Learning Collective Variables from BioEmu with Time-Lagged Generation
Authors: Seonghyun Park
Kiyoung Seong
Soojung Yang
Rafael Gomez-Bombarelli
Sungsoo Ahn
Venue: ICLR 2026 Poster (2026)
Keywords: collective variables
molecular dynamics
protein
enhanced samplings
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
TL;DR: We propose to learn collective variables from the conditions of a unconditional generative models, and extensively validate them by enhanced sampling techniques.

Abstract: Molecular dynamics is crucial for understanding molecular systems but its applicability is often limited by the vast timescales of rare events like protein folding. Enhanced sampling techniques overcome this by accelerating the simulation along key reaction pathways, which are defined by collective variables (CVs). However, identifying effective CVs that capture the slow, macroscopic dynamics of a system remains a major bottleneck. This work proposes a novel framework coined BioEmu-CV that learns these essential CVs automatically from BioEmu, a recently proposed foundation model for generating protein equilibrium samples. In particular, we re-purpose BioEmu to learn time-lagged generation conditioned on the learned CV, i.e., predict the distribution of molecular states after a certain amount of time. This training process promotes the CV to encode only the slow, long-term information while disregarding fast, random fluctuations. We validate our learned CV on fast-folding proteins with two key applications: (1) estimating free energy differences using on-the-fly probability enhanced sampling and (2) sampling transition paths with steered molecular dynamics. Our empirical study also serves as a new systematic and comprehensive benchmark for MLCVs on fast-folding proteins larger than Alanine Dipeptide.

Published as a conference paper at ICLR 2026
LEARNING COLLECTIVE VARIABLES FROM BIOEMU WITH TIME-LAGGED GENERATION
Seonghyun Park'
Kiyoung Seong'
Suojung Yang²
Rafael Gómer-Bombarelli Sungsoo Ahn't
KKIIST 2 MIT
(hyun26, kyseong98, sungsco.. ahn ahn (soojungy, rafagb) (rtagb)@mit.. @mit.edu
ABSTRACT
Molecular dynamics is crucial for understanding molecular systems, but its appli- cability often limited by the vast timescales of rare events like protein folding. Enhanced sampling techniques overcome this by accelerating the simulation along key reaction pathways, which are defined by collective variables (CVs). However, identifying effective CVs that capture the slow, macroscopic dynamics of a sys- tem remains a major bottleneck. This work proposes novel framework coined BIOEMU-CV that learns these essential CVs automatically from BioEmu, re- cently proposed foundation model for generating protein equilibrium samples. particular, re-puros BioEmu to learn time-lagged generation conditioned on the learned CV, i.e., predict the distribution of molecular states after a certain amount of time. This training process promotes the CV encode only the slow, long-term information while disregarding fast, random fluctuations. We validate our learned CV on fast-folding proteins with two key applications: (1) estimating free energy differences using on-the-fly probability enhanced sampling and (2) sampling transition paths with steered molecular dynamics. Our empirical study also serves as a new systematic and comprehensive benchmark for MLCVs on fast-folding proteins larger than Alanine Dipeptide.
INTRODUCTION
Many problems in biomolecules reduce to understanding the complex dynamics of molecular mo- tion and conformational changes, such as estimating drug-target binding affinities (De Vivo et al., 2016; Abel al., 2017) or the folding times of proteins (Piana et al., 2012; Spotte-Smith et al., 2022). Molecular dynamics (MD) simulation is one of the principal methods for studying molecu- lar motion, describing microscopic dynamics by integrating differential equations with femtosecond (10-15) time steps. However, events like protein folding often happen in a much larger timescale, from microseconds (10-6) to milliseconds (10-3) Due to this timescale gap, observing desired events in naive MD requires integrating over a computationally infeasible number of steps, which is considered unrealistic for most real-worde problems.
To overcome this timescale limitation, various enhanced sampling techniques have been stud- ied (Hénin al., 2022). Metadynamies (Barducci et al., 2011) applies biasing force the molec- ular systems to encourage transitions, while replica-exchange MD (Sugita & Okamoto, 1999) ex- changes configurations between parallel simulations different temperatures. Also, accelerated MD (Hamelberg et al., 2004) globally boosts the potential energy surface to overcome energy bar- riers. Their core idea is to add biasing forces throughout the simulation to guide exploration and transitions in the molecular state space, without breaking the equilibrium conditions. Importantly, these biasing forces are computed based on a wiw-iiensioonl representation, denoted as the col- lective variables (CVs). Therefore, CVs well encoding the slow degree of freedom will add biases to numerous seen CVs, resulting in exploration and transition to unseen and less visited states.
CCorrsponningg Author.

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Published as a conference paper at ICLR 2026
However, CVs have been mainly hand-crafted by domain expertise, e.g., selection of specific back- bone dihedral angles for Alenine Dipeptide, which may miss slow modes and has been limited to small systems. To resolve this issue, several works have considered machine-learned CVs (ML- CVs) from MD trajectory data. Supervised methods use ground-truth state definitions and pseudo- labels (Bonati al., 2020; Trizio & Parrinello, 2021), while self-supervised methods rely on time- lagged data to encode the dynamics information (Bonati et al., 2021; Wehmeyer & Noé, 2018; Hernández al., 2018). While prior works have shown promising results on small systems such as alanine dipeptide, they currently lack the ability to scale to larger systems such as proteins and lack a standardized, side-by-side systematic comparison.
In this work, we present simple yet efficient framework for learning collective variables (CVs) from the latent representation of molecular foundation model. Inspired by recent research ex- tracting condition representations from text-to-image diffusion models (Zhang et al., 2023; Mou al., 2024), we train an MICCV encoder to learn the latent representations in an existing molec- ular foundation model, BioEmu (Lewis et al., 2025). Building upon its capability of generating multiple protein conformations, we condition time-lagged data and use them as CVs for enhanced sampling techniques. Additionally, we benchmark prior MLCVs three fast-folding proteins for two downstream tasks by enhanced sampling simulations along with extensive qualitative analysis.
To summarize, contribution is follows:
We propose a framework for extracting collective variables from the time-lagged condition representations of frozen foundation model.
We extensively benchmark MLCVs with two downstream tasks for the slow degree of freedom: free energy difference estimation and transition path sampling for proteins in explicit water solvent simulations.
2 BACKGROUND
Molecular dynamics (MD). MD simulations model the time evolution of molecular systems through atomic coordinates and velocities. An illustrative MD is the underdamped Langevin dy- namics (Bussi & Parrinello, 2007) follows:
dz, v,dt, du, (U)()) dt yo,dt +
2 dw., m
m
where x, and it atomic positions and velocities, m the mass, U(ze) the potential energy, and (x,(), the force. The parameters 7, kg. T, and W, denote the friction coefficient, Boltz- mann constant, temperature, and Brownian motion, respectively. While MD simulations provide atomic-level insights into dynamic process, it remains limited by timescales. The high energy bar- riers between states makes rare events difficult observe such as transition paths, often requiring unrealistic long MD simulations (Valsson et al., 2016).
Enhanced sampling and collective variables (CVs). To overcome the timescale limitations of the standard MD simulations, enhanced sampling methods introduce biasing forces or potentials to accelerate transitions. Popular approaches include metadynamics (Barducei et al., 2011, MTD), well-tempered metadynamies (Barducci et al., 2008, WTMD), replica-exchange molecular dynam- ics (Hukushima Nemoto, 1996, REMD), and on on-the-fly probability enhanced sampling (Invernizzi & Parrinello, 2020, OPES). These methods typically rely low-dimensional descriptors known as collective variables (CVs), which serve as a biasing coordinate in the simulation (Bonati et al., 2023). Formally, the CVs, denoted by c, is represented as set of functions of atomic position
c(z) =
where d < 3N is the number of CVs. In this work, we fix the dimensionality one for simplic- ity and visibility. CVs are designed to capture the system's slow degree of freedom, often chosen based domain knowledge, such as specific backbone dihedral angles or inter-residue contact distances (Piana & Laio, 2007). However, handerafted CVs remain mostly limited to small sys- tems (Pietrucci & Laio, 2009; Noé & Clementi, 2017).
Machine-learned collective variables (MLCVs). Recent methods employ machine learning to automatically identify CVs beyond handcrafted features. Supervised approaches such as
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BioEmu
DAYAQWLKOH HPSSGRPPPS
Evoformer
Sequence
Single Rape
CVs
Free energy estimation
Score model
Mpez
Conditioning CVs encoded from
Transition path sampling
(a) Method overview
(b) Evaluation overview
Figure I: Overview of our framework and evaluation simulation. (Left) We train an encoder on top of the conditions of a frozen molecular foundation model to learn collective variables (CVs) for protein, highlighted in red dotted lines, on top of a frozen pre-trained BioEmu. (Right) Two down- stream tasks for the slow degree of freedom, free energy estimation and transition path sampling.
