{"id":"https://openalex.org/W7117555985","doi":"https://doi.org/10.1016/j.bpj.2025.12.030","title":"Simulation of reaction-diffusion equations with reaction-reaction analog circuits","display_name":"Simulation of reaction-diffusion equations with reaction-reaction analog circuits","publication_year":2025,"publication_date":"2025-12-30","ids":{"openalex":"https://openalex.org/W7117555985","doi":"https://doi.org/10.1016/j.bpj.2025.12.030","pmid":"https://pubmed.ncbi.nlm.nih.gov/41476370","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/13351851"},"language":"en","primary_location":{"id":"doi:10.1016/j.bpj.2025.12.030","doi":"https://doi.org/10.1016/j.bpj.2025.12.030","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.bpj.2025.12.030","pdf_url":null,"source":{"id":"https://openalex.org/S98085912","display_name":"Biophysical Journal","issn_l":"0006-3495","issn":["0006-3495","1542-0086"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-1","medline","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Biophysical Journal","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.bpj.2025.12.030","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5121575425","display_name":"Nathan J. Green","orcid":"https://orcid.org/0009-0002-5144-2493","observed_orcids":["https://orcid.org/0009-0002-5144-2493"]},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nathan Green","raw_affiliation_strings":["Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire"],"raw_orcid":"https://orcid.org/0009-0002-5144-2493","affiliations":[{"raw_affiliation_string":"Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076956293","display_name":"Douglas Raymond Beahm","orcid":"https://orcid.org/0000-0002-8039-020X","observed_orcids":["https://orcid.org/0000-0002-8039-020X"]},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Douglas Beahm","raw_affiliation_strings":["Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011863454","display_name":"A. J. Cressman","orcid":"https://orcid.org/0000-0001-8657-3341","observed_orcids":["https://orcid.org/0000-0001-8657-3341"]},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anthony Cressman","raw_affiliation_strings":["Department of Physics, Dartmouth College, Hanover, New Hampshire"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Dartmouth College, Hanover, New Hampshire","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001601446","display_name":"Jacob Denbeaux","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jacob Denbeaux","raw_affiliation_strings":["Department of Computer Science, Dartmouth College, Hanover, New Hampshire"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Dartmouth College, Hanover, New Hampshire","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116875287","display_name":"Shouka Tavakolian","orcid":"https://orcid.org/0009-0001-9773-0282","observed_orcids":["https://orcid.org/0009-0001-9773-0282"]},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shouka Tavakolian","raw_affiliation_strings":["School of Undergraduate Arts and Sciences, Dartmouth College, Hanover, New Hampshire"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Undergraduate Arts and Sciences, Dartmouth College, Hanover, New Hampshire","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009252030","display_name":"Rahul Sarpeshkar","orcid":"https://orcid.org/0000-0002-5975-0004","observed_orcids":["https://orcid.org/0000-0002-5975-0004"]},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Rahul Sarpeshkar","raw_affiliation_strings":["Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire; Department of Physics, Dartmouth College, Hanover, New Hampshire; The Geisel School of Medicine, Department of Microbiology and Immunology, Dartmouth College, Hanover, New Hampshire; The Geisel School of Medicine, Department of Molecular and Systems Biology, Dartmouth College, Hanover, New Hampshire. Electronic address: rahul.sarpeshkar@dartmouth.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire; Department of Physics, Dartmouth College, Hanover, New Hampshire; The Geisel School of Medicine, Department of Microbiology and Immunology, Dartmouth College, Hanover, New Hampshire; The Geisel School of Medicine, Department of Molecular and Systems Biology, Dartmouth College, Hanover, New Hampshire. Electronic address: rahul.sarpeshkar@dartmouth.edu","institution_ids":["https://openalex.org/I107672454"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009252030"],"corresponding_institution_ids":["https://openalex.org/I107672454"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":{"value":3000,"currency":"USD","value_usd":3000},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"125","issue":"3","first_page":"832","last_page":"855"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.43700000643730164,"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":0.43700000643730164,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.27639999985694885,"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/T12029","display_name":"DNA and Biological