the careful application of these methods, which leads to practical improvements.", "was_revised": true, "final_justification": "The reviewer considers this a valuable contribution that advances conformational sampling by broadening the set of accessible protein states.", "rebuttal": "We thank the reviewer for their careful reading and helpful feedback, and are glad they find that ConforMix demonstrates significant sampling advantages and recapitulates molecular transitions. While our method stands on prior algorithmic work, we believe that applying this combination of methods to protein dynamics is innovative and nontrivial. \n\nAlthough we highlight individual case studies in the paper, we note that we demonstrate application of this method to the domain motion and cryptic pocket protein benchmark sets from BioEmu, which contain 22 and 34 proteins respectively; statistics across these sets are shown in Fig 2. \n\nBased on reviewer comments, we have included or plan to include benchmarking updates including the following:\n\n- We have included additional TM-score analyses of method performance. E.g. for domain motion set:\n\n|Method|Default Boltz|Boltz-AFCluster|Boltz-Conformix|\n|---|---|---|---|\n|TM-score of best models (mean$\\pm$STD)|$0.83\\pm0.13$|$0.84\\pm0.14$|$0.88\\pm0.13$|\n\n- We have updated our Supplementary Material to include detailed RMSD and PCA analyses (similar to those in Fig 2A and 2B) for all proteins. \n\n- We included benchmarking on the open-closed (OC23) dataset from [1]. Summary statistics comparing Boltz-AFCluster and Boltz-ConforMix are as follows:\n|RMSD Threshold (Å)|1|2|3|4|5|\n|-|-|-|-|-|-|\n|Boltz-AFCluster|0.3|0.77|0.83|0.90|0.97|\n|Boltz-ConforMix|0.39|0.81|0.99|1.0|1.0|  \n\n|Method|Boltz-AFCluster|Boltz-Conformix|\n|-|-|-|\n|TM-score of best open state models (mean$\\pm$STD)|$0.82\\pm0.16$|$0.84\\pm0.17$|\n|TM-score of best closed state models (mean$\\pm$STD)|$0.85\\pm0.15$|$0.87\\pm0.16$|\n\n- We will add benchmarking on a set of 92 fold-switching proteins, as suggested by Reviewer pToA. \n\n- We will add additional benchmarking against more recent AF-based models including AFsample2 [1] and CF-Random [2].\n\nWe believe that we demonstrate the wide applicability of our approach by benchmarking on various datasets as well as case studies (see Fig 3).\n\n### Responses to questions\n\nWe hope that our below responses to the reviewer's questions will provide additional information about sampling and estimation. \n\nQ1. The computational cost of generating $n$ samples using our default configuration of ConforMix+Boltz or ConforMix+BioEmu is approximately 3x that of generating $n$ samples from the underlying model via the standard SDE solvers. The twisted diffusion procedure involves two additional operations per denoising timestep compared to standard sampling: gradient-based guidance and particle resampling. There is some flexibility to tune these costs by scheduling these operations at only some steps of the denoising process, though we have not thoroughly explored the accuracy tradeoffs involved in doing so. \n\nThe key question is whether this sampling is ultimately less costly than the alternative: direct estimation from unbiased samples from the underlying model (e.g. Boltz, BioEmu). This depends on the quantity one is trying to estimate. For example, consider free energy estimation. In regimes where conformational states have modest energy differences (1-2 kcal/mol at 300 K), direct unbiased sampling may be sufficient: the higher-energy state will be sampled with probabilities of 1/5 to 1/30. However, important conformational changes often have associated energy differences of  >5 kcal/mol at 300K, resulting in a sampling probability of \\~1/4500 for the higher-energy state. As the free energy difference increases, unbiased sampling becomes exponentially less efficient at estimating the free energies, and so the information provided by guided sampling is of critical value. We believe our results demonstrate that the benefits of exponentially improved rare-event sampling significantly outweigh additional sampling costs of this order. \n\nQ2. For simple choices of the twisting potential, $Z_j$ can often be calculated analytically. For example, if $g_j$ in the harmonic potential described on line 172 is one-dimensional, then the twisting potential has the normalization constant $\\sqrt{\\pi/k}.$ However, it is actually not necessary to estimate $Z_j$ in order to solve the linear system. The unknowns that MBAR estimates from the Eqn (4) system are the partition functions of the conditional distributions we are actually sampling, i.e. the quantities $\\bar Z_j := p(y_j) Z_j$. These combined partition functions are sufficient for our purposes, because they enable us to compute importance sampling weights $w_i$ for all samples in the unbiased distribution $p(x),$ as suggested by Eqn (1). Using the reconstructed unbiased distribution (but with additional information about rare regions, thanks to the conditional sampling), one can then estimate arbitrary observables, including $p(x_j)$.