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Body fat percentage is an increasingly popular alternative to Body Mass Index to measure overweight and obesity, offering a more accurate representation of body composition. In this work, we evaluate three evolutionary computation techniques, Grammatical Evolution, Context-Free Grammar Genetic Programming, and Dynamic Structured Grammatical Evolution, to derive an interpretable mathematical expression to estimate the percentage of body fat that are also accurate. Our primary objective is to obtain a model that balances accuracy with explainability, making it useful for clinical and health applications. We compare the performance of the three variants on a public anthropometric dataset and compare the results obtained with the QLattice framework. Experimental results show that grammatical evolution techniques can obtain competitive results in performance and interpretability., Comment: Accepted at Evostar 2025

The introduction of models like RFDiffusionAA, AlphaFold3, AlphaProteo, and Chai1 has revolutionized protein structure modeling and interaction prediction, primarily from a binding perspective, focusing on creating ideal lock-and-key models. However, these methods can fall short for enzyme-substrate interactions, where perfect binding models are rare, and induced fit states are more common. To address this, we shift to a functional perspective for enzyme design, where the enzyme function is defined by the reaction it catalyzes. Here, we introduce \textsc{GENzyme}, a \textit{de novo} enzyme design model that takes a catalytic reaction as input and generates the catalytic pocket, full enzyme structure, and enzyme-substrate binding complex. \textsc{GENzyme} is an end-to-end, three-staged model that integrates (1) a catalytic pocket generation and sequence co-design module, (2) a pocket inpainting and enzyme inverse folding module, and (3) a binding and screening module to optimize and predict enzyme-substrate complexes. The entire design process is driven by the catalytic reaction being targeted. This reaction-first approach allows for more accurate and biologically relevant enzyme design, potentially surpassing structure-based and binding-focused models in creating enzymes capable of catalyzing specific reactions. We provide \textsc{GENzyme} code at https://github.com/WillHua127/GENzyme.

Enzyme design is a critical area in biotechnology, with applications ranging from drug development to synthetic biology. Traditional methods for enzyme function prediction or protein binding pocket design often fall short in capturing the dynamic and complex nature of enzyme-substrate interactions, particularly in catalytic processes. To address the challenges, we introduce EnzymeFlow, a generative model that employs flow matching with hierarchical pre-training and enzyme-reaction co-evolution to generate catalytic pockets for specific substrates and catalytic reactions. Additionally, we introduce a large-scale, curated, and validated dataset of enzyme-reaction pairs, specifically designed for the catalytic pocket generation task, comprising a total of $328,192$ pairs. By incorporating evolutionary dynamics and reaction-specific adaptations, EnzymeFlow becomes a powerful model for designing enzyme pockets, which is capable of catalyzing a wide range of biochemical reactions. Experiments on the new dataset demonstrate the model's effectiveness in designing high-quality, functional enzyme catalytic pockets, paving the way for advancements in enzyme engineering and synthetic biology. We provide EnzymeFlow code at https://github.com/WillHua127/EnzymeFlow with notebook demonstration at https://github.com/WillHua127/EnzymeFlow/blob/main/enzymeflow_demo.ipynb.

Enhanced sampling simulations make the computational study of rare events feasible. A large family of such methods crucially depends on the definition of some collective variables (CVs) that could provide a low-dimensional representation of the relevant physics of the process. Recently, many methods have been proposed to semi-automatize the CV design by using machine learning tools to learn the variables directly from the simulation data. However, most methods are based on feed-forward neural networks and require as input some user-defined physical descriptors. Here, we propose to bypass this step using a graph neural network to directly use the atomic coordinates as input for the CV model. This way, we achieve a fully automatic approach to CV determination that provides variables invariant under the relevant symmetries, especially the permutational one. Furthermore, we provide different analysis tools to favor the physical interpretation of the final CV. We prove the robustness of our approach using different methods from the literature for the optimization of the CV, and we prove its efficacy on several systems, including a small peptide, an ion dissociation in explicit solvent, and a simple chemical reaction.

