Use of the harmonic mean to the determination of dissociation constants of stereoisomeric mixtures of biologically active compounds
Abstract Herein we introduce the derivation of a mathematical expression to evaluate the dissociation constant of a mixture of stereoisomers in equal amounts (KdMIX), when the corresponding dissociation constants (Kd) or medium response (MR50) of the pure stereoisomers are known; the final equation...
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| Veröffentlicht in: | Journal of enzyme inhibition and medicinal chemistry 2014-12, Vol.29 (6), p.884-894 |
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| creator | Guevara-Salazar, J. Alberto Quintana-Zavala, Delia Jiménez-Vázquez, Hugo A. Trujillo-Ferrara, José |
| description | Abstract
Herein we introduce the derivation of a mathematical expression to evaluate the dissociation constant of a mixture of stereoisomers in equal amounts (KdMIX), when the corresponding dissociation constants (Kd) or medium response (MR50) of the pure stereoisomers are known; the final equation takes the form of the harmonic mean. In order to validate the equation, we carried out a bibliographic search of experimental data of enantiomeric molecules with biological activity, considering the Kd's or MR50's of the isolated enantiomers as well as that of the racemate. The comparisons between the experimental dissociation constants of the mixtures (KdEXP or MR50EXP) and the calculated values (KdMIX or MR50MIX) were consistent; the similarity between these values is supported through statistical analyses of group comparison and simple linear correlation. The equation we obtained, which corresponds to the harmonic mean, was used to predict the values of KdMIX (or MR50MIX) or Kd (or MR50) in systems when only two of the experimental values are known: either the dissociation constants of both enantiomers or the Kd (or MR50) of one of the enantiomers and dissociation constant of the racemate. |
| doi_str_mv | 10.3109/14756366.2013.866656 |
| format | Article |
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Herein we introduce the derivation of a mathematical expression to evaluate the dissociation constant of a mixture of stereoisomers in equal amounts (KdMIX), when the corresponding dissociation constants (Kd) or medium response (MR50) of the pure stereoisomers are known; the final equation takes the form of the harmonic mean. In order to validate the equation, we carried out a bibliographic search of experimental data of enantiomeric molecules with biological activity, considering the Kd's or MR50's of the isolated enantiomers as well as that of the racemate. The comparisons between the experimental dissociation constants of the mixtures (KdEXP or MR50EXP) and the calculated values (KdMIX or MR50MIX) were consistent; the similarity between these values is supported through statistical analyses of group comparison and simple linear correlation. The equation we obtained, which corresponds to the harmonic mean, was used to predict the values of KdMIX (or MR50MIX) or Kd (or MR50) in systems when only two of the experimental values are known: either the dissociation constants of both enantiomers or the Kd (or MR50) of one of the enantiomers and dissociation constant of the racemate.</description><identifier>ISSN: 1475-6366</identifier><identifier>EISSN: 1475-6374</identifier><identifier>DOI: 10.3109/14756366.2013.866656</identifier><identifier>PMID: 24517366</identifier><language>eng</language><publisher>England: Informa UK Ltd</publisher><subject>Animals ; Biological Products - chemistry ; Biological Products - pharmacology ; Dissociation constants ; enantiomers ; Eukaryotic Cells - drug effects ; Eukaryotic Cells - metabolism ; harmonic mean ; Humans ; Inhibitory Concentration 50 ; Kinetics ; medium ; Models, Statistical ; racemate ; Receptors, Cell Surface - agonists ; Receptors, Cell Surface - antagonists & inhibitors ; Receptors, Cell Surface - metabolism ; response ; Stereoisomerism</subject><ispartof>Journal of enzyme inhibition and medicinal chemistry, 