Periodic oscillations of a model for membrane permeability with fluctuating environmental conditions

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• 作者：Pedro J. Torres
• 关键词：Cell volume ; Membrane transport ; Periodic oscillation ; Stability ; Brouwer degree ; 34C25 ; 92C37 ; 92B25
• 刊名：Journal of Mathematical Biology
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：71
• 期：1
• 页码：57-68
• 全文大小：419 KB
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• 作者单位：Pedro J. Torres (1)
  
  1. Departamento de Matem谩tica Aplicada, Universidad de Granada, 18071聽, Granada, Spain
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Biology
  Applications of Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1416

文摘

We perform an analytical study of the dynamics of a multi-solute model for water transport across a cell membrane under periodic fluctuations of the extracellular solute molalities. Under the presence of non-permeating intracellular solute, water volume experiences periodic oscillations if and only if the extracellular non-permeating solute molality is positive in the average. On the other hand, in the absence of non-permeating intracellular solute, a sufficient condition for the existence of an infinite number of periodic solutions of the model is provided. Such sufficient condition holds automatically in the case of only one permeating solute. The proofs are based on classical tools from the qualitative theory of differential equations, namely Brouwer degree, upper and lower solutions and comparison arguments.