Significant interests have recently risen in leveraging sequence-based large language models (LLMs) for drug design. However, most current applications of LLMs in drug discovery lack the ability to comprehend three-dimensional (3D) structures, thereby limiting their effectiveness in tasks that explicitly involve molecular conformations. In this study, we introduced Token-Mol, a token-only 3D drug design model. This model encodes all molecular information, including 2D and 3D structures, as well as molecular property data, into tokens, which transforms classification and regression tasks in drug discovery into probabilistic prediction problems, thereby enabling learning through a unified paradigm. Token-Mol is built on the transformer decoder architecture and trained using random causal masking techniques. Additionally, we proposed the Gaussian cross-entropy (GCE) loss function to overcome the challenges in regression tasks, significantly enhancing the capacity of LLMs to learn continuous numerical values. Through a combination of fine-tuning and reinforcement learning (RL), Token-Mol achieves performance comparable to or surpassing existing task-specific methods across various downstream tasks, including pocket-based molecular generation, conformation generation, and molecular property prediction. Compared to existing molecular pre-trained models, Token-Mol exhibits superior proficiency in handling a wider range of downstream tasks essential for drug design. Notably, our approach improves regression task accuracy by approximately 30% compared to similar token-only methods. Token-Mol overcomes the precision limitations of token-only models and has the potential to integrate seamlessly with general models such as ChatGPT, paving the way for the development of a universal artificial intelligence drug design model that facilitates rapid and high-quality drug design by experts.

Four $SU(5)$ $N=1$ supersymmetric models which exhibit $S_3$ and/or $Z_N$ symmetries are studied, that are finite to two or all loops, and their corresponding mass matrices. The first is an all-loop finite model based on an $S_3\times Z_3\times Z_2$ flavour symmetry, which leads to phenomenologically nonviable mass matrices. The remaining models, based on cyclic symmetries, show various mass textures, some of which are phenomenologically promising. For the two-loop finite models, the parametric solutions to the finiteness conditions determine completely some of the Yukawa couplings, and lead to a restricted range of values for other ones at the GUT scale, with a considerable reduction in the number of free parameters. One particular solution of the two-loop models shows an enhanced symmetry, leading to an all-loop finite model, which has a significant parameter reduction and could in principle reproduce the observed quark masses and mixing pattern. In this case the finiteness conditions determine the absolute value of all the Yukawa couplings at the unification scale. Finally, the minimum number of phases in the mass matrices and their position are determined, a task not previously done in Finite Unified Theories, which contributes towards the reduction of parameters and a better understanding of the Yukawa couplings. the Yukawa couplings., Comment: 42 pages, no figures. Modified abstract, extended introduction and conclusions, added references, and corrected typos. This version corresponds to the published paper in Fortschr. Phys

Diffusion models (DMs) have gained attention in Missing Data Imputation (MDI), but there remain two long-neglected issues to be addressed: (1). Inaccurate Imputation, which arises from inherently sample-diversification-pursuing generative process of DMs. (2). Difficult Training, which stems from intricate design required for the mask matrix in model training stage. To address these concerns within the realm of numerical tabular datasets, we introduce a novel principled approach termed Kernelized Negative Entropy-regularized Wasserstein gradient flow Imputation (KnewImp). Specifically, based on Wasserstein gradient flow (WGF) framework, we first prove that issue (1) stems from the cost functionals implicitly maximized in DM-based MDI are equivalent to the MDI's objective plus diversification-promoting non-negative terms. Based on this, we then design a novel cost functional with diversification-discouraging negative entropy and derive our KnewImp approach within WGF framework and reproducing kernel Hilbert space. After that, we prove that the imputation procedure of KnewImp can be derived from another cost functional related to the joint distribution, eliminating the need for the mask matrix and hence naturally addressing issue (2). Extensive experiments demonstrate that our proposed KnewImp approach significantly outperforms existing state-of-the-art methods.

