DreamFold: A World Model to efficiently generate protein folding pathways in the latent space

Abstract

While there is an abundance of static data for the structure of biological macromolecules, the data regarding their folding mechanisms and dynamics is scarce, posing a challenge to the training of AI models. The World Model approach, which has been very successful in robotics, can come in handy in this regard. From limited data, it can build a latent, approximated representation of the spatio‐temporal folding environment that can be used to train downstream AI models. Here, we developed DreamFold, a World Model‐based generative framework to perform biomolecular simulations. DreamFold encodes protein structures and dihedral angle moves into latent vectors using variational autoencoders. Then, it uses another neural network to rapidly predict the next latent structure after a latent move, allowing the model to develop its own understanding of protein dynamics. Finally, in a “hallucinated” latent environment, an agent learns, through evolutionary algorithms, a policy to drive folding simulations toward a target. Latent configurations can then be decoded back into atomistic structures. DreamFold can compute protein folding pathways four orders of magnitude faster than molecular dynamics (MD), up to ~30,000×. Furthermore, for the monomeric proteins tested here (up to 449 aa), the computational cost scales linearly with the number of atoms (N) as O(N) (in comparison, MD scales as O(NlogN)). We have validated our results against established MD benchmarks and other available experimental data. Finally, we show how DreamFold allows us to identify folding intermediates with cryptic binding sites that are therapeutically valuable. Overall, DreamFold facilitates the study of protein dynamics by generative AI with applications in structure‐based drug discovery.

1. INTRODUCTION

Artificial Intelligence (AI) models often “hallucinate” meaning they generate information that is not grounded in real data but instead synthesized from learned patterns, inventing new scenarios on their own (Ji et al., 2023). While this is often a drawback for many tasks that require strict factual accuracy, the phenomenon can be exploited in the so‐called “World Models” (Ha & Schmidhuber, 2018). They are a class of generative neural networks designed to simulate environments for training reinforcement learning agents. World Models create a latent spatial and temporal representation of an environment—sometimes referred to as a “dream environment”—in which an AI agent can explore, learn, and optimize decision‐making policies. By leveraging this AI's ability to hallucinate possible future states, World Models allow reinforcement learning agents to develop and refine strategies in a controlled, imagined space before being deployed in the real environment, strongly reducing the computational complexity during training. This strategy has been widely applied in robotics, self‐driving cars, and videogames, and can provide enhancement in training time and inference accuracy (Guan et al., 2024; Ha & Schmidhuber, ²⁰¹⁸; Wu et al., ²⁰²²).

A World Model can be particularly useful in contexts where training data are limited and computations in the real environment are heavy or too complex. In the World Models, the training data are only necessary to develop the internal latent spatio‐temporal “dream” environment. Then, the downstream models and agents are trained and compute inside this self‐generated representation of the world. Regularization terms and constraints can be introduced to maintain physical plausibility and limit the models' hallucinations (Saanum et al., 2024).

The original World Model implementation from Ha & Schmidhuber (2018) was developed to teach an agent model to solve a car racing task, or learn to avoid fireballs shot by monsters. The model was compressing visual information into a latent spatio‐temporal representation. Later models were developed for other tasks such as games like Atari (Hafner et al., 2021), Go (Schrittwieser et al., 2020), Chess (Schrittwieser et al., 2020), as well as autonomous driving (Wang et al., 2025), video generation (Du et al., 2023) and robotics (Wu et al., 2022).

In this paper we develop DreamFold, the first generative World Model to evolve a policy to compute protein folding pathways (Figure 1a). Protein folding is a high‐dimensional problem characterized by a vast conformational space, where a protein can adopt an astronomical number of possible configurations (Zwanzig et al., 1992). The process is governed by intricate energetic landscapes, complex atomistic interactions, and stochastic fluctuations, making it a highly nonlinear and computationally intensive process to study.

FIGURE 1.

DreamFold: a generative World Model to compute protein folding pathways. (a) The World Model is employed in a reinforcement learning framework, where a controller is trained to predict actions to be performed on proteins to drive their folding and generate the next structure. (b) Generation of training data by random Monte Carlo simulations on the protein dihedrals. After each move, an energy minimization step (EM) is performed to relax the structure and eliminate atomic clashes. (c) Training of the Variational Autoencoders 1 (VAE1) to encode the protein structure S (Φ, Ψ dihedrals and C_α distances from native) into the latent vector ς. (d) Training of Variational Autoencoders 2 (VAE2) to encode the action (ΔΦ and ΔΨ) into the latent vector α. (e) Training of the Feed Forward Neural Network (FFN) using the trained VAE1 and VAE2, to predict the next latent structure given the current latent structure and action [ς(t + 1)|ς(t), α(t)]. (f) Training of the controller. Starting from an arbitrary unfolded state, the controller is trained to predict the latent action to be performed on the current latent structure [α(t)|ς(t)]. The FFN is used to predict the future configurations. VAE1 can be used to decode the full atomistic structure. MAE, mean average error.

Atomistic protein simulations are very computationally intensive, due to the high number of atoms and degrees of freedom of the system. Efficient optimization methods such as enhanced path sampling techniques and AI‐based methods (Ianeselli et al., 2018; 2024; Laio & Gervasio, ²⁰⁰⁸), are often necessary over equilibrium approaches, such as Molecular Dynamics (Shaw et al., 2010), in order to explore folding mechanisms within feasible timeframes and computational resources. Recently, with the advent of generative AI, some studies tackled this challenge by making use of Variational Autoencoders (VAEs) to reduce the dimensionality, and project the high‐dimensional protein structure onto low‐dimensional latent vectors. This facilitated the study of protein structural ensembles (Mansoor et al., 2024; Tian et al., ²⁰²¹), conformational changes (Schwing et al., 2022; Tian et al., ²⁰²³), and disordered proteins (Gupta et al., 2022; Zhu et al., ²⁰²³).

The method we propose trains on realistic all‐atom Monte Carlo protein simulations (Kolinski & Skolnick, 1994), where random torsions (actions A) of the backbone dihedrals (Φ and Ψ), followed by energy minimization, take place to explore the conformational landscape of proteins. This dataset has the purpose of teaching the model how the atomistic force fields shape the dynamics of the protein's dihedral angles. The energy minimization step is necessary to optimize intermolecular interaction, resolve atomic clashes, and relax the side chains, maintaining the physical plausibility of the conformations of the training set.

First, the dimensionality of the protein configurations (structures S) and actions (A) are reduced by a Variational Autoencoder into smaller latent vectors ς and α. Then, a small Feed Forward Neural Network (FFN) is trained to predict the next latent protein configuration ς(t + 1) given the current latent configuration ς(t) and the latent action α(t) performed on it. In this way, the FFN has built its own understanding of the structural transitions in the folding “dream” environment. Due to the energy minimization process performed after every move, S(t) + A(t) is not equal to S(t + 1) anymore. For this reason, it is necessary to train a model to predict S(t + 1). This is the goal of the FFN, which learns how to do it in the latent space. Finally, a small controller is trained in this dream environment to predict the necessary dihedral action α(t) to be performed on the current structure ς(t) in order to drive the folding toward the target state (i.e., the native state). The decoder of the VAE can then be used to reconstruct the full atomistic representation of the protein configurations (S).