\n\nQ3. For our purposes $J$ (the number of conditional distributions sampled) is typically in the range of 10-50, although larger $J$ can be practically accommodated if necessary. The system of equations has a unique solution, up to a constant factor in all of the estimated partition functions (see [3] and [4]). The practical implication of this free parameter is simply that we are not estimating the absolute partition functions of each state, but rather relative partition functions. Thus, we can use the partition functions as ratios of the form $\\bar Z_a/\\bar Z_b$, which is precisely the case when calculating importance sampling weights. \n\nWe also thank the reviewer for their minor comments. We have updated the manuscript to provide additional references in the introduction and correct the other errors that the reviewer identified.\n\n[1] Kalakoti, Yogesh, and Björn Wallner. \"AFsample2 predicts multiple conformations and ensembles with AlphaFold2.\" Communications Biology 8.1 (2025): 373.\n[2] Lee, Myeongsang, et al. \"Large-scale predictions of alternative protein conformations by AlphaFold2-based sequence association.\" Nature Communications 16.1 (2025): 5622.\n[3] Shirts, Michael R., and John D. Chodera. \"Statistically optimal analysis of samples from multiple equilibrium states.\" The Journal of chemical physics 129.12 (2008).\n[4] Tan, Zhiqiang. \"On a likelihood approach for Monte Carlo integration.\" Journal of the American Statistical Association 99.468 (2004): 1027-1036."}, {"review_id": "Pldnbhgur8", "reviewer": "Reviewer_pToA", "summary": "The authors developed ConforMix, an inference-time scaler for diffusion-based structure predictor of biomolecular systems, to enable multi-state sampling.\nUsing pseudo-potentials under different conditions and Twisted Diffusion Sampling (TDS), they were able to efficiently sample an extensive conformational space.\nBased on these results, the authors connected their method with the long-standing MBAR (multistate Bennett acceptance ratio) method, which is a free energy estimation method based on system perturbation. This allows for faster convergence of MBAR's energy estimation.\nThe authors chose important and quite different biomolecular systems to demonstrate ConforMix's multi-state sampling efficiency and adopted benchmark datasets to show its efficiency in free energy estimation.", "questions": "# Questions\n1. I suggest using supplementary data 1 of [1], which consists of 92 fold-switching protein conformations. In [1], the authors tested the capability of AF-based models to sample multiple conformations of fold-switch proteins and measured the success rate of sampling multi-state conformations. Alternatively, the dataset used in EigenFold (originally constructed from [3]) can be used for benchmarking. This benchmark implicitly evaluates the models' ability to sample multiple states using TM-score and residue-wise flexibility as metrics. Conducting such benchmarks would improve the paper's impact.\n2. Boltz only trained to reproduce the static (mostly stable) PDB structures, not the physical energy function $-\\nabla U(x)$. Thus, the drift that Boltz learned is not a physical force. It seems that using a pseudo-potential like RMSD might lead to highly physically invalid structures. I think that the authors' choice to use a pLDDT value higher than 20% for filtering generated structures implies that most of generated samples are in a physically invalid (off-manifold) state. Could the authors provide the statistics on physical validity of ConforMix-generated samples compared to Vanilla-Boltz-generated samples?\n3. The accuracy of MBAR estimation depends on the number of samples from each state and the overlap between states. To me, efficient sampling of various states and MBAR accuracy seem to be mutually exclusive. Is there any potential bias triggered by a small number of samples due to efficient exploration?\n4. The dynamic state visualization results of ConforMix presented in the main text and supplementary data are very impressive. By what criteria were these examples selected among the numerous structural ensembles generated?\n5. I think multi-state conformation sampling is more important for novel proteins rather than the systems that we know about.\nIs this right?\nIf so, how can one use ConforMix to fully novel protein, where no information about multiple conformational states are available?\nUser may select the suitable pseudo-potential with appropriately consider physical validity, and then should properly select the generated conformations.\nIf the authors provide proper ways to design pseudo-potential and conformer selection criteria (which is related to **W2** and **Q4**), this would enlarge the impact of the work.\n\n# Typos\n1. In Figure 3 caption's 4'th line: applicaation -> application\n2. In line 276: an series -> a series\n3. In line 293: What does mean by hte?\n4. The year is missing from reference 4.\n\n[1] Chakravarty, Devlina, et al. \"AlphaFold predictions of fold-switched conformations are driven by structure memorization.\" Nature communications 15.1 (2024): 7296.  \n[2] Jing, Bowen, et al. \"Eigenfold: Generative protein structure prediction with diffusion models.\" arXiv preprint arXiv:2304.02198 (2023).   \n[3] Chakravarty, Devlina, and Lauren L. Porter. \"AlphaFold2 fails to predict protein fold switching.\" Protein Science 31.6 (2022): e4353.", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "# Strengths\n1. The proposed method uses system-dependent conditions with potentials for TDS and has demonstrated its ability to transform protein structure prediction, such as Boltzmann machines trained with static conformations, into multi-state conformational samplers.\n2. Fast free energy estimation, based on a combination of MBAR, seems to have the potential to be used in the analysis of protein dynamical systems.