Generating diverse, all-atom conformational ensembles of dynamic proteins such as G-protein-coupled receptors (GPCRs) is critical for understanding their function, yet most generative models simplify atomic detail or ignore conformational diversity altogether.

Machine learning force fields (MLFFs) have instigated a groundbreaking shift in molecular dynamics (MD) simulations across a wide range of fields, such as physics, chemistry, biology, and materials science. Incorporating higher order many-body interactions can enhance the expressiveness and accuracy of models. Recent models have achieved this by explicitly including up to four-body interactions. However, five-body interactions, which have relevance in various fields, are still challenging to incorporate efficiently into MLFFs. In this work, we propose the quintuple network (QuinNet), an end-to-end graph neural network that efficiently expresses many-body interactions up to five-body interactions with ab initio accuracy. By analyzing the topology of diverse many-body interactions, we design the model architecture to efficiently and explicitly represent these interactions. We evaluate QuinNet on public datasets of small molecules, such as MD17 and its revised version, and show that it is compatible with other state-of-the-art models on these benchmarks.

The left panelshows the energy profile for arotation around an O-C-C-C dihedral angle. In the right panel of Figure 4, we show energy predictions along a minimum energy path of an intramolecular hydrogen transfer reaction. A.2.2 3BPADataset The 3BPA dataset contains DFT train test splits of a flexible drug-like organic molecule sampled from different temperature molecular dynamics trajectories [33]. The first step of the algorithm is to contract the generalized Clebsch-Gordan coefficients with the weights of the product basis. Then, the last dimension of cν is contracted with theAi-features' last dimension resulting in the a-tensor with correlation orderν 1.

Given a probability distribution $μ$ in $\mathbb{R}^d$ represented by data, we study in this paper the generative modeling of its conditional probability distributions on the level-sets of a collective variable $ξ: \mathbb{R}^d \rightarrow \mathbb{R}^k$, where $1 \le k

Machine learning (ML) is rapidly transforming the way molecular dynamics simulations are performed and analyzed, from materials modeling to studies of protein folding and function. ML algorithms are often employed to learn low-dimensional representations of conformational landscapes and to cluster trajectories into relevant metastable states. Most of these algorithms require selecting a small number of features that describe the problem of interest. Although deep neural networks can tackle large numbers of input features, the training costs increase with input size, which makes the selection of a subset of features mandatory for most problems of practical interest. Here, we show that random nonlinear projections can be used to compress large feature spaces and make computations faster without substantial loss of information. We describe an efficient way to produce random projections and then exemplify the general procedure for protein folding. For our test cases NTL9 and the double-norleucin variant of the villin headpiece, we find that random compression retains the core static and dynamic information of the original high dimensional feature space and makes trajectory analysis more robust.

The complementarity-determining regions of antibodies are loop structures that are key to their interactions with antigens, and of high importance to the design of novel biologics. Since the 1980s, categorizing the diversity of CDR structures into canonical clusters has enabled the identification of key structural motifs of antibodies. However, existing approaches have limited coverage and cannot be readily incorporated into protein foundation models. Here we introduce ImmunoGlobulin LOOp Tokenizer, Igloo, a multimodal antibody loop tokenizer that encodes backbone dihedral angles and sequence. Igloo is trained using a contrastive learning objective to map loops with similar backbone dihedral angles closer together in latent space. Igloo can efficiently retrieve the closest matching loop structures from a structural antibody database, outperforming existing methods on identifying similar H3 loops by 5.9\%. Igloo assigns tokens to all loops, addressing the limited coverage issue of canonical clusters, while retaining the ability to recover canonical loop conformations. To demonstrate the versatility of Igloo tokens, we show that they can be incorporated into protein language models with IglooLM and IglooALM. On predicting binding affinity of heavy chain variants, IglooLM outperforms the base protein language model on 8 out of 10 antibody-antigen targets. Additionally, it is on par with existing state-of-the-art sequence-based and multimodal protein language models, performing comparably to models with $7\times$ more parameters. IglooALM samples antibody loops which are diverse in sequence and more consistent in structure than state-of-the-art antibody inverse folding models. Igloo demonstrates the benefit of introducing multimodal tokens for antibody loops for encoding the diverse landscape of antibody loops, improving protein foundation models, and for antibody CDR design.