It would be challenging to train our agent in the atomistic environment, because the high dimensionality of the parameter space would make the training computationally very demanding. Instead, the training was performed in the dream environment—a compressed (latent) spatio‐temporal representation of the structural transitions. The controller learned to perform the latent rotations on the protein dihedral angles Φ and Ψ, driving the conformational transitions toward the target of interest.

We have applied the method to a variety of small and medium‐sized proteins between 20 and 133 aa: TrpCage miniprotein [Protein Data Bank (PBD): 1L2Y, 20 aa]; Fip35 WW domain (PDB: 2F21, 35 aa); protein G (PDB: 1MI0, 56 aa); λ‐repressor (PDB: 1LMB, 80 aa); prion protein (PrP) (PDB: 1QLX, 124 aa); Ubiquitin (PDB: 1UBQ, 76 aa); human Cellular Retinol Binding Protein II (PDB: 4ZGU, 133 aa). We have computed protein folding pathways, identified and analyzed relevant metastable states such as folding intermediates, transition states (TSs) and unfolded states. We show how the model can be further regularized using a Ramachandran‐based score function during the policy evolution, discouraging structures with unrealistic Φ and Ψ combinations. This yielded folding trajectories that followed lower energy pathways. Our method was tested against long MD simulations, against other enhanced path sampling methods and against available experimental data in the literature. DreamFold showed high accuracy and reproducibility for the computation of the protein folding pathways, for the prediction of the structure of the folding intermediates and of the TSs. The method, however, yields folding trajectories that are out‐of‐equilibrium and cannot directly be used to extract thermodynamic quantities. This is because the Controller was rewarded to only guide the forward folding process (from unfolded to folded), developing a policy that breaks detailed balance. However, performing short relaxations of the structures through MD allowed for the reconstruction of the unbiased dynamics of the proteins via Markov State Modeling (MSM).

DreamFold can be used to compute the folding pathway of biomolecules and obtain the atomistic structure of therapeutically relevant intermediate states using state‐of‐the‐art force fields. It can have applications in structure‐based drug discovery (SBDD), for folding intermediate targeting (Biasini & Faccioli, 2023), as well as to elucidate the biological role of macromolecules and the atomistic details of the conformational transitions.

1.1. Model and training procedure

Building DreamFold involved the following steps:

1. Step 1: collect random rollout training data (Figure 1b). Starting from arbitrary protein conformations (the native or randomly generated unfolded states), we collected trajectories with random dihedral moves (i.e., random ΔΦ and ΔΨ torsions ranging between 0 and ±30°). 30° is a common range for the dihedral moves often used in Monte Carlo simulations. This roughly corresponds to Monte Carlo simulations on Φ and Ψ with a null Metropolis selection criterium (always accept), since the scope of the dataset is to teach the models how to encode moves, structures, and how the moves affect the structures. We are not using this dataset to train the controller, which is instead trained in the “hallucinated” understanding of the structural transitions of the FFN. Right after every move, an energy minimization step was performed to relax the structure and eliminate atomic clashes. The next conformation does not simply correspond to the sum of the previous conformation and the dihedral move Ψ(t) + ΔΨ(t) ≠ Ψ(t + 1) and Φ(t) + ΔΦ(t) ≠ Φ(t + 1), because during the energy minimization process the dihedral angles change to resolve atomic clashes, relax the side chains, and optimize aminoacid interactions. The World Model uses these data to build its internal latent spatio‐temporal representation of the dynamics, where it intrinsically learned how the protein's force fields affect future states given a dihedral move. Structures have been generated with pyRosetta (Python‐based interface to the Rosetta molecular modeling tool; Chaudhury et al., 2010), using a state‐of‐the‐art atomistic force field (Alford et al., 2017). For each protein, the training set corresponded to 50 trajectories of 500 steps each, for a total of 25,000 protein configuration and actions. The validation and test set consisted of five additional trajectories of 500 steps each (total 2500 protein configurations and actions each). This training set contains the information on how different dihedral rotations change the structure of the protein.

2. Step 2: train Variational AutoEncoder 1 (VAE1, the structure module) (Figure 1c). The rollout data were used to train VAE1 to encode the protein features S (a concatenation of Φ dihedrals, Ψ dihedrals, and C_α distance from the native state) into a lower‐dimensional vector that we named ς of length 10. VAE1 is therefore responsible for lowering the dimensionality of the structures into lower‐dimensional vectors, strongly reducing the number of parameters. The decoder of VAE1 can later be used to reconstruct back the full atom structure S from the latent vector ς.

3. Step 3: train Variational AutoEncoder 2 (VAE2, the action module) (Figure 1d). The rollout data were used to train VAE2 to encode the action A (ΔΦ and ΔΨ) into a latent vector that we named α, also of length 10. VAE2 is therefore responsible for reducing the number of dimensions required to describe the action. The VAEs of Steps 2 and 3 ensure that the features are mapped in the latent space continuously. This is important in our context of protein folding because we want to be able to draw realistic configurations when decoding from the latent space back into the real environment. The loss function for both VAE1 and VAE2 consisted in the reconstruction loss (mean average error [MAE]) between the features after decoding (S—Ŝ, A—Â) and the Kullback–Leibner divergence (Kullback & Leibler, 1951) term to ensure that the latent space follows a standard normal distribution. Additional information is provided in Supporting Information S1.

4. Step 4: train the Feed Forward Model (FFN, the future state predictor) (Figure 1e) model to predict the next latent configuration given the current latent configuration and the latent action performed on it (ς[t + 1]|ς[t], α[t]). The FFN is the core of this World Model. It learns how an action affects the current configuration and predicts the next one, entirely in the latent space. First of all, the trained encoders of VAE1 and VAE2 are used to generate ς(t), ς(t + 1) and α(t) vectors from S(t), S(t + 1) and A(t), respectively. Then, ς(t) and α(t) are given as input to the FFN, which predicts the next latent structure ς ^(t+1). The loss function of the FFN consisted of the reconstruction error (MAE) between the true ς(t + 1) and the predicted ς ^(t+1).

