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1.
Lasers Surg Med ; 2024 Sep 22.
Artigo em Inglês | MEDLINE | ID: mdl-39308029

RESUMO

OBJECTIVES: Hirsutism is a widespread condition affecting 5%-15% of females. Laser treatment of hirsutism has the best long-term effect. Patients with nonpigmented or nonterminal hairs are not eligible for laser treatment, and the current patient journey needed to establish eligibility for laser hair removal is problematic in many health-care systems. METHODS: In this study, we compared the ability to assess eligibility for laser hair removal of health-care professionals and convolutional neural network (CNN)-based models. RESULTS: The CNN ensemble model, synthesized from the outputs of five individual CNN models, reached an eligibility assessment accuracy of 0.52 (95% CI: 0.42-0.60) and a κ of 0.20 (95% CI: 0.13-0.27), taking a consensus expert label as reference. For comparison, board-certified dermatologists achieved a mean accuracy of 0.48 (95% CI: 0.44-0.52) and a mean κ of 0.26 (95% CI: 0.22-0.31). Intra-rater analysis of board-certified dermatologists yielded κ in the 0.32 (95% CI: 0.24-0.40) and 0.65 (95% CI: 0.56-0.74) range. CONCLUSION: Current assessment of eligibility for laser hair removal is challenging. Developing a laser hair removal eligibility assessment tool based on deep learning that performs on a par with trained dermatologists is feasible. Such a model may potentially reduce workload, increase quality and effectiveness, and facilitate equal health-care access. However, to achieve true clinical generalizability, prospective randomized clinical intervention studies are needed.

2.
Nucleic Acids Res ; 52(W1): W215-W220, 2024 Jul 05.
Artigo em Inglês | MEDLINE | ID: mdl-38587188

RESUMO

DeepLoc 2.0 is a popular web server for the prediction of protein subcellular localization and sorting signals. Here, we introduce DeepLoc 2.1, which additionally classifies the input proteins into the membrane protein types Transmembrane, Peripheral, Lipid-anchored and Soluble. Leveraging pre-trained transformer-based protein language models, the server utilizes a three-stage architecture for sequence-based, multi-label predictions. Comparative evaluations with other established tools on a test set of 4933 eukaryotic protein sequences, constructed following stringent homology partitioning, demonstrate state-of-the-art performance. Notably, DeepLoc 2.1 outperforms existing models, with the larger ProtT5 model exhibiting a marginal advantage over the ESM-1B model. The web server is available at https://services.healthtech.dtu.dk/services/DeepLoc-2.1.


Assuntos
Proteínas de Membrana , Software , Proteínas de Membrana/química , Proteínas de Membrana/metabolismo , Internet , Sinais Direcionadores de Proteínas , Análise de Sequência de Proteína
3.
Patterns (N Y) ; 5(3): 100943, 2024 Mar 08.
Artigo em Inglês | MEDLINE | ID: mdl-38487804

RESUMO

Although large language models often produce impressive outputs, it remains unclear how they perform in real-world scenarios requiring strong reasoning skills and expert domain knowledge. We set out to investigate whether closed- and open-source models (GPT-3.5, Llama 2, etc.) can be applied to answer and reason about difficult real-world-based questions. We focus on three popular medical benchmarks (MedQA-US Medical Licensing Examination [USMLE], MedMCQA, and PubMedQA) and multiple prompting scenarios: chain of thought (CoT; think step by step), few shot, and retrieval augmentation. Based on an expert annotation of the generated CoTs, we found that InstructGPT can often read, reason, and recall expert knowledge. Last, by leveraging advances in prompt engineering (few-shot and ensemble methods), we demonstrated that GPT-3.5 not only yields calibrated predictive distributions but also reaches the passing score on three datasets: MedQA-USMLE (60.2%), MedMCQA (62.7%), and PubMedQA (78.2%). Open-source models are closing the gap: Llama 2 70B also passed the MedQA-USMLE with 62.5% accuracy.

