scholarly journals Stochastic models and simulation of ion channel dynamics

2010 ◽  
Vol 1 (1) ◽  
pp. 1587-1596 ◽  
Author(s):  
C.E. Dangerfield ◽  
D. Kay ◽  
K. Burrage
Keyword(s):  
Ion Channel ◽  
Stochastic Models ◽  
Channel Dynamics

scholarly journals Computing Optimal Properties of Drugs Using Mathematical Models of Single Channel Dynamics

2018 ◽  
Vol 6 (1) ◽  
pp. 41-64 ◽  
Author(s):  
Aslak Tveito ◽  
Mary M. Maleckar ◽  
Glenn T. Lines
Keyword(s):  
Differential Equations ◽  
Markov Model ◽  
Stochastic Models ◽  
Markov Models ◽  
Single Channel ◽  
Probability Density Functions ◽  
Density Functions ◽  
Mathematical Framework ◽  
Wild Type ◽  
Channel Dynamics

AbstractSingle channel dynamics can be modeled using stochastic differential equations, and the dynamics of the state of the channel (e.g. open, closed, inactivated) can be represented using Markov models. Such models can also be used to represent the effect of mutations as well as the effect of drugs used to alleviate deleterious effects of mutations. Based on the Markov model and the stochastic models of the single channel, it is possible to derive deterministic partial differential equations (PDEs) giving the probability density functions (PDFs) of the states of the Markov model. In this study, we have analyzed PDEs modeling wild type (WT) channels, mutant channels (MT) and mutant channels for which a drug has been applied (MTD). Our aim is to show that it is possible to optimize the parameters of a given drug such that the solution of theMTD model is very close to that of the WT: the mutation’s effect is, theoretically, reduced significantly.We will present the mathematical framework underpinning this methodology and apply it to several examples. In particular, we will show that it is possible to use the method to, theoretically, improve the properties of some well-known existing drugs.

scholarly journals Critical behavior in the artificial axon

2021 ◽  
Author(s):  
Ziqi Pi ◽  
Giovanni Zocchi
Keyword(s):  
Ion Channel ◽  
Critical Behavior ◽  
Delay Time ◽  
Action Potentials ◽  
Scaling Exponent ◽  
Saddle Node Bifurcation ◽  
Channel Dynamics ◽  
A Cell ◽  
Universal Properties ◽  
Fast Ion

Abstract The Artificial Axon is a unique synthetic system, based on biomolecular components, which supports action potentials. Here we examine, experimentally and theoretically, the properties of the threshold for firing in this system. As in real neurons, this threshold corresponds to the critical point of a saddle-node bifurcation. We measure the delay time for firing as a function of the distance to threshold, recovering the expected scaling exponent of −1/2. We introduce a minimal model of the Morris-Lecar type, validate it on the experiments, and use it to extend analytical results obtained in the limit of ”fast” ion channel dynamics. In particular, we discuss the dependence of the firing threshold on the number of channels. The Artificial Axon is a simplified system, an Ur-neuron, relying on only one ion channel species for functioning. Nonetheless, universal properties such as the action potential behavior near threshold are the same as in real neurons. Thus we may think of the Artificial Axon as a cell-free breadboard for electrophysiology research.

scholarly journals Model-order reduction of ion channel dynamics using approximate bisimulation

2015 ◽  
Vol 599 ◽  
pp. 34-46 ◽  
Author(s):  
Md. Ariful Islam ◽  
Abhishek Murthy ◽  
Ezio Bartocci ◽  
Elizabeth M. Cherry ◽  
Flavio H. Fenton ◽  
...  
Keyword(s):  
Ion Channel ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Model Order ◽  
Channel Dynamics

scholarly journals Dynamical model of neuronal activity and ion channel dynamics over the aortic wall

2020 ◽  
Author(s):  
Erhui Wang ◽  
Liancun Zheng ◽  
Xuelan Zhang ◽  
Kheder Suleiman ◽  
Chang Shu
Keyword(s):  
Ion Channel ◽  
Neuronal Activity ◽  
Aortic Wall ◽  
Dynamical Model ◽  
Channel Dynamics
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