DeepLDA (Bonati et al., 2020) and DeepTDA (Trizio & Parrinello, 2021) learn CVs through discriminant analysis. However, they require predefined binary state labels, where one needs to specify a representative folded state and choose an RMSD threshold for classification. In con- trast, soff-supervised and time-lagged methods instead leverage dynamical information from tra- jectories. DeepTICA (Bonati et al., 2021) applies time-lagged independent component analy- sis (Molgedey Schuster, 1994, TICA) as a loss for encoded representations. The time-lagged autoencoder (Wehmeyer & Noé, 2018, TAE) and variational dynamics encoder (Hernández et al., 2018, VDE) reconstructs future configurations Zt+r from the present configuration 2t, deriving latent representations CVs using autoencoders (Rumelhart et al., 1985) and variational autoen- coders (Kingma & Welling, 2014), respectively. However, existing methods mostly focus on small systems such alanine dipeptide, and systematic comparisons across approaches are absent.
METHOD
Overview. We aim to learn an encoder that outputs a low-dimensional vector representing the slow degree of freedom in molecules, known as collective variables (CVs). Inspired by recent works on conditioning frozen foundation models (Zhang et al., 2023; Mou et al., 2024), we re-purpose the BioEmu model. As shown in Figure Ia, instead of using it for its original purpose of generating protein conformation ensemble, we add an encoder to extract its low dimensional representation to serve CV, which call BIOEMU-CV. This CV learns the slow dynamics by approximating the molecular dynamics (MD) propagator with conditional generative model, which generates a subsequent state from a current state and time lag similar to Hernández et al. (2018).
Task formulation. Given a protein configuration represented by atomic coordinates in x E Nx3 where N is the number of atoms, our goal to learn an encoder fe that maps the high-dimensional structure into a low-dimensional representation c = fa(x) E Rd with d << 3N. This representation, the CVs, should qualify three criteria for the use of enhanced samplings: (i) being low-dimensional, (ii) capturing the system's 's slow degree of freedom, and (iii) discriminating the folded and unfolded states in protein (Fu et al., 2024). We fit the first criteria by using a one-dimensional CV, and evaluate the meta-stable state discrimination with secondary structures which are highly correlated to the folded states. For the second and most important criterion, we evaluate MI.CVs with two downstream tasks requiring to encode the slow degree of freedom: (i) free energy estimation and (ii) transition path sampling, each by different enhanced sampling techniques.
Biomolecular Emulator (BioEmu). BioEmu (Lewis et al., 2025) generates the conformational en- semble at full-atom resolution unlike structure prediction models such as AlphaFold (Jumper et al., 2021), which return single low-energy conformation given protein sequence. We focus the capability to generate protein conformation ensemble, and re- re-purpose it for learning collective vari- ables (CVs). Formally, given amino acid sequence A [A1, A2, .2,...7 An) of length n, BioEmu
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DeapTICA
TAE
VDE
BIOEMU-CV
6F [4)mmo]]]
-10
230
500
750
1000
250
500
150
1000
250
750
1000
250
750
3000
[nc]
Time [ns]
Time [ns]
Time [ns]
PMF (elmel)
20-
10-
-1.5
-0.8
CV 0.0
0.0
-1.0
-0.5
0.0
0.5
1.0
-1.0
-0.5
0.0
0.5
1.0
-1.0
-0.5
0.0
0.5
1.0
CV
CV
CV
Figure 2: Free energy (top) and PMF (bottom) estimation from 1 ju8 OPES simulations for Chignolin. We average over four simulations. Green dotted lines indicate the reference value, and blue lines refer to the free energy difference during the OPES simulations. Solid lines refer to the mean, and shaded areas are the standard deviation. Deep shows negative values beyond -1 in PMF even when normalized, and falls short of accurately capturing the reference PMF
a sequence-conditioned denoising diffusion model go(x)) (4) to sample from the equilibrium distri- bution p(x[ To be specific, the protein sequence encoder of the BioEmu produces two represen- tations from the amino acid token with Evoformer (Jumper et al., 2021): the single representations h = { and the pair representations
{ { where i refer to the amino acid index. Based on these two representations, the score model ge generates a-carbon (Ca) coordinates and residue orientations for the protein backbone. Side chains are then reconstructed using the hpacker package (Visani al., 2024), followed by short molecular dynamics (MD) simulations for energy relaxation with OpenMM (Eastman et al., 2017).
Extracting CVs from foundation model. Recent advances in generative models demonstrate that additional condition encoders with lightweight adapters can be trained on top of unconditional gen- erative models for external guidance (Zhang al., 2023; Mou al., 2024). Inspired by this line of research, we propose framework for using low-dimensional encoder output as collective variables (CVs); an overview is shown in Figure 1. We train an encoder fe that maps a configuration æ at time t to a low-dimensional vector, i.e., C2 fo (2x) E IRd. Then, we fuse the encoded representation the single representation h using small MLP to preserve dimensionality to the score model and keep the adapter lightweight (Zhang et al., 2023). The conditioned representation /te = MLP(h, cr) and pair representation are passed to the score model to generate protein conformations.
Learning CVs from time-lagged generation. With this condition pathway in place, we encode CVs of the current conformation but guide the model to generate the time-lagged conformation Tt-r, i.e., the score model generates the time-lagged state 2447 from the CVs with time lag т. Intuitively, the CV c, compresses the information that is shared across I2 and Zi+r, i.c., the slow degree of freedom, while disregarding fast and randomly fluctuating information that is present in the current state v, but not in the time-lagged state r Note that our training objective shares the motivation with VDE (Hernández al., 201 8), but we use scalable diffusion model architecture and do not need the auto-correlation loss.
To keep the training lightweight, freeze parameters ó of BioEmu, and update the encoder and the conditioning MLP via the denoising score-matching objective (Song et al., 2020; Yim et al., 2021):
L(x,, Fetr, A) = E.-24(0.1 A.
V log Pajo Pooo
(2 (6) (1etr 1xt4:: Fr, A) go hr: 2)
(1)
where s is the diffusion time, P.io is the density of x given 2 2t, A, X, > 0 the time schedul- ing weights, and Is the BioEmu's 's score network. This time-lagged reconstruction forces o to capture the slow degree of freedom by incorporating future time-lagged conformation øt+r from the trajectory data, thereby producing CVs suitable for enhanced sampling.
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Table Quantitative results of μs OPES simulations for three fast-folding proteins in explicit water solvent. We report the reference free energy difference (Arrre) from the data, the average free energy difference (AF) from simulations, the absolute error between two energy values (AFrre AF), and the potential of mean force (PMF) MAE. Results are averaged over four simulations for Chignolin, and three simulations for Trp- and BBA. We mark not applicable (N/A) for CVs that fail at meta-stable state discrimination or show a different sign with the reference value.
Molecule
Method
F
AF
A ref
AFI (1)
PMF MAE (1)
Deep
-3.73
-2.02 3.65
1.71
+
TAE
-3.79
-1.26+ 3.69
2.53
3.15+2M.
Chignolin
VDE
-17.24
0.24 5.00
N/A
4.09
BIOEMU-CV
-3.71
-3.19 3.97
0.52
3.07 2.53
DeeP
3.70
6.53 7.31
2.73
8.94 +: 7.43
TAE
-1.45
8.74 1.65
N/A
9.32
Trp-cage
VDE
0.07
N/A
N/A
N/A 6.86 ::: 4.38
BIOEMU-CV
4.15
5.97 3.01
1.82
DeeA
2.76
13.95 13.28
11.19
10.51 + 5.85
TAE
-2.88
-5.46 4.42
N/A
9.97 :: 3.68
BBA
VDE
-2.74
N/A
N/A
N/A
BIOEMU-CV
2.77
9.99 5.43
7.22
8.34
EXPERIMENT RESULTS
Evaluation setup. We consider three fast-folding protein in explicit water solvent from Lindorff- Larsen et al. (2011); Chignolin, Trp-cage, and BBA. For more details protein data, refer to Appendix A. We quantitatively evaluate MLCVs with two downstream tasks that require encoding the slow degree of freedom: (i) free energy difference estimation, and (ii) transition path sampling. We use on-the-fly probability enhanced simulation (Invernizzi & Parrinello, 2020, OPES) and CV- steered MD simulation (Izrailev al., 1999; Fiorin al., 2013b, SMD) for each task, respectively. Furthermore, we extensively investigate the interpretability of CVs with respect to imput descriptors with the sensitivity analysis, and analyze meta- stable state discrimination with secondary structures known to be present in the folded states following Fu et al. (2024). For ablation experiment results regarding architecture components, please refer to Appendix
Baselines. We compare our method against self- supersud CV learning methods: Deep (Bon- ati al., 2021), time-lagged autoencoder (Wehmeyer & Noé, 2018, TAE), and variational dynamics encoder (Hernández et al., 2018, VDE). Since protein types and simulation configuration vary sig- nificantly by methods and lack systematic comparison, we train from scratch on identical data and time-lag with baselines using the ml colvar package (Bonati et al., 2023). We use pairwise C. distances for imputs to ensure rotation and translation invariance following prior works (Trizio Par- All MLCVs
rinello, 2021; Bonati al., 2021), and fix CVs dimensionality to the range [-1, on the full DESRES trajectory after training for simplicity and visibility, with the sign assigning the folded state to positive. For more details baselines, refer Appendix C.
normalized
4.1 FREE ENERGY DIFFERENCE ESTIMATION
We first quantify whether MLCVs encode the slow degree of freedom by estimating the free energy difference AF, with on-the-ffy -fly probability enhanced simulations in explicit water solvent.
