SE(3) diffusion model with application to protein backbone generation (2302.02277v3)

Abstract: The design of novel protein structures remains a challenge in protein engineering for applications across biomedicine and chemistry. In this line of work, a diffusion model over rigid bodies in 3D (referred to as frames) has shown success in generating novel, functional protein backbones that have not been observed in nature. However, there exists no principled methodological framework for diffusion on SE(3), the space of orientation preserving rigid motions in R3, that operates on frames and confers the group invariance. We address these shortcomings by developing theoretical foundations of SE(3) invariant diffusion models on multiple frames followed by a novel framework, FrameDiff, for learning the SE(3) equivariant score over multiple frames. We apply FrameDiff on monomer backbone generation and find it can generate designable monomers up to 500 amino acids without relying on a pretrained protein structure prediction network that has been integral to previous methods. We find our samples are capable of generalizing beyond any known protein structure.

• The paper introduces FrameDiff, a novel SE(3) diffusion model that leverages Lie group metrics to generate realistic protein backbones.
• It simplifies the diffusion process by separating translations and rotations for effective denoising score matching on the non-compact SE(3) manifold.
• Empirical results demonstrate that FrameDiff produces diverse backbone structures up to 500 amino acids, offering a robust alternative to pretrained models.

SE(3) Diffusion Models for Protein Backbone Generation

This paper presents a formal approach to the problem of protein backbone generation utilizing diffusion models on the SE(3) manifold. The authors focus on constructing a principled framework for SE(3) invariant diffusion processes, coupled with the development of 'FrameDiff', a novel machine learning architecture tailored for the task of sampling realistic protein backbones without the necessity for pretrained structure prediction models.

Theoretical and Methodological Advancements

The paper addresses the theoretical gap in diffusion models operating on the SE(3) group, crucial for applications such as protein design that inherently involve 3D rigid body transformations. Unlike Euclidean spaces or compact manifolds, SE(3) requires a specific construction of diffusion processes due to its non-compact nature. The authors introduce a forward process for SE(3) space by leveraging canonical Lie group metrics and Laplacians, achieving a separation of translations and rotations under a specific metric choice. This decision not only simplifies the forward process but also makes it amenable to efficient denoising score matching (DSM) training by establishing independent computations for rotation and translation components.

The introduction of FrameDiff represents a significant methodological contribution. Unlike many practical implementations that rely on heuristic denoising loss or require pretraining, FrameDiff is both theoretically grounded in SE(3) equivariant score learning and demonstrates efficacy in generating realistic and diverse protein structures through purely geometrical diffusion mechanisms.

Empirical Evaluation

Empirically, FrameDiff demonstrates its capacity to generate diverse and novel backbone structures, addressing the task of de novo design which requires adhering to strict physical and chemical constraints. Through a series of experiments on monomer backbone generation, the model showcases the ability to produce backbones up to lengths of 500 amino acids. The researchers highlight the model's success in designing structures such that sequences predicted to fold into these designs achieve low RMSDs, with significant scaffold diversity observed in samples clustered using MaxCluster.

However, the paper does not claim state-of-the-art status outright, acknowledging the superior designability metrics achieved by models like RFdiffusion, which integrate pretraining. Instead, FrameDiff is positioned as a viable alternative that avoids the complexity of pretrained models while still achieving high levels of designability, albeit with some scope for improvement in longer sequences.

Practical and Theoretical Implications

FrameDiff removes the dependency on large pre-trained models, making it suitable for tasks where training on large datasets is infeasible, or where models need to be rapidly developed for novel contexts, such as emergent pathogens. The theoretical constructs pave the way for leveraging SE(3) diffusion models in other domains, such as robotics or physical simulations, where understanding the configurations of spatial bodies under symmetry constraints is paramount.

Overall, this work provides a comprehensive and theoretically rigorous approach to SE(3) diffusion modeling, demonstrating not only how these models can be adapted for complex geometrical spaces but also their practical utility in challenging real-world applications like protein design. Future directions could involve extending this framework to multimeric protein structures or integrating evolved sequence information to improve folding accuracy further. Additionally, the principles highlighted in this work have the potential to advance other fields reliant on SE(3) dynamics, representing a notable cross-disciplinary contribution.