4.
Front Immunol ; 15: 1322712, 2024.
Artigo em Inglês | MEDLINE | ID: mdl-38390326

RESUMO

Accurate computational identification of B-cell epitopes is crucial for the development of vaccines, therapies, and diagnostic tools. However, current structure-based prediction methods face limitations due to the dependency on experimentally solved structures. Here, we introduce DiscoTope-3.0, a markedly improved B-cell epitope prediction tool that innovatively employs inverse folding structure representations and a positive-unlabelled learning strategy, and is adapted for both solved and predicted structures. Our tool demonstrates a considerable improvement in performance over existing methods, accurately predicting linear and conformational epitopes across multiple independent datasets. Most notably, DiscoTope-3.0 maintains high predictive performance across solved, relaxed and predicted structures, alleviating the need for experimental structures and extending the general applicability of accurate B-cell epitope prediction by 3 orders of magnitude. DiscoTope-3.0 is made widely accessible on two web servers, processing over 100 structures per submission, and as a downloadable package. In addition, the servers interface with RCSB and AlphaFoldDB, facilitating large-scale prediction across over 200 million cataloged proteins. DiscoTope-3.0 is available at: https://services.healthtech.dtu.dk/service.php?DiscoTope-3.0.


Assuntos
Epitopos de Linfócito B , Conformação Molecular
5.
Bioinformatics ; 40(2)2024 02 01.
Artigo em Inglês | MEDLINE | ID: mdl-38317052

RESUMO

MOTIVATION: Accurate prediction of RNA subcellular localization plays an important role in understanding cellular processes and functions. Although post-transcriptional processes are governed by trans-acting RNA binding proteins (RBPs) through interaction with cis-regulatory RNA motifs, current methods do not incorporate RBP-binding information. RESULTS: In this article, we propose DeepLocRNA, an interpretable deep-learning model that leverages a pre-trained multi-task RBP-binding prediction model to predict the subcellular localization of RNA molecules via fine-tuning. We constructed DeepLocRNA using a comprehensive dataset with variant RNA types and evaluated it on the held-out dataset. Our model achieved state-of-the-art performance in predicting RNA subcellular localization in mRNA and miRNA. It has also demonstrated great generalization capabilities, performing well on both human and mouse RNA. Additionally, a motif analysis was performed to enhance the interpretability of the model, highlighting signal factors that contributed to the predictions. The proposed model provides general and powerful prediction abilities for different RNA types and species, offering valuable insights into the localization patterns of RNA molecules and contributing to our understanding of cellular processes at the molecular level. A user-friendly web server is available at: https://biolib.com/KU/DeepLocRNA/.


Assuntos
Aprendizado Profundo , Animais , Humanos , Camundongos , RNA/metabolismo , RNA Mensageiro/genética , RNA Mensageiro/metabolismo , Motivos de Nucleotídeos , Proteínas de Ligação a RNA/metabolismo , Biologia Computacional/métodos
6.
NAR Genom Bioinform ; 5(4): lqad088, 2023 Dec.
Artigo em Inglês | MEDLINE | ID: mdl-37850036

RESUMO

When splitting biological sequence data for the development and testing of predictive models, it is necessary to avoid too-closely related pairs of sequences ending up in different partitions. If this is ignored, performance of prediction methods will tend to be overestimated. Several algorithms have been proposed for homology reduction, where sequences are removed until no too-closely related pairs remain. We present GraphPart, an algorithm for homology partitioning that divides the data such that closely related sequences always end up in the same partition, while keeping as many sequences as possible in the dataset. Evaluation of GraphPart on Protein, DNA and RNA datasets shows that it is capable of retaining a larger number of sequences per dataset, while providing homology separation on a par with reduction approaches.

7.
Bioinformatics ; 39(10)2023 10 03.
Artigo em Inglês | MEDLINE | ID: mdl-37812217

RESUMO

MOTIVATION: Peptides are ubiquitous throughout life and involved in a wide range of biological processes, ranging from neural signaling in higher organisms to antimicrobial peptides in bacteria. Many peptides are generated post-translationally by cleavage of precursor proteins and can thus not be detected directly from genomics data, as the specificities of the responsible proteases are often not completely understood. RESULTS: We present DeepPeptide, a deep learning model that predicts cleaved peptides directly from the amino acid sequence. DeepPeptide shows both improved precision and recall for peptide detection compared to previous methodology. We show that the model is capable of identifying peptides in underannotated proteomes. AVAILABILITY AND IMPLEMENTATION: DeepPeptide is available online at ku.biolib.com/DeepPeptide.