Structure-based drug design (SBDD) aims to generate potential drugs that can bind to a target protein and is greatly expedited by the aid of AI techniques in generative models. However, a lack of systematic understanding persists due to the diverse settings, complex implementation, difficult reproducibility, and task singularity. Firstly, the absence of standardization can lead to unfair comparisons and inconclusive insights. To address this dilemma, we propose CBGBench, a comprehensive benchmark for SBDD, that unifies the task as a generative heterogeneous graph completion, analogous to fill-in-the-blank of the 3D complex binding graph. By categorizing existing methods based on their attributes, CBGBench facilitates a modular and extensible framework that implements various cutting-edge methods. Secondly, a single task on \textit{de novo} molecule generation can hardly reflect their capabilities. To broaden the scope, we have adapted these models to a range of tasks essential in drug design, which are considered sub-tasks within the graph fill-in-the-blank tasks. These tasks include the generative designation of \textit{de novo} molecules, linkers, fragments, scaffolds, and sidechains, all conditioned on the structures of protein pockets. Our evaluations are conducted with fairness, encompassing comprehensive perspectives on interaction, chemical properties, geometry authenticity, and substructure validity. We further provide the pre-trained versions of the state-of-the-art models and deep insights with analysis from empirical studies. The codebase for CBGBench is publicly accessible at \url{https://github.com/Edapinenut/CBGBench}., Comment: 9 pages main context

The motivation of this paper is to recognize a geometric shape from a noisy sample in the form of a point cloud. Inspired by the HDBSCAN clustering algorithm, we introduce the core dissimilarity, from which we construct the core bifiltration. We also consider the Delaunay core bifiltration by intersecting with Voronoi cells, giving us a filtered simplicial complex of smaller size. A major advantage of the (Delaunay) core bifiltration is that, for each filtration value, it admits a good cover of balls. By the persistent nerve theorem, the nerve of this cover is homotopy equivalent to the (Delaunay) core bifiltration. We show that the multicover-, core- and Delaunay core bifiltrations are all interleaved, and that they enjoy similar stability properties with respect to the Prohorov distance. We have performed experiments with the Delaunay core bifiltration. In the experiments, we calculated persistent homology along lines in the two-dimensional persistence parameter space, and computed multipersistence module approximations., Comment: 21 pages, 13 figures, 5 tables

The idea of using deep-learning-based molecular generation to accelerate discovery of drug candidates has attracted extraordinary attention, and many deep generative models have been developed for automated drug design, termed molecular generation. In general, molecular generation encompasses two main strategies: de novo design, which generates novel molecular structures from scratch, and lead optimization, which refines existing molecules into drug candidates. Among them, lead optimization plays an important role in real-world drug design. For example, it can enable the development of me-better drugs that are chemically distinct yet more effective than the original drugs. It can also facilitate fragment-based drug design, transforming virtual-screened small ligands with low affinity into first-in-class medicines. Despite its importance, automated lead optimization remains underexplored compared to the well-established de novo generative models, due to its reliance on complex biological and chemical knowledge. To bridge this gap, we conduct a systematic review of traditional computational methods for lead optimization, organizing these strategies into four principal sub-tasks with defined inputs and outputs. This review delves into the basic concepts, goals, conventional CADD techniques, and recent advancements in AIDD. Additionally, we introduce a unified perspective based on constrained subgraph generation to harmonize the methodologies of de novo design and lead optimization. Through this lens, de novo design can incorporate strategies from lead optimization to address the challenge of generating hard-to-synthesize molecules; inversely, lead optimization can benefit from the innovations in de novo design by approaching it as a task of generating molecules conditioned on certain substructures.

Rare event sampling is a central problem in modern computational chemistry research. Among the existing methods, transition path sampling (TPS) can generate unbiased representations of reaction processes. However, its efficiency depends on the ability to generate reactive trial paths, which in turn depends on the quality of the shooting algorithm used. We propose a new algorithm based on the shooting success rate, i.e. reactivity, measured as a function of a reduced set of collective variables (CVs). These variables are extracted with a machine learning approach directly from TPS simulations, using a multi-task objective function. Iteratively, this workflow significantly improves shooting efficiency without any prior knowledge of the process. In addition, the optimized CVs can be used with biased enhanced sampling methodologies to accurately reconstruct the free energy profiles. We tested the method on three different systems: a two-dimensional toy model, conformational transitions of alanine dipeptide, and hydrolysis of acetyl chloride in bulk water. In the latter, we integrated our workflow with an active learning scheme to learn a reactive machine learning-based potential, which allowed us to study the mechanism and free energy profile with an ab initio-like accuracy.