On-the-fly probability enhanced simulations. We run four independent enhanced sampling (Invernizzi & Parrinello, 2020, OPES) simulations initialized from the folded state. OPES iteratively reconstructs the target probability along the CVs pre-defined interval, adding bias that continuously drives transitions between the folded and unfolded states. This enables the estimation of the folding free-energy difference and the potential of mean force (PMF).
on-the-fly probability
Evaluation criteria. Following Yang et al. (2024), we measure (i) the convergence of the estimated reaction free energy of folding (AF), and (ii) the quality of the potential of mean force (PMF).
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Table 2: Quantitative results of steered molecular dynamics on three fast-folding proteins in explicit water solvent. RMSD and THP are averaged over paths obtained from 16 SMD simula- tions, while max energy (Ers) is averaged over paths hitting the target meta-stable state. is the force constant, which is scaling factor of the harmonic bias potential used in SMD. Best results are highlighted in bold and second underline. We mark not applicable (N/A) for CVs that fail at state discrimination and trajectories not arriving at the target meta-stable state.
RMSD (L)
THP (t)
ETS (1) kJ/mol
Molecule
Method
k
Á
%
DeepTICA
10000
2.45 + 0.86
37.5
81102.41 122227
TAE
10000
1.95 0.77
43.8
-81914. 114.30
Chignolin
VDE
10000
2.08 0.56
43.8
-82026. 6.2.6....... 77.63
BIOEMU-CV
10000
1.20 +: 0.33
100.0
-82055.15 + 98.48
DeepTICA
20000
2.37 & 0.47
31.2
-63611
1,88 57.49
TAE
20000
2.75 0.35
0.0
N/A
Trp-cage
VDE
N/A
N/A
N/A
N/A
BIOEMU-CV
20000
2.31 0.52
31.2
-63787.51
31.23
DeepTICA
50000
2.67 10.37
18.8
-130418.55
477.68 N/A
TAE
50000
4.83
0.0
BBA
VDE
N/A
N/A
N/A
N/A
BIOEMU-CV
50000
2.05
93.8
-131315.59 = 116.23
Chigroln
Trp-cage
BBA
Figure 3: 3D Visualization of transition paths. The sampled folding pathways of Chignolin, Trp- cage, and BBA by steered MD with BIOEMU-CV. We visualize only the C. for simplicity.
We compute the two meta-stable state basins, folded and unfolded states, by dividing the CV range in half as in prior work. The reference values for each protein are computed from MLCVs of the full DESRES trajectory with the multi-state Bennett acceptance ratio analysis (Shirts & Chodera, 2008, MBAR). In short, CVs well encoding the slow degree of freedom are expected to have similar distributions between the μs OPES simulation and the long naive reference 100 μs DESRES simulation. Note that we exclude results on MLCVs that fail on the basic criterion of discriminating between the folded and unfolded states; more detail in Section 4.4. Since inadequate CVs produce non non-converged biases and misleading PMFs, OPES cannot reliably drive transition, and its PMFs are meaningless. Results are averaged over four runs for Chignolin and three runs for Trp- cage and BBA, with one outlier excluded from the original four following Yang et al. (2024). For more details on the simulation, evaluation, and outlier criterion, refer to Appendix C.
Results. In Table 1, we report the reference free energy difference Fre).. free energy difference averaged over simulations (AF), and the potential mean force (PMF) MAE. In Figure 2, we addi- tionally plot the free energy difference throughout the OPES simulations. For the full results, please refer to Appendix D. In the following. we interpret the results in both quantitative and qualitative aspects. While most MLCVs fairly converge for Chignolin and work for larger proteins, VDE fails to scale to large proteins. Additionally. TAE appears to converge for Trp-cage, but only because it samples the unfolded state. As shown in Figure 14, the folded state is barely visited, resulting

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DecpTICA
TAE
VDE
BIOEMU CV
Chipnoli
VC.1
TG.1
T61
121
Trp-oage
121
101 T51 153
BBA
Figure 4: Qualitative results transition path sampling. (Left) Transition paths from MLCV- steered MD projected onto TICA coordinates. The white star and circle each refer to the repre- sentative unfolded and folded state. The red convex hulls indicate the folded state regions based on RMSD cutoffs from the representative folded state with cut off 2, 2. and 2.5 Á for Chignolin, Trp-cage, and BBA, respectively. (Right) Diverse intermediate states for Chignolin transition paths using BIOEMU-CV steered MD, with white diamonds representing step 2,400 on TICA coordinates.
in convergence at an incorrect AF, with the wrong sign relative the reference value. Similarly, DeepTICA samples the folded state with high deviation even though the outlier was removed, re- sulting in fluctuation in the PMF We have clarified more interpretationns in detail in Appendix D.
4.2 TRANSITION PATH SAMPLING
We also evaluate the slow degree of freedom in CVs by sampling transition paths of the fast-folding proteins, with CV-steered molecular dynamics simulations in explicit water solvent.
Steered molecular dynamics. We sample transition paths with steered molecular dynam- ics (Izrailev et al., 1999; Fiorin et al., 2013b, SMD). SMD is an enhanced sampling technique that steers the protein conformation towards a pre-defined target state with a time-dependent biasing force. CVs that well encode the slow degree of freedom would produce low-energy transition paths when used with SMD. For each protein, we do 16 NVT simulations for 500 ps using the Langevin Integrator with 1 fs time step. For more detail about SMD, refer to Appendix C.
Evaluation criteria. To evaluate the transition paths from SMD simulations, we first define the target state the local minimum on the potential energy surface corresponding the folded state. We then evaluate the transition paths using three metrics from Seong et al. (2025): (i) C.-RMSD) between the final state of path and the target state, (ii) the target hit percentage (THP) of sampled paths, and (iii) the transition state energy (ETs). i.e., the maximum energy of states of a transition path that hits the target meta-stable state. For THP, a transition path considered hit the target meta-stable state if its final state is within 2 Á C. -MMDD from the target state, regarding the state al. (2011). Again, for the transition path sampling task, any MLCVs
definition in Sidorff--Lrsee that failed to discriminate between the folded and unfolded states of the protein were excluded.
Results. In Table BIOEMU-CY CV shows the best results in hitting the target meta-stable states while achieving low transition state energies. Additionally in Figure 3, we visualize the C. atoms in the folding process under BIOEMU-CV steered MD for qualitative assessment. For the visualization of baseline CV-steered MD, refer to Appendix D. In Figure 4, we also visualize the sampled transition paths of three fast-folding proteins from SMD simulations, by projecting them onto time-lagged independent component analysis (Molgedey & Schuster, 1994, TICA) made from the full DESRES trajectory. We find that transition paths from our MLCVs show better target reaching and follow the region with low PMF value defined two lame-l independent components.
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DeepTICA
TAB
BIDEMU-CV
3.0
2-0
3:5
2-0
3.7
2.8
133 033 034
0.08 031 0.14
3.30 3.0 624
155 633
034
13
Trp
8:17
2:11
0033 0336
0.028
0002 0725
1113 0:03 3009
0103 RER
15-39
3:24
13-32
7-23
9:31
12:30
BBBA
15-30
Figure 5: MLCV sensitivity to -wiwe distances. We plot the top C, distances with the highest sensitivity for each MLCV, where the and y axes each denote the residue index for input distances and the corresponding sensitivity value. For each sensitivity plot, we visualize the top sensitive distances in the unfolded and folded states, with colors highlighted in the sensitivity plot.
4.3 INTERPRETABILITY OF CVs
Beyond enhanced sampling tasks, we further assess the physical interpretability of MICVs.
Sensitivity analysis. We evaluate the interpretability of MLCVs by examining how each MLCV changes to their input descriptors, i.e., the sensitivity to the C.-wise distance (Bonati et al., 2020; Trizio & Parrinello, 2021). To be specific, we use the sensit the ml col colvar library (Bonati et al., 2023), which computes the sensitivity by the gradients each MLCV with respect every input feature. We aggregated the values with the mean of the absolute values, and visualize the top- most sensitive distances in the folded state and unfolded state.
function from
Results. As shown in Figure 5, BIOEMU-CV consistently assigns high sensitivity distances that strongly discriminate the folded and unfolded state, typically long-range contacts spanning the secondary structure for folding. For example in Chignolin, BIOEMU-CV is most sensitive to the distance TYP1- TYR10 and also sensitive to ASP3 TRY8, where a hydrogen bond is observed at folding (Yang et al., 2024). In contrast, TICA and VDE often emphasize distances that provide weaker structural discrimination, e.g.. DeepTICA is sensitive to the distances of ASP3 and TYR1-PRO4 which does not differ much between the folded and unfolded state. Overall, these re- sults indicate that BIOEMU-CY not only captures the slow dynamical modes required for enhanced sampling, but also learn physically meaningful structural relationships.
4.4 META-STABLE STATE DISCRIMINATION ANALYSIS
Finally, we extensively analyze whether MLCVs clearly discriminate folded and unfolded states, following the criteria of Fu et al. (2024). To be specific, we test whether the folded and unfolded state ensemble occupy distinct ranges of MLCVs and report their distribution statistics across proteins. In case of Chignolin, and native hydrogen bond numbers. We also probe sensitivity to structural motifs by analyzing the secondary structure elements involved in the folded state, e.g., a-helix and 3-sheet.
cross- cross-validee validate against standard descriptors, e.g., the committor function
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Table 3: State discrimination analysis of MLCVs. We report the average MLCVs for the folded and unfolded states obtained from the full DESRES trajectory. VDE fails to separate the folded and unfolded states on Trp-cage and BBA, both showing positive ranges.