Computing","score":0.06030000001192093,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reaction-diffusion-systems","display_name":"reaction-diffusion systems","score":0.984000027179718},{"id":"https://openalex.org/keywords/analog-circuits","display_name":"analog circuits","score":0.8100000023841858},{"id":"https://openalex.org/keywords/diffusion-simulation","display_name":"diffusion simulation","score":0.722000002861023},{"id":"https://openalex.org/keywords/turing-patterns","display_name":"Turing patterns","score":0.6029999852180481},{"id":"https://openalex.org/keywords/spatiotemporal-pattern-formation","display_name":"spatiotemporal pattern formation","score":0.8389999866485596},{"id":"https://openalex.org/keywords/systems-medicine","display_name":"systems medicine","score":0.8259999752044678}],"concepts":[{"id":"https://openalex.org/C90915687","wikidata":"https://www.wikidata.org/wiki/Q63759","display_name":"Analog computer","level":2,"score":0.7124000191688538},{"id":"https://openalex.org/C29074008","wikidata":"https://www.wikidata.org/wiki/Q174925","display_name":"Analogue electronics","level":3,"score":0.7013000249862671},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.6922000050544739},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5771999955177307},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5092999935150146},{"id":"https://openalex.org/C2780365114","wikidata":"https://www.wikidata.org/wiki/Q169478","display_name":"MATLAB","level":2,"score":0.5012999773025513},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4787999987602234},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.4666999876499176},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.43549999594688416},{"id":"https://openalex.org/C98142538","wikidata":"https://www.wikidata.org/wiki/Q485005","display_name":"Analog multiplier","level":4,"score":0.3855000138282776},{"id":"https://openalex.org/C55037315","wikidata":"https://www.wikidata.org/wiki/Q5421151","display_name":"Experimental data","level":2,"score":0.37860000133514404},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3702999949455261},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.36579999327659607},{"id":"https://openalex.org/C13412647","wikidata":"https://www.wikidata.org/wiki/Q174948","display_name":"Analog signal","level":3,"score":0.362199991941452},{"id":"https://openalex.org/C530198007","wikidata":"https://www.wikidata.org/wiki/Q80831","display_name":"Integrated circuit","level":2,"score":0.359499990940094},{"id":"https://openalex.org/C187738980","wikidata":"https://www.wikidata.org/wiki/Q182527","display_name":"Chemical equation","level":2,"score":0.351500004529953},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3370000123977661},{"id":"https://openalex.org/C206565188","wikidata":"https://www.wikidata.org/wiki/Q836482","display_name":"Sample and hold","level":3,"score":0.3172000050544739},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3149999976158142},{"id":"https://openalex.org/C62907940","wikidata":"https://www.wikidata.org/wiki/Q1541329","display_name":"Mixed-signal integrated circuit","level":3,"score":0.3091000020503998},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3034999966621399},{"id":"https://openalex.org/C90711627","wikidata":"https://www.wikidata.org/wiki/Q3742408","display_name":"Analog device","level":4,"score":0.2976999878883362},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C32946077","wikidata":"https://www.wikidata.org/wiki/Q618079","display_name":"Network analysis","level":2,"score":0.2904999852180481},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.28360000252723694},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C46205389","wikidata":"https://www.wikidata.org/wiki/Q1270401","display_name":"Electronic circuit simulation","level":3,"score":0.27950000762939453},{"id":"https://openalex.org/C194571574","wikidata":"https://www.wikidata.org/wiki/Q2251187","display_name":"Linear circuit","level":4,"score":0.2685000002384186},{"id":"https://openalex.org/C145366948","wikidata":"https://www.wikidata.org/wiki/Q178947","display_name":"Operational amplifier","level":4,"score":0.2651999890804291},{"id":"https://openalex.org/C23572009","wikidata":"https://www.wikidata.org/wiki/Q964981","display_name":"Equivalent circuit","level":3,"score":0.2605000138282776},{"id":"https://openalex.org/C176046018","wikidata":"https://www.wikidata.org/wiki/Q359205","display_name":"Analogue filter","level":4,"score":0.250900000333786}],"mesh":[{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D004058","descriptor_name":"Diffusion","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008954","descriptor_name":"Models, Biological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":3,"locations":[{"id":"doi:10.1016/j.bpj.2025.12.030","doi":"https://doi.org/10.1016/j.bpj.2025.12.030","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.bpj.2025.12.030","pdf_url":null,"source":{"id":"https://openalex.org/S98085912","display_name":"Biophysical