Mathematical contributions to dynamics and optimization of gene-environment networks

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dc.contributor.authorWeber, Gerhard-Wilhelm
dc.contributor.authorTezel, Aysun
dc.contributor.authorTaylan, Pakize
dc.contributor.authorSoyler, Alper
dc.contributor.authorCetin, Mehmet
dc.date.accessioned2024-04-24T16:24:31Z
dc.date.available2024-04-24T16:24:31Z
dc.date.issued2008
dc.departmentDicle Üniversitesien_US
dc.description.abstractThis article contributes to a further introduction of continuous optimization in the field of computational biology which is one of the most challenging and emerging areas of science, in addition to foundations presented and the state-of-the-art displayed in [C.A. Floudas and P.M. Pardalos, eds., Optimization in Computational Chemistry and Molecular Biology: Local and Global Approaches, Kluwer Academic Publishers, Boston, 2000]. Based on a summary of earlier works by the coauthors and their colleagues, it refines the model on gene-environment patterns by a problem from generalized semi-infinite programming (GSIP), and characterizes the condition of its structural stability. Furthermore, our paper tries to detect and understand structural frontiers of our methods applied to the recently introduced gene-environment networks and tries to overcome them. Computational biology is interdisciplinary, but it also looks for its mathematical foundations. From data got by DNA microarray experiments, non-linear ordinary differential equations are extracted by the optimization of least-squares errors; then we derive corresponding time-discretized dynamical systems. Using a combinatorial algorithm with polyhedra sequences we can detect the regions of parametric stability, contributing to a testing the goodness of data fitting of the model. To represent and interpret the dynamics, certain matrices, genetic networks and, more generally, gene-environment networks serve. Here, we consider n genes in possible dependence with m special environmental factors and a cumulative one. These networks are subject of discrete mathematical questions, but very large structures, such that we need to simplify them. This is undertaken in a careful optimization with constraints, aiming at a balanced connectedness, incorporates any type of a priori knowledge or request and should be done carefully enough to be robust against disturbation by the environment. In this way, we take into account attacks on the network, knockout phenomena and catastrophies, but also changes in lifestyle and effects of education as far as they can approximately be quantified. We characterize the structural stability of the GSIP problem against perturbations like changes between data series or due to outliers. We give explanations on the numerics and the use of splines. This study is an attempt to demonstrate some beauty and applicabilty of continuous optimization which might together one day give a support in health care, food engineering, biomedicine and -technology, including elements of bioenergy and biomaterials.en_US
dc.identifier.doi10.1080/02331930701780037
dc.identifier.endpage377en_US
dc.identifier.issn0233-1934
dc.identifier.issn1029-4945
dc.identifier.issue2en_US
dc.identifier.scopus2-s2.0-40549112675en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage353en_US
dc.identifier.urihttps://doi.org/10.1080/02331930701780037
dc.identifier.urihttps://hdl.handle.net/11468/16753
dc.identifier.volume57en_US
dc.identifier.wosWOS:000253762200012en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoenen_US
dc.publisherTaylor & Francis Ltden_US
dc.relation.ispartofOptimizationen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectComputational Biologyen_US
dc.subjectGeneralized Semi-Infinite Programmingen_US
dc.subjectMathematical Modelingen_US
dc.subjectDynamical Systemsen_US
dc.subjectGene-Expression Dataen_US
dc.subjectEnvironmenten_US
dc.subjectStabilityen_US
dc.subjectStructural Stabilityen_US
dc.subjectStructural Frontiersen_US
dc.subjectContinuousen_US
dc.subjectDiscreteen_US
dc.subjectHybriden_US
dc.subjectSplineen_US
dc.subjectInverse Problemen_US
dc.titleMathematical contributions to dynamics and optimization of gene-environment networksen_US
dc.typeArticleen_US

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