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Sleiman JL, Conforto F, Fosado YAG, Michieletto D. Geometric learning of knot topology. SOFT MATTER 2023; 20:71-78. [PMID: 37877330 PMCID: PMC10732224 DOI: 10.1039/d3sm01199b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2023] [Accepted: 10/18/2023] [Indexed: 10/26/2023]
Abstract
Knots are deeply entangled with every branch of science. One of the biggest open challenges in knot theory is to formalise a knot invariant that can unambiguously and efficiently distinguish any two knotted curves. Additionally, the conjecture that the geometrical embedding of a curve encodes information on its underlying topology is, albeit physically intuitive, far from proven. Here we attempt to tackle both these outstanding challenges by proposing a neural network (NN) approach that takes as input a geometric representation of a knotted curve and tries to make predictions of the curve's topology. Intriguingly, we discover that NNs trained with a so-called geometrical "local writhe" representation of a knot can distinguish curves that share one or many topological invariants and knot polynomials, such as mutant and composite knots, and can thus classify knotted curves more precisely than some knot polynomials. Additionally, we also show that our approach can be scaled up to classify all prime knots up to 10-crossings with more than 95% accuracy. Finally, we show that our NNs can also be trained to solve knot localisation problems on open and closed curves. Our main discovery is that the pattern of "local writhe" is a potentially unique geometric signature of the underlying topology of a curve. We hope that our results will suggest new methods for quantifying generic entanglements in soft matter and even inform new topological invariants.
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Affiliation(s)
- Joseph Lahoud Sleiman
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
| | - Filippo Conforto
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
| | | | - Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
- MRC Human Genetics Unit, Institute of Genetics and Cancer, University of Edinburgh, Edinburgh EH4 2XU, UK
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2
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Azizogli AR, Pai V, Coppola F, Jafari R, Dodd-o JB, Harish R, Balasubramanian B, Kashyap J, Acevedo-Jake AM, Král P, Kumar VA. Scalable Inhibitors of the Nsp3-Nsp4 Coupling in SARS-CoV-2. ACS OMEGA 2023; 8:5349-5360. [PMID: 36798146 PMCID: PMC9923439 DOI: 10.1021/acsomega.2c06384] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Accepted: 11/29/2022] [Indexed: 06/18/2023]
Abstract
The human Betacoronavirus SARS-CoV-2 is a novel pathogen claiming millions of lives and causing a global pandemic that has disrupted international healthcare systems, economies, and communities. The virus is fast mutating and presenting more infectious but less lethal versions. Currently, some small-molecule therapeutics have received FDA emergency use authorization for the treatment of COVID-19, including Lagevrio (molnupiravir) and Paxlovid (nirmaltrevir/ritonavir), which target the RNA-dependent RNA polymerase and the 3CLpro main protease, respectively. Proteins downstream in the viral replication process, specifically the nonstructural proteins (Nsps1-16), are potential drug targets due to their crucial functions. Of these Nsps, Nsp4 is a particularly promising drug target due to its involvement in the SARS-CoV viral replication and double-membrane vesicle formation (mediated via interaction with Nsp3). Given the degree of sequence conservation of these two Nsps across the Betacoronavirus clade, their protein-protein interactions and functions are likely to be conserved as well in SARS-CoV-2. Through AlphaFold2 and its recent advancements, protein structures were generated of Nsp3 and 4 lumenal loops of interest. Then, using a combination of molecular docking suites and an existing library of lead-like compounds, we virtually screened 7 million ligands to identify five putative ligand inhibitors of Nsp4, which could present an alternative pharmaceutical approach against SARS-CoV-2. These ligands exhibit promising lead-like properties (ideal molecular weight and log P profiles), maintain fixed-Nsp4-ligand complexes in molecular dynamics (MD) simulations, and tightly associate with Nsp4 via hydrophobic interactions. Additionally, alternative peptide inhibitors based on Nsp3 were designed and shown in MD simulations to provide a highly stable binding to the Nsp4 protein. Finally, these therapeutics were attached to dendrimer structures to promote their multivalent binding with Nsp4, especially its large flexible luminal loop (Nsp4LLL). The therapeutics tested in this study represent many different approaches for targeting large flexible protein structures, especially those localized to the ER. This study is the first work targeting the membrane rearrangement system of viruses and will serve as a potential avenue for treating viruses with similar replicative function.