\n3. The motivation of the paper and the method and the experimental results are well aligned.\nThe paper's core result is that Boltz-ConforMix performs well in multi-state sampling, demonstrating its performance on domain and cryptic pocket motion datasets.\nTwo systems, which used for case studies, are quite different (SemiSWEET sugar transporter is a relatively less dynamic protein system where the hammerhead ribozyme is a more dynamic RNA system), demonstrating the proposed method's effectiveness.\n\n# Weakness\n1. **Lack of validations for generated conformations**. [related to **Q2**]  \nBoltz-ConforMix in Figure 2(c) shows that it beats the BioEmu's performance under the range around 3Å.\nHow can it be possible only using RMSD compared to the initially generated conformation from Boltz?\nGiven the fact that (a) BioEmu learned vast conformational space with dynamical data (b) Boltz only learned mostly stable data, I think it is still hard with ConforMix to generate physically validated structures while covering more extensive conformational space than BioEmu.\nThe authors should provide an analysis about the structural validity of Boltz-ConforMix.\n\n2. **Potential biased selection of structural visualzation**. [related to **Q4**]  \nHow did author selected the visualization results from data?\nSince several results are picked from low-density region of the PCA results, it seems that the authors chose the results with specific criteria, which should be mentioned in the manuscript.\nFor example, were structures chosen based on their distance from a cluster center, their energy, a specific structural motif, or another quantitative measure?\n\n3. **Incomplete manuscript**.\nAlthough the final quality of the paper does not depend on its initial completeness, most papers submitted to the conference are well-formatted, with complete citations and figures.\nHowever, this paper has several critical issues.\n- Incomplete citations (lines 83 and 157)\n- Line 157 reveals the authors' names, which violates the anonymity requirement\n- In Figure 2(b), the label under *hinge outward* structure seems to be fixed (0.46Å to 1DV2) -> (?Å to 1DV1)\n- In supplementary figures S3(c) and S3(d), it seems that the axes are swapped, making it difficult to understand whether BioEmu and ConforMix generated similar conformational distributions\n\n4. **Understanding the manuscript is quite hard due to the lack of information**.\n- RMSD metrics used for each domain motion and cryptic pocket sets seems to be global and local RMSDs (inferred from BioEmu). These information is critical for evaluating the results of the paper so the authors should give more information about each results' metrics.\n- In the algorithm section, RMSD first appears, but there is no explanation of why the mask is generated from the rigid element or what the mask does in RMSD. (A detailed explanation is provided in Section 4.1, especially in line 274.) Using captions for detailed explanations would help readers better understand.\n- The authors should explicitly inform the readers about related supplementary section. (e.g. supplement -> supplementary figure 4)", "was_revised": true, "final_justification": "My previous questions were considered well. In particular, the addition of new benchmark results, the conformation selection strategy in PCA, the detailed explanation of the trade-off in MBAR, the applicability to novel proteins (as well as characterized proteins) and its importance, were helpful. The authors also provided additional empirical results about physically valid structures and their reasoning behind filtration schemes to obtain them.", "rebuttal": "We thank the reviewer for their thorough reading and very constructive suggestions. We are glad they observe the potential of our method to predict protein dynamics. Based on their comments, we have significantly updated our manuscript and run further benchmarking metrics and comparisons. We hope that our responses below address their concerns.\n\n### 1. Validating generated conformations\nThis is an excellent question. We believe our findings add to the growing literature (primarily based on MSA perturbations) that shows that even models trained for single-structure prediction can generate varied conformations. \n\nAlthough BioEmu is finetuned on MD simulations and experimental stability data, it is initially pretrained on only clustered PDB data. This pretrained  model still performs remarkably well at conformational sampling (see e.g. BioEmu Fig 2, S1, S2, S4). In fact, for many proteins, the finetuning does not appear to significantly improve the conformational coverage. Thus, there is precedent for diffusion-based sampling of conformational changes given only training on static structures. \n\nWe appreciate the reviewer's suggestion to analyze structural validity of these samples. We now include statistics on outliers in Ramachandran angles, backbone bond angles, and bond lengths in the manuscript. These results show slightly increased outliers for Boltz-ConforMix samples compared to vanilla Boltz samples. We summarize results on the domain motion protein set below. A bond length or bond angle is an outlier if its value is beyond $4 \\sigma$ of the reference value. A residue, excluding Gly and Pro, is a Ramachandran outlier if its $\\phi/\\psi$ angles lie outside standard regions. Each table entry gives the outlier rate (number of outliers divided by total number of backbone bonds, backbone bond angles, or residues), averaged across all samples collected of all proteins.  