{"id":"https://openalex.org/W2288694364","doi":"https://doi.org/10.1109/tsp.2015.2455515","title":"Constrained Maximum Likelihood Estimation of Relative Abundances of Protein Conformation in a Heterogeneous Mixture From Small Angle X-Ray Scattering Intensity Measurements","display_name":"Constrained Maximum Likelihood Estimation of Relative Abundances of Protein Conformation in a Heterogeneous Mixture From Small Angle X-Ray Scattering Intensity Measurements","publication_year":2015,"publication_date":"2015-07-13","ids":{"openalex":"https://openalex.org/W2288694364","doi":"https://doi.org/10.1109/tsp.2015.2455515","mag":"2288694364","pmid":"https://pubmed.ncbi.nlm.nih.gov/26924916"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2015.2455515","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2015.2455515","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084242647","display_name":"A. Emre Onuk","orcid":null},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Emre Onuk","raw_affiliation_strings":["Electrical and Computer Engineering Department, Northeastern University, Boston, MA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, Northeastern University, Boston, MA","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007822978","display_name":"Murat Ak\u00e7akaya","orcid":"https://orcid.org/0000-0001-5094-1931"},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Murat Akcakaya","raw_affiliation_strings":["Electrical and Computer Engineering Department, University of Pittsburgh, Pittsburgh, PA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, University of Pittsburgh, Pittsburgh, PA","institution_ids":["https://openalex.org/I170201317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021584861","display_name":"Jaydeep P. Bardhan","orcid":"https://orcid.org/0000-0002-6051-8499"},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jaydeep P. Bardhan","raw_affiliation_strings":["Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083261801","display_name":"Deniz Erdo\u011fmu\u015f","orcid":"https://orcid.org/0000-0002-1114-3539"},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Deniz Erdogmus","raw_affiliation_strings":["Electrical and Computer Engineering Department, Northeastern University, Boston, MA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, Northeastern University, Boston, MA","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079980080","display_name":"Dana H. Brooks","orcid":"https://orcid.org/0000-0003-3231-6715"},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dana H. Brooks","raw_affiliation_strings":["Electrical and Computer Engineering Department, Northeastern University, Boston, MA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, Northeastern University, Boston, MA","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025862507","display_name":"Lee Makowski","orcid":"https://orcid.org/0000-0003-0202-9264"},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lee Makowski","raw_affiliation_strings":["Bioengineering Department, Northeastern University, Boston, MA; Department of Chemistry and Chemical Biology, Northeastern University, Boston, MA","Bioengineering Department, Northeastern University, Boston, MA","Department of Chemistry and Chemical Biology, Northeastern University, Boston, MA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bioengineering Department, Northeastern University, Boston, MA; Department of Chemistry and Chemical Biology, Northeastern University, Boston, MA","institution_ids":["https://openalex.org/I12912129"]},{"raw_affiliation_string":"Bioengineering Department, Northeastern University, Boston, MA","institution_ids":["https://openalex.org/I12912129"]},{"raw_affiliation_string":"Department of Chemistry and Chemical Biology, Northeastern University, Boston, MA","institution_ids":["https://openalex.org/I12912129"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2639,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.78879123,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"63","issue":"20","first_page":"5383","last_page":"5394"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11162","display_name":"Enzyme Structure and Function","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11162","display_name":"Enzyme Structure and Function","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10044","display_name":"Protein Structure and Dynamics","score":0.9997000098228455,"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/T10211","display_name":"Computational Drug Discovery Methods","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/small-angle-x-ray-scattering","display_name":"Small-angle X-ray scattering","score":0.6941137313842773},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.6003638505935669},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5888983607292175},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.5393490791320801},{"id":"https://openalex.org/keywords/scattering","display_name":"Scattering","score":0.5056946277618408},{"id":"https://openalex.org/keywords/biological-system","display_name":"Biological system","score":0.38195884227752686},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.37794214487075806},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35484278202056885},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.32975438237190247},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.301098108291626},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2975640296936035},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15160927176475525},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.12647464871406555},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.08260685205459595}],"concepts":[{"id":"https://openalex.org/C131888329","wikidata":"https://www.wikidata.org/wiki/Q3027679","display_name":"Small-angle X-ray