Str2Str: A Score-based Framework for Zero-shot Protein Conformation Sampling (2306.03117v3)

Abstract: The dynamic nature of proteins is crucial for determining their biological functions and properties, for which Monte Carlo (MC) and molecular dynamics (MD) simulations stand as predominant tools to study such phenomena. By utilizing empirically derived force fields, MC or MD simulations explore the conformational space through numerically evolving the system via Markov chain or Newtonian mechanics. However, the high-energy barrier of the force fields can hamper the exploration of both methods by the rare event, resulting in inadequately sampled ensemble without exhaustive running. Existing learning-based approaches perform direct sampling yet heavily rely on target-specific simulation data for training, which suffers from high data acquisition cost and poor generalizability. Inspired by simulated annealing, we propose Str2Str, a novel structure-to-structure translation framework capable of zero-shot conformation sampling with roto-translation equivariant property. Our method leverages an amortized denoising score matching objective trained on general crystal structures and has no reliance on simulation data during both training and inference. Experimental results across several benchmarking protein systems demonstrate that Str2Str outperforms previous state-of-the-art generative structure prediction models and can be orders of magnitude faster compared to long MD simulations. Our open-source implementation is available at https://github.com/lujiarui/Str2Str

• The paper presents a novel zero-shot framework, Str2Str, that leverages score-based generative modeling to efficiently sample protein conformations.
• It reformulates conformation sampling as a structure-to-structure translation using a forward-backward diffusion process with roto-translation equivariance.
• Experimental results demonstrate that Str2Str improves validity, fidelity, and diversity over state-of-the-art MD and MC methods while significantly reducing computational costs.

A Score-based Framework for Zero-shot Protein Conformation Sampling

The paper under review introduces an innovative framework called "Str2Str" for achieving zero-shot protein conformation sampling, leveraging a score-based approach. This research is grounded in the fundamental understanding that proteins exhibit dynamic properties pivotal for their biological functions, which require exhaustive conformational sampling to be comprehensively understood. Traditional methodologies for such tasks have predominantly relied on Monte Carlo (MC) and molecular dynamics (MD) simulations guided by empirical force fields. However, Str2Str proposes a compelling alternative rooted in score-based generative modeling.

Methodology and Contributions

The core methodological contribution of this work is the formulation of protein conformation sampling as a structure-to-structure translation problem. Str2Str employs a forward-backward (FB) diffusion process over Riemannian manifolds, specifically targeting the $\rm{SE(3)}^n$ space where sequences of protein backbone frames reside. This approach is inspired by simulated annealing, designed to incorporate both exploration (enhanced by stochastic perturbation) and exploitation (through score-based annealing) within its translation dynamics.

A significant feature of Str2Str is its zero-shot capability, which implies that the model can generalize to unseen proteins without requiring simulation data or prior knowledge specific to the test proteins. The training is carried out on general protein crystal structures from databases such as the Protein Data Bank (PDB), allowing for broad applicability without additional simulation data during inference.

The framework is underlying defined by several formal mathematical formulations, including the denoising score matching objective and the equivariance properties of the scoring model. The training leverages a Denoising Invariant Point Attention (DenoisingIPA) module, which maintains roto-translation equivariance, thereby ensuring that predicted conformations remain physically plausible with respect to the input structure's spatial orientation.

Experimental Evaluation and Findings

The experiments conducted with Str2Str focused on fast-folding protein systems to demonstrate its performance in generating conformational ensembles. The results were benchmarked against multiple state-of-the-art models, including EigenFold and idpGAN. Str2Str consistently outperformed these baselines across several key metrics:

• Validity: The structural validity of generated samples was demonstrated with high scores in metrics like bond and clash checks.
• Fidelity: Str2Str showed improved fidelity in approximating the reference MD trajectories, as measured by metrics such as Jensen-Shannon divergence on pairwise distances.
• Diversity: The approach also maintained a better balance between fidelity and diversity, capturing a wider range of conformational states effectively.

Furthermore, the framework exhibited significant efficiency advantages over traditional MD approaches, delivering comparable performance in terms of conformational sampling but with orders of magnitude less computational time required.

Implications and Future Directions

Str2Str opens up compelling opportunities for protein dynamics research, specifically by providing a markedly more efficient approach to exploring the conformational space of proteins. This capability can directly impact areas such as drug design, where understanding the various protein states is crucial.

Practically, the framework suggests a scalable way to derive insights into proteins' structural transitions without the prohibitive costs traditionally associated with MD simulations. Theoretically, Str2Str pushes the boundaries of score-based generative models within the biological sciences, demonstrating how they can be applied beyond typical image or text data to complex three-dimensional biological structures.

Future work could explore integrating energy-based optimization post-sampling to further refine sampled ensembles towards true Boltzmann distributions. Additionally, extensions of the model might involve hybrid approaches that combine simulations with Str2Str's generative modeling to enhance predictive precision and expand upon the temporal aspects absent in the current model.

Str2Str thus stands as a significant contribution to protein modeling, offering a robust, efficient, and scalable tool for conformation sampling in complex biological systems.