These results show that ConforMix samples are generally physically valid. \n\n| Fraction of outliers in: | Boltz | Boltz-ConforMix no filtering | Boltz-ConforMix w/ filtering |\n|-|-|-|-|\n| Rama. angles |  $0.0088 \\pm 0.0055 $ | $0.0142 \\pm 0.0047$ | $0.0124 \\pm 0.0054$| \n| Backbone bond angles | $(2.2 \\pm 4.2) \\times 10^{-5}$ | $(31.4 \\pm 32.1) \\times 10^{-5}$ | $(8.2 \\pm 4.7) \\times 10^{-5}$|\n| Backbone bond distances |  $(2.3 \\pm 1.8) \\times 10^{-5}$ | $(28.2 \\pm 21.3) \\times 10^{-5}$ | $(14.1 \\pm 8.7) \\times 10^{-5}$| \n\n\n### 2. Selection of visualized structures\n\nThis is a good question. For each protein sampled with Boltz-ConforMix, we perform a principal component analysis on the generated samples. We chose samples to visualize with the primary goal of illustrating what motion is captured by the largest PCs. Please see our response 1a to reviewer 61jC for more details. \n\nTo address the reviewer's concern and better demonstrate how ConforMix samples physically-relevant transitions, we have:\n- Expanded our description of the PCA procedure (including how visualized samples were selected) and what these analyses indicate about transition paths between experimental structures.\n- Provided PCAs for all proteins in the supplement.\n- Included analyses of the \"trajectories\" generated by Boltz-ConforMix samples. E.g. projection analyses quantifying on- vs off-pathway conformational variation between the experimental states and fill ratio analyses (quantifies how well samples map onto the path between known states, from [1]).\n\nPlease also see our response to Q4. \n\n### 3 and 4. Corrections\nWe thank the reviewer for pointing out errors. \n- We have corrected the citations, figure axes, and Fig. 2B labels. We also reference supplementary figures in the text. \n- We apologize for the inadvertent internal comment on line 157. However, we wish to note that this comment referred to citing material from an external source and does not reveal the name of any authors of this work. \n\n- The reviewer is correct that we use the metrics from BioEmu (global RMSDs for domain motion and local RMSDs for cryptic pocket sets). We have updated the text to reference this. \n\n- The question about the choice of residue mask for computing RMSDs is an excellent one. Most proteins contain both flexible loop regions and rigid secondary structure elements. During initial testing we computed RMSD on all residues, which revealed that models preferentially sampled loop motion. Though these are usually physically valid, loop flexibility is typically easy to predict via other means, so we aimed to concentrate sampling efforts on larger changes that rely on rigid element motion. We thus compute RMSD only on residues within rigid secondary structure elements (helices and sheets). Forcing RMSD changes measured on these regions guides Boltz-ConforMix to recapitulate larger dynamics such as domain motions and transporter cycling. This mask does not limit loop regions from moving during diffusion; indeed, loops often must move to allow rearrangements of rigid elements. We updated the text to better describe this idea. \n\n## Questions\n\nQ1. We agree that further metrics and benchmarks would improve our paper. Following the reviewer's recommendation, we updated our analyses and manuscript to include TM-score analyses. E.g. for domain motion set:\n\n|Method|Default Boltz|Boltz-AFCluster|Boltz-Conformix|\n|-|-|-|-|\n|TM-score of best models (mean$\\pm$STD)|$0.83\\pm0.13$|$0.84\\pm0.14$|$0.88\\pm0.13$|\n\nWe are also exploring residue-wise flexibility metrics.\n\nThe recommendation to test the fold-switching benchmark is a good one. We are running these proteins and will include the results in the final version of the manuscript. In the interim, we have also run the open-closed (OC23) dataset from [1], excluding six proteins that overlap with the domain motion set. Please see our response to reviewer YdFU for statistics on this dataset. \n\nWe are also benchmarking against more recent AF-based models including AFsample2 [1] and CF-Random [2].\n\nQ2. The reviewer identifies a key design consideration in our filtering approach. Our conditional diffusion framework allows generation under arbitrary constraints, but some constraints would require a protein to assume a physically implausible conformation. Since we do not always know a priori if a given constraint is reasonable, our goal in filtering is to screen out samples that violate physical norms. The 10-residue sliding window pLDDT approach serves as our mechanism for identifying when biasing constraints exceed a protein's natural flexibility limits. We expect that proteins that undergo large motions relative to the initial structure will remain physically plausible at greater RMSD values, while proteins with limited motion will show validity dropoffs at lower RMSD values. Based on the reviewer's question, we analyzed filtering statistics across our datasets and confirm this trend. The fraction of filtered structures increases with the biasing RMSD value, e.g. for the domain motion set:\n\n|RMSD|Filter Ratio|\n|-|-|\n|0|$0.0\\pm0.0$|\n|6|$0.02\\pm0.06$|\n|10|$0.18\\pm0.36$|\n|18|$0.36\\pm0.44$|\n\nThese statistics vary substantially between proteins based on their degree of conformational flexibility. For example, P06766 (10.3 Å experimental RMSD) accepts 97\\% of structures up to 12 Å, then drops to zero acceptance. P02911 (5.0 Å experimental RMSD) accepts 98\\% under 6 Å, with no acceptance above 9 Å. RMSD acceptance thresholds don't always match experimental ranges exactly, Boltz-ConforMix samples conformations beyond experimentally observed states while often remaining physically plausible. For example, biotin carboxylase (Fig 2B) samples states more extended than the known \"outward hinge\" conformation. We have added a figure showing filtering statistics across proteins and RMSD ranges. W also provide physical validity statistics (see W1).