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Affiliation(s)
- Abdul-Rahman Azizogli
- Department
of Biological Sciences, New Jersey Institute
of Technology, Newark, New Jersey 07102, United States
| | - Varun Pai
- Department
of Biological Sciences, New Jersey Institute
of Technology, Newark, New Jersey 07102, United States
| | - Francesco Coppola
- Department
of Chemistry, University of Illinois at
Chicago, Chicago, Illinois 60607, United States
| | - Roya Jafari
- Department
of Chemistry, University of Illinois at
Chicago, Chicago, Illinois 60607, United States
| | - Joseph B. Dodd-o
- Department
of Biomedical Engineering, New Jersey Institute
of Technology, Newark, New Jersey 07102, United States
| | - Rohan Harish
- Department
of Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, New Jersey 07102, United States
| | - Bhavani Balasubramanian
- Department
of Chemistry and Environmental Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, United States
| | - Jatin Kashyap
- Department
of Biomedical Engineering, New Jersey Institute
of Technology, Newark, New Jersey 07102, United States
| | - Amanda M. Acevedo-Jake
- Department
of Biomedical Engineering, New Jersey Institute
of Technology, Newark, New Jersey 07102, United States
| | - Petr Král
- Department
of Chemistry, University of Illinois at
Chicago, Chicago, Illinois 60607, United States
- Departments
of Physics, Pharmaceutical Sciences, and Chemical Engineering, University of Illinois at Chicago, Chicago, Illinois 60607, United States
| | - Vivek A. Kumar
- Department
of Biological Sciences, New Jersey Institute
of Technology, Newark, New Jersey 07102, United States
- Department
of Biomedical Engineering, New Jersey Institute
of Technology, Newark, New Jersey 07102, United States
- Department
of Chemical and Materials Engineering, New
Jersey Institute of Technology, Newark, New Jersey 07102, United States
- Department
of Endodontics, Rutgers School of Dental
Medicine, Newark, New Jersey 07103, United States
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3
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Muneer A, Fati SM, Arifin Akbar N, Agustriawan D, Tri Wahyudi S. iVaccine-Deep: Prediction of COVID-19 mRNA vaccine degradation using deep learning. JOURNAL OF KING SAUD UNIVERSITY. COMPUTER AND INFORMATION SCIENCES 2022; 34:7419-7432. [PMID: 38620874 PMCID: PMC8513509 DOI: 10.1016/j.jksuci.2021.10.001] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/15/2021] [Revised: 08/29/2021] [Accepted: 10/05/2021] [Indexed: 12/14/2022]
Abstract
Messenger RNA (mRNA) has emerged as a critical global technology that requires global joint efforts from different entities to develop a COVID-19 vaccine. However, the chemical properties of RNA pose a challenge in utilizing mRNA as a vaccine candidate. For instance, the molecules are prone to degradation, which has a negative impact on the distribution of mRNA among patients. In addition, little is known of the degradation properties of individual RNA bases in a molecule. Therefore, this study aims to investigate whether a hybrid deep learning can predict RNA degradation from RNA sequences. Two deep hybrid neural network models were proposed, namely GCN_GRU and GCN_CNN. The first model is based on graph convolutional neural networks (GCNs) and gated recurrent unit (GRU). The second model is based on GCN and convolutional neural networks (CNNs). Both models were computed over the structural graph of the mRNA molecule. The experimental results showed that GCN_GRU hybrid model outperform GCN_CNN model by a large margin during the test time. Validation of proposed hybrid models is performed by well-known evaluation measures. Among different deep neural networks, GCN_GRU based model achieved best scores on both public and private MCRMSE test scores with 0.22614 and 0.34152, respectively. Finally, GCN_GRU pre-trained model has achieved the highest AuC score of 0.938. Such proven outperformance of GCNs indicates that modeling RNA molecules using graphs is critical in understanding molecule degradation mechanisms, which helps in minimizing the aforementioned issues. To show the importance of the proposed GCN_GRU hybrid model, in silico experiments has been contacted. The in-silico results showed that our model pays local attention when predicting a given position's reactivity and exhibits interesting behavior on neighboring bases in the sequence.
