Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This work aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science.

We introduce RNA-FrameFlow, the first generative model for 3D RNA backbone design. We build upon S E ( 3 ) flow matching for protein backbone generation and establish protocols for data preparation and evaluation to address unique challenges posed by RNA modeling. We formulate RNA structures as a set of rigid-body frames and associated loss functions which account for larger, more conformationally flexible RNA backbones (13 atoms per nucleotide) vs. proteins (4 atoms per residue). Toward tackling the lack of diversity in 3D RNA datasets, we explore training with structural clustering and cropping augmentations. Additionally, we define a suite of evaluation metrics to measure whether the generated RNA structures are globally self-consistent (via inverse folding followed by forward folding) and locally recover RNA-specific structural descriptors. The most performant version of RNA-FrameFlow generates locally realistic RNA backbones of 40-150 nucleotides, over 40% of which pass our validity criteria as measured by a self-consistency TM-score ≥ 0.45, at which two RNAs have the same global fold. Open-source code: github.com/rish-16/rna-backbone-design.

Computational RNA design tasks are often posed as inverse problems, where sequences are designed based on adopting a single desired secondary structure without considering 3D conformational diversity. We introduce gRNAde, a geometric RNA design pipeline operating on 3D RNA backbones to design sequences that explicitly account for structure and dynamics. gRNAde uses a multi-state Graph Neural Network and autoregressive decoding to generates candidate RNA sequences conditioned on one or more 3D backbone structures where the identities of the bases are unknown. On a single-state fixed backbone re-design benchmark of 14 RNA structures from the PDB identified by Das et al. (2010), gRNAde obtains higher native sequence recovery rates (56% on average) compared to Rosetta (45% on average), taking under a second to produce designs compared to the reported hours for Rosetta. We further demonstrate the utility of gRNAde on a new benchmark of multi-state design for structurally flexible RNAs, as well as zero-shot ranking of mutational fitness landscapes in a retrospective analysis of a recent ribozyme. Experimental wet lab validation on 10 different structured RNA backbones finds that gRNAde has a success rate of 50% at designing pseudoknotted RNA structures, a significant advance over 35% for Rosetta. Open source code and tutorials are available at: github.com/chaitjo/geometric-rna-design.

Antibodies, crucial for immune defense, primarily rely on complementarity-determining regions (CDRs) to bind and neutralize antigens, such as viruses. The design of these CDRs determines the antibody's affinity and specificity towards its target. Generative models, particularly denoising diffusion probabilistic models (DDPMs), have shown potential to advance the structure-based design of CDR regions. However, only a limited dataset of bound antibody-antigen structures is available, and generalization to out-of-distribution interfaces remains a challenge. Physics based force-fields, which approximate atomic interactions, offer a coarse but universal source of information to better mold designs to target interfaces. Integrating this foundational information into diffusion models is, therefore, highly desirable. Here, we propose a novel approach to enhance the sampling process of diffusion models by integrating force field energy-based feedback. Our model, DiffForce, employs forces to guide the diffusion sampling process, effectively blending the two distributions. Through extensive experiments, we demonstrate that our method guides the model to sample CDRs with lower energy, enhancing both the structure and sequence of the generated antibodies.

Protein design and directed evolution have separately contributed enormously to protein engineering. Without being mutually exclusive, the former relies on computation from first principles, while the latter is a combinatorial approach based on chance. Advances in ultrahigh throughput (uHT) screening, next generation sequencing and machine learning may create alternative routes to engineered proteins, where functional information linked to specific sequences is interpreted and extrapolated in silico. In particular, the miniaturisation of functional tests in water-in-oil emulsion droplets with picoliter volumes and their rapid generation and analysis (>1 kHz) allows screening of >10(7)-membered libraries in a day. Subsequently, decoding the selected clones by short or long-read sequencing methods leads to large sequence-function datasets that may allow extrapolation from experimental directed evolution to further improved mutants beyond the observed hits. In this work, we explore experimental strategies for how to draw up 'fitness landscapes' in sequence space with uHT droplet microfluidics, review the current state of AI/ML in enzyme engineering and discuss how uHT datasets may be combined with AI/ML to make meaningful predictions and accelerate biocatalyst engineering.