Chignolin
Trp-cage
BBA
Method
Folded
Unfolded
Folded
Unfolded
Folded
Unfolded
DeAA
0.85 0.06
-0.49
0.70
-0.74
0.75 0.07
-0.51 0.00
TAE
0.78 0.07
.0.82
0.04
-0.95 = 0.02
0.00
-0.90
VDE
0.84 0.07
-0.74 0.13
1.00 0.00
0.87 +: 0.13
1.00 0.00
1.00 +
BIOEMU-CV
0.82
-0.0s
0.96
.0.90
0.04
-0093
Folded state
Unfolded state
DeepTICA
TAE
VDE
BIOEMU-CV
Chignolin
V
05
Trp
1C1
BBA
-10
Figure 6: (Left) Visualizations of the folded and unfolded states for three protein. (Right) TICA projections of the full DESRES trajectory, colored by each MLCVs. The folded and unfolded states are marked by white circle and a white star, respectively. All MLCVs are normalized to the range [-1, 1], with signs flipped such that folded state corresponds + 1 for consistency and visibility. As the protein size increases, prior methods struggle with state discrimination, for instance, VDE.
Meta-stable state discrimination. First, we verify whether the CVs truly distinguish the folded and unfolded states of proteins. Figure 6, we color each TICA coordinates with its MLCVs. We time lag of r 1000 for BBA and 7 10 otherwise for TICA plots. While most methods distinguish the folded and unfolded states, prior works tend to fail at BBA. In Table 3, we report the average MI.CV for the folded and unfolded states gathered from the full DESRES trajectory. Noticeably, VDE shows similar values for Trp-cage and BBA. We plot the detailed distribution of MLCVs for the folded and unfolded states in Appendix D. where VDE fails at meta-stable state discrimination showing almost identical results between MLCVs of the folded and unfolded states.
Chignolin analysis. We also analyze CVs for Chignolin with well-known descriptors, the committor function. The commit- tor function provides a quantitative measure of progress along the folding pathway on scale from [0, 1). We use the commit- tor function from Kang et al. (2024), estimated in data-driven manner. In Table 4, we report the Pearson correlation between the committor function and MLCVs. DeepTICA shows rel- atively weak correlation with the committor values, whereas other methods demonstrate stronger alignment. For more de- tails Chignolin descriptors, refer to Appendix C.
Table 4: Pearson correlation be- tween MICVs and the Chignolin committor function.
Method
Pearson corr.
DeepTICA
0.682
TAE
0.744
VDE
0.778
B10EMU-CV
0.748
Secondary structure analysis. Finally, we analyze the correlation between CVs and the sec- ondary structure of proteins. As seen in Table secondary structures mostly observed in the

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Published as a conference paper at ICLR 2026
DeepTICA
TAE
VDE
BIOEMU-CV
LY98
ARG10
f-sheet
ARG10 f-sheet
GUU17
GLU17
TiepTTCA
R10EMU-CV
-0.59
1,00
-0.15
-0.01
1,00
1.00
1.00
1,00
Figure 7: Secondary structure analysis on BBA. (Top) Folded-state visualization of the BBA protein, with a-helix and ß-sheet highlighted orange and green, respectively. We also plot the MLCVs distribution for the residues included in the secondary structures, for residues showing specific secondary structures in the folded state. Letters C, H, and each correspond to coil (irregular elements), a-helix, and 8-sheet secondary structures. TAE and VDE fail to assign distinct values to helix and sheet structures. (Bottom) Visualizations and MLCVs on states the DESRES trajectory having partial secondary structures. Residues colored according to the DSSP value. DeepTICA and BIOEMU- CV align with the secondary structures.
folded state clearly distinguished from the unfolded states (Lindorff-Larsen al., 2011), therefore CVs should capture their presence to describe the folding dynamics (Ahalawat & Mondal, 2018).
We compute the residue-level secondary structure using the dictionary of secondary structures in proteins (Kabsch & Sander, 1983; McGibbon et al., 2015, DSSP), which classi- fies structures based on hydrogen-bond patterns. In Figure 7, we plot the MLCV distribution against the known secondary structures BBA. While the folded states BBA contain one a-helix and two ß-sheets (Lindorff-Larsen et al., 2011), TAE and VDE encode nearly identical CVs regardless of the secondary structures in contrast to DeepTICA and BIOEMU- CV successfully separating them.
Table 5: Average fraction of residues forming the secondary structure in unfolded states. Un- folded refers the fraction of residues regardless of type.
Protein
a-helix
f-sheet
Unfolded
Chignolin Trp-cuge
0.00
0.00
0.00
0.02
0.01
0.03
BBA
5 CONCLUSION
We present BIoEMU-CV, lightweight framework that learns collective variables (CVs) from time- lagged conditioning signals on frozen BioEmu foundation model. Given the current structure, we derive low-dimensional CV and inject it into BioEmu's single representation, where only this conditioning path trained with a denoising score-matching objective, leaving the backbone un- touched. We systematically evaluate MLCVs three fast-folding proteins for two downstream tasks, estimating free-energy differences using OPES simulations and transition-patt sampling using CV-steered MD. Our experiments show that BIOEMU-CT CV successfully identifies important macro- scopic movements related to the slow degree of freedom, and our qualitative evaluation of state discrimination corroborates this.
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ETHICS STATEMENT
Our work introduces a method to accelerate the study of protein dynamics using the generative model. This work aims to advance scientific understanding of bimolecular mechanisms for disease analysis and drug discovery. We believe the potential for the misuse of this research is low.
REPRODUCIBILLTY STATEMENT
All protein trajectory data used in this study publicly available from the D. E. Shaw Research (DESRES) database. The detailed description of the dataset can be found in Lindorff-Larse et al. (2011). We provided brief explanation of the dataset in Appendix A.2. Implementation details for our method and all baselines, including model and training hyperparameters, are specified in Ap- pendix C.2. Furthermore, the experimental setups for our downstream evaluation tasks are provided in the appendix; Appendix C.4 contains the configurations for the on-the-fly fly probability enhanced sampling (OPES) simulations, and Appendix C.6 outlines the setup for the steered molecular dy- namics (SMD) simulations. For reproduction, we provide our code for training & simulation, and simulation environment set up.
ACKNOWLEDGMENTS
This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Ministry of Science and ICT(MSIT) (No. 2S-2202--NR721880
Korea Health Industry Develop- ment Institute(KHIDD) grant funded by the Ministry of Health & Welfare(MOHH) (No. N0425208, Developing a Highly Multimodal (Drug, Protein, Gene, Cell Imaging, Literature) Foundation Model for ADMET Property Prediction), the Institute for Information & communications Technology Plan- ning & Evaluation(IITP)gram funded by the Korea govermeet(MSIT) (RS- R8S-2019-11100755 Artifi- cial Intelligence Graduate School Program(KAIST),, and the Institute of Information & Commu- nications Technology Planning & (Valuation(IITP) grant funded by the Korea govermeen((MSIT) (RS-2025-02304967,, AI Star Fellowship(KAISTT)
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A DATA DETAILS
A. PROTEIN DATA
Proteins are sequence of amino acid building blocks, each represented by one letter. Below, we provide statistics on the proteins we used in this work. Protein size ranges from 10 to 35 residues, 166 504 atoms. C The PDB ID the Table 6 refers to the discovered experimental structures in the PDB with the smallest error. In case of Chignolin, it is closest to the NMR structure of CLN025 reported by Honda et al. (2008), Trp-cage corresponds to the K8A mutant the thermostable Trp- cage variant TC10b in Barua et al. (2008), and BBA, i.c., short for beta-beta- corresponds to the FDS-EY peptide in Sarisky Mayo (2001).
Table 6: Details on three proteins used in this work, selected among the DESRES fast folding proteins.
Protein
PDB
Residues
# of Atoms
of CA pairs
Sequence
Chignolin
CLN025
10
166
YYDPETGIWY
Trp-cuge
2JOF
20
272
190
DATAOWLKDEHHSSSGREPSS LADDDDPKKATEEEMTTSSAAAAARR XKEKGLE
28
A.2 DESRES TRAJECTORY DATASET
Lindorff-Larsen et al. (2011) provides twelve fast-folding proteins. Among them, we chose three proteins to test MLCVs. For proteins given with multiple simulations, we sample from the longest length simulation to use as the data. other words, we use the simulation of length 223 μas for the BBA protein. In Table 7, denote the simulation time, average folding time, simulation tem- perature, and the cubic box size of the simulations. Since DESRES simulations are recorded in 0.2 picoseconds intervals and reach millions of frames, chose randomly sample 50,000 frames as in Lewis et al. (2025).
Table 7: Simulation details of three DESRES fast-folding proteins.
