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The work proposes a minimal, non-genetic learning mechanism inspired by Boltzmann neural networks: dense reversible interaction networks use mediator “hidden” species whose concentrations are modulated, and a rate-sensitive autoregulatory scheme implements a local Hebbian-like training rule. The approach is model-free, applies to reversible multimerization networks, and supports diverse learning behaviors including conditioning, supervised classification, and bet-hedging generation.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/trainable-computation-in-molecular-networks-paper/442951/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/trainable-computation-in-molecular-networks-paper/442951.png","ImageObject",300,407,{"name":92,"@type":93},"CatatanPagi","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-03","2026-09-29",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What problem does the paper tackle?","Question",{"text":112,"@type":113},"It tackles the lack of an accepted molecular mechanism for training in single cells without genetic change, comparable to gradient-based or Hebbian learning.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What minimal ingredients are proposed to enable non-genetic learning?",{"text":117,"@type":113},"The mechanism uses dense reversible interaction networks plus modulation of mediator species concentrations, combined with a rate-sensitive autoregulatory scheme that yields a local Hebbian-like training rule.",{"name":119,"@type":110,"acceptedAnswer":120},"What learning behaviors can the trained molecular networks perform?",{"text":121,"@type":113},"The autoregulatory rule enables Pavlovian conditioning, supervised classification, and generative tuning for bet-hedging ratios matching environmental statistics.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},442951,1790993668,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145},962090894170,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","bioRxiv preprint doi: [https://doi.org/10.64898/2025.12.28.696421](https://doi.org/10.64898/2025.12.28.696421); this version posted December 30, 2025. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made  \navailable under aCC-BY-NC-ND 4.0 International license.  \nTrainable computation in molecular networks  \nKristina Trifonova 1 ,∗ , Martin J. Falk 1 ,∗ , Mason Rouches 1 ,  \nSuriyanarayanan Vaikuntanathan 1 , Michael Elowitz2 , Arvind Murugan 1  \n1 James Franck Institute, University of Chicago, Chicago, IL 60637,  \n2 Howard Hughes Medical Institute and Division of Biology and Biological Engineering,  \nCalifornia Institute of Technology, Pasadena, CA 91125  \nReports of learning in single cells without genetic change span decades yet remain controversial, in part because there is no accepted general molecular mechanism for training comparable to gradient-based training or Hebbian learning in neural circuits. Here we identify a minimal set of ingredients sufficient to realize non-genetic learning, drawing inspiration from Boltzmann neural networks. First, dense reversible interaction networks provide an expressive substrate in which modulating the concentrations of a small set of mediator species can reprogram function without altering the underlying interaction parameters. Second, a simple rate-sensitive autoregulatory scheme that adjusts these mediator levels provides a local Hebbian-like training rule that can train the same network for diverse tasks, including Pavlovian conditioning, supervised classification, and generative tuning of bet-hedging ratios to match environmental statistics. We show that this autoregulatory training rule is model free and applies to reversible multimerization networks of arbitrary complexity, so training can compensate for unknown or unmodeled interactions present in vivo. These results suggest design principles for trainable synthetic cellular circuits and indicate how molecular systems could learn statistical features of their environments through experience.  \nNatural selection is often invoked to explain how cells come to embody the statistics of their past environments. In this view, regulatory programs encode those statistics, shaping cellular responses based on how frequently different conditions occurred in the past and not just on their immediate presence. These evolved programs can be remarkably sophisticated: microbes can anticipate nutrient depletion [1–4], populations hedge their bets by adopting diverse phenotypes at characteristic frequencies [5–9], and stress response pathways activate in anticipation of correlated environmental changes [10–12] . Here, memory of environmental statistics is genetically hardwired over evolutionary timescales through mutation and selection.  \nYet many observations hint that cells can learn environmental statistics on much shorter timescales, via parameter remodeling within a lineage rather than differential survival of variants. These observations [8, 13–26] include habituation, priming, Pavlovian associative conditioning, anticipatory regulation, and learned bet hedging in cells ranging from bacteria to protists, yeast, and immune and cancer cells. While intriguing, many of these observations remain controversial, especially since the mechanisms underlying these phenomena are not fully clear.  \nHere, we define learning as experience-dependent reprogramming of regulatory programs: repeated exposure to a structured environment adjusts internal parameters so that future responses reflect correlations in past stimuli rather than only their immediate presence [27–29]; see Fig.1a. Biologically, learning within a lifetime would allow cells and organisms to adapt to evolutionarily novel or fluctuating environments on short timescales and without the cost of deleterious mutations. In a synthetic biology context, it would enable","cbCaiesJ2QGUa1pt","https://ap.wps.com/l/cbCaiesJ2QGUa1pt","pdf",11418329,15,"English","# Overview\n## Non-genetic learning challenge\n## Proposed minimal mechanism\n# Learning rule and model-free training\n## Dense reversible interaction networks\n## Rate-sensitive autoregulation\n# Applications and implications\n## Conditioning, classification, and bet hedging\n## Design principles for synthetic circuits","[{\"question\":\"What problem does the paper tackle?\",\"answer\":\"It tackles the lack of an accepted molecular mechanism for training in single cells without genetic change, comparable to gradient-based or Hebbian learning.\"},{\"question\":\"What minimal ingredients are proposed to enable non-genetic learning?\",\"answer\":\"The mechanism uses dense reversible interaction networks plus modulation of mediator species concentrations, combined with a rate-sensitive autoregulatory scheme that yields a local Hebbian-like training rule.\"},{\"question\":\"What learning behaviors can the trained molecular networks perform?\",\"answer\":\"The autoregulatory rule enables Pavlovian conditioning, supervised classification, and generative tuning for bet-hedging ratios matching environmental statistics.\"}]","Trainable computation in molecular networks - Paper | PDF",1790702283,38]