scattering","level":3,"score":0.6941137313842773},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.6003638505935669},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5888983607292175},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.5393490791320801},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.5056946277618408},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.38195884227752686},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.37794214487075806},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35484278202056885},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.32975438237190247},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.301098108291626},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2975640296936035},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15160927176475525},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.12647464871406555},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.08260685205459595},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsp.2015.2455515","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2015.2455515","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmid:26924916","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26924916","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,"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":"IEEE transactions on signal processing : a publication of the IEEE Signal Processing Society","raw_type":null},{"id":"pmh:oai:europepmc.org:4015998","is_oa":false,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/4767180","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6527971152","display_name":null,"funder_award_id":"R01 GM085648","funder_id":"https://openalex.org/F4320337354","funder_display_name":"National Institute of General Medical Sciences"},{"id":"https://openalex.org/G782234075","display_name":null,"funder_award_id":"R01-GM85648","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"}],"funders":[{"id":"https://openalex.org/F4320322421","display_name":"Orta Do\u011fu Teknik \u00dcniversitesi","ror":"https://ror.org/014weej12"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320332434","display_name":"ExxonMobil Research and Engineering Company","ror":"https://ror.org/01xcepn55"},{"id":"https://openalex.org/F4320337354","display_name":"National Institute of General Medical Sciences","ror":"https://ror.org/04q48ey07"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W630005112","https://openalex.org/W1584865998","https://openalex.org/W1814500939","https://openalex.org/W1970454429","https://openalex.org/W1972738934","https://openalex.org/W1979154012","https://openalex.org/W1980571928","https://openalex.org/W1982126789","https://openalex.org/W1984530381","https://openalex.org/W1986888461","https://openalex.org/W1996122875","https://openalex.org/W2005667072","https://openalex.org/W2015016494","https://openalex.org/W2042467250","https://openalex.org/W2042928151","https://openalex.org/W2066088601","https://openalex.org/W2075564615","https://openalex.org/W2086412408","https://openalex.org/W2086469512","https://openalex.org/W2134474324","https://openalex.org/W2142654956","https://openalex.org/W2154539002","https://openalex.org/W2164361934","https://openalex.org/W2167693135","https://openalex.org/W2170408275","https://openalex.org/W2406525321","https://openalex.org/W2799148064","https://openalex.org/W4206180546","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4385780251","https://openalex.org/W2793358973","https://openalex.org/W2130897203","https://openalex.org/W2170146374","https://openalex.org/W62419374","https://openalex.org/W2154850011","https://openalex.org/W3037884287","https://openalex.org/W3002700256","https://openalex.org/W4310722055","https://openalex.org/W4223456432"],"abstract_inverted_index":{"In":[0],"this":[1,188],"paper,":[2],"we":[3,44,103,136,147,155,198],"describe":[4],"a":[5,20,23,46,66,85,113],"model":[6,98,108],"for":[7,99,161,180],"maximum":[8,189],"likelihood":[9],"estimation":[10,62,143,186],"(MLE)":[11],"of":[12,16,19,80,84,140,177,187,191],"the":[13,37,55,59,72,76,81,89,94,97,100,106,119,138,141,166,171,175,196],"relative":[14,178],"abundances":[15,179],"different":[17],"conformations":[18,83,127,192],"protein":[21,123],"in":[22],"heterogeneous":[24],"mixture":[25,60],"from":[26],"small":[27],"angle":[28],"X-ray":[29],"scattering":[30],"(SAXS)":[31],"intensities.":[32],"To":[33],"consider":[34],"cases":[35],"where":[36],"solution":[38],"includes":[39],"intermediate":[40],"or":[41],"unknown":[42],"conformations,":[43],"develop":[45],"subset":[47],"selection":[48],"method":[49],"based":[50],"on":[51,58,96],"k-means":[52],"clustering":[53,167],"and":[54,93,124,131,154],"Cram\u00e9r-Rao":[56],"bound":[57],"coefficient":[61],"error":[63],"to":[64,195],"find":[65],"sparse":[67],"basis":[68,91],"set":[69,92],"that":[70,105,170],"represents":[71],"space":[73],"spanned":[74],"by":[75],"measured":[77],"SAXS":[78],"intensities":[79],"known":[82,126],"protein.":[86],"Then,":[87],"using":[88,132],"selected":[90],"assumptions":[95],"intensity":[101],"measurements,":[102],"show":[104],"MLE":[107],"can":[109],"be":[110],"expressed":[111],"as":[112,128],"constrained":[114],"convex":[115],"optimization":[116],"problem.":[117],"Employing":[118],"adenylate":[120],"kinase":[121],"(ADK)":[122],"its":[125],"an":[129],"example,":[130],"Monte":[133],"Carlo":[134],"simulations,":[135],"demonstrate":[137],"performance":[139],"proposed":[142],"scheme.":[144],"Here,":[145],"although":[146],"use":[148],"45":[149],"crystallographically":[150],"determined":[151],"experimental":[152],"structures":[153],"could":[156],"generate":[157],"many":[158],"more":[159,181],"using,":[160],"instance,":[162],"molecular":[163],"dynamics":[164],"calculations,":[165],"technique":[168],"indicates":[169],"data":[172],"cannot":[173],"support":[174],"determination":[176],"than":[182],"5":[183],"conformations.":[184],"The":[185],"number":[190],"is":[193],"intrinsic":[194],"methodology":[197],"have":[199],"used":[200],"here.":[201]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-24T13:16:06.693445","created_date":"2025-10-10T00:00:00"}