scholarly journals Computational Study on Hysteresis of Ion Channels: Multiple Solutions to Steady-State Poisson-Nernst-Planck Equations

Author(s):  
Jie Ding ◽  
Hui Sun ◽  
Zhongming Wang ◽  
Shenggao Zhou
2012 ◽  
Vol 8 (4) ◽  
pp. 417-423
Author(s):  
Przemysław Korohoda ◽  
Przemysław Sypka ◽  
Jacek A. Pietrzyk

ABSTRACT The paper presents an application of the Lopot-plot, which compares the timeaveraged concentration (TAC) and the time-averaged deviation (TAD) of the weekly dialysis cycle, to comprise the results of intensive computational study. The presented case is based on 420 one-week-cycle simulations to verify the consequences implied by the change of the treatments schedule from nonuniformly to uniformly distributed over the week. The concept of steady state is explained and utilized to obtain periodical runs of the urea concentration. The presented graphs encouragingly indicate the potential of such plots in presenting results of multivariable intensive computations that should be advisably performed during the planning process of hemodialysis treatment.


2022 ◽  
Vol 9 (1) ◽  
pp. 28
Author(s):  
Henry Sutanto

The excitation, contraction, and relaxation of an atrial cardiomyocyte are maintained by the activation and inactivation of numerous cardiac ion channels. Their collaborative efforts cause time-dependent changes of membrane potential, generating an action potential (AP), which is a surrogate marker of atrial arrhythmias. Recently, computational models of atrial electrophysiology emerged as a modality to investigate arrhythmia mechanisms and to predict the outcome of antiarrhythmic therapies. However, the individual contribution of atrial ion channels on atrial action potential and reentrant arrhythmia is not yet fully understood. Thus, in this multiscale in-silico study, perturbations of individual atrial ionic currents (INa, Ito, ICaL, IKur, IKr, IKs, IK1, INCX and INaK) in two in-silico models of human atrial cardiomyocyte (i.e., Courtemanche-1998 and Grandi-2011) were performed at both cellular and tissue levels. The results show that the inhibition of ICaL and INCX resulted in AP shortening, while the inhibition of IKur, IKr, IKs, IK1 and INaK prolonged AP duration (APD). Particularly, in-silico perturbations (inhibition and upregulation) of IKr and IKs only minorly affected atrial repolarization in the Grandi model. In contrast, in the Courtemanche model, the inhibition of IKr and IKs significantly prolonged APD and vice versa. Additionally, a 50% reduction of Ito density abbreviated APD in the Courtemanche model, while the same perturbation prolonged APD in the Grandi model. Similarly, a strong model dependence was also observed at tissue scale, with an observable IK1-mediated reentry stabilizing effect in the Courtemanche model but not in the Grandi atrial model. Moreover, the Grandi model was highly sensitive to a change on intracellular Ca2+ concentration, promoting a repolarization failure in ICaL upregulation above 150% and facilitating reentrant spiral waves stabilization by ICaL inhibition. Finally, by incorporating the previously published atrial fibrillation (AF)-associated ionic remodeling in the Courtemanche atrial model, in-silico modeling revealed the antiarrhythmic effect of IKr inhibition in both acute and chronic settings. Overall, our multiscale computational study highlights the strong model-dependent effects of ionic perturbations which could affect the model’s accuracy, interpretability, and prediction. This observation also suggests the need for a careful selection of in-silico models of atrial electrophysiology to achieve specific research aims.


2014 ◽  
Vol 763 ◽  
pp. 1-23 ◽  
Author(s):  
Z. Liu ◽  
D. L. Xu ◽  
J. Li ◽  
T. Peng ◽  
A. Alsaedi ◽  
...  

