{"corpus_id":82515951,"paper_sha":"efc822383886d5004f472777fa55b890e5af41c8","doi":"10.1016/s0021-9258(18)97473-9","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":141700673,"dblp_id":null,"acl_id":null,"title":"A Procedure for the Analysis of Countercurrent Distribution Data I. CURVE FITTING, PARAMETER ESTIMATES, AND ERROR ANALYSIS","year":1960,"publication_date":"1960-11-01","venue":"","journal":{"name":"Journal of Biological Chemistry","pages":"3033-3041","volume":"235"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics","Chemistry"],"reference_count":5,"citation_count":11,"influential_citation_count":0,"is_open_access":false,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"The need for a comprehensive analysis of data obtained from countercurrent distribution studies has led to the adoption of the procedure of fitting these data to polynomial curves. Although mathematical models of the countercurrent process are available for the fundamental operation and for single and double withdrawal operations (l-3), our experience with highly purified steroids distributed in the basic operation, including recycling, has often shown appreciable deviations from the expected normal or binomial curves. It is emphasized that operational deviations from the ideal model, rather than detectable heterogeneity, resulted in distributions which were skewed or more broadened or peaked than expected. These deviations, anticipated and discussed in detail by Craig et al. (4-6), may be due to situations where: (a) volume irregularities occur in the transfer process; (b) actual equilibrium conditions are not realized at each transfer; (c) the partition coefficient is a function of concentration; (d) the partition coefficient is not independent of transfer number due to changes in phase composition and temperature; and (e) design problems occur such as that introduced by the extra half tube for transfer of the upper layer only in the recycle operation. Because an error at a particular transfer stage affects all subsequent stages, the occurrence of any of the above irregularities during the countercurrent process may produce a final distribution that is not adequately represented by the binomial distribution. In addition, the usual representation of countercurrent distribution data by a binomial curve (or normal curve where a large number of transfers has been completed) requires selection of the peak tube number by inspection, or more elaborately by successive approximations. For comparison of analyses of distribu-","claims":[{"public_id":"cl_67517724bac233940a8f571adc8f2043","status":"active","text":"A binomial or normal-curve representation of countercurrent distribution data requires choosing the peak tube number by inspection or by successive approximations.","confidence":0.9,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_67517724bac233940a8f571adc8f2043"},{"public_id":"cl_8bd856dcc6d96c6732171ffc5db5e0ae","status":"active","text":"Irregularities such as volume transfer errors, failure to reach equilibrium at each transfer, concentration-dependent partition coefficients, transfer-number-dependent partition coefficients, and recycle-design problems can prevent the final distribution from being adequately represented by a binomial distribution.","confidence":0.92,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_8bd856dcc6d96c6732171ffc5db5e0ae"},{"public_id":"cl_1906ff6f51d0ab2fa67e7be566582fb3","status":"active","text":"Operational deviations from the ideal countercurrent distribution model, rather than detectable heterogeneity, can produce skewed, broadened, or peaked distributions in highly purified steroids.","confidence":0.95,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_1906ff6f51d0ab2fa67e7be566582fb3"},{"public_id":"cl_d338f18f241eab393cb09ceba4c08195","status":"active","text":"Polynomial-curve fitting is adopted as a comprehensive procedure for analyzing countercurrent distribution 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