Numerical Solution of the Coupled Nernst-Planck and Poisson Equations for Ion-Selective Membrane Potentials

2002 ◽  
Vol 752 ◽  
Author(s):  
Peter Lingenfelter ◽  
Tomasz Sokalski ◽  
Andrzej Lewenstam
Keyword(s):  
Electrical Potential ◽  
Membrane System ◽  
Contact Boundary ◽  
Poisson Equations ◽  
Space And Time ◽  
Boundary Potential ◽  
Time Domains ◽  
Selective Membrane ◽  
Linear Differential ◽  
And Migration

ABSTRACTA numerical model is presented for analyzing the propagation of ionic concentrations and electrical potential in space and time in the solution ion-exchanging membrane system. Diffusion and migration according to the Nernst-Planck (NP) flux equation govern the transport of ions, and the electrical interaction of the species is described by the Poisson (P) equation. These two equations and the continuity equation form a system of partial non-linear differential equations that is solved numerically. As a result of the physicochemical properties of the system, both the contact/boundary potential and the diffusion potential contribute to the overall membrane potential. It is shown that interpreting the electrical potential of ion-exchanging membranes exclusively in terms of boundary potential at steady-state is incorrect. The Nernst-Planck-Poisson (NPP) model is general and applies to ions of any charge in space and time domains.

scholarly journals Spatial and space-time correlations in systems of subpopulations with genetic drift and migration.

Genetics ◽  
1993 ◽  
Vol 133 (3) ◽  
pp. 711-727
Author(s):  
B K Epperson
Keyword(s):  
Population Genetics ◽  
Time Correlation ◽  
Space Time ◽  
Spatial Correlations ◽  
Gene Frequencies ◽  
Migration Patterns ◽  
Migration Rates ◽  
Space And Time ◽  
Time Correlations ◽  
And Migration

Abstract The geographic distribution of genetic variation is an important theoretical and experimental component of population genetics. Previous characterizations of genetic structure of populations have used measures of spatial variance and spatial correlations. Yet a full understanding of the causes and consequences of spatial structure requires complete characterization of the underlying space-time system. This paper examines important interactions between processes and spatial structure in systems of subpopulations with migration and drift, by analyzing correlations of gene frequencies over space and time. We develop methods for studying important features of the complete set of space-time correlations of gene frequencies for the first time in population genetics. These methods also provide a new alternative for studying the purely spatial correlations and the variance, for models with general spatial dimensionalities and migration patterns. These results are obtained by employing theorems, previously unused in population genetics, for space-time autoregressive (STAR) stochastic spatial time series. We include results on systems with subpopulation interactions that have time delay lags (temporal orders) greater than one. We use the space-time correlation structure to develop novel estimators for migration rates that are based on space-time data (samples collected over space and time) rather than on purely spatial data, for real systems. We examine the space-time and spatial correlations for some specific stepping stone migration models. One focus is on the effects of anisotropic migration rates. Partial space-time correlation coefficients can be used for identifying migration patterns. Using STAR models, the spatial, space-time, and partial space-time correlations together provide a framework with an unprecedented level of detail for characterizing, predicting and contrasting space-time theoretical distributions of gene frequencies, and for identifying features such as the pattern of migration and estimating migration rates in experimental studies of genetic variation over space and time.

scholarly journals Electrodiffusion Phenomena in Neuroscience and the Nernst–Planck–Poisson Equations

Electrochem ◽  
2021 ◽  
Vol 2 (2) ◽  
pp. 197-215
Author(s):  
Jerzy J. Jasielec
Keyword(s):  
Electrical Potential ◽  
Signal Propagation ◽  
Liquid Junction Potential ◽  
Liquid Junction ◽  
Patch Clamp Technique ◽  
Poisson Equations ◽  
Cellular Environment ◽  
Electrochemical Transport ◽  
Insight Into ◽  
Junction Potential

This work is aimed to give an electrochemical insight into the ionic transport phenomena in the cellular environment of organized brain tissue. The Nernst–Planck–Poisson (NPP) model is presented, and its applications in the description of electrodiffusion phenomena relevant in nanoscale neurophysiology are reviewed. These phenomena include: the signal propagation in neurons, the liquid junction potential in extracellular space, electrochemical transport in ion channels, the electrical potential distortions invisible to patch-clamp technique, and calcium transport through mitochondrial membrane. The limitations, as well as the extensions of the NPP model that allow us to overcome these limitations, are also discussed.

Estimating Effective Population Size and Migration Rates From Genetic Samples Over Space and Time

Genetics ◽  
2003 ◽  
Vol 163 (1) ◽  
pp. 429-446 ◽  
Author(s):  
Jinliang Wang ◽  
Michael C Whitlock
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Joint Estimation ◽  
Large Sample Size ◽  
Effective Population ◽  
Likelihood Methods ◽  
Marker Allele ◽  
Migration Rates ◽  
Space And Time ◽  
And Migration

Abstract In the past, moment and likelihood methods have been developed to estimate the effective population size (Ne) on the basis of the observed changes of marker allele frequencies over time, and these have been applied to a large variety of species and populations. Such methods invariably make the critical assumption of a single isolated population receiving no immigrants over the study interval. For most populations in the real world, however, migration is not negligible and can substantially bias estimates of Ne if it is not accounted for. Here we extend previous moment and maximum-likelihood methods to allow the joint estimation of Ne and migration rate (m) using genetic samples over space and time. It is shown that, compared to genetic drift acting alone, migration results in changes in allele frequency that are greater in the short term and smaller in the long term, leading to under- and overestimation of Ne, respectively, if it is ignored. Extensive simulations are run to evaluate the newly developed moment and likelihood methods, which yield generally satisfactory estimates of both Ne and m for populations with widely different effective sizes and migration rates and patterns, given a reasonably large sample size and number of markers.

scholarly journals Crossing the digital divide: an interoperable solution for sharing time series and coverages in Earth sciences

2012 ◽  
Vol 12 (10) ◽  
pp. 3013-3029 ◽  
Author(s):  
F. R. Salas ◽  
E. Boldrini ◽  
D. R. Maidment ◽  
S. Nativi ◽  
B. Domenico
Keyword(s):  
Time Series ◽  
Information Science ◽  
Atmospheric Science ◽  
Data Types ◽  
Continuous Space ◽  
Space And Time ◽  
Accessible Information ◽  
Time Space ◽  
Time Domains ◽  
The Web

Abstract. In a world driven by the Internet and the readily accessible information it provides, there exists a high demand to easily discover and collect vast amounts of data available over several scientific domains and numerous data types. To add to the complexity, data is not only available through a plethora of data sources within disparate systems but also represents differing scales of space and time. One clear divide that exists in the world of information science and technology is the disjoint relationship between hydrologic and atmospheric science information. These worlds have long been split between observed time series at discrete geographical features in hydrologic science and modeled or remotely sensed coverages or grids over continuous space and time domains in atmospheric science. As more information becomes widely available through the Web, data are being served and published as Web services using standardized implementations and encodings. This paper illustrates a framework that utilizes Sensor Observation Services, Web Feature Services, Web Coverage Services, Catalog Services for the Web and GI-cat Services to index and discover data offered through different classes of information. This services infrastructure supports multiple servers of time series and gridded information, which can be searched through multiple portals, using a common set of time, space and concept query filters.

Sign in / Sign up

Export Citation Format

Share Document