\n\nQ3. MBAR provides unbiased estimators of the partition functions. As the reviewer notes, the variance of those estimates depends on the number of samples and the overlap between states. Please see our response to reviewer YdFU Q1 for further discussion. \n\nQ4. Fig 2: these are typical cases where ConforMix captures experimental states and motion, a pattern seen across many proteins (see coverage plots) but not all. Our supplement now shows visualizations for each tested protein. We also updated Fig 2 to include one domain motion and one cryptic pocket representative. \nTransporters and RNA (Fig 3, S1): we consulted with collaborators on proteins with physically relevant motion. We focused on these transporters as they have >1 chain (not accessible with most previous methods) and exhibit >2 relevant states, allowing us to test whether ConforMix can recapitulate the full set. The ribozyme was chosen as MD data was available to validate our generated  states.\n\nQ5. The reviewer raises an excellent point about novel protein applications. Our RMSD-based approach can be applied to any protein sequence without prior knowledge: it uses only the structure prediction model's default output to systematically bias sampling at progressive RMSD distances, and relies solely on model-derived confidence metrics for filtering.  While ConforMix supports different potentials (see our response to PcUq), this RMSD approach (used for Fig 2-3) is applicable without information about multiple conformational states. For any protein, users can: 1) predict a default structure, 2) sample with bias potentials at increasing RMSD distances (e.g. 2-20 Å used here), and 3) filter for plausible conformations. \n\nWe note that conformational sampling is valuable not only for novel proteins but also for characterized proteins where dynamics remain experimentally challenging to capture (e.g., transporter mechanisms, binding transitions).\n\n[1] Kalakoti & Wallner. \"AFsample2 predicts multiple conformations and ensembles with AlphaFold2.\" Comm Bio (2025). \n[2] Lee et al. \"Large-scale predictions of alternative protein conformations by AlphaFold2-based sequence association.\" Nat Comm (2025)."}, {"review_id": "Y8LNAjUaL4", "reviewer": "Reviewer_PcUq", "summary": "In this paper, the authors propose ConforMix, a sampling method that employs Twisted Diffusion and Sequential Monte Carlo within a diffusion model. This method allows us to sample a wide variety of conformations, enabling us to capture the most important conformational changes for understanding biomolecular function.", "questions": "You might be planned as the next step, but will it yield results for predicting protein complexes and extending docking simulations?", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strengths:\nThis is an interesting method of extending a diffusion model-based generative model, which essentially predicts static three-dimensional structures, to dynamic three-dimensional structures that can be predicted without information on degrees of freedom. This method uses sampling with Twisted Diffusion and Sequential Monte Carlo and reweighting with the Multi-State Bennett Acceptance Ratio (MBAR) free energy estimation algorithm to guide and reweight conditioning generation. When incorporated into Boltz, it can predict structures closer to those revealed by experiments that Boltz alone cannot predict. This method is more sophisticated and scalable than the previously reported AFCluster, and its performance is comparable to that of BioEmu.\n\nWeaknesses:\nIt seems that three-dimensional coordinate information is essential for input. The prediction accuracy is affected by the statistical uncertainty of MBAR, as mentioned in the limitations, and it may depend heavily on the accuracy of the extended diffusion model predictions. Therefore, validation experiments in a wet lab are ultimately required. However, this is not reason to lower the paper's rating, as this applies to all in silico models.\n\nMinor point: \nI found several typographical errors in the text. The following is a list of the ones we noticed:\nLine 78: Excessive parentheses.\nLines 83 and 157: The reference appears to be incomplete.\nFigure 3: \"applicaation\" is a typo for \"application.\"\nLine 235: “MDLu” is a typo for “MD Lu”.