5. Step 5: assemble the World Model and train the controller (Figure 1f) to predict the action to be performed on the current structure [α(t)|ς(t)], in order to drive the trajectory closer to the target (i.e., the folded state), starting from an arbitrary unfolded state. The trained FFN is used to predict the next ς(t + 1) given the current ς(t) and the α(t) output of the controller. As in the original paper from Ha and Schmidhuber, the controller was trained using the evolutionary strategy Covariance Matrix Adaptation (CMA; Hansen, ²⁰⁰⁶). CMA is a powerful evolutionary optimization algorithm that is particularly well‐suited for training controllers in complex, high‐dimensional search spaces. For protein folding, credit assignment—the process of determining which parameters contributed most to a successful outcome—is highly nontrivial. CMA explores solution spaces through evolutionary strategies, refining a population of candidate solutions over successive generations (further details in Supporting Information S1: section 10). Note how the training of the controller is performed entirely in the latent space and in the FFN's own understanding of the environment (aka “in‐dream” training). At each generation, each agent (population size of 20) performs 100 (n) iterations starting from the unfolded state. The reward to the agent corresponded to the distance (MAE) between the last latent configuration ς(t + n) and the native latent configuration, plus a Ramachandran‐based regularization term (further details in the later section). For simplicity, the objective of the training was to minimize the reward. The overall architecture and training procedures are shown in Figure 1. Additional model details can be found in Supporting Information S1: section 1.

The trained model is then employed for the inference of folding trajectories, starting from an arbitrary unfolded conformation and predicting the conformational changes that lead to the target state (in our case, the folded state). The atomistic structures S at each step can be reconstructed using the decoder of VAE1 (Figure 1c). The reconstruction procedure is indicated in Supporting Information S1: section 3.

2. RESULTS

2.1. Regularization

To reduce overfitting during policy evolution, we have introduced a path‐dependent Ramachandran‐based energy score as reward during the training of the controller. The Ramachandran score is calculated on the normalized frequency distribution of the protein backbone dihedral angles Φ, Ψ, computed from ~8000 high‐resolution protein PDBs (obtained from Chen et al., ²⁰¹⁰; Sobolev et al., ²⁰²⁰). The Ramachandran score discourages structures with unrealistic Φ and Ψ combinations, which would be sterically unfavorable.

During controller training, the latent structure s of each step was decoded back using the decoder from VAE1 in order to reconstruct the values of Φ and Ψ and calculate the Ramachandran‐based energy score. The total reward, in our case to be minimized, can be defined as following:

$$\sum _{t=1}^T\sum _{i=1}^{N}R\left(\mathrm{\Phi },\mathrm{\Psi }\right)+\frac{1}{L}\sum _{i=1}^L\mid \mathit{\varsigma }\left(t+n\right)-{\mathbf{\varsigma }}_{\text{target}}\mid ,$$

where R(Φ,Ψ) corresponds to the Ramachandran matrix shown in Figure 2a, summed over N protein residues for every frame t of the trajectory of length T. The second term corresponds to the MAE between the target latent ς vector ( ς _target) and the last ς vector of the trajectory ς (t + n), with L being the length of the latent vector (10).

FIGURE 2.

Controller training and regularization. (a) Ramachandran frequency matrix R used to compute the regularization term. (b) Training progress of the controller by CMA‐ES, example of TrpCage. Each generation has a population size of 20 trajectories, for a total of 500 generations. (c) RMSD of Protein G folding trajectories (each color corresponds to a different trajectory). Generally, we consider a conformation to be folded when its RMSD becomes <0.3 nm. (d) Cumulative Ramachandran score of the folding trajectories of the four proteins of interest. As expected, controller regularization decreases the cumulative Ramachandran score. (e) Cumulative Rosetta energy calculated on the folding trajectories of the four proteins. In two cases, the controller regularization significantly reduced the cumulative Rosetta energy of the folding pathways, making them follow lower energy routes. *indicates p value < 0.05.

We have used CMA‐evolution strategy to evolve the controller weights for 1000 generations, with a population size of 20, starting from a different unfolded state at every generation and performing 100 moves. Controller training progress for Protein G is shown in Figure 2b. Folding trajectories for Protein G are shown in Figure 2c.

As expected, the regularization term reduced the cumulative Ramachandran score of the folding trajectories during inference (Figure 2d) (except for the case of Protein G which was not significant). Interestingly, in two cases (Fip35 and hCRBP2), it also significantly reduced the cumulative Rosetta energy score of the trajectories, indicating that the folding pathways are following more energetically favored routes (Figure 2e).

2.2. Computation of folding pathways and validation

Folding trajectories are computed by starting from randomly generated unfolded states s and using the trained controller and FFN to iteratively perform 100 steps. We have computed 50 trajectories for each protein. Figure 2c shows the RMSD root mean squared displacement (RMSD) to native of trajectories computed for Protein G. Figure 3 shows the folding mechanism and the energy landscape (Rosetta energy score) for our proteins of interest. The folding proceeds from regions of high energy (unfolded) toward regions of low energy, with the native state always being the basin with the lowest energy. The energy of the protein configurations has been obtained using the default full atom score function of Rosetta (Alford et al., 2017), which is a weighted sum of energy terms that represent physical forces and statistical terms, measured in Rosetta Energy Units (REU; Chaudhury et al., ²⁰¹⁰). While it does not correspond to the thermodynamic energy landscape of the protein (because it lacks entropic contributions), it still contains valuable information about the relative stability between the conformations, the folding pathways, and the structural intermediates.

1. Fip35 WW domain

FIGURE 3.

Protein folding pathways computed by the World Model. Folding mechanism and Rosetta energy landscape as a function of various collective variables for Fip 35 WW domain (a–c), TrpCage (d–f), Protein G (g–i), and λ‐repressor (j–l). The plots (b‐h‐k) show how the protein residues (y‐axis, ordered from N‐ to C‐terminal) assume their secondary structure over time (x‐axis, iterations). Starting from an unstructured unfolded state, the proteins progressively form their secondary structures during their pathway toward the native state (E = extended strand, B = β‐sheet, T = turn, G = 3–10 helix, C = coil, and H = α‐helix). The plots in (e) show the folding progression of TrpCage measured as RMSD heliix versus gyration radius. This allows to distinguish two folding pathways of TrpCage characterized by the differential order of formation of the protein core and of the helix. The plots (c‐f‐i‐l) show the conformational landscape of the proteins measured with Rosetta Energy Units (REU): These units are not directly transferable into a physical unit of measure but can be used to compare the relative energy of different conformations of the same protein. One single folding trajectory of choice is drawn on top of each energy landscape. The pink triangular and hexagonal points in the energy landscape indicate the starting (unfolded) and ending (folded) states, and correspond to the structures marked with the same symbols in the trajectory on the left. The curved purple arrows shown in (i–l) indicate the folding mechanism measured by Lapidus et al. and Liu et al., respectively.

Fip35 WW domain is a small protein of 35 aa whose structure mainly consists of a three‐stranded antiparallel β‐sheet. Past studies indicate that its folding pathway proceeds in a heterogeneous manner, even though two main pathways can be identified which mostly differ by the order of formation of the two hairpins (Beccara et al., 2012; Ensign & Pande, ²⁰⁰⁹): pathway I where hairpin 1 folds before hairpin 2, and pathway II the opposite. In our simulations (Figure 3a–c) pathway I was prevalent, with 94% of the simulations following it, while pathway II was followed only 6% of the time. A similar preference toward pathway I was observed in a past study (Ianeselli et al., 2025), pointing to the hypothesis that pathway I might be energetically favorable.

