title: A comprehensive mathematical model for three-body binding equilibria.
abstract: Three-component systems are often more complex than their two-component counterparts. Although the reversible association of three components in solution is critical for a vast array of chemical and biological processes, no general physical picture of such systems has emerged. Here we have developed a general, comprehensive framework for understanding ternary complex equilibria, which relates directly to familiar concepts such as EC50 and IC50 from simpler (binary complex) equilibria. Importantly, application of our model to data from the published literature has enabled us to achieve new insights into complex systems ranging from coagulation to therapeutic dosing regimens for monoclonal antibodies. We also provide an Excel spreadsheet to assist readers in both conceptualizing and applying our models. Overall, our analysis has the potential to render complex three-component systems--which have previously been characterized as "analytically intractable"--readily comprehensible to theoreticians and experimentalists alike.
authors.affiliation: Department of Chemistry, Yale University, New Haven, Connecticut 06520, USA.
authors.forename: Eugene F
authors.initials: EF
authors.lastname: Douglass
authors.forename: Chad J
authors.initials: CJ
authors.lastname: Miller
authors.forename: Gerson
authors.initials: G
authors.lastname: Sparer
authors.forename: Harold
authors.initials: H
authors.lastname: Shapiro
authors.forename: David A
authors.initials: DA
authors.lastname: Spiegel
mesh_terms: D000465:Algorithms; D000911:Antibodies, Monoclonal / Q000737:chemistry; D000920:Antibody-Dependent Cell Cytotoxicity; D000925:Anticoagulants / Q000494:pharmacology; D004305:Dose-Response Relationship, Drug; D057166:High-Throughput Screening Assays; D006801:Humans; D007700:Kinetics; D008297:Male; D015233:Models, Statistical; D011471:Prostatic Neoplasms / Q000175:diagnosis; D011485:Protein Binding; D036104:Receptor, EphA2 / Q000737:chemistry; D011961:Receptors, Fc / Q000737:chemistry; D012996:Solutions
chemical_list: D000911:Antibodies, Monoclonal; D000925:Anticoagulants; D011961:Receptors, Fc; D012996:Solutions; D036104:Receptor, EphA2
references.citation: J Immunol. 1978 Aug;121(2):593-601
references.pmid: 79608
references.citation: Proc Natl Acad Sci U S A. 1997 Dec 9;94(25):13493-8
references.pmid: 9391053
references.citation: Math Biosci. 2011 Aug;232(2):164-73
references.pmid: 21683720
references.citation: Nat Biotechnol. 2005 Sep;23(9):1105-16
references.pmid: 16151404
references.citation: Angew Chem Int Ed Engl. 2011 Feb 18;50(8):1762-8
references.pmid: 21328640
references.citation: FEBS Lett. 1995 Feb 27;360(2):111-4
references.pmid: 7875313
references.citation: J Am Chem Soc. 2003 Apr 2;125(13):3692-3
references.pmid: 12656587
references.citation: Cancer Metastasis Rev. 1999;18(4):483-90
references.pmid: 10855791
references.citation: Biochem Soc Trans. 1978;6(1):258-60
references.pmid: 640181
references.citation: J Gen Physiol. 1943 Jul 20;26(6):559-85
references.pmid: 19873367
references.citation: Nat Struct Mol Biol. 2007 Feb;14(2):169-71
references.pmid: 17220897
references.citation: Infect Immun. 2007 Apr;75(4):1904-15
references.pmid: 17283107
references.citation: Dalton Trans. 2004 Dec 21;(24):4096-105
references.pmid: 15573160
references.citation: AAPS J. 2010 Dec;12(4):592-601
references.pmid: 20652780
references.citation: J Am Chem Soc. 2009 Dec 2;131(47):17090-2
references.pmid: 19888723
references.citation: Immunochemistry. 1978 Feb;15(2):77-82
references.pmid: 631868
references.citation: J Biol Chem. 1980 Aug 10;255(15):7108-17
references.pmid: 6248546
references.citation: Int J Mol Sci. 2012;13(7):8273-92
references.pmid: 22942702
references.citation: Biochemistry. 2002 Apr 23;41(16):5177-84
references.pmid: 11955066
references.citation: Biochemistry. 2004 May 11;43(18):5406-13
references.pmid: 15122906
references.citation: J Biol Chem. 1998 Jul 3;273(27):16824-7
references.pmid: 9642241
references.citation: J Phys Chem A. 2005 Jul 14;109(27):6128-34
references.pmid: 16833950
references.citation: Biochem Biophys Res Commun. 1976 Aug 9;71(3):738-45
references.pmid: 962952
references.citation: PLoS Comput Biol. 2010 Nov 04;6(11):e1000975
references.pmid: 21079669
references.citation: J Immunol. 2003 Apr 1;170(7):3621-30
references.pmid: 12646626
references.citation: Nat Commun. 2010 Nov 16;1:119
references.pmid: 21081917
references.citation: J Exp Med. 1935 Aug 31;62(3):359-74
references.pmid: 19870421
references.citation: Nature. 2001 Nov 1;414(6859):31-2
references.pmid: 11689928
references.citation: ACS Chem Biol. 2011 Nov 18;6(11):1223-31
references.pmid: 21936526
references.citation: Anal Chem. 2008 Jul 15;80(14):5550-5
references.pmid: 18543951
references.citation: Mol Syst Biol. 2009;5:313
references.pmid: 19888208
references.citation: Proc Natl Acad Sci U S A. 2000 May 23;97(11):5818-23
references.pmid: 10823939
references.citation: J Biol Chem. 1995 Apr 21;270(16):9043-51
references.pmid: 7721817
references.citation: J Med Res. 1905 Aug;13(5):431-59
references.pmid: 19971681
references.citation: Biochem J. 1978 Sep 1;173(3):869-75
references.pmid: 708377
references.citation: Neoplasia. 2009 Jun;11(6):509-17, 2 p following 517
references.pmid: 19484140
references.citation: Mol Cancer Ther. 2006 Dec;5(12):3122-9
references.pmid: 17172415