Assuntos
Peptídeo Hidrolases , Peptídeos , Peptídeos/química , Sequência de Aminoácidos , Peptídeo Hidrolases/metabolismo , Proteoma/metabolismo
8.
Phys Chem Chem Phys ; 25(37): 25828-25837, 2023 Sep 27.
Artigo em Inglês | MEDLINE | ID: mdl-37724552

RESUMO

Inexpensive machine learning (ML) potentials are increasingly being used to speed up structural optimization and molecular dynamics simulations of materials by iteratively predicting and applying interatomic forces. In these settings, it is crucial to detect when predictions are unreliable to avoid wrong or misleading results. Here, we present a complete framework for training and recalibrating graph neural network ensemble models to produce accurate predictions of energy and forces with calibrated uncertainty estimates. The proposed method considers both epistemic and aleatoric uncertainty and the total uncertainties are recalibrated post hoc using a nonlinear scaling function to achieve good calibration on previously unseen data, without loss of predictive accuracy. The method is demonstrated and evaluated on two challenging, publicly available datasets, ANI-1x (Smith et al. J. Chem. Phys., 2018, 148, 241733.) and Transition1x (Schreiner et al. Sci. Data, 2022, 9, 779.), both containing diverse conformations far from equilibrium. A detailed analysis of the predictive performance and uncertainty calibration is provided. In all experiments, the proposed method achieved low prediction error and good uncertainty calibration, with predicted uncertainty correlating with expected error, on energy and forces. To the best of our knowledge, the method presented in this paper is the first to consider a complete framework for obtaining calibrated epistemic and aleatoric uncertainty predictions on both energy and forces in ML potentials.

9.
Genome Biol ; 24(1): 180, 2023 08 04.
Artigo em Inglês | MEDLINE | ID: mdl-37542318

RESUMO

We present RBPNet, a novel deep learning method, which predicts CLIP-seq crosslink count distribution from RNA sequence at single-nucleotide resolution. By training on up to a million regions, RBPNet achieves high generalization on eCLIP, iCLIP and miCLIP assays, outperforming state-of-the-art classifiers. RBPNet performs bias correction by modeling the raw signal as a mixture of the protein-specific and background signal. Through model interrogation via Integrated Gradients, RBPNet identifies predictive sub-sequences that correspond to known and novel binding motifs and enables variant-impact scoring via in silico mutagenesis. Together, RBPNet improves imputation of protein-RNA interactions, as well as mechanistic interpretation of predictions.


Assuntos
Sequência de Bases , Simulação por Computador , Aprendizado Profundo , Proteínas de Ligação a RNA , RNA , Humanos , Alelos , Viés , Sítios de Ligação , Sequência Consenso , Conjuntos de Dados como Assunto , Internet , Mutação , Motivos de Nucleotídeos , Nucleotídeos/metabolismo , RNA/química , RNA/genética , RNA/metabolismo , Sítios de Splice de RNA , RNA Mensageiro/química , RNA Mensageiro/genética , RNA Mensageiro/metabolismo , RNA Viral/química , RNA Viral/genética , RNA Viral/metabolismo , Proteínas de Ligação a RNA/química , Proteínas de Ligação a RNA/metabolismo
10.
Sci Data ; 10(1): 528, 2023 08 08.
Artigo em Inglês | MEDLINE | ID: mdl-37553439

RESUMO

Large language models (LLMs) such as GPT-4 have recently demonstrated impressive results across a wide range of tasks. LLMs are still limited, however, in that they frequently fail at complex reasoning, their reasoning processes are opaque, they are prone to 'hallucinate' facts, and there are concerns about their underlying biases. Letting models verbalize reasoning steps as natural language, a technique known as chain-of-thought prompting, has recently been proposed as a way to address some of these issues. Here we present ThoughtSource, a meta-dataset and software library for chain-of-thought (CoT) reasoning. The goal of ThoughtSource is to improve future artificial intelligence systems by facilitating qualitative understanding of CoTs, enabling empirical evaluations, and providing training data. This first release of ThoughtSource integrates seven scientific/medical, three general-domain and five math word question answering datasets.