• 2 TrpCage miniprotein

TrpCage is a miniprotein of 20 aa whose structure is composed of an α‐helix, a 3–10 helix and a C‐terminal poly‐proline tail. According to past computational and experimental studies, its folding mechanism mostly consists in two pathways (Andryushchenko & Chekmarev, 2017; Byrne et al., ²⁰¹⁴; Culik et al., ²⁰¹¹; Meuzelaar et al., ²⁰¹³; Mok et al., ²⁰⁰⁷; Mou et al., ²⁰¹⁴). Pathway I, in which the hydrophobic collapse of the core precedes the formation of the α‐helix. Pathway II, in which the events occur in the opposite order, that is, the α‐helix forms first followed by the hydrophobic collapse. In our simulations (Figure 3d–f), we found both pathways to be almost equiprobable. Pathway I, where radius of gyration rapidly drops (indicating an hydrophobic collapse) followed by the folding of the α‐helix, was followed 48% of the times (Figure 3e bottom). Pathway II, where the helix forms first and the hydrophobic collapse happens later, was followed 52% of the times (Figure 3e, top). We have also observed the formation of the folding intermediate of TrpCage (Meuzelaar et al., 2013; Zhou, ²⁰⁰³), which is characterized by the premature formation of a salt bridge between Asp9 and Arg16. This interaction temporarily blocks the protein in an intermediate metastable state, because the salt bridge needs to be broken to continue folding. In some of our simulations, we could see the protein remaining stuck in this metastable conformation for a few iterations (see the conformation indicated with an * in Figure 3d), before being able to continue folding toward the native state.

• 3 Protein G and λ‐repressor

The folding pathways of Fip35 (35 aa) and TrpCage (20 aa) are relatively easy to measure because these proteins are small in size and possess a simple topology that limits the conformational space. Things become more complicated as protein size increases, as for example Protein G (56 aa) and λ‐repressor (80 aa). There is not a general consensus on the folding mechanism of these proteins (Lapidus et al., 2014; Liu et al., ²⁰¹²; McCallister et al., ²⁰⁰⁰; Morrone et al., ²⁰¹¹; Prigozhin et al., ²⁰¹¹; Yang & Gruebele, ²⁰⁰⁴), but rather only qualitative observations that are not always consistent between different studies. In this section, we will perform high‐level comparisons to verify whether the folding pathways computed with DreamFold satisfy such general constraints. A more quantitative approach is pursued later when our trajectories are compared against MD data.

Protein G is a small protein (56 aa) with a relatively complex topology, where one α‐helix is packed against a four‐stranded β‐sheet. Its folding mechanism involves an initial hydrophobic collapse followed by a slow structure fine‐tuning (Camilloni et al., 2008; Kmiecik & Kolinski, ²⁰⁰⁸; Lindorff‐Larsen et al., ²⁰¹¹). The protein follows multiple routes toward the native state which nonetheless belong to two major folding pathways. In both, the α‐helix forms first. Then, the first path (pathway I) forms the N‐terminal hairpin first, whereas the second path (pathway II) forms the C‐terminal hairpin first (Lapidus et al., 2014). The folding continues with the formation of the β‐sheets and the core rearranging into a native state. In our simulations (Figure 3g–i), the first part of the pathway is governed by the hydrophobic collapse (i.e., reducing the radius of gyration). Then, the protein is seen taking two routes: pathway I, where hairpin1 forms before hairpin 2; and pathway II, with the opposite order. The structures at these points resemble those computed by Lapidus et al. (2014). The folding continues with the progressive formation of the remaining structures, that is, the β‐sheets and the core rearrangements.

The λ‐repressor is a protein of 80 aa composed of five α‐helices. Past studies indicate that it folds very fast following a two‐state kinetics where a hydrophobic collapse is followed by a heterogeneous progressive rearrangement of the backbone and of the α‐helices (Adhikari et al., 2012; Liu et al., ^{2010, 2012}; Pogorelov & Luthey‐Schulten, ²⁰⁰⁴). In our simulations (Figure 3j–l), we could not distinguish a specific order of formation of the helices. We, however, observed an initial hydrophobic collapse (i.e., decreasing radius of gyration) followed by the folding of the α‐helices and their positioning. The RMSD versus gyration radius landscape plot (Figure 3l) looks very similar to the one obtained by Liu et al. (2012).

These observations highlight a qualitative agreement between the folding mechanisms computed by DreamFold and experimental or computational data found in the literature.

2.3. Performance

In MD, the computational cost scales approximately as O(NlogN), where N is the number of atoms. This scaling arises because short‐range interactions are handled with neighbor lists (linear cost O(N)), while long‐range electrostatics are computed using Particle Mesh Ewald (PME), which adds a logN factor (Phillips et al., 2005). Our World Model scales instead as O(N). The time required for training the model is constant (O(1)) since it takes place in the latent space which has the same dimensionality for all the proteins (up to a certain size). Rollout data generation and inference scale instead linearly (O(N)) with the number of atoms. This is due to the full‐atom energy minimization step that takes place at every iteration. In this energy minimization step (pyRosetta's FastRelax), the computational cost scales as O(N). This is because pairwise interactions are evaluated with neighbors lists within Rosetta's empirical score function, without performing long‐range electrostatic calculations using PME.

We have also calculated the difference of speed between pure MD and DreamFold, on a standard computer cluster to compute 50 folding trajectories. DreamFold was 3800× faster for TrpCage, 8000× faster for Fip35, and 30,000× faster for ProteinG. Thanks to these speed advantages, DreamFold is a valuable approach to study the folding dynamics of large molecular systems. In the later sections, we study and valid the folding pathway of larger proteins such as hCRBP2 (133 aa) and the PrP (124 aa). It would be computationally challenging to study their folding dynamics via standard MD, while computation is instead cheap using our World Model. DreamFold has also been successful in studying the folding of the human α‐tubulin, a large protein of 449 aa which is computationally prohibitive to be studied by standard MD (Supporting Information S1: section 11). Due to the lack of available literature data about its folding mechanism, we could not perform a proper validation. These simulations have, therefore, been performed just to demonstrate the feasibility and computational efficiency of DreamFold for larger proteins.

The highest computational cost of DreamFold is during the creation of the training set, which requires the generation of numerous atomistic structures and, therefore, energy minimizations. This cost represents an effective “reverse‐amortization” of expensive physical calculations necessary during conventional MD. Thus, after this cost is paid, during DreamFold inference the generation of folding pathways becomes extremely fast (up to 30,000× faster than MD).

More information about model performance in Supporting Information S1: section 5.