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Affiliation(s)
- Amgad Muneer
- Department of Computer and Information Sciences, Universiti Teknologi PETRONAS, Seri Iskandar 32160, Malaysia
| | - Suliman Mohamed Fati
- Information Systems Department, College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
| | - Nur Arifin Akbar
- Research Department, Idenitive Mashable Prototyping, Banyumas 53124, Indonesia
| | - David Agustriawan
- Faculty of Bioinformatics, Indonesia International Institute for Life Sciences, Jakarta Timur 13210, Indonesia
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Errica F, Giulini M, Bacciu D, Menichetti R, Micheli A, Potestio R. A Deep Graph Network-Enhanced Sampling Approach to Efficiently Explore the Space of Reduced Representations of Proteins. Front Mol Biosci 2021; 8:637396. [PMID: 33996896 PMCID: PMC8116519 DOI: 10.3389/fmolb.2021.637396] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2020] [Accepted: 02/17/2021] [Indexed: 12/12/2022] Open
Abstract
The limits of molecular dynamics (MD) simulations of macromolecules are steadily pushed forward by the relentless development of computer architectures and algorithms. The consequent explosion in the number and extent of MD trajectories induces the need for automated methods to rationalize the raw data and make quantitative sense of them. Recently, an algorithmic approach was introduced by some of us to identify the subset of a protein's atoms, or mapping, that enables the most informative description of the system. This method relies on the computation, for a given reduced representation, of the associated mapping entropy, that is, a measure of the information loss due to such simplification; albeit relatively straightforward, this calculation can be time-consuming. Here, we describe the implementation of a deep learning approach aimed at accelerating the calculation of the mapping entropy. We rely on Deep Graph Networks, which provide extreme flexibility in handling structured input data and whose predictions prove to be accurate and-remarkably efficient. The trained network produces a speedup factor as large as 105 with respect to the algorithmic computation of the mapping entropy, enabling the reconstruction of its landscape by means of the Wang-Landau sampling scheme. Applications of this method reach much further than this, as the proposed pipeline is easily transferable to the computation of arbitrary properties of a molecular structure.
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Affiliation(s)
- Federico Errica
- Department of Computer Science, University of Pisa, Pisa, Italy
| | - Marco Giulini
- Physics Department, University of Trento, Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Davide Bacciu
- Department of Computer Science, University of Pisa, Pisa, Italy
| | - Roberto Menichetti
- Physics Department, University of Trento, Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Alessio Micheli
- Department of Computer Science, University of Pisa, Pisa, Italy
| | - Raffaello Potestio
- Physics Department, University of Trento, Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
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Swanson K, Trivedi S, Lequieu J, Swanson K, Kondor R. Deep learning for automated classification and characterization of amorphous materials. SOFT MATTER 2020; 16:435-446. [PMID: 31803878 DOI: 10.1039/c9sm01903k] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
It is difficult to quantify structure-property relationships and to identify structural features of complex materials. The characterization of amorphous materials is especially challenging because their lack of long-range order makes it difficult to define structural metrics. In this work, we apply deep learning algorithms to accurately classify amorphous materials and characterize their structural features. Specifically, we show that convolutional neural networks and message passing neural networks can classify two-dimensional liquids and liquid-cooled glasses from molecular dynamics simulations with greater than 0.98 AUC, with no a priori assumptions about local particle relationships, even when the liquids and glasses are prepared at the same inherent structure energy. Furthermore, we demonstrate that message passing neural networks surpass convolutional neural networks in this context in both accuracy and interpretability. We extract a clear interpretation of how message passing neural networks evaluate liquid and glass structures by using a self-attention mechanism. Using this interpretation, we derive three novel structural metrics that accurately characterize glass formation. The methods presented here provide a procedure to identify important structural features in materials that could be missed by standard techniques and give unique insight into how these neural networks process data.
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Affiliation(s)
- Kirk Swanson
- Department of Computer Science, The University of Chicago, Chicago, IL 60637, USA.
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Erban R, Harris S, Potestio R. Multi-resolution simulations of intracellular processes. Interface Focus 2019. [DOI: 10.1098/rsfs.2019.0028] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
This is an introduction to the Thematic Issue of
Interface Focus
containing papers by speakers of the Theo Murphy International Scientific Meeting on ‘Multi-resolution simulations of intracellular processes’
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Affiliation(s)
- Radek Erban
- Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
| | - Sarah Harris
- School of Physics and Astronomy and Astbury Centre for Structural and Molecular Biology, University of Leeds, Leeds, UK
| | - Raffaello Potestio
- Physics Department, University of Trento, via Sommarive, 14 38123 Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, 38123 Trento, Italy
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