11.
Brief Bioinform ; 24(5)2023 09 20.
Artigo em Inglês | MEDLINE | ID: mdl-37466130

RESUMO

RNA localization is essential for regulating spatial translation, where RNAs are trafficked to their target locations via various biological mechanisms. In this review, we discuss RNA localization in the context of molecular mechanisms, experimental techniques and machine learning-based prediction tools. Three main types of molecular mechanisms that control the localization of RNA to distinct cellular compartments are reviewed, including directed transport, protection from mRNA degradation, as well as diffusion and local entrapment. Advances in experimental methods, both image and sequence based, provide substantial data resources, which allow for the design of powerful machine learning models to predict RNA localizations. We review the publicly available predictive tools to serve as a guide for users and inspire developers to build more effective prediction models. Finally, we provide an overview of multimodal learning, which may provide a new avenue for the prediction of RNA localization.


Assuntos
Transporte de RNA , RNA , RNA/genética , Transporte de RNA/fisiologia , Aprendizado de Máquina , Biologia Computacional/métodos
12.
ACS Omega ; 8(26): 23566-23578, 2023 Jul 04.
Artigo em Inglês | MEDLINE | ID: mdl-37426277

RESUMO

Therapeutic peptides and proteins derived from either endogenous hormones, such as insulin, or de novo design via display technologies occupy a distinct pharmaceutical space in between small molecules and large proteins such as antibodies. Optimizing the pharmacokinetic (PK) profile of drug candidates is of high importance when it comes to prioritizing lead candidates, and machine-learning models can provide a relevant tool to accelerate the drug design process. Predicting PK parameters of proteins remains difficult due to the complex factors that influence PK properties; furthermore, the data sets are small compared to the variety of compounds in the protein space. This study describes a novel combination of molecular descriptors for proteins such as insulin analogs, where many contained chemical modifications, e.g., attached small molecules for protraction of the half-life. The underlying data set consisted of 640 structural diverse insulin analogs, of which around half had attached small molecules. Other analogs were conjugated to peptides, amino acid extensions, or fragment crystallizable regions. The PK parameters clearance (CL), half-life (T1/2), and mean residence time (MRT) could be predicted by using classical machine-learning models such as Random Forest (RF) and Artificial Neural Networks (ANN) with root-mean-square errors of CL of 0.60 and 0.68 (log units) and average fold errors of 2.5 and 2.9 for RF and ANN, respectively. Both random and temporal data splittings were employed to evaluate ideal and prospective model performance with the best models, regardless of data splitting, achieving a minimum of 70% of predictions within a twofold error. The tested molecular representations include (1) global physiochemical descriptors combined with descriptors encoding the amino acid composition of the insulin analogs, (2) physiochemical descriptors of the attached small molecule, (3) protein language model (evolutionary scale modeling) embedding of the amino acid sequence of the molecules, and (4) a natural language processing inspired embedding (mol2vec) of the attached small molecule. Encoding the attached small molecule via (2) or (4) significantly improved the predictions, while the benefit of using the protein language model-based encoding (3) depended on the used machine-learning model. The most important molecular descriptors were identified as descriptors related to the molecular size of both the protein and protraction part using Shapley additive explanations values. Overall, the results show that combining representations of proteins and small molecules was key for PK predictions of insulin analogs.

13.
PLOS Digit Health ; 2(6): e0000269, 2023 Jun.
Artigo em Inglês | MEDLINE | ID: mdl-37384616

RESUMO

Early diagnosis is crucial for well-being and life quality of the rare disease patient. Access to the most complete knowledge about diseases through intelligent user interfaces can play an important role in supporting the physician reaching the correct diagnosis. Case reports may offer information about heterogeneous phenotypes which often further complicate rare disease diagnosis. The rare disease search engine FindZebra.com is extended to also access case report abstracts extracted from PubMed for several diseases. A search index for each disease is built in Apache Solr adding age, sex and clinical features extracted using text segmentation to enhance the specificity of search. Clinical experts performed retrospective validation of the search engine, utilising real-world Outcomes Survey data on Gaucher and Fabry patients. Medical experts evaluated the search results as being clinically relevant for the Fabry patients and less clinically relevant for the Gaucher patients. The shortcomings for Gaucher patients mainly reflect a mismatch between the current understanding and treatment of the disease and how it is reported in PubMed, notably in the older case reports. In response to this observation, a filter for the publication date was added in the final version of the tool available from deep.findzebra.com/ with = gaucher, fabry, hae (Hereditary angioedema).