Most earlier 3D structure-based molecular generation approaches follow an atom-wise paradigm, incrementally adding atoms to a partially built molecular fragment within protein pockets. These methods, while effective in designing tightly bound ligands, often overlook other essential properties such as synthesizability. The fragment-wise generation paradigm offers a promising solution. However, a common challenge across both atom-wise and fragment-wise methods lies in their limited ability to co-design plausible chemical and geometrical structures, resulting in distorted conformations. In response to this challenge, we introduce the Deep Geometry Handling protocol, a more abstract design that extends the design focus beyond the model architecture. Through a comprehensive review of existing geometry-related models and their protocols, we propose a novel hybrid strategy, culminating in the development of FragGen - a geometry-reliable, fragment-wise molecular generation method. FragGen marks a significant leap forward in the quality of generated geometry and the synthesis accessibility of molecules. The efficacy of FragGen is further validated by its successful application in designing type II kinase inhibitors at the nanomolar level.

This work explores the dimension reduction problem for Bayesian nonparametric regression and density estimation. More precisely, we are interested in estimating a functional parameter $f$ over the unit ball in $\mathbb{R}^d$, which depends only on a $d_0$-dimensional subspace of $\mathbb{R}^d$, with $d_0 < d$.It is well-known that rescaled Gaussian process priors over the function space achieve smoothness adaptation and posterior contraction with near minimax-optimal rates. Moreover, hierarchical extensions of this approach, equipped with subspace projection, can also adapt to the intrinsic dimension $d_0$ (\cite{Tokdar2011DimensionAdapt}).When the ambient dimension $d$ does not vary with $n$, the minimax rate remains of the order $n^{-\beta/(2\beta +d_0)}$.%When $d$ does not vary with $n$, the order of the minimax rate remains the same regardless of the ambient dimension $d$. However, this is up to multiplicative constants that can become prohibitively large when $d$ grows. The dependences between the contraction rate and the ambient dimension have not been fully explored yet and this work provides a first insight: we let the dimension $d$ grow with $n$ and, by combining the arguments of \cite{Tokdar2011DimensionAdapt} and \cite{Jiang2021VariableSelection}, we derive a growth rate for $d$ that still leads to posterior consistency with minimax rate.The optimality of this growth rate is then discussed.Additionally, we provide a set of assumptions under which consistent estimation of $f$ leads to a correct estimation of the subspace projection, assuming that $d_0$ is known.

Therapeutic peptides have proven to have great pharmaceutical value and potential in recent decades. However, methods of AI-assisted peptide drug discovery are not fully explored. To fill the gap, we propose a target-aware peptide design method called \textsc{PPFlow}, based on conditional flow matching on torus manifolds, to model the internal geometries of torsion angles for the peptide structure design. Besides, we establish a protein-peptide binding dataset named PPBench2024 to fill the void of massive data for the task of structure-based peptide drug design and to allow the training of deep learning methods. Extensive experiments show that PPFlow reaches state-of-the-art performance in tasks of peptide drug generation and optimization in comparison with baseline models, and can be generalized to other tasks including docking and side-chain packing., Comment: 18 pages

Accurate prediction of protein-ligand binding structures, a task known as molecular docking is crucial for drug design but remains challenging. While deep learning has shown promise, existing methods often depend on holo-protein structures (docked, and not accessible in realistic tasks) or neglect pocket sidechain conformations, leading to limited practical utility and unrealistic conformation predictions. To fill these gaps, we introduce an under-explored task, named flexible docking to predict poses of ligand and pocket sidechains simultaneously and introduce Re-Dock, a novel diffusion bridge generative model extended to geometric manifolds. Specifically, we propose energy-to-geometry mapping inspired by the Newton-Euler equation to co-model the binding energy and conformations for reflecting the energy-constrained docking generative process. Comprehensive experiments on designed benchmark datasets including apo-dock and cross-dock demonstrate our model's superior effectiveness and efficiency over current methods.