\nLine 293: “hte” is a typo for “the”.", "was_revised": true, "final_justification": "ConforMix is an interesting study that proposes a method for sampling multiple conformations of important biomedical proteins. I increased my rating by one because I gained a better understanding during the peer review process, and I believe this manuscript will be useful for subsequent research.", "rebuttal": "We thank the reviewer for their positive evaluation of our method, observing that it allows us to sample a wide variety of conformations. We are glad they found the approach to be sophisticated and scalable. We appreciate their useful feedback and believe we address the limitations they describe in our responses below. \n\nThe procedure we describe in Algorithm 1, which we used to produce the data visualized in Figures 2 and 3, does not require external 3D coordinate information to be supplied. Instead, an initial 3D conformation is generated at runtime from the diffusion model with default sampling (line 1) and this is then used as a reference state to construct biasing potentials (lines 2 and 3).  For instance, all results from Boltz-ConforMix shown in Figs 2, 3, and S1 are generated without any user-input 3D coordinates. \n\nNevertheless, ConforMix readily accommodates alternative sampling objectives. For example, a user may provide a reference 3D conformation or other coordinates of interest (e.g. distances between regions of interest in a protein), and ConforMix can perform sampling along those degrees of freedom. E.g. samples in Fig S2 were generated using distance-based coordinates (biasing the diffusion model to generate samples with user-input distances between protein regions of interest). Based on the reviwer's comments, we have revised the manuscript to highlight the versatility of the method in accommodating objectives **with** or **without** input coordinates.  \n\nWe acknowledge that because our method runs at inference time, the quality of its predictions necessarily depends on the behavior of the underlying diffusion model, as well as the performance of Twisted Diffusion Sampling and MBAR. Despite these limitations, we believe our results demonstrate the utility of ConforMix. We also acknowledge that wet lab validation experiments for computational results play an essential role in the scientific process. We hope that our tool will be useful to wet lab scientists in guiding their experimental investigations. \n\nWe thank the reviewer for their careful reporting of typographical errors, which we address in the revised manuscript."}, {"review_id": "SLdEbFpD96", "reviewer": "Reviewer_61jC", "summary": "The paper presents ConforMix, a method for guiding diffusion-based biomolecular generative models (e.g., Boltz, AlphaFold3) to produce conformational ensembles—rather than single static structures—at inference time, without any model retraining or fine-tuning.", "questions": "1.\tThe 10-residue sliding window for pLDDT (Section 3.2) is an interesting idea. Why was this chosen over, for example, simply averaging pLDDT over all residues?\n2.\tIn Algorithm 1, are samples with specific RMSD thresholds R guaranteed? For example, in Figure 2A, there appear to be no samples within 1Å RMSD for 13PK, despite this threshold being mentioned on line 190.", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 4, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n1.  The paper tackles a highly relevant and open challenge: predicting conformational ensembles of biomolecules, which has broad applications in structural biology and drug design.\n2.  The proposed method, ConforMix, is both novel and promising. Notably, it appears to outperform BioEmu—a state-of-the-art method trained on molecular dynamics data—in at least two respects: (i) recovery of native conformations under varying RMSD thresholds (Figures 2C and 2D), (ii) efficiency in free energy estimation (Section 4.1).\n3.  The proposed approach requires no retraining and could be widely applicable to pretrained diffusion models.\n\n**Weaknesses**\n\n1.  Experimental details are missing, making it hard to fully interpret the results:\n  - How were the proteins in Figures 2A and 2B selected? What exactly is being projected in the PCA plots?\n  - Are the protein sets in Figures 2C and 2D the same as those used in the BioEmu paper? Please explain the metrics.\n  - The conclusions from the RNA modeling experiment (starting line 230) are insufficiently supported. Are the grey structures in Figure 3B experimental references? Please support both the claim of lower performance on RNA than on proteins, as well as recapitulation of conformations from MDLu et al. 2025.\n2.  Although Section 3.3 discusses free energy prediction and sample reweighting, these components do not appear to be used or evaluated in the experiments. In Section 4.1, free energy estimation seems to be performed using the BioEmu method rather than the proposed one. A comparison is needed.\n3.  Runtime performance is not discussed.\n4.  Some parts lack clarity:\n  - TwistedSampling, central to ConforMix, is not described. A brief intuitive explanation in the main text and a detailed description in the appendix would be very helpful.\n  - [Line 7] Mentions classifier guidance, but it does not appear in the methods—this is also mentioned on line 113.\n  - [Line 149] It’s unclear what the variable j represents.\n  - [Lines 280–283] The discussion is confusing. Is the proposed method actually faster than existing ones?\n  - [Line 99] The conditioning variable is inconsistently denoted as both $input$ and $s$ later.\n5.  Typos and minor errors\n  - Line 78: “(,”\n  - Line 83: “[ cite …”\n  - Line 157: “[ CITE …”\n  - Figure 2: Floating letter “B” in the figure", "was_revised": true, "final_justification": "I maintain my \"Accept\" score. The paper presents a novel idea and the results are strong. My rebuttal comments were addressed well.", "rebuttal": "We thank the reviewer for their enthusiastic evaluation of our method and for their helpful feedback. We are glad they found the approach to be \"novel and promising.