Engineering enzyme biocatalysts for higher efficiency is key to enabling sustainable, ‘green’ production processes for the chemical and pharmaceutical industry. This challenge can be tackled from two angles: by directed evolution, based on labor-intensive experimental testing of enzyme variant libraries, or by computational methods, where sequence-function data are used to predict biocatalyst improvements. Here, we combine both approaches into a two-week workflow, where ultra-high throughput screening of a library of imine reductases (IREDs) in microfluidic devices provides not only selected ‘hits’, but also long-read sequence data linked to fitness scores of >17 thousand enzyme variants. We demonstrate engineering of an IRED for chiral amine synthesis by mapping functional information in one go, ready to be used for interpretation and extrapolation by protein engineers with the help of machine learning (ML). We calculate position-dependent mutability and combinability scores of mutations and comprehensively illuminate a complex interplay of mutations driven by synergistic, often positively epistatic effects. Interpreted by easy-to-use regression and tree-based ML algorithms designed to suit the evaluation of random whole-gene mutagenesis data, 3-fold improved ‘hits’ obtained from experimental screening are extrapolated further to give up to 23-fold improvements in catalytic rate after testing only a handful of designed mutants. Our campaign is paradigmatic for future enzyme engineering that will rely on access to large sequence-function maps as profiles of the way a biocatalyst responds to mutation. These maps will chart the way to improved function by exploiting the synergy of rapid experimental screening combined with ML evaluation and extrapolation. ### Competing Interest Statement The authors have declared no competing interest.

Current protein generative models are able to design novel backbones with desired shapes or functional motifs. However, despite the importance of a protein’s dynamical properties for its function, conditioning on dynamical properties remains elusive. We present a new approach to protein generative modeling by leveraging Normal Mode Analysis that enables us to capture dynamical properties too. We introduce a method for conditioning the diffusion probabilistic models on protein dynamics, specifically on the lowest non-trivial normal mode of oscillation. Our method, similar to the classifier guidance conditioning, formulates the sampling process as being driven by conditional and unconditional terms. However, unlike previous works, we approximate the conditional term with a simple analytical function rather than an external neural network, thus making the eigenvector calculations approachable. We present the corresponding SDE theory as a formal justification of our approach. We extend our framework to conditioning on structure and dynamics at the same time, enabling scaffolding of the dynamical motifs. We demonstrate the empirical effectiveness of our method by turning the open-source unconditional protein diffusion model Genie into the conditional model with no retraining. Generated proteins exhibit the desired dynamical and structural properties while still being biologically plausible. Our work represents a first step towards incorporating dynamical behaviour in protein design and may open the door to designing more flexible and functional proteins in the future.

Generative modelling paradigms based on denoising diffusion processes have emerged as a leading candidate for conditional sampling in inverse problems. In many real-world applications, we often have access to large, expensively trained unconditional diffusion models, which we aim to exploit for improving conditional sampling. Most recent approaches are motivated heuristically and lack a unifying framework, obscuring connections between them. Further, they often suffer from issues such as being very sensitive to hyperparameters, being expensive to train or needing access to weights hidden behind a closed API. In this work, we unify conditional training and sampling using the mathematically well-understood Doob's h-transform. This new perspective allows us to unify many existing methods under a common umbrella. Under this framework, we propose DEFT (Doob's h-transform Efficient FineTuning), a new approach for conditional generation that simply fine-tunes a very small network to quickly learn the conditional $h$-transform, while keeping the larger unconditional network unchanged. DEFT is much faster than existing baselines while achieving state-of-the-art performance across a variety of linear and non-linear benchmarks. On image reconstruction tasks, we achieve speedups of up to 1.6$\times$, while having the best perceptual quality on natural images and reconstruction performance on medical images. Further, we also provide initial experiments on protein motif scaffolding and outperform reconstruction guidance methods.

We introduce ProteinWorkshop, a comprehensive benchmark suite for representation learning on protein structures with Geometric Graph Neural Networks. We consider large-scale pre-training and downstream tasks on both experimental and predicted structures to enable the systematic evaluation of the quality of the learned structural representation and their usefulness in capturing functional relationships for downstream tasks. We find that: (1) large-scale pretraining on AlphaFold structures and auxiliary tasks consistently improve the performance of both rotation-invariant and equivariant GNNs, and (2) more expressive equivariant GNNs benefit from pretraining to a greater extent compared to invariant models. We aim to establish a common ground for the machine learning and computational biology communities to rigorously compare and advance protein structure representation learning. Our open-source codebase reduces the barrier to entry for working with large protein structure datasets by providing: (1) storage-efficient dataloaders for large-scale structural databases including AlphaFoldDB and ESM Atlas, as well as (2) utilities for constructing new tasks from the entire PDB. ProteinWorkshop is available at: github.com/a-r-j/ProteinWorkshop.

Deep generative models for structure-based drug design (SBDD), where molecule generation is conditioned on a 3D protein pocket, have received considerable interest in recent years. These methods offer the promise of higher-quality molecule generation by explicitly modelling the 3D interaction between a potential drug and a protein receptor. However, previous work has primarily focused on the quality of the generated molecules themselves, with limited evaluation of the 3D molecule \emph{poses} that these methods produce, with most work simply discarding the generated pose and only reporting a "corrected" pose after redocking with traditional methods. Little is known about whether generated molecules satisfy known physical constraints for binding and the extent to which redocking alters the generated interactions. We introduce PoseCheck, an extensive analysis of multiple state-of-the-art methods and find that generated molecules have significantly more physical violations and fewer key interactions compared to baselines, calling into question the implicit assumption that providing rich 3D structure information improves molecule complementarity. We make recommendations for future research tackling identified failure modes and hope our benchmark can serve as a springboard for future SBDD generative modelling work to have a real-world impact.

