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10.1007/s11538-014-0040-x http://scihub22266oqcxt.onion/10.1007/s11538-014-0040-x C4258194!4258194!25412739     free     free     free Warning: file_get_contents(https://eutils.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&id=25412739&cmd=llinks): Failed to open stream: HTTP request failed! HTTP/1.1 500 Internal Server Error in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 215 Deprecated: Implicit conversion from float 213.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 213.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534       Bull+Math+Biol 2014 ; 76 (12): 2945-84 Nephropedia Template TP {{tp|p=25412739|t=2014. Piecewise linear and Boolean models of chemical reaction networks |pdf=|usr=}}{{25412739}} gab.com Text Piecewise linear and Boolean models of chemical reaction networks JO: Bull Math Biol http://www.kidney.de/pget.php?&tw=1&pmid=25412739 #FOAvip Models of biochemical networks are frequently complex and high-dimensional. Reduction methods that preserve important dynamical properties are therefore essential for their study. Interactions in biochemical networks are frequently modeled using Hill functions (xn/(Jn + xn)). Reduced ODEs and Boolean approximations of such model networks have been studied extensively when the exponent n is large. However, while the case of small constant J appears in practice, it is not well understood. We provide a mathematical analysis of this limit, and show that a reduction to a set of piecewise linear ODEs and Boolean networks can be mathematically justified. The piecewise linear systems have closed form solutions that closely track those of the fully nonlinear model. The simpler, Boolean network can be used to study the qualitative behavior of the original system. We justify the reduction using geometric singular perturbation theory and compact convergence, and illustrate the results in network models of a toggle switch and an oscillator. Twit Text FOAVip Piecewise linear and Boolean models of chemical reaction networks ????Bull Math Biol http://www.kidney.de/pget.php?&tw=1&pmid=25412739 #FOAvip Twit Text # Free Paper on # # # # # LINK http://www.kidney.de/pget.php?&tw=1&pmid=25412739 #FOAvip English Wikipedia <ref>{{Cite pmid|25412739}}</ref> Piecewise linear and Boolean models of chemical reaction networks #MMPMID25412739 Veliz-Cuba A; Kumar A; Josi? K Bull Math Biol 2014[Dec]; 76 (12): 2945-84 PMID25412739show ga Models of biochemical networks are frequently complex and high-dimensional. Reduction methods that preserve important dynamical properties are therefore essential for their study. Interactions in biochemical networks are frequently modeled using Hill functions (xn/(Jn + xn)). Reduced ODEs and Boolean approximations of such model networks have been studied extensively when the exponent n is large. However, while the case of small constant J appears in practice, it is not well understood. We provide a mathematical analysis of this limit, and show that a reduction to a set of piecewise linear ODEs and Boolean networks can be mathematically justified. The piecewise linear systems have closed form solutions that closely track those of the fully nonlinear model. The simpler, Boolean network can be used to study the qualitative behavior of the original system. We justify the reduction using geometric singular perturbation theory and compact convergence, and illustrate the results in network models of a toggle switch and an oscillator. äPiecewise linear and Boolean models of chemical reaction networks (epmc).pdf DeepDyve Pubget Overpricing