\" We have updated the text significantly based on the reviewer's comments and provide answers to their questions below. \n\n## 1. Experimental details:\n### a)\n**Selection of proteins Fig 2:** The proteins in Fig. 2A and 2B are meant to provide case studies of the behavior summarized in Fig. 2C and 2D, where Boltz-ConforMix captures experimental states and relevant motions for domain motion and cryptic pocket proteins. We selected examples that represent good multi-conformation sampling, which is seen across many but not all proteins in these sets. We have added similar visualizations for every tested protein to the Supplement so that a detailed comparison can be made. \n\n**PCA plots in Fig 2:** We have updated our text to better describe the principal component analysis and our interpretation of it. For these analyses, we transform each generated sample to internal coordinates by computing a distance matrix between all alpha-carbons, then perform a PCA across all Boltz-ConforMix generated samples for a given protein. To investigate what the principal components capture, we visualize samples at different positions along PC1. We also project experimental structures onto this PCA space to visualize where known conformations are positioned relative to our generated ensemble. For many, though not all, proteins, we find that Boltz-ConforMix produces samples along physically meaningful transition pathways that connect experimental conformational states (e.g., hinge open-to-close, domain in-to-out, transporter inward-to-outward facing). For instance, Fig. 2A/B show domain motions progressing from closed/hinge-inward to open/hinge-outward conformations through physically plausible intermediate states. These motions dominate the sampling of these systems. We now include PCAs for all proteins tested in the Supplement. \n\n### b)\nYes, the domain motion and cryptic pocket protein sets depicted in Figs 2C and 2D are the same datasets as in the BioEmu paper. The global and local RMSD metrics, respectively, are the ones used by BioEmu on these sets. Specifically, the global RMSD metric is the RMSD of the entire protein to the reference structures, which is used on the domain motion set. The local RMSD metric is the RMSD of a predefined region of the protein around the location of the cryptic pocket. We have updated the text to clarify these details and better reference their origin from BioEmu.\n\n### c) \nRegarding the comparison of RNA modeling to molecular dynamics results, the grey structures depicted in Fig 3B are frames from MD simulations performed by Lu et al., which we use as reference data for this system since experimental structures do not exist for all of the states depicted. Thus, Fig 3B illustrates the extent to which Boltz-ConforMix sampling can recapitulate RNA conformational heterogeneity found in MD simulations. We have expanded our explanation of the reference structures accordingly. With regard to the performance on RNA modeling, we agree with the reviewer that the claim of lower performance is not sufficiently supported. We have not evaluated a larger dataset of RNA conformational variability and thus intended our remarks simply as a caution that performance may vary between proteins and other systems such as RNA. We have clarified the text accordingly.\n\n## Free energy prediction and sample reweighting\nWe believe that the quantitative components of our approach complement the qualitative understanding available from the conditional sampling alone. We have indeed evaluated these components with both BioEmu-ConforMix (described in the text) and Boltz-ConforMix (which we agree is not sufficiently covered in the text). With BioEmu, we compare the convergence of free energy estimates via our procedure and convergence of free energy estimates via direct unbiased sampling of BioEmu. Figure S4B illustrates a set of such convergence comparisons, showing that our procedure (\"mbar\", orange line) is more sample-efficient than unbiased estimation. We purposely selected these examples to be achievable via unbiased sampling. Consider a free energy difference of interest, $\\Delta G_{a,b}$, between states $a$ and $b$. As $\\Delta G_{a,b}$ becomes greater, convergence of the free energy estimate $\\Delta \\hat G_{a,b}$ derived from unbiased sampling becomes exponentially slower. Our approach of biased sampling followed by reweighting makes estimating such free energy differences substantially more practical. \n\nIt is logical to examine the performance of our free energy estimation machinery with Boltz-ConforMix as well. A feasible amount of unbiased Boltz sampling will never sample much of the conformational heterogeniety we access with Boltz-ConforMix. This makes a quantitative comparison between our method and unbiased sampling almost trivial, since the (inaccurate) free energy estimate from unbiased sampling is simply $\\infty$ for states not visited. Our approach enables more precise quantification of the Boltz distribution. We have revised our manuscript to describe these additional observations.