[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120431-en":3,"doc-seo-120431-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},120431,962075114765,"Quinn","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Pointwise prediction of protein diffusive properties using machine learning","Accurate determination of protein diffusive properties is central to interpreting cellular mechanisms, yet conventional analyses based on mean square displacements struggle with heterogeneous proteins, time-varying environments, and state transitions. The Anomalous Diffusion Challenge 2024 motivates machine-learning inference of diffusion coefficients, anomalous exponents, and biological states from trajectories with time-dependent changepoints. This work introduces M3, an LSTM-based method for pointwise estimation that achieves small mean absolute errors for diffusion parameters and high state accuracies (>90%), followed by changepoint detection for behavioral transition times. The approach avoids expert fine-tuning and is computationally efficient, reaching Top 5 performance with subsequent improvements.","J. Phys. Photonics 7 (2025) 035025 [https://doi.org/10.1088/2515-7647/adede9](https://doi.org/10.1088/2515-7647/adede9)  \nJournal of Physics: Photonics  \nPAPER  \nOPEN ACCESS  \nRECEIVED  \n17 January 2025  \nREVISED  \n2 June 2025  \nACCEPTED FOR PUBLICATION  \n8 July 2025  \nPUBLISHED  \n17 July 2025  \nOriginal content from this work may be used under the terms of the  \nCreative Commons Attribution 4 .0 licence.  \nAny further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.  \nPointwise prediction of protein diffusive properties using machine learning  \nRasched Haidari1,2, ∗􀁂 and Achillefs N Kapanidis1,2􀁂  \n1 Gene Machines Group, Clarendon Laboratory, Department of Physics, University of Oxford, Oxford, United Kingdom  \n2 Kavli Institute of Nanoscience Discovery, Dorothy Crowfoot Hodgkin Building, University of Oxford, Oxford, United Kingdom  \n∗ Author to whom any correspondence should be addressed.  \n[E-mail: rasched.haidari@linacre.ox.ac.uk](E-mail: rasched.haidari@linacre.ox.ac.uk)  \nKeywords: anomalous diffusion, pointwise inference, diffusion, AnDi2 challenge, machine learning, LSTM, changepoint analysis  \nAbstract  \nThe understanding of cellular mechanisms benefits substantially from accurate determination of protein diffusive properties. Prior work in this field primarily focuses on traditional methods, such as mean square displacements, for calculation of protein diffusion coefficients and biological states. This proves difficult and error-prone for proteins undergoing heterogeneous behaviour, particularly in complex environments, limiting the exploration of new biological behaviours. The importance of determining protein diffusion coefficients, anomalous exponents, and biological behaviours led to the Anomalous Diffusion Challenge 2024, exploring machine learning methods to infer these variables in heterogeneous trajectories with time-dependent changepoints. In response to the challenge, we present M3, a machine learning method for pointwise inference of diffusive coefficients, anomalous exponents, and states along noisy heterogenous protein trajectories. M3 makes use of long short-term memory cells to achieve small mean absolute errors for the diffusion coefficient and anomalous exponent alongside high state accuracies (>90%) . Subsequently, we implement changepoint detection to determine timepoints at which protein behaviour changes. M3 removes the need for expert fine-tuning required in most conventional statistical methods while being computationally inexpensive to train. The model finished in the Top 5 of the Anomalous Diffusive Challenge 2024, with small improvements made since challenge closure.  \n1. Introduction  \nProtein diffusion is vital to understanding cellular processes and the mechanisms which govern cellular functionality [1–4]. Advancements in fields such as single-molecule imaging and single-particle tracking have allowed for direct experimental observation of protein movement [4–15] . These studies have made extensive use of spatial-temporal properties of protein trajectories such as mean square displacements (MSD) and diffusion coefficients. Subsequent hard thresholding of diffusion coefficients allows for categorisation of proteins into different states, with each state representing underlying biological behaviour (e.g. a RNA polymerase molecule with a low diffusion coefficient may be interacting with the DNA) [14, 16–18] .  \nAlthough successful for a small number of states with relatively simple behaviours, MSD approaches are difficult to extend to complex behaviours such as changes in environment (e.g. viscosity), confinement or directed motion [19–21]. This is further complicated with proteins transitioning between different states, leading to inaccurate diffusion coefficients and overlapping states causing misclassifications [22] .  \nTo address these issues, Mun˜oz–Gil et al introduced the Anomalous Diffusion (AnDi) Challenge in ","cbCaiclrUxZ9sDeo","https://ap.wps.com/l/cbCaiclrUxZ9sDeo","pdf",1314028,1,13,"English","en",105,"# Introduction\n## Protein diffusion and trajectory-based measurements\n## Limitations of mean square displacement methods\n## Anomalous Diffusion Challenge background (AnDi 2020)\n## Diffusion models and anomalous exponent interpretation\n# Methods (M3) and pointwise inference","[{\"question\":\"Why are mean square displacement methods difficult for heterogeneous protein trajectories?\",\"answer\":\"MSD-based diffusion coefficient estimation becomes error-prone when proteins exhibit complex behaviors, transition between states, or experience changing environments, leading to overlapping states and misclassifications.\"},{\"question\":\"What variables does the proposed M3 method infer from protein trajectories?\",\"answer\":\"M3 performs pointwise inference of diffusion coefficients, anomalous exponents, and protein states along noisy heterogeneous trajectories.\"},{\"question\":\"How does M3 handle changes in protein behavior over time?\",\"answer\":\"M3 uses long short-term memory for pointwise estimation and then applies changepoint detection to identify timepoints where protein behavior changes.\"}]","Pointwise prediction of protein diffusive properties using machine learning | 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are mean square displacement methods difficult for heterogeneous protein trajectories?","Question",{"text":76,"@type":77},"MSD-based diffusion coefficient estimation becomes error-prone when proteins exhibit complex behaviors, transition between states, or experience changing environments, leading to overlapping states and misclassifications.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What variables does the proposed M3 method infer from protein trajectories?",{"text":81,"@type":77},"M3 performs pointwise inference of diffusion coefficients, anomalous exponents, and protein states along noisy heterogeneous trajectories.",{"name":83,"@type":74,"acceptedAnswer":84},"How does M3 handle changes in protein behavior over time?",{"text":85,"@type":77},"M3 uses long short-term memory for pointwise estimation and then applies changepoint detection to identify timepoints where protein behavior 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