SE(3)-Stochastic Flow Matching for Protein Backbone Generation (2310.02391v4)

Abstract: The computational design of novel protein structures has the potential to impact numerous scientific disciplines greatly. Toward this goal, we introduce FoldFlow, a series of novel generative models of increasing modeling power based on the flow-matching paradigm over $3\mathrm{D}$ rigid motions -- i.e. the group $\text{SE}(3)$ -- enabling accurate modeling of protein backbones. We first introduce FoldFlow-Base, a simulation-free approach to learning deterministic continuous-time dynamics and matching invariant target distributions on $\text{SE}(3)$. We next accelerate training by incorporating Riemannian optimal transport to create FoldFlow-OT, leading to the construction of both more simple and stable flows. Finally, we design FoldFlow-SFM, coupling both Riemannian OT and simulation-free training to learn stochastic continuous-time dynamics over $\text{SE}(3)$. Our family of FoldFlow, generative models offers several key advantages over previous approaches to the generative modeling of proteins: they are more stable and faster to train than diffusion-based approaches, and our models enjoy the ability to map any invariant source distribution to any invariant target distribution over $\text{SE}(3)$. Empirically, we validate FoldFlow, on protein backbone generation of up to $300$ amino acids leading to high-quality designable, diverse, and novel samples.

• The paper introduces the novel FoldFlow framework that combines deterministic continuous-time dynamics, simulation-free stochastic training, and Riemannian optimal transport for protein backbone generation.
• It demonstrates that FoldFlow models can generate protein backbones of up to 300 amino acids more efficiently and stably than traditional diffusion-based methods.
• The work offers significant implications for drug design and protein engineering by enabling rapid, diversified, and designable protein structure generation.

Overview of $SE(3)$ Stochastic Flow Matching for Protein Backbone Generation

The paper "$SE(3)$ Stochastic Flow Matching for Protein Backbone Generation" presents novel methodologies for the computational design of protein structures, a task that holds significant promise across scientific domains, including drug design and therapeutic development. The work introduces the FoldFlow model family, leveraging the structural group $SE(3)$ to accurately generate protein backbones. The authors target three primary innovations: deterministic continuous-time dynamics, Riemannian optimal transport (OT), and simulation-free stochastic training. These adaptations collectively advance the generative modeling landscape beyond standard diffusion-based approaches, which the authors argue are less stable and slower to converge.

FoldFlow encompasses three distinct models—FoldFlow-Base, FoldFlow-OT, and FoldFlow-SFM—each progressively more sophisticated in capturing the geometric nuances of $SE(3)$. The foundational model, FoldFlow-Base, employs simulation-free training to learn deterministic continuous-time dynamics. This is augmented in FoldFlow-OT with Riemannian optimal transport, aiming to simplify and stabilize the generative flows. The most comprehensive model, FoldFlow-SFM, combines stochastic continuous-time dynamics with both the prior innovations, thereby integrating Riemannian optimal transport and simulation-free training methodologies.

Strong Numerical Results and Claims

The authors deliver empirical validations showing FoldFlow’s capability to generate protein backbones of up to 300 amino acids efficiently. The results highlight the designability, diversity, and novelty of samples generated using FoldFlow. Specific metrics validated against standard baselines illustrate FoldFlow models outperforming diffusion-based approaches across these parameters. The development of Conditional Flow Matching (CFM) methods - allowing mapping from any invariant source distribution to any invariant target distribution within $SE(3)$ - is noted as a key feature enabling higher processing speeds and stability. Furthermore, stochastic aspects were emphasized in FoldFlow-SFM to accommodate biological variability inherent in protein structures.

Implications and Future Directions

The practical implications span across computational biology and protein engineering, offering a robust toolset for rational protein design aligned with evolutionary biology's methodologies. Theoretically, FoldFlow models provide structured generative architectures that may inspire future research across manifold-based deep learning, stochastic processes, and geometric machine learning.

Given these advancements, pathways for future exploration include broadening the models' application to include conditional generation, thus allowing more targeted protein engineering tasks. Moreover, integrating sequence-level data with structure could propel the models into more sophisticated design spaces—aligning with biological functionalities. Additionally, advancing these models' capacity to handle larger protein complexes and detailed interactions could further augment their utility and alignment with empirical biological processes.

In conclusion, FoldFlow underscores a meaningful leap in protein structure modeling, aligning computational capabilities with biological insights adaptively and efficiently. These contributions unravel vast possibilities in pharmacology, biotechnology, and synthetic biology by supporting informed rational design strategies.