Protein
Simulation time (us)
Avg. folding time (us)
Temperature (K)
Cubic box (A)
Chignolin
106
0.6
340
40
Trp-cage
208
14
290
BBA
223, 102
2.8
325
47
A.3 TIME-LAGGED INDEPENDENT COMPONENT ANALYSIS
Time-lagged independent component analysis (Molgedey & Schuster, 1994, TICA) is a linear trans- formation method commonly used for dimensionality reduction, first used for molecular dynamics in Naritomi & Fuchigami (2011). In short, it maps the given data to the slow process for given time-lag r, by finding the coordinates of maximal auto correlation between time-lagged data pairs. Therefore, TICA, combined with a long MD trajectory, will likely capture the slow degree of free- dom well. In this work, we use the TICA model in pyemma (Scherer et al., 2015). All TICA plots in the paper, e.g., Figure 4 and Figure 6, are made with the full DESRES trajectory with a log norm applicd. We use Ca pairwise distances for the input descriptors, and apply the switching function to obtain the contact st in the case of Chignolin follows:
(Faj/ro)"
8ig
(m
where Tay refers to the distances between C, atoms i and j. 80mm n 6, and m 12. Intuitively, the contacts sij are a continuous version of the coordinate numbers.
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B ABLATION EXPERIMENTS RESULTS
In this section, we present various ablation experiments on BIOEMU-CV.
B.1 TIME-LAGGED CONDITIONING AND FIXED BIOEMU WEIGHTS
Here, we conduct ablation experiment on not using time-lagged conditions and unfreezing BioEmu's parameters, with OPES simulations and Steered MD.
Table 8: Ablation experiments for the components of BIOEMU-CV in OPES and steered MD simulations. Time-lag indicates whether the model is trained to generated time-lagged target conformation, and freezing indicates whether BioEmu's 's parameters are kept fixed during the training of the encoder. Our current design choice shows high performance for SMD results.
Components
OPES simulations
Steered MI)
Time-lag
Freezing
A
AF
AF (F)
PMF MAE (1)
RMSD (U)
THP (t)
Eys (1)
Á
%
kJ/mol
-3.71
33,19
0.52
3.07
=,30
100.0
-82055.13
/
-3.68
+32
2,10
+.4
1.57 o.36
81.3
-82084.68 62,86
-3.25
1.22
3,53
1631
100.0
-82076.42
Time-lagged conditioning. We input conformation 2; the MLCV encoder, and condition the BioEmu to generate instead of using time-lagged data Te+r. Formally, are testing the denois- ing score-matching objective modified from Equation (1) as follows:
st (5) [o] sn, A) go(s, h4, 2) 1)]
L(x,, A) [0.11
A
V VogPP40
In Table 8, one see that time-lagged conditioning results in better performance for both down- stream tasks, i.e. OPES and steered MD simulations. Intuitively, time-lagged data will inject dy- namic information into the MLCVs, resulting enrich representations.
Unfrozen BioEmu weights. We also test whether unfreezing the BioEmu parameters would im- prove performance, while B1oEMU-CV only trains the parameters of the MLCV encoder. In Ta- ble 8, MLCV trained with a frozen BioEmu results in a lower RMSD in SMD and better OPES results. Since the performance is slightly better in unfrozen cases, keeping the lightweight training scheme is reasonable.
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B.2 ENCODER SIZES AND PLACEMENT
Table 9: Quantitative results steered MD for different encoder sizes. The performance remains
largely unchanged across the encoder size.
RMSD (1)
THP (1)
Ers (4) kJ kJ/mol
Param.
Repr.
Â
%
48K
single
1.20 0.33
100.0
-82055.15
98.48
1.27M
single
1.30
100.0
-82071.
100.08
196K
single
1.41 0.3.2
93.8
-82049, 40 i 98.52
48K
pair
1.79 0.45
56.3
-82088.33 76.61
48K
single, pair
1.66 0.56
68.8
-82086.6 61 74.80
TIC
TIC
TIC
Figure 8: Qualitative results of steered MD for different encoder sizes. From left to right, each visualizes the paths from the steered MD from the encoder with 48K, 196K, and 1.27M parameters.
Encoder size. We test 48K, 196K, 1.27M parameters with layers {2, 4, 8} and hidden dimension {100, 200, 400) for Chignolin, where the main paper encoder corresponds the 48K parameter setting. All MICVs were mixed with C. RMSD CVs at a 5:5 ratio. In Figure 8 and Table 9, per- formance remains largely unchanged across the encoder size. Since the encoder is inferred millions of times during the OPES simulation, keeping relatively smaller size would be practical.
Conditioning placement. Additionally, we test whether on how selecting the conditioning repre- sentation affects on the performance. While BIOEMU-CV conditions the single representation as h4 = MLP (h, ct). we additionally test conditioning the pair representation, i.c. 2, = MLP(2, c.) and both the single and pair representation. In Table 9, RMSD and THP both fall behind the case of only conditioning the single representation, while the energy shows little improvement.
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B.3 STEERED MD WITHOUT MIXING CVs
Table 10: Ablation experiments of steered molecular dynamics on three fast-folding proteins in explicit water solvent, without C.-RMSD CVs. We mark not applicable (N/A) for CVs that fail at state discrimination and trajectories not arriving at the target meta-stable state.
RMSD (1)
THP (1)
Ers (L) kJ/mo
Molecule
k
Method
A
DeepTICA
7.24 1.49
0.0
N/A
TAE
5.72
6.2
-81951.53
1000
VDE
N/A
N/A
N/A
BIOEMU-CV
7.82
0.0
N/A
Chignolin
DeepTICA
7.01 1.71
0.0
N/A
TAE
6.39 +: 1.74
0.0
N/A
2000
VDE
N/A
N/A
N/A
BIOEMU-CV
6.09 2.21
6.2
-82023.05
DeepTICA
2.23
0.0
N/A
TAE
8.62 + 3.25
0.0
N/A
2000
VDE
N/A
N/A
N/A
BIOEMU-CV
12.17
0.0
N/A
Trp-cage
DeepTICA
10.78 1.15
0.0
N/A
TAE
7.22 + 1.71
0.0
N/A
5000
VDE
N/A
N/A
N/A
BIOEMU-CV
7.14
0.0
N/A
DeepTICA
7.39 22771
0.0
N/A
TAE
9.87
0.0
N/A
50000
VDE
N/A
N/A
N/A
BIOEMU-CV
6,03 2.56
0.0
N/A
BBA
DeepTICA
N/A
N/A
N/A
TAE
10.20 1.59
0.0
N/A
100000
VDE
N/A
N/A
N/A
BIOEMU-CV
6.64 1.95
0.0
N/A
Steered MD without C.-RMSD CVs. Here, report the performance of steered MD using MLCVs without C. RMSD. In Table 10, MLCV steered MD mostly fails to reach the target. The force constant & was to the maximum value with simulations not exploding, resulting in different k values compared to Table 2. Due to this, we have incorporated C. RMSD for all MLCVs in Table 2.
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C SIMULATION AND EVALUATION DETAILS
C.I QUALITATIVE VERIFICATION
CLN025 descriptors. CLN025 known to form several hydrogen bonds at the folded state (Yang et al., 2024). The criteria for hydrogen bonds are (i) the donor-accepton distance being smaller than 0.35 um, and (ii) the angle formed by the donor, acceptor, and hydrogen being bigger than 110%. The donor acceptor atom list is follows:
1. TYRI N, TYRIO OTI
2. TYRI N, TYRIO OXT
3. ASP3 N, TRY8 O
4. THR6 OGI, ASP3
5. THR6 N, ASP3 ODI
6. THR6 ASP3 OD2
7. GLY7 N, ASP3 O
8. TYRI0 N, TYR1 O
The committor function g(x) is the probability that trajectory initiated from a configuration x reaches the folded state before the unfolded state A. is the solution to the wark Kolmogorov equation with the boundary conditions g(x) 0 for E A and g(x) for x E B. We use the committor function from Kang et al. (2024) to evaluate its correlation with MLCVs. In their approach, solving the Kolmogorov equation is reformulated minimizing a variational functional. To this end, they parameterize the committor function as neural network and train using self-consistent iterative procedure optimize the functional.
Committor function.
14
+15
-10
Figure 9: TICA coordinates colored with committor values.
DeepTICA
TAE
VDE
BIOEMU-CV
Committor
Caredax
Bond Numbers
Oxe Narze
Dund Nartbrr
Temd Number
Figure 10: Correlation known descriptors for Chignolin. (Top) Scatter plot of correlation to the committor function. (Bottom) Violin plot of correlation to the number of hydrogen bonds.
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Secondary structure. Protein secondary structures are local spatial structures made from the back- bone excluding the side chain, key structures observed in the folded states. The two most common structures the a-helix and B-sheet shown in Figure i..., spiral coil-like structure and flattened zig-zag-shaped structure, respectively. Secondary structures are formally defined by the pattern of hydrogen bonds between the hydrogen atoms in the amino part and the oxygen atoms in the car- boxyl. In this work, we use the dictionary of secondary structures proteins (Kabsch & Sander, 1983, DSSP) for the definition of secondary structures, implemented in the MDtraj library (MeGib- bon et al., 2015). Note that secondary structures are assigned for each residue, and three more consecutive residues with the same hydrogen bond are usually considered a full secondary structure. For proteins simulated in Lindorff-Larse unfolded state as stated Table 5. Additionally, in Table 11, we list the percentage of secondary structures throughout the whole DESRES trajectory for each residue and protein. Thrre classes of DSSP: C, E, and H each correspond to irregular elements, B-sheets, and a-helix. While DDSP provides a detailed classification with eight classes, selected the simplified one for this work.
al. (2011), secondary structures are rarely observed in
Table 11: DSSP class percentage of each residue in Chignolin, Trp-cage, and BBA.