Journal","issn_l":"0006-3495","issn":["0006-3495","1542-0086"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-1","medline","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Biophysical Journal","raw_type":"journal-article"},{"id":"pmh:oai:pubmedcentral.nih.gov:13351851","doi":null,"is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13351851/","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13351851/pdf/","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Biophys J","raw_type":"Text"},{"id":"pmid:41476370","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41476370","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Biophysical journal","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1016/j.bpj.2025.12.030","doi":"https://doi.org/10.1016/j.bpj.2025.12.030","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.bpj.2025.12.030","pdf_url":null,"source":{"id":"https://openalex.org/S98085912","display_name":"Biophysical Journal","issn_l":"0006-3495","issn":["0006-3495","1542-0086"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-1","medline","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Biophysical Journal","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6858785568","display_name":"FET: Small: Rapid and Rational Drug-Cocktail Formulation and Discovery Via Electronic Circuits","funder_award_id":"2240264","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320310400","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7117555985.pdf","grobid_xml":"https://content.openalex.org/works/W7117555985.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1668206751","https://openalex.org/W1669342238","https://openalex.org/W1980661496","https://openalex.org/W1991325491","https://openalex.org/W2003095799","https://openalex.org/W2014362480","https://openalex.org/W2030638423","https://openalex.org/W2039888453","https://openalex.org/W2050492893","https://openalex.org/W2057119480","https://openalex.org/W2071803641","https://openalex.org/W2086333769","https://openalex.org/W2089840306","https://openalex.org/W2091643574","https://openalex.org/W2099530148","https://openalex.org/W2100995199","https://openalex.org/W2102653059","https://openalex.org/W2116074901","https://openalex.org/W2125010820","https://openalex.org/W2127071442","https://openalex.org/W2139983563","https://openalex.org/W2140281076","https://openalex.org/W2148114554","https://openalex.org/W2151847832","https://openalex.org/W2161045785","https://openalex.org/W2166705426","https://openalex.org/W2566193534","https://openalex.org/W2790737510","https://openalex.org/W2791666466","https://openalex.org/W3092734034","https://openalex.org/W3216953587","https://openalex.org/W4390542491","https://openalex.org/W4396886376","https://openalex.org/W4404919358","https://openalex.org/W4406749449","https://openalex.org/W4408669091"],"related_works":["https://openalex.org/W7130532808","https://openalex.org/W2279359657","https://openalex.org/W2183428067","https://openalex.org/W2122526344","https://openalex.org/W2791666466","https://openalex.org/W7096066664","https://openalex.org/W2140574265","https://openalex.org/W4229698491","https://openalex.org/W2073305540","https://openalex.org/W7098598921"],"abstract_inverted_index":{"In":[0],"1952,":[1],"Alan":[2],"Turing":[3],"showed":[4],"that":[5,86,99,112],"analog":[6,69,88,108],"reaction-diffusion":[7,92,102,164],"equations":[8,61],"were":[9,81],"extremely":[10],"powerful":[11],"models":[12],"of":[13,17,30,36,57,62,135,162],"biological":[14,136],"development":[15],"and":[16,50,132,149],"distributed":[18],"cellular":[19],"automata.":[20],"Analog":[21],"circuits":[22,111,116,126],"have":[23,114],"been":[24],"shown":[25],"to":[26,66,75,146],"accelerate":[27],"the":[28,55,58,100,156],"simulation":[29,56],"chemical":[31,83],"reactions":[32],"by":[33],"many":[34],"orders":[35],"magnitude,":[37],"including":[38],"in":[39,51,68,107],"stochastic":[40],"(noisy)":[41],"cytomorphic":[42,109,139],"chips,":[43],"which":[44],"are":[45],"useful":[46],"for":[47],"drug-cocktail":[48],"formulation":[49],"systems":[52,89],"medicine.":[53],"However,":[54],"partial":[59],"differential":[60],"diffusion":[63,77,120],"is":[64,155],"expensive":[65],"architect":[67],"systems.":[70,93],"Here,":[71],"we":[72,97],"show":[73,98,127],"how":[74],"simulate":[76,91],"as":[78],"though":[79],"it":[80],"a":[82],"reaction":[84,115],"such":[85],"reaction-reaction":[87,125],"can":[90,104],"As":[94],"an":[95],"example,":[96],"BMP-SOX9-WNT":[101],"system":[103],"be":[105],"simulated":[106],"integrated":[110],"only":[113],"but":[117],"no":[118],"explicit":[119],"circuits.":[121],"Experimental":[122],"data":[123],"from":[124],"excellent":[128],"agreement":[129],"with":[130,141],"MATLAB":[131],"COPASI":[133],"simulations":[134,161],"models.":[137],"Even":[138],"chips":[140],"relatively":[142],"sparse":[143],"sampling":[144],"appear":[145],"demonstrate":[147],"decaying":[148],"unstable":[150],"growing":[151],"waves.":[152],"Our":[153],"work":[154],"first":[157],"step":[158],"toward":[159],"large-scale":[160],"spatiotemporal":[163],"equations.":[165]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2025-12-30T00:00:00"}