TEMPO: Temporal Multi-scale Autoregressive Generation of Protein Conformational Ensembles

TL;DR

TEMPO addresses the challenge of generating temporally coherent, physically plausible protein dynamics by introducing a two-scale autoregressive framework that couples slow, global conformational transitions with fast, local fluctuations through stochastic differential equations. A spatiotemporal encoder with SE(3)–equivariant representation and invariant attention enables stable, physics-informed trajectory generation, while hierarchical inference anchors detailed dynamics to coarse-grained states. Across mdCATH and ATLAS, TEMPO achieves state-of-the-art performance on structural and thermodynamic metrics, significantly outperforming baselines in trajectory fidelity and efficiency (approximately 22 seconds to generate 400 frames on a single A100). These results demonstrate the practicality of trajectory-aware, multi-scale generative modeling for protein dynamics, offering a scalable alternative to MD with strong biomechanical realism. TEMPO’s framework also provides a foundation for future extensions to side-chain dynamics, ligand binding, and multi-molecule systems.

Abstract

Understanding the dynamic behavior of proteins is critical to elucidating their functional mechanisms, yet generating realistic, temporally coherent trajectories of protein ensembles remains a significant challenge. In this work, we introduce a novel hierarchical autoregressive framework for modeling protein dynamics that leverages the intrinsic multi-scale organization of molecular motions. Unlike existing methods that focus on generating static conformational ensembles or treat dynamic sampling as an independent process, our approach characterizes protein dynamics as a Markovian process. The framework employs a two-scale architecture: a low-resolution model captures slow, collective motions driving major conformational transitions, while a high-resolution model generates detailed local fluctuations conditioned on these large-scale movements. This hierarchical design ensures that the causal dependencies inherent in protein dynamics are preserved, enabling the generation of temporally coherent and physically realistic trajectories. By bridging high-level biophysical principles with state-of-the-art generative modeling, our approach provides an efficient framework for simulating protein dynamics that balances computational efficiency with physical accuracy.

Figures (13)

• Figure 1: Overview of our multi-scale protein dynamics generation framework. a) The hierarchical free energy landscape of protein dynamics, where slow motions (upper) guide fast local fluctuations (lower). b) Our two-stage generation process: the low-resolution model $f^s_\theta$ captures slow collective motions, while the high-resolution model $f^f_\phi$ fills in detailed dynamics. c) The neural architecture that parameterizes both models features spatial-temporal encoding of protein conformations.
• Figure 2: Comparison of PC projections between MD and generated conformations. (a-c) PC1 trajectories from MD (blue) and our slow-scale trajectories (red) for three representative proteins. (d) Box plot of cosine similarity scores comparing TEMPO and MDGen across the test set.
• Figure 3: FES comparison between MD trajectories (a,c) and generated ensembles (b,d) for proteins 2eyzA03 (a,b) and 3gyxA02 (c,d). Colors represent free energy values from low (blue) to high (red).
• Figure 4: Comparison of conformational transitions in PC space between TEMPO and MDGen baseline (bottom). Ground truth MD trajectories are shown in blue, while generated trajectories are in green. The polynomial fitting curves highlight the temporal evolution of conformational changes (Protein from left to right: 2e9xB01, 1s79A00, 1bl0A02, 3cx5E01).
• Figure 5: FES comparison between TEMPO (top row) and ESMFlow (bottom row) on four randomly selected test proteins. TEMPO's dynamic modeling shows more focused exploration of conformational space, whereas ESMFlow's independent sampling achieves broader coverage across the PCA-derived free energy surface (Protein from left to right: 1s79A00, 1x4tA01, 2e9xB01, 5b58T02).