AbstractThis paper describes an experimental investigation of steady-state resonant waves. Several co-propagating short-crested wave trains are generated in a basin at the State Key Laboratory of Ocean Engineering (SKLOE) in Shanghai, and the wavefields are measured and analysed both along and normal to the direction of propagation. These steady-state resonant waves are first calculated theoretically under the exact resonance criterion with sufficiently high nonlinearity, and then are generated in the basin by means of the main wave components that contain at least 95 % of the wave energy. The steady-state wave spectra are quantitatively observed within the inherent system error of the basin and identified by means of a contrasting experiment. Both symmetrical and anti-symmetrical steady-state resonant waves are observed and the experimental and theoretical results show excellent agreement. These results offer the first experimental evidence of the existence of steady-state resonant waves with multiple solutions.


EP Europace ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 1594-1602
Author(s):  
Massimiliano Zaniboni ◽  
Francesca Cacciani

Abstract Aims This computational study refines our recently published pacing protocol to measure short-term memory (STM) of cardiac action potential (AP), and apply it to five numerical models of human ventricular AP. Methods and results Several formulations of electrical restitution (ER) have been provided over the years, including standard, beat-to-beat, dynamic, steady-state, which make it difficult to compare results from different studies. We discuss here the notion of dynamic ER (dER) by relating it to its steady-state counterpart, and propose a pacing protocol based on dER to measure STM under periodically varying pacing cycle length (CL). Under high and highly variable-pacing rate, all models develop STM, which can be measured over the entire sequence by means of dER. Short-term memory can also be measured on a beat-to-beat basis by estimating action potential duration (APD) adaptation after clamping CL constant. We visualize STM as a phase shift between action potential (AP) parameters over consecutive cycles of CL oscillations, and show that delay between CL and APD oscillation is nearly constant (around 92 ms) in the five models, despite variability in their intrinsic AP properties. Conclusion dER, as we define it and together with other approaches described in the study, provides an univocal way to measure STM under extreme cardiac pacing conditions. Given the relevance of AP memory for repolarization dynamics and stability, STM should be considered, among other usual biomarkers, to validate and tune cardiac AP models. The possibility of extending the method to in vivo cellular and whole organ models can also be profitably explored.


Characteristics of observed bursts of single channel openings were derived recently for two particular ion channel mechanisms. In this paper these methods are generalized so that the observable characteristics of bursts can be calculated directly for any mechanism that has transition probabilities that are independent of time as long as the process is at equilibrium or is maintained in a steady state by an energy supply. General expressions are given for the distributions of the open time, the number of openings per burst, the total open time per burst, the gaps within and between bursts, and so on. With the aid of these general results a single computer program can be written that will provide numerical values for such distributions for postulated mechanism, given only the transition rates between the various states. The results are illustrated by a numerical example of a mechanism in which two agonist molecules can bind sequentially, and either singly or doubly occupied receptor ion channels may open. The analogous theory is also given for the case where bursts of channel openings are grouped into clusters; many of the results bear a close analogy with those found for simple bursts.


2012 ◽  
Vol 32 (8) ◽  
pp. 1472-1483 ◽  
Author(s):  
Daniela Calvetti ◽  
Erkki Somersalo

This work is a computational study based on a new detailed metabolic network model comprising well-mixed compartments representing separate cytosol and mitochondria of astrocytes, glutamatergic and gamma aminobutyric acid (GABA)ergic neurons, communicating through an extracellular space compartment and fed by arterial blood flow. Our steady-state analysis assumes statistical mass balance of both carbons and amino groups. The study is based on Bayesian flux balance analysis, which uses Markov chain Monte Carlo sampling techniques and provides a quantitative description of steady states when the two exchangers aspartate-glutamate carrier (AGC1) and oxoglutarate carrier (OGC) in the malate-aspartate shuttle in astrocyte are not in equilibrium, as recent studies suggest. It also highlights the importance of anaplerotic reactions, pyruvate carboxylase in astrocyte and malic enzyme in neurons, for neurotransmitter synthesis and recycling. The model is unbiased with respect to the glucose partitioning between cell types, and shows that determining the partitioning cannot be done by stoichiometric constraints alone. Furthermore, the intercellular lactate trafficking is found to depend directly on glucose partitioning, suggesting that a steady state may support different scenarios. At inhibitory steady state, characterized by high rate of GABA release, there is elevated oxidative activity in astrocyte, not in response to specific energetic needs.


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