2014-12, Vol.29 (6), p.884-894</ispartof><rights>2014 Informa UK Ltd. All rights reserved: reproduction in whole or part not permitted 2014</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c490t-ac460963126b1ba19f4d20e2d72e4fb2c798c6fc9b1420a4c122ea371b5a0da13</citedby><cites>FETCH-LOGICAL-c490t-ac460963126b1ba19f4d20e2d72e4fb2c798c6fc9b1420a4c122ea371b5a0da13</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/24517366$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Guevara-Salazar, J. Alberto</creatorcontrib><creatorcontrib>Quintana-Zavala, Delia</creatorcontrib><creatorcontrib>Jiménez-Vázquez, Hugo A.</creatorcontrib><creatorcontrib>Trujillo-Ferrara, José</creatorcontrib><title>Use of the harmonic mean to the determination of dissociation constants of stereoisomeric mixtures of biologically active compounds</title><title>Journal of enzyme inhibition and medicinal chemistry</title><addtitle>J Enzyme Inhib Med Chem</addtitle><description>Abstract
Herein we introduce the derivation of a mathematical expression to evaluate the dissociation constant of a mixture of stereoisomers in equal amounts (KdMIX), when the corresponding dissociation constants (Kd) or medium response (MR50) of the pure stereoisomers are known; the final equation takes the form of the harmonic mean. In order to validate the equation, we carried out a bibliographic search of experimental data of enantiomeric molecules with biological activity, considering the Kd's or MR50's of the isolated enantiomers as well as that of the racemate. The comparisons between the experimental dissociation constants of the mixtures (KdEXP or MR50EXP) and the calculated values (KdMIX or MR50MIX) were consistent; the similarity between these values is supported through statistical analyses of group comparison and simple linear correlation. The equation we obtained, which corresponds to the harmonic mean, was used to predict the values of KdMIX (or MR50MIX) or Kd (or MR50) in systems when only two of the experimental values are known: either the dissociation constants of both enantiomers or the Kd (or MR50) of one of the enantiomers and dissociation constant of the racemate.</description><subject>Animals</subject><subject>Biological Products - chemistry</subject><subject>Biological Products - pharmacology</subject><subject>Dissociation constants</subject><subject>enantiomers</subject><subject>Eukaryotic Cells - drug effects</subject><subject>Eukaryotic Cells - metabolism</subject><subject>harmonic mean</subject><subject>Humans</subject><subject>Inhibitory Concentration 50</subject><subject>Kinetics</subject><subject>medium</subject><subject>Models, Statistical</subject><subject>racemate</subject><subject>Receptors, Cell Surface - agonists</subject><subject>Receptors, Cell Surface - antagonists & inhibitors</subject><subject>Receptors, Cell Surface - metabolism</subject><subject>response</subject><subject>Stereoisomerism</subject><issn>1475-6366</issn><issn>1475-6374</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNp9kE9v1DAQxSMEon-_AUI5ctnFdhwnuYBQBQWpUi_0bE2cCevK9iy2Q9kzX5ykaSv10pPtN--9sX5F8Y6zbcVZ95HLplaVUlvBeLVtlVK1elUcL_JGVY18_XRX6qg4SemWMcEFl2-LIyFr3sz6cfHvJmFJY5l3WO4gegrWlB4hlJnuxQEzRm8DZEthcQ42JTJ2fRsKKUPIaZmk2YlkE3mMS4v9m6eI96PekqNf1oBzhxJMtn9wzvo9TWFIZ8WbEVzC84fztLj59vXnxffN1fXlj4svVxsjO5Y3YKRinaq4UD3vgXejHARDMTQC5dgL03StUaPpei4FA2m4EAhVw_sa2AC8Oi0-rL37SL8nTFl7mww6BwFpSpor0daibflilavVREop4qj30XqIB82ZXvDrR_x6wa9X_HPs_cOGqfc4PIUeec-Gz6vBhpGihzuKbtAZDo7iGCEYm5b6F1d8etawQ3B5ZyCivqUphhngy3_8D259qtg</recordid><startdate>20141201</startdate><enddate>20141201</enddate><creator>Guevara-Salazar, J. Alberto</creator><creator>Quintana-Zavala, Delia</creator><creator>Jiménez-Vázquez, Hugo A.