Many protein design applications, such as binder or enzyme design, require scaffolding a structural motif with high precision. Generative modelling paradigms based on denoising diffusion processes emerged as a leading candidate to address this motif scaffolding problem and have shown early experimental success in some cases. In the diffusion paradigm, motif scaffolding is treated as a conditional generation task, and several conditional generation protocols were proposed or imported from the Computer Vision literature. However, most of these protocols are motivated heuristically, e.g. via analogies to Langevin dynamics, and lack a unifying framework, obscuring connections between the different approaches. In this work, we unify conditional training and conditional sampling procedures under one common framework based on the mathematically well-understood Doob's h-transform. This new perspective allows us to draw connections between existing methods and propose a new variation on existing conditional training protocols. We illustrate the effectiveness of this new protocol in both, image outpainting and motif scaffolding and find that it outperforms standard methods.

The expressive power of Graph Neural Networks (GNNs) has been studied extensively through the Weisfeiler-Leman (WL) graph isomorphism test. However, standard GNNs and the WL framework are inapplicable for geometric graphs embedded in Euclidean space, such as biomolecules, materials, and other physical systems. In this work, we propose a geometric version of the WL test (GWL) for discriminating geometric graphs while respecting the underlying physical symmetries: permutations, rotation, reflection, and translation. We use GWL to characterise the expressive power of geometric GNNs that are invariant or equivariant to physical symmetries in terms of distinguishing geometric graphs. GWL unpacks how key design choices influence geometric GNN expressivity: (1) Invariant layers have limited expressivity as they cannot distinguish one-hop identical geometric graphs; (2) Equivariant layers distinguish a larger class of graphs by propagating geometric information beyond local neighbourhoods; (3) Higher order tensors and scalarisation enable maximally powerful geometric GNNs; and (4) GWL's discrimination-based perspective is equivalent to universal approximation. Synthetic experiments supplementing our results are available at \url{https://github.com/chaitjo/geometric-gnn-dojo}

The success of therapeutic antibodies relies on their ability to selectively bind antigens. AI-based antibody design protocols have shown promise in generating epitope-specific designs. Many of these protocols use an inverse folding step to generate diverse sequences given a backbone structure. Due to prohibitive screening costs, it is key to identify candidate sequences likely to bind in vitro. Here, we compare the efficacy of 8 common scoring paradigms based on open-source models to classify antibody designs as binders or non-binders. We evaluate these approaches on a novel surface plasmon resonance (SPR) dataset, spanning 5 antigens. Our results show that existing methods struggle to detect binders, and performance is highly variable across antigens. We find that metrics computed on flexibly docked antibody-antigen complexes are more robust, and ensembles scores are more consistent than individual metrics. We provide experimental insight to analyze current scoring techniques, highlighting that the development of robust, zero-shot filters is an important research gap.

Pre-trained models have been successful in many protein engineering tasks. Most notably, sequence-based models have achieved state-of-the-art performance on protein fitness prediction while structure-based models have been used experimentally to develop proteins with enhanced functions. However, there is a research gap in comparing structure- and sequence-based methods for predicting protein variants that are better than the wildtype protein. This paper aims to address this gap by conducting a comparative study between the abilities of equivariant graph neural networks (EGNNs) and sequence-based approaches to identify promising amino-acid mutations. The results show that our proposed structural approach achieves a competitive performance to sequence-based methods while being trained on significantly fewer molecules. Additionally, we find that combining assay labelled data with structure pre-trained models yields similar trends as with sequence pre-trained models. Our code and trained models can be found at: https://github.com/semiluna/partIII-amino-acid-prediction.

Computational RNA design tasks are often posed as inverse problems, where sequences are designed based on adopting a single desired secondary structure without considering 3D geometry and conformational diversity. We introduce gRNAde, a geometric RNA design pipeline operating on 3D RNA backbones to design sequences that explicitly account for structure and dynamics. Under the hood, gRNAde is a multi-state Graph Neural Network that generates candidate RNA sequences conditioned on one or more 3D backbone structures where the identities of the bases are unknown. On a single-state fixed backbone re-design benchmark of 14 RNA structures from the PDB identified by Das et al. [2010], gRNAde obtains higher native sequence recovery rates (56% on average) compared to Rosetta (45% on average), taking under a second to produce designs compared to the reported hours for Rosetta. We further demonstrate the utility of gRNAde on a new benchmark of multi-state design for structurally flexible RNAs, as well as zero-shot ranking of mutational fitness landscapes in a retrospective analysis of a recent RNA polymerase ribozyme structure. Open source code: https://github.com/chaitjo/geometric-rna-design

Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes transform according to the inherent physical symmetries of 3D atomic systems, including rotations and translations in Euclidean space, as well as node permutations. In recent years, Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. Their specificity lies in the inductive biases they leverage - such as physical symmetries and chemical properties - to learn informative representations of these geometric graphs. In this opinionated paper, we provide a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems. We cover fundamental background material and introduce a pedagogical taxonomy of Geometric GNN architectures: (1) invariant networks, (2) equivariant networks in Cartesian basis, (3) equivariant networks in spherical basis, and (4) unconstrained networks. Additionally, we outline key datasets and application areas and suggest future research directions. The objective of this work is to present a structured perspective on the field, making it accessible to newcomers and aiding practitioners in gaining an intuition for its mathematical abstractions.

Tropical secondary forests are ecosystems of critical importance for protecting biodiversity, buffering primary forest loss, and sequestering atmospheric carbon. Monitoring growth and carbon sequestration in secondary forests is difficult, with inventory plots sampling <0.001% of secondary forests. The Global Ecosystem Dynamics Investigation (GEDI), a space-borne LiDAR sampler, provides billions of aboveground carbon density (ACD) estimates across the tropics. We fuse these carbon density estimates with a time series of forest change maps to identify their age since last deforestation and thus estimate the average rate of carbon sequestration in secondary forests across the Amazon biome. To our knowledge, this is the first estimate of these rates made using the new GEDI dataset. Moreover, this paper addresses key statistical and computational challenges of GEDI data fusion and analysis. We propagate both GEDI ACD and geolocation uncertainty to the regrowth rate estimate through a Monte Carlo approach, and we handle heteroskedasticity, outliers, and spatial autocorrelation using robust statistical methods. The large size of the GEDI dataset combined with the proposed Monte Carlo bootstrap can be highly computationally intensive, with a naive implementation taking over a month to complete. Nevertheless, we demonstrate the feasibility of our method by developing optimized open-source code that performs this computation on the 151 million quality-filtered GEDI shots available for the Amazon biome from April 2019–August 2021 in under 25 min in benchmark tests. By resolving these statistical and computational challenges with an efficient open-source pipeline, we create a standard approach that can be used more broadly in any work seeking to combine the GEDI dataset with high-resolution classification maps. Using this approach, we identify approximately 23, 000 GEDI samples of regrowing forest at least 60 m × 60 m wide across the Amazon biome and estimate a carbon sequestration rate of 1.86 MgC/ha/yr with a 95% empirical confidence interval of 1.75–1.97 MgC/ha/yr, with rates varying from 1.27 to 1.99 MgC/ha/yr across smaller subregions.

Scaffold hopping is a drug discovery strategy to generate new chemical entities by modifying the core structure, the \emph{scaffold}, of a known active compound. This approach preserves the essential molecular features of the original scaffold while introducing novel chemical elements or structural features to enhance potency, selectivity, or bioavailability. However, there is currently a lack of generative models specifically tailored for this task, especially in the pocket-conditioned context. In this work, we present DiffHopp, a conditional E(3)-equivariant graph diffusion model tailored for scaffold hopping given a known protein-ligand complex.

Underground infrastructure networks form the backbone of vital supply and disposal systems. However, they are under-monitored in comparison to their value. This is due, in large part, to the lack of energy supply for monitoring and data transmission. In this paper, we investigate a novel, energy harvesting system used to power underground sewer infrastructure monitoring networks. The system collects the required energy from ambient sources, such as temperature differences or residual light in sewer networks. A prototype was developed that could use either a thermoelectric generator (TEG) or a solar cell to capture the energy needed to acquire and transmit ultrasonic water level data via LoRaWAN. Real-world field trials were satisfactory and showed the potential power output, as well as, possibilities to improve the system. Using an extrapolation model, we proved that the developed solution could work reliably throughout the year.

We introduce a software package that allows users to design and run simulations of thought experiments in quantum theory. In particular, it covers cases where several reasoning agents are modelled as quantum systems, such as Wigner's friend experiment. Users can customize the protocol of the experiment, the inner workings of agents (including a quantum circuit that models their reasoning process), the abstract logical system used (which may or not allow agents to combine premises and make inferences about each other's reasoning), and the interpretation of quantum theory used by different agents. Our open-source software is written in a quantum programming language, ProjectQ, and runs on classical or quantum hardware. As an example, we model the Frauchiger-Renner extended Wigner's friend thought experiment, where agents are allowed to measure each other's physical memories, and make inferences about each other's reasoning.