2.4. Path similarity and structure formation analysis

To obtain a quantifiable value of the accuracy of the folding pathways generated by the DreamFold, we computed their path similarity (Camilloni et al., 2011; Wang et al., ²⁰¹⁸) to available data from ultra‐long equilibrium MD (DE Shaw Research (Lindorff‐Larsen et al., 2011) aka DESRES) and other trajectories from different enhanced path sampling methods, such as the so‐called Bias Functional scheme (Ianeselli et al., 2018; Orioli et al., ²⁰¹⁷) ratcheted Molecular Dynamics Bias Functional (rMDBF)], an enhanced path sampling method that generates folding pathways using ratchet‐and‐pawl MD and then selects the least biased trajectories), and the “Discard‐and‐Restart” MD method (Ianeselli et al., 2024) (D&R, an efficient algorithm to compute folding pathways by repeatedly running short simulations and discarding those that do not fold forward). The trajectories from DESRES are often used as references in the validation of enhanced sampling methods and algorithms (Ianeselli et al., 2025; Janson et al., ²⁰²⁵; Lewis et al., ²⁰²⁵; Riccabona et al., ²⁰²⁴; Strahan et al., ²⁰²¹). The reason is that those simulations cover long timescales and are performed at thermodynamic equilibrium by plain MD.

The folding trajectories of the D&R and Bias Functional methods were directly available from their data repositories. The folding trajectories from DESRES were extracted from their long MD simulations (publicly available upon request) by cutting out the folding transition regions. Results are shown in Figure 4. Further details about the calculation of the path similarity can be found in Supporting Information S1: section 2. The path similarity was computed against the trajectories of DESRES (World Model  vs. DESRES, rMDBF vs. DESRES, or D&R vs. DESRES). We have also computed a measure of the self‐consistency between the DESRES trajectories themselves (DESRES vs. DESRES) which measures the heterogeneity of the folding pathways and is to be used as a measure of the upper boundary of the path similarity. Finally, we also calculate the path similarity between processes of random formation of native contacts (random vs. DESRES), which is to be used as a lower‐end baseline to help in the interpretation of the results.

FIGURE 4.

Validation of the folding mechanism to molecular dynamics. Path similarity and order of formation analysis for Fip35 WW domain (a, e), TrpCage (b, f), Protein G (c, g) and λ‐repressor (d, h). DESRES: David E Shaw Research; D&R: Discard and Restart algorithm; rMDBF: Ratcheted MD Bias Functional. Asterisk indicates that the difference is statistically significant. When the asterisk is alone, it indicates statistical significance against all the other comparisons in the same plot. (a–d) Path similarity analysis versus DESRES. (e–h) Order of formation of the residues: DreamFold simulations (thick lines) versus DESRES (thin lines). The cartoons at the top indicate the secondary structures of the protein (yellow = β‐sheet, purple = α‐helix). The transparent gray boxes highlight the regions of high correlation between the signals. For all proteins, the Spearman correlation values are positive with a p‐value of less than 0.0001 (unpaired t‐test).

Our trajectories of the Fip35 WW domain have a high path similarity to DESRES MD folding trajectories (Figure 4a), meaning that the order of formation of its native contacts is indistinguishable from the DESRES trajectories. DreamFold in this case is also more accurate than the rMDBF method. For what concerns the TrpCage miniprotein, the order of formation of native contacts slightly deviates from DESRES MD folding trajectories, and DreamFold does not outperform the D&R method (Figure 4b). For both Protein G and the λ‐repressor (Figure 4c,d), our trajectories are indistinguishable from those generated by DESRES (in terms of native contact order formation). A comparison to other methods for Protein G and λ‐repressor was not possible, because we have not been able to find publicly available folding trajectories for these proteins. The path similarity results indicate that the trajectories obtained with DreamFold maintain a high level of accuracy for what concerns the order of formation of their native contacts over the course of folding.

As a further method of comparison, we have calculated the order of formation of local native structures during the folding transitions and, again, compared the results against the MD folding trajectories from DESRES. Following the procedure developed in (Lindorff‐Larsen et al., 2011) and explained in Supporting Information S1: section 6, we plotted the order of formation of local native structures for each folding trajectory as a function of the residue number. A value close to 0 indicates that the residue adopts a native‐like structure early during the folding process, while a value close to 1 indicates later folding. In this manner, each trajectory obtains an interpretable fingerprint that describes its folding mechanism. Lindorff‐Larsen et al. (2011) has shown that even when a protein has multiple folding pathways, they still share the same folding nuclei and have a similar order of formation of the native structures. They also show that initiation sites for folding are preferentially located in regions that have a high propensity to form native structures in the unfolded state, which often correspond to the most stable secondary structures. This means that, up to a certain degree, the fingerprints shown in Figure 4e–h describe the overall folding mechanism of the protein.

The lines of the World Model folding trajectories and those from DESRES show similar fingerprints, even though sometimes scaled differently. Note that what matters in the comparison is not the scale of the values, but rather the shape of the line. The reason is that the values are integrated over time and the scale is relative to how much time each conformation spends in the trajectory, which strongly differs between DreamFold and DESRES trajectories (also, DreamFold's trajectories do not possess the concept of time). We have quantified the similarity between the fingerprints by calculating their Spearman's correlation coefficient (ρ), which measures whether two variables are monotonically related without caring about their absolute scale. A Spearman value of +1 or −1 indicates perfect positive or negative monotonic relationship, while a value of 0 indicates no relationship (e.g., random). The ρ value of each protein corresponds to the average of all combinations between the World Model and DESRES trajectories. For all proteins, we have obtained ρ values higher than 0, indicating a positive monotonic correlation between the fingerprints. This implies that the overall folding landscape computed with DreamFold shows a degree of similarity to MD.

Taken together, the qualitative comparison of the folding pathways, the results of the path similarity analysis and the correlation values between the folding fingerprints indicate that DreamFold is an accurate and reliable method to compute protein folding pathways with atomistic accuracy.

2.5. Thermodynamics

DreamFold is able to generate pathways connecting two structural states (e.g., unfolded to native). However, thermodynamic and kinetic properties cannot be directly inferred from these trajectories, because they are not generated by a physical dynamical process obeying detailed balance. Consequently, the trajectories lack a well‐defined notion of reversibility, and the frequency with which states are visited cannot be interpreted as equilibrium populations.