We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes. TopoX consists of three packages: TopoNetX facilitates constructing and computing on these domains, including working with nodes, edges and higher-order cells; TopoEmbedX provides methods to embed topological domains into vector spaces, akin to popular graph-based embedding algorithms such as node2vec; TopoModelX is built on top of PyTorch and offers a comprehensive toolbox of higher-order message passing functions for neural networks on topological domains. The extensively documented and unit-tested source code of TopoX is available under MIT license at https://pyt-team.github.io/}{https://pyt-team.github.io/.

The probabilistic design of offshore wind turbines aims to ensure structural safety in a cost-effective way. This involves conducting structural reliability assessments for different design options and considering different structural responses. There are several structural reliability methods, and this paper will apply and compare different approaches in some simplified case studies. In particular, the well known environmental contour method will be compared to a more novel approach based on sequential sampling and Gaussian processes regression for an ultimate limit state case study. For one of the case studies, results will also be compared to results from a brute force simulation approach. Interestingly, the comparison is very different from the two case studies. In one of the cases the environmental contours method agrees well with the sequential sampling method but in the other, results vary considerably. Probably, this can be explained by the violation of some of the assumptions associated with the environmental contour approach, i.e. that the short-term variability of the response is large compared to the long-term variability of the environmental conditions. Results from this simple comparison study suggests that the sequential sampling method can be a robust and computationally effective approach for structural reliability assessment.

Protein structure-based property prediction has emerged as a promising approach for various biological tasks, such as protein function prediction and sub-cellular location estimation. The existing methods highly rely on experimental protein structure data and fail in scenarios where these data are unavailable. Predicted protein structures from AI tools (e.g., AlphaFold2) were utilized as alternatives. However, we observed that current practices, which simply employ accurately predicted structures during inference, suffer from notable degradation in prediction accuracy. While similar phenomena have been extensively studied in general fields (e.g., Computer Vision) as model robustness, their impact on protein property prediction remains unexplored. In this paper, we first investigate the reason behind the performance decrease when utilizing predicted structures, attributing it to the structure embedding bias from the perspective of structure representation learning. To study this problem, we identify a Protein 3D Graph Structure Learning Problem for Robust Protein Property Prediction (PGSL-RP3), collect benchmark datasets, and present a protein Structure embedding Alignment Optimization framework (SAO) to mitigate the problem of structure embedding bias between the predicted and experimental protein structures. Extensive experiments have shown that our framework is model-agnostic and effective in improving the property prediction of both predicted structures and experimental structures. The benchmark datasets and codes will be released to benefit the community.

This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competition asked participants to provide open-source implementations of topological neural networks from the literature by contributing to the python packages TopoNetX (data processing) and TopoModelX (deep learning). The challenge attracted twenty-eight qualifying submissions in its two-month duration. This paper describes the design of the challenge and summarizes its main findings.

Understanding the origin(s) of life (OoL) is a fundamental challenge for science in the 21st century. Research on OoL spans many disciplines, including chemistry, physics, biology, planetary sciences, computer science, mathematics and philosophy. The sheer number of different scientific perspectives relevant to the problem has resulted in the coexistence of diverse tools, techniques, data, and software in OoL studies. This has made communication between the disciplines relevant to the OoL extremely difficult because the interpretation of data, analyses, or standards of evidence can vary dramatically. Here, we hope to bridge this wide field of study by providing common ground via the consolidation of tools and techniques rather than positing a unifying view on how life emerges. We review the common tools and techniques that have been used significantly in OoL studies in recent years. In particular, we aim to identify which information is most relevant for comparing and integrating the results of experimental analyses into mathematical and computational models. This review aims to provide a baseline expectation and understanding of technical aspects of origins research, rather than being a primer on any particular topic. As such, it spans broadly -- from analytical chemistry to mathematical models -- and highlights areas of future work that will benefit from a multidisciplinary approach to tackling the mystery of life's origin. Ultimately, we hope to empower a new generation of OoL scientists by reviewing how they can investigate life's origin, rather than dictating how to think about the problem.