We present a novel theoretical interpretation of AlphaFold1 that reveals the potential of generalized Bayesian updating for probabilistic deep learning. The seminal breakthrough of AlphaFold1 in protein structure prediction by deep learning relied on a learned potential energy function, in contrast to the later end-to-end architectures of AlphaFold2 and AlphaFold3. While this potential was originally justified by referring to physical potentials of mean force (PMFs), we reinterpret AlphaFold1's potential as an instance of {\em probability kinematics} -- also known as {\em Jeffrey conditioning} -- a principled but under-recognised generalization of conventional Bayesian updating. Probability kinematics accommodates uncertain or {\em soft} evidence in the form of updated probabilities over a partition. This perspective reveals AlphaFold1's potential as a form of generalized Bayesian updating, rather than a thermodynamic potential. To confirm our probabilistic framework's scope and precision, we analyze a synthetic 2D model in which an angular random walk prior is updated with evidence on distances via probability kinematics, mirroring AlphaFold1's approach. This theoretical contribution connects AlphaFold1 to a broader class of well-justified Bayesian methods, allowing precise quantification, surpassing merely qualitative heuristics based on PMFs. Our contribution is theoretical: we replace AlphaFold1's heuristic analogy with a principled probabilistic framework, tested in a controlled synthetic setting where correctness can be assessed. More broadly, our results point to the considerable promise of probability kinematics for probabilistic deep learning, by allowing the formulation of complex models from a few simpler components.

Deployable structures inspired by origami have provided lightweight, compact, and reconfigurable solutions for various robotic and architectural applications. However, creating an integrated structural system that can effectively balance the competing requirements of high packing efficiency, simple deployment, and precise morphing into multiple load-bearing configurations remains a significant challenge. This study introduces a new class of hyper-Yoshimura origami, which exhibits a wide range of kinematically admissible and locally metastable states, including newly discovered symmetric "self-packing" and asymmetric "pop-out" states. This metastability is achieved by breaking a design rule of Yoshimura origami that has been in place for many decades. To this end, this study derives a new set of mathematically rigorous design rules and geometric formulations. Based on this, forward and inverse kinematic strategies are developed to stack hyper-Yoshimura modules into deployable booms that can approximate complex 3D shapes. Finally, this study showcases the potential of hyper-Yoshimura with a meter-scale pop-up cellphone charging station deployed at our university's bus transit station, along with a 3D-printed, scaled prototype of a space crane that can function as an object manipulator, solar tracking device, or high-load-bearing structure. These results establish hyper-Yoshimura as a promising platform for deployable and adaptable robotic systems in both terrestrial and space environments.

Generating diverse, all-atom conformational ensembles of dynamic proteins such as G-protein-coupled receptors (GPCRs) is critical for understanding their function, yet most generative models simplify atomic detail or ignore conformational diversity altogether. We present latent diffusion for full protein generation (LD-FPG), a framework that constructs complete all-atom protein structures, including every side-chain heavy atom, directly from molecular dynamics (MD) trajectories. LD-FPG employs a Chebyshev graph neural network (ChebNet) to obtain low-dimensional latent embeddings of protein conformations, which are processed using three pooling strategies: blind, sequential and residue-based. A diffusion model trained on these latent representations generates new samples that a decoder, optionally regularized by dihedral-angle losses, maps back to Cartesian coordinates. Using D2R-MD, a 2-microsecond MD trajectory (12 000 frames) of the human dopamine D2 receptor in a membrane environment, the sequential and residue-based pooling strategy reproduces the reference ensemble with high structural fidelity (all-atom lDDT of approximately 0.7; C-alpha-lDDT of approximately 0.8) and recovers backbone and side-chain dihedral-angle distributions with a Jensen-Shannon divergence of less than 0.03 compared to the MD data. LD-FPG thereby offers a practical route to system-specific, all-atom ensemble generation for large proteins, providing a promising tool for structure-based therapeutic design on complex, dynamic targets. The D2R-MD dataset and our implementation are freely available to facilitate further research.