Understanding the structural dynamics of biomolecules is crucial for uncovering biological functions. As molecular dynamics (MD) simulation data becomes more available, deep generative models have been developed to synthesize realistic MD trajectories. However, existing methods produce fixed-length trajectories by jointly denoising high-dimensional spatiotemporal representations, which conflicts with MD’s frame-by-frame integration process and fails to capture time-dependent conformational diversity. Inspired by MD's sequential nature, we introduce a new probabilistic autoregressive (ProAR) framework for trajectory generation. ProAR uses a dual-network system that models each frame as a multivariate Gaussian distribution and employs an anti-drifting sampling strategy to reduce cumulative errors. This approach captures conformational uncertainty and time-coupled structural changes while allowing flexible generation of trajectories of arbitrary length. Experiments on ATLAS, a large-scale protein MD dataset, demonstrate that for long trajectory generation, our model achieves a 7.5% reduction in reconstruction RMSE and an average 25.8% improvement in conformation change accuracy compared to previous state-of-the-art methods. For conformation sampling task, it performs comparably to specialized time-independent models, providing a flexible and dependable alternative to standard MD simulations.

Vision modeling has advanced rapidly with Transformers, whose attention mechanisms capture visual dependencies but lack a principled account of how semantic information propagates spatially. We revisit this problem from a wave-based perspective: feature maps are treated as spatial signals whose evolution over an internal propagation time (aligned with network depth) is governed by an underdamped wave equation. In this formulation, spatial frequency—from low-frequency global layout to high-frequency edges and textures—is modeled explicitly, and its interaction with propagation time is controlled rather than implicitly fixed. We derive a closed-form, frequency–time decoupled solution and implement it as the Wave Propagation Operator (WPO), a lightweight module that models global interactions in O(NlogN) time—far lower than attention. Building on WPO, we propose a family of WaveFormer models as drop-in replacements for standard ViTs and CNNs, achieving competitive accuracy across image classification, object detection, and semantic segmentation, while delivering up to 1.6× higher throughput and 30% fewer FLOPs than attention-based alternatives. Furthermore, our results demonstrate that wave propagation introduces a complementary modeling bias to heat-based methods, effectively capturing both global coherence and high-frequency details essential for rich visual semantics.

Three-dimensional atomic arrangements of biomolecules are key to demystifying biological functions. The rapid expansion of accessible structural data, driven by advances in AI for science, highlights the critical challenge of efficiently modeling large-scale biomolecular structures, which are high-dimensional systems shaped by biological assembly principles. To address this, we introduce BiHiTo, a multi-level Biomolecular Hierarchy-inspired Tokenizer that intrinsically mimics natural biological assembly hierarchies. Specifically, we design a multi-codebook quantizer that mirrors the natural hierarchy of biomolecular structure, enabling simultaneous capture of representations spanning atomic motifs to global conformational variations. This hierarchical alignment markedly improves the biological interpretability and reconstruction fidelity of biomolecular structure.Extensive experiments demonstrate that BiHiTo delivers state-of-the-art performance and robust generalization across molecular dynamics trajectories and macromolecular complexes, facilitating advances in structure generation and dynamic conformation exploration. In the reconstruction of the CASP14 and OOD test set FastFolding protein multi-conformation data, our method achieves a 17% and 51% reduction in RMSD compared to Bio2Token, respectively.

Despite high-resolution structural studies on the USP14-proteasome-substrate complexes, time-resolved cryo-electron microscopy (cryo-EM) results on USP14-regulated allostery of the 26S proteasome are still very limited and a quantitative understanding of substrate degradation dynamics remains elusive. In this study, we propose a mean field model of ordinary differential equations (ODEs) for USP14 regulated substrate degradation in 26S proteasome. The kinetic model incorporates recent cryo-EM findings on the allostery of 26S proteasome and generates results in good agreement with time-resolved experimental observations. The model elucidates that USP14 typically reduces the substrate degradation rate and reveals the functional dependence of this rate on the concentrations of substrate and adenosine triphosphate (ATP). The half-maximal effective concentration (EC50) of the substrate for different ATP concentrations is predicted. When multiple substrates are present, the model suggests that substrates that are easier to insert into the OB-ring and disengage from the proteasome, or less likely to undergo deubiquitination would be more favored to be degraded by the USP14-bound proteasome. The mean field model proposed here quantitatively considers the process of proteasomal substrate degradation from the perspective of chemical kinetics, and provides a quantitative framework to decode the dynamic interplay between USP14 and the proteasome.

BACKGROUND: The detection of weak signals and selection of single particles from low-contrast micrographs of frozen hydrated biomolecules by cryo-electron microscopy (cryo-EM) represents a major practical bottleneck in cryo-EM data analysis. Template-based particle picking by an objective function using fast local correlation (FLC) allows computational extraction of a large number of candidate particles from micrographs. Another independent objective function based on maximum likelihood estimates (MLE) can be used to align the images and verify the presence of a signal in the selected particles. Despite the widespread applications of the two objective functions, an optimal combination of their utilities has not been exploited. Here we propose a bi-objective function (BOF) approach that combines both FLC and MLE and explore the potential advantages and limitations of BOF in signal detection from cryo-EM data. RESULTS: The robustness of the BOF strategy in particle selection and verification was systematically examined with both simulated and experimental cryo-EM data. We investigated how the performance of the BOF approach is quantitatively affected by the signal-to-noise ratio (SNR) of cryo-EM data and by the choice of initialization for FLC and MLE. We quantitatively pinpointed the critical SNR (~ 0.005), at which the BOF approach starts losing its ability to select and verify particles reliably. We found that the use of a Gaussian model to initialize the MLE suppresses the adverse effects of reference dependency in the FLC function used for template-matching. CONCLUSION: The BOF approach, which combines two distinct objective functions, provides a sensitive way to verify particles for downstream cryo-EM structure analysis. Importantly, reference dependency of the FLC does not necessarily transfer to the MLE, enabling the robust detection of weak signals. Our insights into the numerical behavior of the BOF approach can be used to improve automation efficiency in the cryo-EM data processing pipeline for high-resolution structural determination.

BACKGROUND: Single-particle cryo-electron microscopy (cryo-EM) has become a mainstream tool for the structural determination of biological macromolecular complexes. However, high-resolution cryo-EM reconstruction often requires hundreds of thousands of single-particle images. Particle extraction from experimental micrographs thus can be laborious and presents a major practical bottleneck in cryo-EM structural determination. Existing computational methods for particle picking often use low-resolution templates for particle matching, making them susceptible to reference-dependent bias. It is critical to develop a highly efficient template-free method for the automatic recognition of particle images from cryo-EM micrographs. RESULTS: We developed a deep learning-based algorithmic framework, DeepEM, for single-particle recognition from noisy cryo-EM micrographs, enabling automated particle picking, selection and verification in an integrated fashion. The kernel of DeepEM is built upon a convolutional neural network (CNN) composed of eight layers, which can be recursively trained to be highly "knowledgeable". Our approach exhibits an improved performance and accuracy when tested on the standard KLH dataset. Application of DeepEM to several challenging experimental cryo-EM datasets demonstrated its ability to avoid the selection of un-wanted particles and non-particles even when true particles contain fewer features. CONCLUSIONS: The DeepEM methodology, derived from a deep CNN, allows automated particle extraction from raw cryo-EM micrographs in the absence of a template. It demonstrates an improved performance, objectivity and accuracy. Application of this novel method is expected to free the labor involved in single-particle verification, significantly improving the efficiency of cryo-EM data processing.