14.
Nucleic Acids Res ; 51(12): e67, 2023 07 07.
Artigo em Inglês | MEDLINE | ID: mdl-37224538

RESUMO

Polygenic risk scores (PRSs) are expected to play a critical role in precision medicine. Currently, PRS predictors are generally based on linear models using summary statistics, and more recently individual-level data. However, these predictors mainly capture additive relationships and are limited in data modalities they can use. We developed a deep learning framework (EIR) for PRS prediction which includes a model, genome-local-net (GLN), specifically designed for large-scale genomics data. The framework supports multi-task learning, automatic integration of other clinical and biochemical data, and model explainability. When applied to individual-level data from the UK Biobank, the GLN model demonstrated a competitive performance compared to established neural network architectures, particularly for certain traits, showcasing its potential in modeling complex genetic relationships. Furthermore, the GLN model outperformed linear PRS methods for Type 1 Diabetes, likely due to modeling non-additive genetic effects and epistasis. This was supported by our identification of widespread non-additive genetic effects and epistasis in the context of T1D. Finally, we constructed PRS models that integrated genotype, blood, urine, and anthropometric data and found that this improved performance for 93% of the 290 diseases and disorders considered. EIR is available at https://github.com/arnor-sigurdsson/EIR.


Assuntos
Modelos Genéticos , Herança Multifatorial , Polimorfismo de Nucleotídeo Único , Humanos , Predisposição Genética para Doença , Genoma Humano , Estudo de Associação Genômica Ampla , Genômica/métodos , Genótipo , Fatores de Risco
15.
NAR Genom Bioinform ; 5(2): lqad026, 2023 Jun.
Artigo em Inglês | MEDLINE | ID: mdl-37007588

RESUMO

Dysfunction of regulatory elements through genetic variants is a central mechanism in the pathogenesis of disease. To better understand disease etiology, there is consequently a need to understand how DNA encodes regulatory activity. Deep learning methods show great promise for modeling of biomolecular data from DNA sequence but are limited to large input data for training. Here, we develop ChromTransfer, a transfer learning method that uses a pre-trained, cell-type agnostic model of open chromatin regions as a basis for fine-tuning on regulatory sequences. We demonstrate superior performances with ChromTransfer for learning cell-type specific chromatin accessibility from sequence compared to models not informed by a pre-trained model. Importantly, ChromTransfer enables fine-tuning on small input data with minimal decrease in accuracy. We show that ChromTransfer uses sequence features matching binding site sequences of key transcription factors for prediction. Together, these results demonstrate ChromTransfer as a promising tool for learning the regulatory code.

16.
J Chem Inf Model ; 63(9): 2651-2655, 2023 05 08.
Artigo em Inglês | MEDLINE | ID: mdl-37092865

RESUMO

Many endogenous peptides rely on signaling pathways to exert their function, but identifying their cognate receptors remains a challenging problem. We investigate the use of AlphaFold-Multimer complex structure prediction together with transmembrane topology prediction for peptide deorphanization. We find that AlphaFold's confidence metrics have strong performance for prioritizing true peptide-receptor interactions. In a library of 1112 human receptors, the method ranks true receptors in the top percentile on average for 11 benchmark peptide-receptor pairs.


Assuntos
Peptídeos , Transdução de Sinais , Humanos , Peptídeos/metabolismo
17.
Telemed J E Health ; 29(9): 1342-1348, 2023 09.
Artigo em Inglês | MEDLINE | ID: mdl-36735575

RESUMO

Background and Objectives: Image quality is a crucial factor in the effectiveness and efficiency of teledermatological consultations. However, up to 50% of images sent by patients have quality issues, thus increasing the time to diagnosis and treatment. An automated, easily deployable, explainable method for assessing image quality is necessary to improve the current teledermatological consultation flow. We introduce ImageQX, a convolutional neural network for image quality assessment with a learning mechanism for identifying the most common poor image quality explanations: bad framing, bad lighting, blur, low resolution, and distance issues. Methods: ImageQX was trained on 26,635 photographs and validated on 9,874 photographs, each annotated with image quality labels and poor image quality explanations by up to 12 board-certified dermatologists. The photographic images were taken between 2017 and 2019 using a mobile skin disease tracking application accessible worldwide. Results: Our method achieves expert-level performance for both image quality assessment and poor image quality explanation. For image quality assessment, ImageQX obtains a macro F1-score of 0.73 ± 0.01, which places it within standard deviation of the pairwise inter-rater F1-score of 0.77 ± 0.07. For poor image quality explanations, our method obtains F1-scores of between 0.37 ± 0.01 and 0.70 ± 0.01, similar to the inter-rater pairwise F1-score of between 0.24 ± 0.15 and 0.83 ± 0.06. Moreover, with a size of only 15 MB, ImageQX is easily deployable on mobile devices. Conclusion: With an image quality detection performance similar to that of dermatologists, incorporating ImageQX into the teledermatology flow can enable a better, faster flow for remote consultations.


