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Mathematical Models for Sensing Devices Constructed out of Artificial Cell Membranes

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Hoiles W., Krishnamurthy V., Cornell B.
Nanoscale Systems: Mathematical Modeling, Theory and Applications
|
2012
|
tom 1
143-171
EN
This paper presents a review of ion channel based biosensors with a focus on the mathematical modeling of the stateof- the-art ion channel switch (ICS) biosensor and the novel cation specific (CS) sensor. The characteristics of the analyte present in the electrolyte, the ionic transport of chemical species, and the bioelectronic interface present in the ICS biosensor and CS sensor are modeled using ordinary and partial differential equations. The methodologies presented are important for modeling similar bioelectronic devices. Biosensors have applications in the fields of medicine, engineering, and biology. The recent emergence of biomimetically engineered nanomachine devices capable of measuring femto-molar concentrations of chemical species and the detection of channelopathies (ion channel disorders) makes them an attractive tool due to their high sensitivity and rapid detection rates. Beyond the continuum models used for the ICS and CS sensors, we present methods by which firstprinciple approaches such as molecular dynamics combined with stochastic methodologies can be used to obtain macrolevel parameters such as conductance and chemical reaction rates.
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Some global results for nonlinear fourth order eigenvalue problems

100%
Aliyev Z.
Open Mathematics
|
2014
|
tom 12
|
nr 12
1811-1828
EN
In this paper, we consider the nonlinear fourth order eigenvalue problem. We show the existence of family of unbounded continua of nontrivial solutions bifurcating from the line of trivial solutions. These global continua have properties similar to those found in Rabinowitz and Berestycki well-known global bifurcation theorems.
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