</creator><creator>Trujillo-Ferrara, José</creator><general>Informa UK Ltd</general><general>Taylor & Francis</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope></search><sort><creationdate>20141201</creationdate><title>Use of the harmonic mean to the determination of dissociation constants of stereoisomeric mixtures of biologically active compounds</title><author>Guevara-Salazar, J. Alberto ; Quintana-Zavala, Delia ; Jiménez-Vázquez, Hugo A. ; Trujillo-Ferrara, José</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c490t-ac460963126b1ba19f4d20e2d72e4fb2c798c6fc9b1420a4c122ea371b5a0da13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Animals</topic><topic>Biological Products - chemistry</topic><topic>Biological Products - pharmacology</topic><topic>Dissociation constants</topic><topic>enantiomers</topic><topic>Eukaryotic Cells - drug effects</topic><topic>Eukaryotic Cells - metabolism</topic><topic>harmonic mean</topic><topic>Humans</topic><topic>Inhibitory Concentration 50</topic><topic>Kinetics</topic><topic>medium</topic><topic>Models, Statistical</topic><topic>racemate</topic><topic>Receptors, Cell Surface - agonists</topic><topic>Receptors, Cell Surface - antagonists & inhibitors</topic><topic>Receptors, Cell Surface - metabolism</topic><topic>response</topic><topic>Stereoisomerism</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Guevara-Salazar, J. Alberto</creatorcontrib><creatorcontrib>Quintana-Zavala, Delia</creatorcontrib><creatorcontrib>Jiménez-Vázquez, Hugo A.</creatorcontrib><creatorcontrib>Trujillo-Ferrara, José</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><jtitle>Journal of enzyme inhibition and medicinal chemistry</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Guevara-Salazar, J. Alberto</au><au>Quintana-Zavala, Delia</au><au>Jiménez-Vázquez, Hugo A.</au><au>Trujillo-Ferrara, José</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Use of the harmonic mean to the determination of dissociation constants of stereoisomeric mixtures of biologically active compounds</atitle><jtitle>Journal of enzyme inhibition and medicinal chemistry</jtitle><addtitle>J Enzyme Inhib Med Chem</addtitle><date>2014-12-01</date><risdate>2014</risdate><volume>29</volume><issue>6</issue><spage>884</spage><epage>894</epage><pages>884-894</pages><issn>1475-6366</issn><eissn>1475-6374</eissn><abstract>Abstract
Herein we introduce the derivation of a mathematical expression to evaluate the dissociation constant of a mixture of stereoisomers in equal amounts (KdMIX), when the corresponding dissociation constants (Kd) or medium response (MR50) of the pure stereoisomers are known; the final equation takes the form of the harmonic mean. In order to validate the equation, we carried out a bibliographic search of experimental data of enantiomeric molecules with biological activity, considering the Kd's or MR50's of the isolated enantiomers as well as that of the racemate. The comparisons between the experimental dissociation constants of the mixtures (KdEXP or MR50EXP) and the calculated values (KdMIX or MR50MIX) were consistent; the similarity between these values is supported through statistical analyses of group comparison and simple linear correlation. The equation we obtained, which corresponds to the harmonic mean, was used to predict the values of KdMIX (or MR50MIX) or Kd (or MR50) in systems when only two of the experimental values are known: either the dissociation constants of both enantiomers or the Kd (or MR50) of one of the enantiomers and dissociation constant of the racemate.</abstract><cop>England</cop><pub>Informa UK Ltd</pub><pmid>24517366</pmid><doi>10.3109/14756366.2013.866656</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
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| source | MEDLINE; EZB-FREE-00999 freely available EZB journals |
| subjects | Animals Biological Products - chemistry Biological Products - pharmacology Dissociation constants enantiomers Eukaryotic Cells - drug effects Eukaryotic Cells - metabolism harmonic mean Humans Inhibitory Concentration 50 Kinetics medium Models, Statistical racemate Receptors, Cell Surface - agonists Receptors, Cell Surface - antagonists & inhibitors Receptors, Cell Surface - metabolism response Stereoisomerism |
| title | Use of the harmonic mean to the determination of dissociation constants of stereoisomeric mixtures of biologically active compounds |
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