\n\n## Runtime performance\nThe computational cost of generating $n$ samples using our default configuration of ConforMix+Boltz or ConforMix+BioEmu is approximately 3x that of generating $n$ samples from the underlying model via the standard SDE solvers. The twisted diffusion procedure involves two additional operations per denoising timestep compared to standard sampling: gradient-based guidance and particle resampling. There is some flexibility to tune these costs by scheduling these operations at only some steps of the denoising process, though we have not thoroughly explored the accuracy tradeoffs involved in doing so. However, we believe our results demonstrate that the benefits of exponentially improved rare-event sampling significantly outweigh additional sampling costs of this magnitude. \n\n## Clarity\nWe thank the reviewer for their notes on clarity and have updated the text to better explain the points they have identified. \n- TwistedSampling refers to the sequential Monte Carlo procedure of Twisted Diffusion Sampling [1]. We have included a description of this method in the revised text. \n- We have updated the text to describe the classifier guidance approach we leverage here. \n- The variable $j$ on line 149 indexes the set of conditional distributions we sample; these correspond to the bias potentials constructed from the set of RMSDs in line 4 of Algorithm 1. \n- Our method is overall substantially faster than unbiased sampling in cases where the states of interest are sufficiently different in free energy (one is rarely sampled), which is frequently the case in these models as well as in actual Boltzmann distributions. Please see also our remarks on runtime performance above. \n- The conditioning variable was indeed inconsistently denoted; we have corrected this in the text. \n\n## Typos\nWe thank the reviewer for identifying these typos and minor errors. We have resolved them. \n    \n## Questions\n\n### Q1. \nWe thank the reviewer for highlighting our pLDDT structure filtering approach. Their insightful question has prompted us to include a clearer explanation of and justification for this approach. ConforMix enables structure generation with arbitrary constraints, thus requiring a way to determine when the samples generated under these constraints (e.g. specific RMSD values from default predictions) are compatible with a protein's conformational flexibility. We initially tried filtering for physically feasible samples using average pLDDT over all residues, as the reviewer suggests. We found, however, that when we bias structure generation away from default predictions with RMSD values incompatible with a protein's physical constraints, the resulting samples often exhibit non-physical structure only in small protein segments. Since the majority of the predicted structure remains physically valid, the average pLDDT over all residues typically shows minimal decrease, making such a filter unreliable. In contrast, the pLDDT of these small non-physical segments decreases dramatically. We thus implemented a sliding window approach to ensure every sub-region of the protein maintains relatively high pLDDT/physical validity. We have updated the manuscript text to describe our rationale for choosing this metric. We also refer the reviewer to our response to Q2 from reviewer pToA for further details on the behavior of this filtering. Based on feedback from both reviewers, we have added a supplementary figure demonstrating filtering statistics across different proteins and RMSD ranges.\n\n### Q2.\nThe RMSD guarantees the reviewer asks about are an important point to clarify. As we note elsewhere, ConforMix can be used with arbitrary biasing potentials, but in the procedure outlined in Algorithm 1, we bias structure prediction $R$ Å away from the \\textit{default conformation} predicted by Boltz/BioEmu/etc (considering only regions with secondary structure), rather than $R$ Å away from an experimental structure. In general, we find that generated samples satisfy their respective RMSD targets, although some of these samples contain physically implausible features and are removed by our filtering procedure. This process does not guarantee that generated samples will have a specific RMSD to experimental reference structures, however. The ability to recapitulate reference structures (e.g. open 16PK and closed 13PK for phosphoglycerate kinase) varies by protein and is summarized in Fig. 2C. We have added the best match RMSD values to each reference structure for all tested proteins to the Supplement.\n\n[1] Wu et al, \"Practical and Asymptotically Exact Conditional Sampling in Diffusion Models\", NeurIPS 2023."}]

Author rebuttal:

Meta-review: This paper introduces ConforMix, an inference-time sampling framework for biomolecular diffusion models. It integrates (a) twisted diffusion sampling, (b) pseudo-potentials for conformation landscape exploration, and (c) MBAR-based sample reweighting for free energy estimation. The method is implemented for Boltz and BioEmu and verified on proteins and RNAs.

The paper is quite strong in a sense that it points out a novel research direction with high practical relevance. I also find the experiments on BioEmu and Boltz to be appealing for practitioners.  

During the rebuttal period, reviewers raised concerns about (a) computational cost, (b) unclear details on MBAR, (c) Boltz training on static structures, and (d) frequent typos. A reviewer also suggested additional benchmarks like fold-switching proteins and OC23 dataset. The authors have resolved this concerns in a satisfiable way, and all the reviewers expressed excitement about this paper. 

Overall, I believe this is a strong paper and recommend acceptance.
Decision: Accept (spotlight)