Protein loop modeling is the most challenging yet highly non-trivial task in protein structure prediction. Despite recent progress, existing methods including knowledge-based, ab initio, hybrid and deep learning (DL) methods fall significantly short of either atomic accuracy or computational efficiency. Moreover, an overarching focus on backbone atoms has resulted in a dearth of attention given to side-chain conformation, a critical aspect in a host of downstream applications including ligand docking, molecular dynamics simulation and drug design. To overcome these limitations, we present KarmaLoop, a novel paradigm that distinguishes itself as the first DL method centered on full-atom (encompassing both backbone and side-chain heavy atoms) protein loop modeling. Our results demonstrate that KarmaLoop considerably outperforms conventional and DL-based methods of loop modeling in terms of both accuracy and efficiency, with the average RMSD improved by over two-fold compared to the second-best baseline method across different tasks, and manifests at least two orders of magnitude speedup in general. Consequently, our comprehensive evaluations indicate that KarmaLoop provides a state-of-the-art DL solution for protein loop modeling, with the potential to hasten the advancement of protein engineering, antibody-antigen recognition, and drug design., Comment: 20 pages, 6 figures, journal articles and keywords:Protein loop modeling, Loop prediction, Antibody H3 loop, Deep Learning

In recent years, AI-assisted drug design methods have been proposed to generate molecules given the pockets' structures of target proteins. Most of them are atom-level-based methods, which consider atoms as basic components and generate atom positions and types. In this way, however, it is hard to generate realistic fragments with complicated structures. To solve this, we propose D3FG, a functional-group-based diffusion model for pocket-specific molecule generation and elaboration. D3FG decomposes molecules into two categories of components: functional groups defined as rigid bodies and linkers as mass points. And the two kinds of components can together form complicated fragments that enhance ligand-protein interactions. To be specific, in the diffusion process, D3FG diffuses the data distribution of the positions, orientations, and types of the components into a prior distribution; In the generative process, the noise is gradually removed from the three variables by denoisers parameterized with designed equivariant graph neural networks. In the experiments, our method can generate molecules with more realistic 3D structures, competitive affinities toward the protein targets, and better drug properties. Besides, D3FG as a solution to a new task of molecule elaboration, could generate molecules with high affinities based on existing ligands and the hotspots of target proteins., Comment: 9 pages

We study landmark-based SLAM with unknown data association: our robot navigates in a completely unknown environment and has to simultaneously reason over its own trajectory, the positions of an unknown number of landmarks in the environment, and potential data associations between measurements and landmarks. This setup is interesting since: (i) it arises when recovering from data association failures or from SLAM with information-poor sensors, (ii) it sheds light on fundamental limits (and hardness) of landmark-based SLAM problems irrespective of the front-end data association method, and (iii) it generalizes existing approaches where data association is assumed to be known or partially known. We approach the problem by splitting it into an inner problem of estimating the trajectory, landmark positions and data associations and an outer problem of estimating the number of landmarks. Our approach creates useful and novel connections with existing techniques from discrete-continuous optimization (e.g., k-means clustering), which has the potential to trigger novel research. We demonstrate the proposed approaches in extensive simulations and on real datasets and show that the proposed techniques outperform typical data association baselines and are even competitive against an "oracle" baseline which has access to the number of landmarks and an initial guess for each landmark., Comment: Accepted at ICRA 2023. Correcting a typo (missing parentheses) in eq. (1) and following equations

We introduce an exploration bonus for deep reinforcement learning methods calculated using self-organising feature maps. Our method uses adaptive resonance theory (ART) providing online, unsupervised clustering to quantify the novelty of a state. This heuristic is used to add an intrinsic reward to the extrinsic reward signal for then to optimize the agent to maximize the sum of these two rewards. We find that this method was able to play the game Ordeal at a human level after a comparable number of training epochs to ICM arXiv:1705.05464. Agents augmented with RND arXiv:1810.12894 were unable to achieve the same level of performance in our space of hyperparameters., Comment: 10 pages, 4 figures. Code publicly available at https://github.com/mariuslindegaard/curiosity_baselines