However, it is possible to reconstruct (up to a certain degree) the underlying unbiased dynamics of the system by performing local relaxations of the structures along a predefined collective variable (e.g., RMSD to native), by means of running short MD simulations (Orioli et al., 2017). In contrast to extracting slow properties from long MD simulations, Markov State Models (MSM) can construct the dynamics from short simulations starting from different conformations (Noé & Fischer, 2008; Schwantes et al., ²⁰¹⁴). In MSM, simulations only need to reach local equilibrium (which is achieved in a few nanoseconds; Orioli et al., ²⁰¹⁷) within individual substates and eventually transition to neighboring ones. The short unbiased trajectories give the conditional transition probabilities to start from the RMSD bin i and end up in bin j. The goal is to measure the probability that, after some short time Δt, you find yourself in bin j. This allows you to build the transition matrix T:

$${\mathbf{T}}_{\mathit{ij}}\left(\mathrm{\Delta }t\right)=\frac{P\left(j,t+\mathrm{\Delta }t|i,t\right)}{P\left(i,t\right)},$$

where $P\left(j,t+\mathrm{\Delta }t|i,t\right)$ is the probability of being in state j at time t + Δt given that the system was in state i at time t, and $P\left(i,t\right)$ is the probability of the system being in state i at time t. Each row of the transition matrix is then normalized to represent a conditional probability distribution $\sum _j{\mathbf{T}}_{\mathit{ij}}\left(\mathrm{\Delta }t\right)=1$. The stationary probability distribution then corresponds to the eigenvector corresponding to eigenvalue 1. Δt has been chosen to be 2 ns, which is on the same timescale as the local thermalization of metastable states, that is, the degrees of freedom orthogonal to a collective variable (such as Q, the fraction of native contacts, or RMSD to native) (Orioli et al., 2017). Moreover, it also corresponds to the frequency of which coordinates have been printed in the reference trajectories from DESRES.

For each protein, we have divided the RMSD space in 50 bins and extracted a structure representing each bin. Then, we have run 40 ns of MD in explicit solvent (protocol in Section 4). A cartoon scheme of the procedure is shown in Figure 5a. This reconstruction method works under the assumption that even if the original trajectories were biased, these short runs (done without any bias) reflect how the system evolves locally. It also assumes that we can treat the dynamics as a Markov chain on the RMSD bins (i.e., the future state depends only on the current bin and not on the full history; and the microstates represent separated regions of the state space). Unfortunately, these assumptions cannot easily be verified in our case and, therefore, MSM should not be considered a reliable method to reconstruct the true kinetics and thermodynamics from our trajectories. It should rather be used to obtain general insights and qualitative information.

FIGURE 5.

Reconstruction of unbiased dynamics by Markov State Modeling. (a) Cartoon scheme of the Markov State Modeling approach for the reconstruction of the true dynamics. Short molecular dynamics (MD) relax simulations are started from RMSD bins from randomly chosen World Model trajectories. (b) Transition matrix of the MD relaxation for the Fip35 WW domain at 360 K (total run time 40 ns, Δt = 2 ns). (c) Reconstruction of the folding landscape for Fip35 WW domain. World Model after relaxation is shown in blue, MD from DESRES is shown in orange. The landscape identified a three‐state folding mechanism: Native (N), intermediate (I), and unfolded (U). (d) Folding landscape for Protein G and TrpCage, respectively.

Figure 5b shows the transition matrix for Fip35 WW domain, and the reconstruction of the stationary probability is shown in Figure 5c. The shape of the distribution is not identical to equilibrium MD, but both methods identified three basins corresponding to a three‐state folding (native, intermediate, and unfolded). With some discrepancies, the method was able to generally reconstruct the folding landscape of our proteins, with a shape and magnitude reasonably similar to equilibrium MD (Figure 5c,d). The discrepancies might arise from different MD protocols and from the fact that the process of local relaxation cannot be entirely described as a Markovian process by a single collective variable such as RMSD, as it might fail to capture the conformational separation of states.

2.6. PrP folding intermediate

Past studies have shown that the cellular PrP, a cell surface glycoprotein that is involved in numerous regulatory cellular pathways, has a metastable folding intermediate in its folding pathway (Ianeselli et al., 2025; Spagnolli et al., ²⁰²¹). We wanted to investigate if DreamFold is successful at identifying such conformation. The PrP folding intermediate presents a native‐like conformation where helix 1 (H1) is displaced and misses its docking contacts with helix 3 (H3), exposing to the solvent several residues that, in the native state, would be buried inside the protein core. We trained the models to compute the folding pathway of the structured C‐terminal domain of the human PrP protein (residues 125–228, 1696 atoms, PDB: 1QLX). Results are shown in Figure 6. Out of a total of 50 trajectories, 7 of them showed a folding trajectory that passes through the folding intermediate. These intermediates found in the World Model trajectories display an RMSD of less than 0.5 nm to the structure identified by Spagnolli et al. (2021). (shown in blue in Figure 6b) and Ianeselli et al. (2025). This folding intermediate is of great therapeutic interest. Numerous attempts to pharmacologically target the PrP native state have failed, suggesting that the native conformation could be an undruggable target (Poncet‐Montange et al., 2011). Instead, it has been possible to develop drugs against this folding intermediate, in a pocket present only in this particular conformation. We have used p2rank (Krivák & Hoksza, 2018) to screen the surface of the folding intermediate to identify such pocket binding site. We could identify the same therapeutic pocket as identified by Spagnolli et al. (2021) (Figure 6c) positioned between the displaced H1 and the central H3. The residues that make up the pocket consist of Arg136, Pro137, Ile139, Glu146, Asp147, Tyr150, Tyr157, Met205, Arg208, Val209, and Gln212. These results indicate that our method can successfully identify folding intermediates and maintain the key structural interaction between the residues that are responsible for the formation of binding pockets.

FIGURE 6.

Prion protein (PrP) folding intermediate. (a) Structure of the native PrP. (b) Structure of the folding intermediate of PrP superimposed to the one from Spagnolli et al. (in blue). (c) Surface binding pocket (cyan) of the PrP folding intermediate predicted with P2Rank.

2.7. Ubiquitin's transition state

Ubiquitin is a protein of 76 aa that folds in a two‐state manner. Its folding TS has been measured by Ψ and Φ analyses (Sosnick et al., 2004) (not to be confused with Ψ and Φ dihedral angles), where specific residues of the protein are mutated or engineered and the response of the folding rate is measured. These methods can quantify the extent to which a residue is involved in the formation of the TS and can give information about its structure. The Ψ and Φ analysis revealed that the TS of Ubiquitin has a native‐like conformation consisting of a nucleus made of a partially formed four‐stranded sheet network (β1–β4) and the carboxyl terminus of the major helix.

We have trained the World Model to compute the folding trajectories of Ubiquitin starting from the unfolded states. As a computational reference, we have analyzed the folding simulations of Ubiquitin from DESRES (Lindorff‐Larsen et al., 2011). We selected 30 frames from the DreamFold trajectories and 460 from DESRES that sampled the TS ensemble, defined as structures with an RMSD to native between 0.5 and 0.8 nm, and a gyration radius smaller than 1.5 nm (which corresponds to the transition region between the native and unfolded basins in the folding landscape, Figure 7a). The study from Sosnick et al. (2004) measured the Ψ value for numerous residue pairs. The Ψ value of a pairwise interaction between residues quantifies its involvement in the structure and formation of the TS. A Ψ value of 1 indicates full involvement, while 0 indicates none. To obtain a comparable computational measurement of such Ψ values from our simulations, we measured how often these residue pairs appear in contact in the TS structures. For each structure k, a contact (C _ij ) between residue i and residue j was considered formed (1) when their distance d _ij was smaller than a threshold (d _c), otherwise 0. The threshold d _c was defined as the d _ij found in the native state multiplied by 1.3, an arbitrary parameter to account for the looser structures of non‐native configurations. The computational Ψ value was then calculated as:

$${\mathrm{\Psi }}_{\mathit{ij}}=\frac{1}{N}\sum _{k=1}^N{C}_{\mathit{ij}}.$$

FIGURE 7.