Assuntos
Aplicativos Móveis , Consulta Remota , Neoplasias Cutâneas , Humanos , Neoplasias Cutâneas/diagnóstico , Redes Neurais de Computação , Fotografação
18.
Ultramicroscopy ; 243: 113641, 2023 Jan.
Artigo em Inglês | MEDLINE | ID: mdl-36401890

RESUMO

Reconstruction of the exit wave function is an important route to interpreting high-resolution transmission electron microscopy (HRTEM) images. Here we demonstrate that convolutional neural networks can be used to reconstruct the exit wave from a short focal series of HRTEM images, with a fidelity comparable to conventional exit wave reconstruction. We use a fully convolutional neural network based on the U-Net architecture, and demonstrate that we can train it on simulated exit waves and simulated HRTEM images of graphene-supported molybdenum disulphide (an industrial desulfurization catalyst). We then apply the trained network to analyse experimentally obtained images from similar samples, and obtain exit waves that clearly show the atomically resolved structure of both the MoS2 nanoparticles and the graphene support. We also show that it is possible to successfully train the neural networks to reconstruct exit waves for 3400 different two-dimensional materials taken from the Computational 2D Materials Database of known and proposed two-dimensional materials.

19.
Med Image Anal ; 83: 102647, 2023 Jan.
Artigo em Inglês | MEDLINE | ID: mdl-36272237

RESUMO

Dermatological diagnosis automation is essential in addressing the high prevalence of skin diseases and critical shortage of dermatologists. Despite approaching expert-level diagnosis performance, convolutional neural network (ConvNet) adoption in clinical practice is impeded by their limited explainability, and by subjective, expensive explainability validations. We introduce DermX, an end-to-end framework for explainable automated dermatological diagnosis. DermX is a clinically-inspired explainable dermatological diagnosis ConvNet, trained using DermXDB, a 554 image dataset annotated by eight dermatologists with diagnoses, supporting explanations, and explanation attention maps. DermX+ extends DermX with guided attention training for explanation attention maps. Both methods achieve near-expert diagnosis performance, with DermX, DermX+, and dermatologist F1 scores of 0.79, 0.79, and 0.87, respectively. We assess the explanation performance in terms of identification and localization by comparing model-selected with dermatologist-selected explanations, and gradient-weighted class-activation maps with dermatologist explanation maps, respectively. DermX obtained an identification F1 score of 0.77, while DermX+ obtained 0.79. The localization F1 score is 0.39 for DermX and 0.35 for DermX+. These results show that explainability does not necessarily come at the expense of predictive power, as our high-performance models provide expert-inspired explanations for their diagnoses without lowering their diagnosis performance.

20.
Sci Data ; 9(1): 779, 2022 12 24.
Artigo em Inglês | MEDLINE | ID: mdl-36566281

RESUMO

Machine Learning (ML) models have, in contrast to their usefulness in molecular dynamics studies, had limited success as surrogate potentials for reaction barrier search. This is primarily because available datasets for training ML models on small molecular systems almost exclusively contain configurations at or near equilibrium. In this work, we present the dataset Transition1x containing 9.6 million Density Functional Theory (DFT) calculations of forces and energies of molecular configurations on and around reaction pathways at the ωB97x/6-31 G(d) level of theory. The data was generated by running Nudged Elastic Band (NEB) with DFT on 10k organic reactions of various types while saving intermediate calculations. We train equivariant graph message-passing neural network models on Transition1x and cross-validate on the popular ANI1x and QM9 datasets. We show that ML models cannot learn features in transition state regions solely by training on hitherto popular benchmark datasets. Transition1x is a new challenging benchmark that will provide an important step towards developing next-generation ML force fields that also work far away from equilibrium configurations and reactive systems.

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