DSSP
1
3
5
7
9
C
100.0
25.5
53.8
99.2
98.6
98.4
98.5
52.7
24.7
100.0
E
0.0
74.5
46.2
0.0
0.2
0.1
0.1
46.3
74.6
0.0
H
0.0
0.0
0.0
0.8
1.2
1.5
1.5
1.0
0.6
0.0
Trp-cage
0
2
3
5
8
9
C
100.0
85.7
75.1
70.9
67.1
67.8
72.3
78.2
88.8
97.7
0.0
0.3
1.4
1.2
3.0
4.0
2.7
1.3
0.5
0.1
H
0.0
14.0
23.6
27.9
29.8
28.3
25.0
20.5
10.7
2.2
Trp-cage
10
11
12
13
14
15
16
17
18
19
C
83.6
80.9
75.7
80.1
95.6
94.6
100.0
100.0
99.8
100.0
E
1.7
2.1
4.6
2.4
0.6
5.4
0.0
0.0
0.2
0.0
14.7
17.0
19.7
17.5
3.8
0.0
0.0
0.0
0.0
0.0
BBA
0
2
3
4
5
6
7
9
C
100.0
96.4
79.1
75.5
68.1
64.6
70.1
89.2
93.7
73.9
E
0.0
3.0
9.5
10.7
16.0
21.0
23.1
5.1
1.3
20.2
H
0.0
0.6
11.4
13.8
15.9
14.4
6.8
5.6
5.0
5.9
BBA
10
12
14
16
17
19
C
70.8
75.5
91.0
94.6
71.6
67.5
67.3
67.3
67.4
67.7
E
23.8
19.4
5.9
3.8
3.0
4.6
4.3
2.9
2.7
2.6
H
5.5
5.1
3.2
1.5
25.4
27.9
28.4
29.8
30.0
29.7
BBA
20
21
22
23
24
25
26
27
C
61.2
61.5
65.6
71.2
83.6
94.0
98.5
100.0
E
4.6
5.6
4.1
2.4
4.6
2.3
0.6
0.0
H
34.2
32.9
30.2
26.4
11.8
3.7
0.9
0.0
C.2 BASELINE DETAILS
We test three self- supervised time-lagged MILV baselines: DeepTICA (Bonati et al., 2021), TAE (Wehmeyer & Noé, 2018), and VDE (Hernández et al., 2018). Since simulation configurations vary each paper, we retrain all models with the same data using the ml cllolvar library (Bonati et al., 2023). All models have the following identical configurations. We use neural network size of [45, 100, 100, 1] with tanh as the activation function, and dropout of 0.5. We split the dataset into 80% for training and 20% for validation. Models, including ours, epochs, with early stopping applied with a minimum delta 0.1 and patience of epochs. Unless mentioned, follow the basic configuration of the m col varv (Bonati al., 2023).
trained for maximum of 1000
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C.3 SIMPLE BASELINES
Experiment setup. Additionally, we show that simple baselines, e.g., PCA and TICA, on C. -wise distance fail for Trp-cage. We the first principal component and the first time-lagged principal component as CVs. All other details are identical; the training data is for the baseline and BIOEMU- CV, normalization to the range [-1, over the whole DESRES trajectory data.
(a) PCA-CVs
(b) TICA-CVs
Figure 11: Simple method CVs on TICA projections of the full DESRES trajectory. PCA-CVs fails discriminate the folded and unfolded state, while TICA-CVs obviously shows correlation with the TICA using the full DESRES trajectory.
Qualitative results. Figure 11, we color TICA plot with the CVs. Since the axes were computed with TICA on the full DESRES dataset, TICA-CVs show high correlation with the axis. Nonethe- less, PCA-CVs show meaningless values in Trp-cage compared to MLCVs in Figure 6, failing to discriminate between the folded and unfolded state.
PCA-CVs
TICA-CVs
RMSD (L)
3.78 0.33
2.57 = 1.03
THP (1)
0.0 N/A
25.0
Ers (L)
-63660.34
T 1
T
(a) PCA-CVs
(b) TICA-CVs
(c) Stecred MD with TICA-CVs
Figure 12: Visualization of transition paths and quantitative results of steered MD. PCA-CVs fails to reach the target state, where TICA-CVs sometimes reach the target state with a low energy.
Steered MD results. For steered MD, identically mix with the C. RMSD CVs in ratio of 5:5, as for our baselines and BIOEMU-CV. In Figure 12, PCA-CVs fail to reach the target state, while TICA-CVs often reach the target state with low energy. However, its THP is low compared to baselines, failing to find meaningful transition pathways.
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C.4 OPES SIMULATION DETAILS
Simulation settings. OPES simulations for all proteins were performed with GROMACS 2024.3 (Abraham et al., 2015) patched with PLUMED 2.10 (Tribello et al., 2014), on top of Docker containers. Proteins were solvated in a cubic water with the same size as the reference simulation data, and each neutralized using sodium or chloride ions. The protein molecule was parameterized by the CHARMM27 force field (Piana et al., 201 1). i.e., CHARMM22 plus CMAP backbone correc- tion, and the modified TIP3P water model compatible with the CHARMM force field (MacKerell Jr et al., 1998), analogously to the reference simulation data (Lindorff-Larr tions were all performed in the NVT ensemble, Initial states were selected from folded states among the original DESRES trajectory, where the folded state was identified with native contacts and sec- ondary structures. Afterward, the state was equilibrated through short NVT and NPT simulations, each of length 50 and 500 picoseconds, respectively. Temperatures were controlled with the veloc- ity rescaling thermostat (v-rescale) (Bussi et al., 2007). Equations of motion were integrated with time step of femtoseconds with the leap-frog algorithm (Hockney et al., 1974). Additionally, the LINCS algorithm (Hess et al., 1997) was used to constrain all bonds involving the hydrogen bonds. All simulations were run on a single GPU of RTX 3090 or RTX 4090, with four to nine days depending on the protein size. Approximately 8,000 GPU hours were used for a single evaluation.
et al., 2011). Simula-
OPES configurations. We use configurations as in Table 12 for PLUMED, differing only in tem- peratures. A PACE of 500 steps is applied, i.e., 1 picoseconds. We use the same SIGMA value 0.05 and BARRIER value 30 for all systems. Temperatures are identical the reference simulation. The first 100 ns are discarded as equilibration time with 50 ns window unit time steps for Figures 2 and 14.
Table 12: OPES Simulation details of three DESRES fosding proteins.
Protein
PACE
SIGMA
BARRIER (kJ/mol)
Temperature (K)
Chignolin
500
0.05
30
340
Trp-cage (TC10b)
500
0.05
30
290
BBA
500
0.05
30
325
Evaluation metrics. We evaluate the learned collective variables (CVs) using two complementary metries from Yang et al. (2024): the free energy difference AF and the mean absolute eтror (MAE) of the potential of mean force (PMF). The free energy difference AF quantifies the stability gap between the folded and unfolded states. It is computed by integrating the PMF A(s) for CVs over the corresponding metastable basins,
exp( (((3))))) ds
AF -knnToog log T
ds
where kn is the Boltzmann constant and T is the temperature. A lower AF error indicates that the CV preserves the free energy difference between metastable states more accurately. For the folded and unfolded basins, we divided the reference CVs range to half and use them for each one.
In addition, we use the mean absolute error (MAE) of the PMF to evaluate the agreement between the biased and reference free-energy landscapes. PMF, The MAE is defined as Attres ds
MAE(A, A Ass) A
(3)
[[(Are((s) < AAtres) ds
where A(s) and (st(() are the PMFs from enhanced sampling and a long unbiased trajectory, respectively, and T[-] is an indicator function restricting the comparison to regions with reference free energy below a threshold Athres = 25 kJ/mol. This metric captures deviations in both metastable basins and transition regions.
Outlier simulation exclusion. As discussed Yang et al. (2024), enhanced sampling simulations driven by CVs may often get trapped in a local minima, leading to outlier simulation results. To address this issue, we follow the standard practice of computing the metrics after removing a single outlier run. Specifically, among the four simulations, free energy difference, i.c., the run whose value deviates the most from the mean, and exclude it. Afterwards, the metrics re-computed using the remaining three runs.
identify the outlier based on the final
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C.5 LONGER SIMULATION RESULTS
Here, we report the results of longer OPES simulations. To be specific, we report 9829 ns ~ 9.8 Srf length simulation for Trp-cage using Deep computed four RTX 3090 GPUs for month.
Table 13:
Quantitative results of long OPES simulation on Trp-cage with DICA MLCVs.
Time horizon
A
AF
Frrff
AF (4)
PMF MAE (L)
uss
3.70
6.53
7731
2.73
8.94 7.43
9.8 ps
-3.36
2.76
7.60
7.64 + 3.81
30
20
AF [kj/ml]]
PMF [k/mal]
20
10
0
10
-10
0
2000
4000
6000 Time [ns]
8000
-1.0
-0.5
0.0
0.5
1.0
CV
Figure 13: Free energy (left) and PMF (right) estimation from 9.8 μ. OPES simulations for Trp-cage with TICA MLCVs. Green dotted lines indicated the reference value, and blue lines refer to the free energy difference during the OPES simulations. Solid line refer to the mean, and shaded areas are standard deviation.
