{"id":"https://openalex.org/W7220698100","doi":"https://doi.org/10.64898/2026.10.01.756064","title":"Activation thresholds set the speed of biochemical trigger waves","display_name":"Activation thresholds set the speed of biochemical trigger waves","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220698100","doi":"https://doi.org/10.64898/2026.10.01.756064"},"language":"en","primary_location":{"id":"doi:10.64898/2026.10.01.756064","doi":"https://doi.org/10.64898/2026.10.01.756064","is_oa":true,"landing_page_url":"https://doi.org/10.64898/2026.10.01.756064","pdf_url":"https://www.biorxiv.org/content/biorxiv/early/2026/10/06/2026.10.01.756064.full.pdf","source":{"id":"https://openalex.org/S4306402567","display_name":"bioRxiv (Cold Spring Harbor Laboratory)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2750212522","host_organization_name":"Cold Spring Harbor Laboratory","host_organization_lineage":["https://openalex.org/I2750212522"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"bioRxiv","raw_type":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.biorxiv.org/content/biorxiv/early/2026/10/06/2026.10.01.756064.full.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101819916","display_name":"Zhengda Li","orcid":"https://orcid.org/0000-0002-9960-4394","observed_orcids":["https://orcid.org/0000-0002-9960-4394"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhengda Li","raw_affiliation_strings":["Stanford University"],"raw_orcid":"https://orcid.org/0000-0002-9960-4394","affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007372909","display_name":"James E. Ferrell","orcid":"https://orcid.org/0000-0003-4767-3926","observed_orcids":["https://orcid.org/0000-0003-4767-3926"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"James E Ferrell","raw_affiliation_strings":["Stanford University"],"raw_orcid":"https://orcid.org/0000-0003-4767-3926","affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007372909"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.6342999935150146,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.6342999935150146,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10294","display_name":"Cell death mechanisms and regulation","score":0.23180000483989716,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.06300000101327896,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/trigger-waves","display_name":"trigger waves","score":0.9779999852180481},{"id":"https://openalex.org/keywords/activation-threshold","display_name":"activation threshold","score":0.6949999928474426},{"id":"https://openalex.org/keywords/wave-speed","display_name":"wave velocity","score":0.7170000076293945},{"id":"https://openalex.org/keywords/apoptosis","display_name":"apoptosis","score":0.8040000200271606},{"id":"https://openalex.org/keywords/caspase-activity","display_name":"caspase activity","score":0.9150000214576721},{"id":"https://openalex.org/keywords/positive-feedback","display_name":"positive feedback","score":0.871999979019165},{"id":"https://openalex.org/keywords/cell-cycle","display_name":"cell cycle","score":0.6359999775886536},{"id":"https://openalex.org/keywords/cytostatic-factor","display_name":"cytostatic factor","score":0.7789999842643738},{"id":"https://openalex.org/keywords/xenopus-egg-extracts","display_name":"Xenopus egg extracts","score":0.7599999904632568},{"id":"https://openalex.org/keywords/diffusion-coefficient","display_name":"diffusion coefficient","score":0.5759999752044678},{"id":"https://openalex.org/keywords/scaling-laws","display_name":"scaling laws","score":0.6269999742507935},{"id":"https://openalex.org/keywords/interphase","display_name":"interphase","score":0.3490000069141388},{"id":"https://openalex.org/keywords/m-phase-arrest","display_name":"M phase arrest","score":0.6430000066757202}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5860999822616577},{"id":"https://openalex.org/C2779535977","wikidata":"https://www.wikidata.org/wiki/Q1342298","display_name":"Xenopus","level":3,"score":0.5515999794006348},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5194000005722046},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5092999935150146},{"id":"https://openalex.org/C29452124","wikidata":"https://www.wikidata.org/wiki/Q835950","display_name":"Interphase","level":2,"score":0.5040000081062317},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.4169999957084656},{"id":"https://openalex.org/C106978608","wikidata":"https://www.wikidata.org/wiki/Q1412691","display_name":"Wave packet","level":2,"score":0.4090000092983246},{"id":"https://openalex.org/C2986045365","wikidata":"https://www.wikidata.org/wiki/Q1163350","display_name":"Wave speed","level":2,"score":0.3765000104904175},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.3580999970436096},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.3537999987602234},{"id":"https://openalex.org/C12554922","wikidata":"https://www.wikidata.org/wiki/Q7100","display_name":"Biophysics","level":1,"score":0.35260000824928284},{"id":"https://openalex.org/C2988430800","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Scaling