Analysis of Ubiquitin's transition state. (a) Folding landscape of Ubiquitin measured by RMSD and gyration radius calculated for the World Model trajectories (larger plot) and for molecular dynamics (MD) (DESRES, smaller inset), shown as a frequency histogram. (b) Ψ value analysis of various contacts of Ubiquitin transition state (TS), calculated for the World Model, DESRES and from the experiments of Sosnick et al. (c) Deviation (absolute error) of the computational Ψ values from the experimental ones from Sosnick et al. (d) Native state of Ubiquitin. (e) Some conformations of Ubiquitin TS extracted from the World Model folding simulations.

Results are shown in Figure 7b. The best agreement between DreamFold's simulations and the experimental data from Sosnick et al. regards the shorter‐range contacts (aa distance ≤8). The structures of the TS states (Figure 7e) are visually very similar to those reconstructed by Sosnick et al. However, we have observed a better agreement for what concerns short‐range contacts rather than long‐range ones. This also parallels with what is observed in the simulations from DESRES, indicating that the discrepancy might be attributed to the force fields that tend to overstabilize local secondary structures.

2.8. Ubiquitin's unfolded state

The unfolded state of Ubiquitin has been studied by hydrogen/deuterium (H/D) exchange using two‐dimensional Nuclear Magnetic Resonance ‐ (Yagi‐Utsumi et al., 2020). This technique allows to characterize the residual structures persistent in the unfolded state. H/D exchange occurs when a backbone amide hydrogen becomes exposed to the solvent and is not protected by burial. The exchange rates correlate with structural protection (protection factor P). Residues with a high P belong to portions of the protein that are still structured in the unfolded state, where the amide is protected from the solvent and from the H/D exchange. A low P instead indicates that the residue was in an unstructured region of the protein and was exposed to the solvent, so that a high H/D rate could occur. In the study from Yagi‐Utsumi et al. (2020), Ubiquitin was unfolded in 6M guanidium chloride and then H/D exchange was initiated. In this manner, they could characterize the residual structures persistent in the unfolded state. They distinguish between exposed residues (p < 2), protected residues (2 < p < 3) and very protected (p > 3). Their results indicated that most of the protein was unstructured, but maintained residual native‐like structures in the central α‐helix α1 (p > 3, very protected) and the N‐terminal β‐hairpins β1 and β2 (2 < p < 3, protected).

We studied the conformation of Ubiquitin's unfolded ensemble of our DreamFold simulations, to characterize the residual structures. First of all, we identified the unfolded structures as the ones residing in the unfolded basin of the folding landscape shown in Figure 8a, obtaining a total of 613 structures. To obtain a metric that correlates with the protection factor P of H/D studies, we have quantified the buriedness (aka number of neighbors) of the amide of each residue of the protein, that is, the number of atoms closer than 0.75 nm to the amide. We classified a residue as exposed when its buriedness was lower than 112: the buriedness value of the N‐term amine that is very exposed to the solvent. A residue was classified as very protected when its buriedness exceeded 131: the value of the mildly exposed region between helix α1 and the 3–10 helix α2. Protected residues belonged between these boundaries. Results are shown in Figure 8b–e. Our results indicate residual structures in the N‐terminal hairpins β1 and β2 and in the central helix α1, confirming the experimental observations. However, our results indicate further residual structures in the regions corresponding to the 3–10 helix α2 and the 3–10 helix α3, which are instead expected to be unstructured according to the experimental data. This discrepancy is likely to arise by the fact that force fields in atomistic simulations tend to produce over‐collapsed unfolded states with excessive residual structures (Skinner et al., 2014). DreamFold employs atomistic force fields in the training set and during the reconstruction of the 3D structures from the latent space. Therefore, our method is subject to the artifacts caused by these atomistic force fields.

FIGURE 8.

Analysis of Ubiquitin's unfolded state. (a) Folding landscape (frequency histogram) of Ubiquitin. Black dots indicate the conformations sampled from the unfolded basin. (b) Buriedness of each residue. Green and red boxes indicate regions of agreement or disagreement with experimental data, respectively. (c) Protection factor of each residue from the study of Yagi‐Utsumi et al. calculated through hydrogen/deuterium exchange. (d, e) Structure of Ubiquitin with residues colored to show their level of residual structure (i.e., protection). Red corresponds to very protected, purple to protected and black to exposed to the solvent.

We have also calculated the free energy landscape of Ubiquitin and compared our results against MD and against an advanced Machine Learning Coarse‐Grained method. Results are shown in Supporting Information S1: section 12.

2.9. Structural ensemble of hCRBP2

We have then used DreamFold to infer the folding pathway of the human Cellular Retinol Binding Protein 2 (hCRBP2, PDB: 4ZGU). Due to its medium‐large size (133 aa, 2163 atoms), it would be challenging to study its folding via standard MD. DreamFold is instead a fast method to obtain a good approximation of its folding landscape (Figure 9a).

FIGURE 9.

Conformational landscape for the human Cellular Retinol Binding Protein 2 (hCRBP2) protein. (a) Folding landscape visualized as RMSD to native versus binding pocket solvent accessible surface area. (b) Crystal structure of the domain‐swapped dimer. Monomers drawn in different colors. (c) In the native state, the retinol binding pocket is buried in the β‐barrel and is inaccessible for retinol binding. (c–f) Structure of the native state and of the native‐like folding intermediates computed with the World Model. They display a partially formed but accessible retinol binding site. Binding affinities to retinol have been calculated with Vina. (g–i) Structures of the open monomer folding intermediates computed by the World Model. Their structure is resemblant of the monomer of the crystal, with the N‐terminal and C‐terminal partially formed and separated by a central hinge loop. (k) Structure of the hCRBP2 unfolded state. REU, Rosetta Energy Units.

HCRBP2 is an intracellular chaperone for retinol (vitamin A). It binds dietary retinol in the intestine, protects it from degradation, and directs it to enzymes for storage or conversion to retinoic acid. By doing so, it regulates vitamin A absorption, metabolism, and signaling: essential for development and epithelial health. In the native state, the protein has a tightly packed β‐barrel fold that buries the retinol binding pocket, making it inaccessible (Figure 9c). This raises the question of how retinol can enter, suggesting that structural changes must take place to allow retinol binding (Lu et al., 1999). The “portal hypothesis” (Vaezeslami et al., 2006) suggests that the α1‐loop‐α2 motif together with the two loops connecting β‐strands 3–4 and 5–6, near the entrance of the barrel, can transiently open to expose the barrel and let retinol in. Another hypothesis is that local breathing motions of the protein create temporary openings large enough for retinol to slip through (Ragona et al., 2014). Nonetheless, the B‐factors of the portal region of the crystal of hCRBP2 indicate increased backbone mobility in this region when the protein is in the apo form. This suggests a looser structure of the portal in the apo form which becomes more rigid upon retinol binding, locking the ligand inside (Silvaroli et al., 2016).