As seen in Table 13 and Figure 13, simulations with approximately ten times longer results do not fully converge and still exhibit uncertainty. While the folded state is sampled many times, the unfolded states not sampled properly, resulting in gap in the negative range of CVs in the PMF plot. Overall, longer OPES evaluations do not provide more meaningful insights.
C.6 STEERED MD SIMULATION DETAILS
Steered MD (Izrailev et al., 1999; Fiorin al., 2013b, SMD) is an enhanced sampling method for sampling transition paths. It drives the state toward the target meta-stable state along the time- dependent reference CV using an additional harmonic potential. This biasing potential of SMD
defined as
initial
Uzx,t) =
--r initial
(4)
where & the force constant, the molecular configuration, t is the current step, the total number of steps, and initial carget are the CV values at the respective meta-stable states. The reference CV starts the initial CV cinitial and ends the target CV Jarget with constant rate (carrget cinitia) I/T. The bias potential (ar, L) restrains the current state to follow the reference states. To hit the target meta-stable states better, in our experiments, we combine the MI.CVs fo(x) with (Kabsch aligned) CMMRMSD CV c(x) fa(z) RMSD(2,, Trarget, following the technique supported in Fiorin et al. (2013a).
We perform SMD simulations with the OpenMM software package (Eastman et al., 2023) to gener- ate transition pathways. We use the CHARMM36 force field (Best et al., 2012) for the fast-folding proteins and the modified TIP3P model (Jorgensen et al., 1983) for water molecules. We handle long-range electrostatics via the Particle Mesh Fwald (PME) method (Ewald, 1921) with a 0.95 nm cutoff. Constraining all bonds involving hydrogen atoms allow for fs integration timestep. We run the simulations in the canonical (NVT) ensemble at 340 K. A Langevin integrator with a ps friction coefficient is used for the 500 ps NVT equilibration. Finally, since the CV depends only on the C. atom coordinates, we apply the biasing force, - V. V (x, exclusively to them through the OpenMM external force class.
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D ADDITIONAL RESULTS
D.1 OPES SIMULATION RESULTS
DeepTICA
TAE
VDE
Ours
Chignolin
-10
1800
1030
Time (ns)
Time (rs]
Time inc]
Time Indl
-1.8
-0.38
-05
80
-10
0.5
1.0
-30
00
03
Trp ca-cage
1056
530
750
10
CV
01
0V
BBA
250
900
750
1966
350
500
753
1000
250
515
750
105c
250
500
750
1050
1.0
-0.
0..
-2.
Figure 14: Free energy difference (top) and PMF (bottom) for three proteins from ps OPES simulation. Green dotted lines indicate the reference value computed by CVs along the full DESRES trajectory, while blue lines refer values computed by CVs from the OPES simulations.
In Figure 14, Chignolin fairly converges while Trp-cage and BBA show relatively big deviations. In the following, we qualitatively evaluate MICVs for each protein averaged three simulations.
Trp-cage. Although TAE converged with a small deviation, this due to failing to sample enough folded states. Also, the PMF for the folded state does not align with the reference, especially re- garding the folded state region, i.c., the positive range of CVs. This indicates the failure of sampling folded states, which leads incorrect energy value convergence. Additionally, DeepTICA shows very low PMF compared to the reference PMF near CV ~ 0. This indicates that while the unfolded states were sampled properly, the folded states were not sampled enough CVs identified as the folded states were actually transition states, resulting in severe mismatch between PMFs.
BBA. Once again, although TAE appears to converge closely to the reference value, we can identify that only the folded states are exclusively sampled from the PMF plot. Unfolded states, i.e., CVs being close -1, are not sampled at all, resulting in a convergence to an incorrect value. Furthermore, the reference PMF shows only one distinct local minimum, indicating that the trained CV itself did not properly discriminate between the folded and unfolded states. While one outlier simulation has been excluded for DeepTICA, the PMF plot shows divergence between simulations near the folded states. This indicates that TICA has failed to sample folded states properly, such as assigning diverse CV values to similar folded states.
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D.2 STATE DISCRIMINATION
In this section, we present the full qualitative results extended from Section 4.4. In Figure 15, we visualize the MLCV value the z-axis top of the TICA plane. In Figure 16, visualize the violin plot of the MLCV of the folded and unfolded state. The states are collected from the full DESRES trajectory, with an RMSD threshold cutoff.
DeepTICA
RIDEMU-DV
Chignaiin
8
Trp-cage
BBA
Figure 15: 3D visualization of protein conformations projected to TICA coordinates, with ML-
CVs the axis.
DeepTICA
TAE
VDE
BIOEMU-CV
Chignolin
Unloed
Trp cage
Folded
BBA
Figure 16: MLCV distribution the folded and unfolded states. Average MLCV of the folded and unfolded state is stated the black dot, with the standard deviation in black lines.
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D.3 STEERED MD VISUALIZATION
We also visualize C. of MLCV-steered MD trajectory for all baselines, following Figure 3. For the folded state visualization in the DESRES data, refer the in Figure 6.
Chignolin
DeapTICA
TAE
8
2
7
4
VDE
3
3
BIOBMU-CV
Tip-cago
mmm som
DeepTTCA
E
mmm mar
20z
&
TAE
mmm mam
VDE
BIOEMU-CV
DeepTIcA
E
2
fr
TAE
208
BIOENU-CV VDE
$
Figure 17: 3D Visualization of MLCV-steered MD paths. The sampled folding pathways of Chignolin, Trp-cage, and BBA by steered MD with MLCVs from DeepTICA, TAE, VDE, and BIOEMU-CV.
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D.4
VAMP SCORE
Here, we evaluate the VAMP score (Noé & Nuske, 2013; McGibbon & Pande, 2015; Noé & Clementi, 2015; Wu & Noé, 2020) MLCVs, where higher VAMP score indicates preserva- tion of dynamic contents. We use VAMP from deept im library (Hoffmann et al., 2021), with time-lag of 10 the DESRES trajectory data. Table 14, TAE and VDE show a relatively low score for bigger molecules compared to other methods. DeepTICA yields a high score since its training objective is similar the definition of the VAMP score, and BIOEMU-CV shows similar VAMP scores in big molecules. However, VAMP scores should not be simply trusted since highly correlated values could result in high VAMP scores (Noé & Nuske, 2013; Wang et al., 2024).
Table 14: VAMP scores of MLCVs Chignolin, Trp-cage, and BBA. higher score indicates better preservation of dynamic content.
Chignolin
Trp-cage
BBA
Method
VAMP-1
VAMP-2
VAMP-E
VAMP-1
VAMP-2
VAMP-E
VAMP-1
VAMP-2
VAMP-E
DeepTICA
1,9803
1.961
1.9611
1.9920
1.9840
1.9840
1.9898
1.9796
1.9796
TAE
1.9686
1.9381
1.9381
1.8787
1.7722
1.7722
1.8902
1.7925
1.7925
VDE
1.9850
1.9702
1.9702
1.9947
1.9894
1.9894
1.8469
1.7172
1.7172
BIOEMU-CV
1.9199
1.9446
1.9446
1.9939
1.9878
1.9878
1.9859
1.9721
1.9721
28


Reviews:
[{"review_id": "7MEFEcujdq", "reviewer": "Reviewer_H3Mz", "summary": "The paper proposes a method for efficient molecular dynamics by learning collective variables (CV) from the BioEmu model. The paper adds a small encoder on top of a frozen BioEmu diffusion model to learn a one-dimensional collective variable (CV) using a time-lagged objective. The authors evaluate the learned CV on three fast-folding proteins using OPES (for free-energy and PMF error) and SMD (for target hitting and maximum energy along paths). All CV’s are restricted to 1 dimension.", "questions": "- How much of the gain comes from time-lagging itself versus using BioEmu features?\n\n\n- Does partially fine-tuning BioEmu help or hurt compared to freezing it?\n\n\n- How sensitive are results to encoder size and to the choice of where conditioning is attached within the model?\n\n\n- Does the approach generalize to larger proteins or multi-path systems, and to higher-dimensional CVs?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The integration is simple and practical: keep BioEmu frozen and train only a small conditioning head. This is an attractive engineering path if it works broadly.\n\n\n- On SMD tasks, the method often reports better target-hitting probability and lower maximum energy along the path, which suggests the CV is useful for guiding transitions.\n\n\n- The paper provides reasonably clear setup details for OPES and SMD, which helps with reproducibility.", "weaknesses": "- The paper needs more ablation. It is unclear which components matter most. For example, comparisons for time-lagged vs. non-time-lagged training, frozen BioEmu vs. partial fine-tuning, different encoder sizes and placements, and SMD runs without mixing the learned CV with RMSD. Without these tests, it is hard to attribute the reported gains to the proposed choices, and hard to evaluate the novelty of the proposed method vs. the reported baseline methods.\n- Restricting the CV to one dimension and forcing a fixed range can hide multi-modal kinetics or make methods look closer or farther apart depending on alignment. While reported CV’s don’t need to be that high dimensional, understanding if the method scales to multi-dimensional CV’s at all is important for future practitioners.\n\n\n- Several results have large standard deviations. In Tables 1 and 2, many method averages fall within each other’s uncertainty ranges. This weakens the ranking of methods and makes performance differences difficult to trust.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "fFj9b5vOyn", "reviewer": "Reviewer_F5dg", "summary": "This work proposes a novel framework for learning collective variables. The model trains an encoder to extract CVs by enabling the frozen generative model BioEMU to generate molecular conformations under time-lagged conditions. The paper benchmarked MLCVs for two slow degree freedom tasks and demonstrated the model's effectiveness.", "questions": "1. How physically interpretable are the learned CVs?\n2. If BioEmu’s modeling capabilities are insufficiently accurate, will the learned CV still reflect the system's true slow degrees of freedom? How can this issue be mitigated?