law","level":3,"score":0.34700000286102295},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.34599998593330383},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.3440999984741211},{"id":"https://openalex.org/C190283241","wikidata":"https://www.wikidata.org/wiki/Q14599311","display_name":"Apoptosis","level":2,"score":0.3361999988555908},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3046000003814697},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.28049999475479126},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.27399998903274536},{"id":"https://openalex.org/C44886760","wikidata":"https://www.wikidata.org/wiki/Q1758425","display_name":"Wave propagation","level":2,"score":0.2540999948978424},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2531000077724457}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.64898/2026.10.01.756064","doi":"https://doi.org/10.64898/2026.10.01.756064","is_oa":true,"landing_page_url":"https://doi.org/10.64898/2026.10.01.756064","pdf_url":"https://www.biorxiv.org/content/biorxiv/early/2026/10/06/2026.10.01.756064.full.pdf","source":{"id":"https://openalex.org/S4306402567","display_name":"bioRxiv (Cold Spring Harbor Laboratory)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2750212522","host_organization_name":"Cold Spring Harbor Laboratory","host_organization_lineage":["https://openalex.org/I2750212522"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"bioRxiv","raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.64898/2026.10.01.756064","doi":"https://doi.org/10.64898/2026.10.01.756064","is_oa":true,"landing_page_url":"https://doi.org/10.64898/2026.10.01.756064","pdf_url":"https://www.biorxiv.org/content/biorxiv/early/2026/10/06/2026.10.01.756064.full.pdf","source":{"id":"https://openalex.org/S4306402567","display_name":"bioRxiv (Cold Spring Harbor Laboratory)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2750212522","host_organization_name":"Cold Spring Harbor Laboratory","host_organization_lineage":["https://openalex.org/I2750212522"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"bioRxiv","raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220698100.pdf","grobid_xml":"https://content.openalex.org/works/W7220698100.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4243730356"],"related_works":["https://openalex.org/W2885028350","https://openalex.org/W7135015583","https://openalex.org/W7077973512","https://openalex.org/W4400509159","https://openalex.org/W2886004308","https://openalex.org/W2049414718","https://openalex.org/W4391133142","https://openalex.org/W2001165708","https://openalex.org/W2613036297","https://openalex.org/W2902840862"],"abstract_inverted_index":{"Trigger":[0],"waves":[1,6,32,59],"are":[2],"positive":[3],"feedback-mediated":[4],"traveling":[5],"that":[7,58],"propagate":[8],"without":[9],"slowing":[10],"down":[11],"or":[12],"diminishing":[13],"in":[14,38,49,63,71,133,138],"amplitude,":[15],"enabling":[16],"biochemical":[17,216],"coordination":[18],"over":[19],"distances":[20],"where":[21,168],"diffusion":[22,89],"alone":[23],"would":[24],"be":[25],"insufficient.":[26],"Apoptosis":[27],"can":[28],"spread":[29,213],"as":[30,36,195],"trigger":[31,134,144,200],"of":[33,121,199,214],"caspase":[34],"activity,":[35],"demonstrated":[37],"Xenopus":[39],"eggs":[40],"and":[41,56,92,100,108,137,174,203],"egg":[42],"extracts.":[43],"We":[44,154],"measured":[45],"apoptotic":[46,182],"wave":[47,85,135,201],"speeds":[48],"extracts":[50,69,73,107],"at":[51],"two":[52,106],"cell":[53,151],"cycle":[54,152],"states":[55],"found":[57,147],"propagated":[60],"more":[61],"slowly":[62],"M-phase":[64],"arrested":[65],"cytostatic":[66],"factor":[67],"(CSF)":[68],"than":[70],"interphase":[72],"(21":[74],"versus":[75],"27":[76],"\u03bcm":[77],"min":[78],"-1":[79],").":[80],"Luther's":[81,157],"equation,":[82],"v=2\u221aD\u03ba,":[83],"predicts":[84],"speed":[86,113,202],"from":[87],"the":[88,93,105,112,122,140,171,178,185,192,212],"coefficient":[90],"D":[91,99],"positive-feedback":[94],"doubling":[95],"rate":[96,173],"\u03ba.":[97],"However,":[98],"\u03ba":[101],"were":[102],"comparable":[103],"between":[104,150],"could":[109],"not":[110,127],"explain":[111],"difference.":[114],"This":[115],"discrepancy":[116],"highlighted":[117],"a":[118,162,196,205],"key":[119,197],"limitation":[120],"classical":[123],"equation:":[124],"it":[125],"does":[126],"account":[128],"for":[129,210],"an":[130],"activation":[131,179,193],"threshold":[132,141,194],"initiation,":[136],"fact":[139],"required":[142],"to":[143,148,159],"apoptosis":[145],"was":[146],"differ":[149],"states.":[153],"therefore":[155],"extended":[156],"equation":[158],"include":[160],"such":[161],"threshold,":[163],"obtaining":[164],"v\u221d\u221a(AD/U":[165],"c":[166,176],"),":[167],"A":[169],"is":[170,177],"reaction":[172],"U":[175],"threshold.":[180],"Perturbing":[181],"sensitivity":[183],"confirmed":[184],"predicted":[186],"threshold-speed":[187],"relationship.":[188],"These":[189],"findings":[190],"establish":[191],"determinant":[198],"provide":[204],"broadly":[206],"applicable":[207],"scaling":[208],"law":[209],"predicting":[211],"switch-like":[215],"signals.":[217]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-07T00:00:00"}