We have analyzed the structures of the hCRBP2 folding trajectories to check if we could capture such conformational transitions. Indeed, we could identify three native‐like conformations, where the retinol binding site is formed but also accessible for retinol entry.

1. One conformation is characterized by a relaxed β‐barrel structure (Figure 9f), which loosened and exposed the binding site, allowing retinol to slip in. This conformation is compatible with the hypothesis of the breathing motions that create temporary openings in the protein (a similar mechanism to cryptic pockets).

2. Another conformation is characterized by the displacement of the first N‐terminal β‐sheet up until helix α1, while the rest of the protein stays in its final folded state (Figure 9e). The displaced N‐terminal exposed the inside of the barrel and therefore, the binding site.

3. Finally, one conformation (Figure 9d) characterized by the displaced α1‐loop‐α2 motif, exposing the barrel, while the rest of the protein is in its final folded state. This conformation supports the “portal hypothesis” discussed before, where the α1‐loop‐α2 motif transiently opens to let retinol enter and bind. In these intermediates, the binding pockets are accessible and show binding affinity to retinol (Figure 9d–f).

HCRBP2 also has an intermediate earlier in the folding pathway. It is the so‐called “open monomer” folding intermediate, which was identified and crystallized as a domain‐swapped dimer (Assar et al., 2016) (Figure 9b). The folding intermediate of hCRBP2 is comprised of the N‐terminal and C‐terminal regions that are separated at a central hinge loop region. In this conformation, the protein is able to dimerize if it finds another open monomer, and then this extended conformation becomes stabilized. However, the structure of the non‐dimerized open monomer is still unknown. It is unlikely to be the same as in the dimer, since it lacks many of the interactions that can stabilize it. It is probably structurally heterogeneous due to the central flexible loop and the low number of stabilizing interactions. In three‐folding simulation, we could observe the transient formation of an intermediate structure resemblant of the open monomer found in the dimer. The structures are shown in Figure 9g–i. The N‐terminal is separated from the C‐terminal by a central hinge loop. The β‐barrel is partially formed, as well as the α1‐loop‐α2 motif.

3. CONCLUSIONS

We have demonstrated that generative World Models for policy evolution in the latent space can be implemented in the context of biomolecular simulations. Folding policy evolution becomes possible in the latent space, overcoming the need of high computational resources necessary to compute the real atomistic environment. We successfully computed the folding pathway for proteins of variable sizes, including two medium‐large proteins (PrP 124 aa and hCRBP2 133 aa) whose folding dynamics is inaccessible by standard simulation methods, thanks to the World Model's linear scaling O(N). DreamFold showed high accuracy for the simulation of protein folding mechanisms, for the prediction of the structure of the folding intermediates and of the TSs. We show that structure‐based regularization terms (Ramachandran score) can be used to influence the folding dynamics, making folding trajectories follow lower energy pathways. The inference on hCRBP2 identified in detail some crucial conformations involved in its biology, such as retinol binding and protein dimerization, that were before only hypothesized based on limited experimental observations. The conformations that can be identified with DreamFold are valuable for drug discovery. For example, they could be used as targets to design drugs that inhibit the binding to retinol, or that modulate the dimerization propensity of the protein.

Even though the method does not provide kinetics or thermodynamics information, we showed that it can be coupled with equilibrium MD to restore a general overview of the real dynamics of the system under the assumptions of MSM. To our knowledge, this is the first application of generative World Models in the context of biomolecular simulations. Future developments of the method could include its refinement to perform unguided molecular simulations (i.e., without the need to specify the target), or to generate thermodynamically consistent trajectories to provide kinetics and free energy insights.

3.1. Limitations

The major shortcoming of this method is its inability of directly computing kinetics and thermodynamics quantities. This limitation arises from the fact that the Controller of the World Model does not preserve detailed balance, because it is trained to only guide the folding forward toward the (latent) target state. Thanks to its high computational speed DreamFold is, therefore, more suited for obtaining the atomistic structure of folding intermediates along the folding pathways, rather than obtaining kinetics, thermodynamics, or free energy quantities. This is a different approach than, for example, Gō models (Takada, 2019) or coarse‐grained models (Souza et al., 2021) that by being well grounded to statistical physics are able to yield kinetics and thermodynamics values together with computational efficiency. Moreover, our method inherits the biases of atomistic force fields from the training data, such as low accuracy for long‐range interaction and the preference for local structure formation.

4. METHODS

DreamFold has been built via custom‐made code written in Python using Keras and tensorflow. Training data and structural calculations on the proteins have been made using pyRosetta, the Python‐based interface to the Rosetta molecular modeling tool. The energy minimization step was performed with pyRosetta's FastRelax function using the all‐atom force field (Alford et al., 2017) and default parameters, allowing the movement of the backbone and side chains torsion angles. Controller training (CMA) has been performed using the Python cma library.

Molecular dynamics simulations have been performed using GROMACS. Protein structures were positioned in a dodecahedral box with 12 Å minimum distance from the box walls. Water molecules have been modeled with TIP3P water and charges neutralized with Na⁺ and Cl⁻ counter ions. Each system was then energy minimized by steepest gradient descent (5000 steps), followed by constant number of particles, volume and temperature (NVT) equilibration (500 ps) and constant number of particles, pressure and temperature (NPT) equilibration (500 ps). Temperature was chosen to match available MD data and is shown in Figure 5. MD was run at the same temperature as the equilibrations and was performed using the leap‐frog integrator with a dt of 2 fs for 20,000,000 steps (total 40 ns). Non‐bonded interactions such as Van‐der‐Waals and Coulomb were set with a cutoff of 1.6 nm and have been computed on central processing unit). PME was employed for long‐range electrostatics and was computed on graphics processing unit. Parrinello‐Rahman barostat was used for pressure coupling of the system, and Nose‐Hoover thermostat for temperature coupling. GROMACS protocol files (.mdp files) for energy minimization, for NVT/NPT equilibration and for MD can be found in the GitHub repository. The force field used was AMBER99SB‐ILDN.

The computations have been performed on the High Performance Computing facility of Yale University.

AUTHOR CONTRIBUTIONS

AI developed the models, designed the study, wrote the code, analyzed the data. EC and JI provided data analysis support. MBG supervised the study and designed the scientific workflow. MBG and AI wrote the manuscript.

CONFLICT OF INTEREST STATEMENT

The authors declare no competing financial interests.

Supporting information

Data S1. Supporting Information.

Ianeselli A, Im J, Cavallin E, Gerstein MB. DreamFold: A World Model to efficiently generate protein folding pathways in the latent space. Protein Science. 2026;35(11):e70794. 10.1002/pro.70794

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are openly available in Zenodo at https://doi.org/10.5281/zenodo.17369796.