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dc.contributor.authorFan, G.
dc.contributor.authorCummins, Bree
dc.contributor.authorGedeon, Tomas
dc.date.accessioned2017-01-20T20:30:13Z
dc.date.available2017-01-20T20:30:13Z
dc.date.issued2016-06
dc.identifier.citationFan, G., B. Cummins, and T. Gedeon. "Convergence Properties of Posttranslationally Modified Protein-Protein Switching Networks with Fast Decay Rates." Bulletin of Mathematical Biology 78, no. 6 (June 2016): 1077-1120.en_US
dc.identifier.issn1522-9602
dc.identifier.urihttps://scholarworks.montana.edu/xmlui/handle/1/12422
dc.description.abstractA significant conceptual difficulty in the use of switching systems to model regulatory networks is the presence of so-called "black walls" co-dimension 1 regions of phase space with a vector field pointing inward on both sides of the hyperplane. Black walls result from the existence of direct negative self-regulation in the system. One biologically inspired way of removing black walls is the introduction of intermediate variables that mediate the negative self-regulation. In this paper, we study such a perturbation. We replace a switching system with a higher-dimensional switching system with rapidly decaying intermediate proteins, and compare the dynamics between the two systems. We find that the while the individual solutions of the original system can be approximated for a finite time by solutions of a sufficiently close perturbed system, there are always solutions that are not well approximated for any fixed perturbation. We also study a particular example, where global basins of attraction of the perturbed system have a strikingly different form than those of the original system. We perform this analysis using techniques that are adapted to dealing with non-smooth systems.en_US
dc.titleConvergence Properties of Posttranslationally Modified Protein-Protein Switching Networks with Fast Decay Ratesen_US
dc.typeArticleen_US
mus.citation.extentfirstpage1077en_US
mus.citation.extentlastpage1120en_US
mus.citation.issue6en_US
mus.citation.journaltitleBulletin of Mathematical Biologyen_US
mus.citation.volume78en_US
mus.identifier.categoryPhysics & Mathematicsen_US
mus.identifier.doi10.1007/s11538-016-0175-zen_US
mus.relation.collegeCollege of Letters & Scienceen_US
mus.relation.departmentMathematical Sciences.en_US
mus.relation.universityMontana State University - Bozemanen_US
mus.data.thumbpage6en_US
mus.contributor.orcidGedeon, Tomas|0000-0001-5555-6741en_US


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