MoDyGAN: Exploring Protein Conformational Spaces

• MoDyGAN is an innovative framework combining molecular dynamics and GANs to simulate protein conformations using 2D pairwise feature matrices.
• The approach reconstructs accurate 3D protein structures from 2D matrices, employing ProGAN for generative modeling and dual discriminators for error correction.
• Findings show MoDyGAN produces precise, plausible protein forms and interpolates between conformations, with applications for complex molecular systems.

MoDyGAN is a computational framework designed to combine molecular dynamics (MD) simulations with generative adversarial networks (GANs) to efficiently explore protein conformational spaces. The core innovation of MoDyGAN lies in its reversible representation of 3D protein conformations as 2D “pairwise feature matrices,” enabling the application of advanced image-based GAN architectures to biomolecular data. MoDyGAN’s modular pipeline supports the generation of physically plausible protein structures, interpolation in conformational space, and potential extension to other complex 3D molecular systems (Liang et al., 18 Jul 2025).

1. Pipeline Structure and Methodological Innovations

MoDyGAN operates via three primary stages: generative modeling, coordinate recovery, and refinement.

1. Generative Modeling: The generator, based on the Progressive Growing of GANs (ProGAN) architecture, receives a 100-dimensional vector sampled from a multivariate Gaussian distribution. This input is mapped to an image-like pairwise feature matrix, where each matrix element encodes the spatial relationship between two protein backbone atoms as a vector in spherical coordinates (radius $r$, inclination $\phi$, azimuthal angle $\theta$).
2. 3D Recovery: Recovery of Cartesian coordinates from the matrix utilizes a deterministic mapping:

$$x = r \sin(\phi) \cos(\theta),\quad y = r \sin(\phi) \sin(\theta),\quad z = r \cos(\phi)$$

This process is performed for each atom, referencing its spherical relationships to others, resulting in $O(n^2)$ computational complexity for $n$ backbone atoms.

1. Refinement Module:

The initial 3D conformation—recovered from the generator’s output—may exhibit local geometric errors (e.g., unusual bond angles, minor backbone distortions). To address this, MoDyGAN employs a Pix2Pix-based image-to-image translation module augmented with ensemble learning and a dual-discriminator scheme: - The global discriminator evaluates structural plausibility at the whole-protein level. - The secondary structure–focused discriminator specializes in correcting errors in well-defined regions (such as alpha helices or beta sheets).

The full training objective is:

$G^* = \arg\min_G \max_{D_1, D_2}\, L(G, D_1, D_2)$

where:

$$L(G, D_1, D_2) = L(G, D_1) + L(G, D_2) + \lambda_{L_1} L_{L_1}(G)$$

here, $L(G, D_i)$ is the adversarial loss for discriminator $D_i$ and $L_{L_1}$ is the pixel-wise $L_1$ reconstruction loss weighted by a large constant.

2. Representation of Protein Structures

Central to MoDyGAN is the conversion of protein conformations from 3D Cartesian coordinates to a 2D pairwise feature matrix, compatible with convolutional image-processing architectures. For a protein with $n$ backbone atoms, the approach operates as follows:

• Each atom $i$ is treated as a local origin.
• For all pairs $(i, j)$, the vector from $i$ to $j$ is computed and recorded in spherical coordinates.
• These are assembled into an $n \times n \times 3$ matrix: dimensions correspond to atom pairs, and the three channels are $r$, $\phi$, and $\theta$.

This representation is reversible: the original 3D geometry can be recovered without loss of information, and orientation-invariant, simplifying the learning task for convolutional networks.

3. Generator and Refinement Modules

The generator utilizes ProGAN’s coarse-to-fine progression, harnessing convolutional layers for upscaling and detail enrichment in the image-like matrix. This enables MoDyGAN to leverage advances from computer-vision GANs for molecular structures.

Due to the generator’s likelihood of introducing local steric clashes or unphysical dihedral angles, the refinement module maps initial outputs to physically acceptable conformations. The module is trained with two discriminators:

• The global discriminator ensures the matrices correspond to overall native-like protein folds.
• The secondary structure–focused discriminator penalizes feature matrices violating known helix or strand motifs.

Ensemble learning combines outputs of several refinement paths to further enhance accuracy in both rigid and flexible regions.

4. Empirical Evaluation and Case Studies

MoDyGAN's effectiveness is demonstrated in two principal experiments:

Protein/System	Purpose	Outcomes
Phospholipase A₂ (1POA), αB-crystallin (2WJ7), α-toxin (1BMR)	Rigid structure generation	Average N–Cα–C bond angle errors reduced (e.g., from 144.92° ± 13.85° to ~112.59° ± 3.84° in 1POA) after refinement. Backbone energy and RMSD also showed improvement.
Deca-alanine	Conformational interpolation (helix–coil)	GAN-generated intermediates aligned with steered MD (SMD) paths despite being trained only on endpoint conformations. Statistical measures showed significant overlap with SMD trajectories; KNN analysis indicated novelty.

The results indicate that the system produces structures with corrected geometric properties and enables plausibly smooth transitions between major conformational states (Liang et al., 18 Jul 2025).

5. Extensions and Generality

The methodology is not limited to proteins. The reversible matrix representation can, in principle, be adapted to RNA, supramolecular complexes, or nanostructures. Potential directions outlined in the original work include:

• Energy-aware refinement to enforce native-state energies.
• Temporal dynamic forecasting of structure evolution.
• Protein loop or flexible region modeling and rapid conformational sampling for drug design.

A plausible implication is that similar workflows might be developed for a broader class of 3D molecular sampling problems.

6. Significance Within Molecular Simulation and Deep Learning

MoDyGAN represents an intersection of physics-based and data-driven modeling:

• By learning a continuous mapping from a latent Gaussian to physically plausible conformational space, it enables sampling of new structures at a fraction of MD’s computational cost.
• The use of image-based neural architectures, in tandem with a modular refinement system, yields enhanced ability to capture both global and local features of protein folds.
• Latent variable interpolation enables the paper of folding pathways and transition intermediates in a manner not directly accessible by traditional MD.

This design opens a route to integrating generative modeling and simulation for efficient, flexible exploration of biochemical conformational landscapes (Liang et al., 18 Jul 2025).

7. Relationship to Modular Architectures

MoDyGAN builds on the principle of modularity exemplified by ModularGAN (Zhao et al., 2018). ModularGAN's architecture employs reusable modules (encoder, transformer, reconstructor) that operate on shared feature spaces, thereby supporting flexible composition and scalability. Similarly, MoDyGAN’s sequential generator, recovery, and refinement modules provide well-defined interfaces between stages, enabling independent development and targeted improvements at each phase. This modular approach is essential to both scalability and adaptability in high-dimensional generative tasks.

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MoDyGAN offers a rigorous framework for bridging the statistical power of advanced GANs with molecular simulation, providing efficient mechanisms for conformational sampling, structural refinement, and generalization to arbitrary 3D molecular systems. The pipeline’s orientation-invariant representations, dual-discriminator refinement, and empirical validation across diverse scenarios position MoDyGAN as a capable tool for contemporary computational biology and molecular modeling research.