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The idea of capturing collective variables through a conditional generative task is novel. \n2. The paper is well-structured, clearly presented, and supported by thorough experiments.", "weaknesses": "1. The method heavily relies on the model capabilities of BioEmu. The captured CV may contain model bias.\n2. The paper a bit overstates the scope of its CVs, especially in the title. It should make clear that the method focuses on CVs for enhanced sampling, rather than general CV learning.\n3. The dataset is quite limited, and the selected proteins are all very small. The method should be tested on a broader set of proteins with varying sizes to better demonstrate its generality and robustness.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "dy4iHrgNO2", "reviewer": "Reviewer_UdyY", "summary": "Enhanced sampling uses collective variables (CVs) for sampling from long timescales which can represent rare events. However, finding good CVs is not trivial. This paper proposes to learn these from BioEmu. Concretely, an encoder is trained to embed the input structure to a low-dimensional vector, which represents the CVs. This vector is added to the single representation in BioEmu so that the time-lagged conformation is generated.\n\nTo evaluate the model, it looks at the free energy difference estimation and transition path sampling, which requires correct long timescale encoding. Comparisons to the baselines show comparable/better performance of the proposed model.", "questions": "* There are two downstream tasks used: free energy difference estimation and transition path sampling. What could be other metrics to used to measure the effective encoding of slow dynamics?\n* The proposed model is compared against self-supervised models. Are there any supervised models for the task?\n* Line309: 'not meaningless'->'meaningless'?\n* line317: 'through out'->'throughout'\n* Fig1 caption: 'earn'->'learn'\n* Fig4, the circle represents the folded state. Why is the red convex hull not around it for chignolin, while it is for others? Also, would it be better to draw lines for transition paths somehow, to clearly see the paths?\n* Fig3, it would be interesting to also show the transitions of samples from compared models.\n* Have you tried using other models than BioEmu, e.g. Boltz, AlphaFlow? I guess it should be straightforward to do it and should be interesting to compare the results.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* originality \n Learning latent representations from a fixed pretrained model is not new but this paper adapts it for learning CVs for slow dynamics which is a novel application.  \n * quality \n The model's predictions are compared against state-of-the-arts quantitatively while it would have been better if more that 3 proteins were tested.\n * clarity\n It is mostly clear to understand except for some typos and sentences.\n * significance\n Running MD simulations to investigate slow dynamics of proteins, e.g. folding, is challenging due to the required computation resource and error accumulation. Enhanced sampling methods can tackle this challenge but it needs good VCs. This paper introduces an effective way of learning them by wrapping around an existing protein ensemble generation model, BioEmu. The results are competitive and extensive comparisons were conducted. The folding path sampling results show a good performance of the model.", "weaknesses": "* To see if the model works well on a variety of proteins, it would make the paper stronger if more than 3 proteins were tested.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ugzU460NFm", "reviewer": "Reviewer_VbbS", "summary": "This paper introduces BIOEMU-CV, a novel framework for automatically learning collective variables (CVs) for molecular dynamics (MD) simulations. The authors identify that existing machine-learning-based CVs (MLCVs) often struggle to scale from small toy systems to more complex proteins.\n\nThe proposed method cleverly leverages a large, pre-trained protein foundation model, BioEmu, as a \"scaffolding\" to train a new, lightweight CV encoder. The core idea is to train this encoder to find a low-dimensional CV ($c_t$) from a protein's current state ($x_t$) that is maximally predictive of a future, time-lagged state ($x_{t+\\tau}$). This is achieved by freezing the weights of the powerful BioEmu model and training only the small encoder and an adapter to \"condition\" BioEmu to generate $x_{t+\\tau}$ based on $c_t$. This time-lagged objective theoretically forces the CV to capture only the slow, persistent dynamics (e.g., folding) while discarding fast, random fluctuations.\n\nThe method is benchmarked against three other self-supervised MLCVs (DeepTICA, TAE, VDE) on three fast-folding proteins (Chignolin, Trp-cage, BBA). The evaluation is performed on two key downstream tasks: (1) free energy difference estimation using On-the-fly Probability Enhanced Sampling (OPES) and (2) transition path sampling using Steered Molecular Dynamics (SMD).", "questions": "1. The target state $x_{t+\\tau}$ is not a pure simulation frame but a synthetic construct (BioEmu C$\\alpha$ + hpacker side chains + OpenMM relaxation). This pipeline may introduce its own biases. How can the authors be sure that the learned CV isn't just learning to predict the artifacts of the hpacker algorithm rather than the true underlying slow dynamics of the protein? An ablation study training on \"native\" MD frames vs. the synthetic targets would seem necessary to resolve this.\n\n2. Given the massive standard deviations in Table 1, the 1µs OPES simulations are clearly unconverged. Can the authors provide longer-run data or, failing that, justify why any conclusions are being drawn from this specific task? As it stands, the $\\Delta F$ results are statistically inconclusive and weaken the paper's overall argument.\n\n3. The study is limited to a 1-dimensional CV ($d=1$) for simplicity. However, complex folding events often require more than one coordinate. How does the method perform when tasked with finding 2 or 3 CVs? Does the time-lagged generation approach successfully separate multiple slow modes?\n\n4. The steering variable for the SMD task is a combination of the learned CV and C$\\alpha$-RMSD. This is a significant confounding variable. Can the authors please provide results for the SMD task using only the learned CV as the steering variable? This is necessary to prove that BIOEMU-CV itself, and not the C$\\alpha$-RMSD helper, is responsible for the high target hit percentage.\n\n5. The paper does not include \"simple baseline\" controls. How does the learned CV's performance (e.g., in SMD THP) compare to a simple, non-learned CV, such as a linear PCA or TICA component derived from either the input coordinates or the internal latents of the frozen BioEmu model? This is needed to demonstrate that the complex, time-lagged training is necessary.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. The paper's most significant contribution is demonstrating a clear failure of popular baseline methods (VDE and TAE) to scale beyond the 10-residue Chignolin protein. As shown in Table 3 and Figure 5, VDE is completely incapable of separating the folded and unfolded states for Trp-cage and BBA. BIOEMU-CV, by contrast, scales robustly and provides excellent state discrimination for all three proteins. This finding alone reframes the problem, suggesting that foundation-model approaches may be a necessary solution.\n\n2. The method demonstrates superior qualitative performance. The CV provides a clear, unambiguous separation between the folded and unfolded basins (Table 3), which is the primary prerequisite for any useful CV. Furthermore, Figure 6 shows it successfully assigns distinct values to different secondary structures ($\\alpha$-helix vs. $\\beta$-sheet) in BBA, a task where VDE and TAE fail.\n\n3. The SMD results (Table 2) provide the strongest quantitative evidence for the method's utility. BIOEMU-CV achieves a 93.8% target hit percentage (THP) for BBA, compared to just 18.8% for DeepTICA (the only other baseline to even run the task). This is a decisive result and shows the CV is highly effective as a reaction coordinate for guiding folding pathways.\n\n4. The approach of re-purposing a large, frozen foundation model is computationally appealing. It avoids the cost of training a massive new model from scratch and instead produces a small, fast, and practical CV encoder that can be easily plugged into existing MD simulation packages.", "weaknesses": "1. This is the most significant weakness in the paper's evaluation: The OPES simulations (Table 1) are demonstrably not converged. The reported standard deviations for the free energy difference ($\\Delta F$) are often larger than the mean values themselves (e.g., $1.36 \\pm 7.92$ kJ/mol for Trp-cage and $0.82 \\pm 16.57$ kJ/mol for BBA). With such massive error bars, it is statistically impossible to compare the methods. The authors' claims of \"winning\" based on the mean value are unsupportable. These results should be treated as inconclusive.\n\n2. Even within the inconclusive OPES results, the \"win\" is not uniform. For Chignolin (the most well-behaved system), DeepTICA achieves a notably better PMF-MAE (2.64) than BIOEMU-CV (3.07).\n\n3. The target state $x_{t+\\tau}$ is a synthetic construct (BioEmu C$\\alpha$ + hpacker + relaxation), not a pure MD frame. This introduces a significant potential for bias, where the CV may be learning the artifacts of the hpacker algorithm rather than the true, all-atom slow dynamics. This concern is not addressed with an ablation study (this point is expanded in Question 1).\n\n4. The method is benchmarked on three \"fast-folding proteins\". While this is an improvement over systems like alanine dipeptide, these are still relatively small proteins (10-28 residues). Its scalability to much larger, more complex proteins (e.g., 100+ residues) is not demonstrated.\n\n5. The study is limited to a 1-dimensional CV ($d=1$) for simplicity. While this is readable, it is likely limiting for multi-pathway kinetics or larger proteins; the paper doesn’t probe $d>1$ (this point is expanded in Question 3).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)