{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T13:42:03Z","timestamp":1777902123707,"version":"3.51.4"},"reference-count":23,"publisher":"SAGE Publications","issue":"7","license":[{"start":{"date-parts":[[2007,7,1]],"date-time":"2007-07-01T00:00:00Z","timestamp":1183248000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIMULATION"],"published-print":{"date-parts":[[2007,7]]},"abstract":"<jats:p>The budding yeast cell cycle can be modeled by a set of ordinary differential equations with 143 rate constant parameters. The quality of the model (and an associated vector of parameter settings) is measured by comparing simulation results to the eXperimental data derived from observing the cell cycles of over 100 selected mutated forms. Unfortunately, determining whether the simulated phenotype matches eXperimental data is difficult since the eXperimental data tend to be qualitative in nature (i.e., whether the mutation is viable, or which development phase it died in). Because of this, previous methods for automatically comparing simulation results to eXperimental data used a discontinuous penalty function, which limits the range of techniques available for automated estimation of the differential equation parameters. This paper presents a system of smooth inequality constraints that will be satisfied if and only if the model matches the eXperimental data. Results are presented for evaluating the mutants with the two most frequent phenotypes. This nonlinear inequality formulation is the first step toward solving a large-scale feasibility problem to determine the ordinary differential equation model parameters.<\/jats:p>","DOI":"10.1177\/0037549707085075","type":"journal-article","created":{"date-parts":[[2007,11,9]],"date-time":"2007-11-09T03:27:51Z","timestamp":1194578871000},"page":"497-514","source":"Crossref","is-referenced-by-count":2,"title":["A Mathematical Programming Formulation for the Budding Yeast Cell Cycle"],"prefix":"10.1177","volume":"83","author":[{"given":"Thomas D.","family":"Panning","sequence":"first","affiliation":[{"name":"Department of Computer Science"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Layne T.","family":"Watson","sequence":"additional","affiliation":[{"name":"Departments of Computer Science and Mathematics"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Clifford A.","family":"Shaffer","sequence":"additional","affiliation":[{"name":"Department of Computer Science"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John J.","family":"Tyson","sequence":"additional","affiliation":[{"name":"Department of Biological Sciences Virginia Polytechnic Institute and State University Blacksburg, VA 24061"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2007,7,1]]},"reference":[{"key":"atypb1","volume-title":"Computational Software for Building Biochemical Reaction Network Models with Differential Equations.\u201d Ph.D. thesis","author":"Allen, N.A.","year":"2005"},{"key":"atypb2","volume-title":"Modeling regulatory networks at Virginia Tech.\u201d OMICS, Vol. 7, pp 285\u2014299","author":"Allen, N.A.","year":"2003"},{"key":"atypb3","first-page":"13","volume":"153","author":"Allen, N.A.","year":"2006","journal-title":"Biology"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1177\/0037549703040944"},{"key":"atypb5","volume-title":"Jr., J.E., \u201cMesh adaptive direct search algorithms for constrained optimization.\u201d SIAM J. 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