Continuous Modeling of Calcium Transport Through Biological Membranes

Abstract

In this work an approach to the modeling of the biological membranes where a membrane is treated as a continuous medium is presented. The Nernst-Planck-Poisson model including Poisson equation for electric potential is used to describe transport of ions in the mitochondrial membrane-the interface which joins mitochondrial matrix with cellular cytosis. The transport of calcium ions is considered. Concentration of calcium inside the mitochondrion is not known accurately because different analytical methods give dramatically different results. We explain mathematically these differences assuming the complexing reaction inside mitochondrion and the existence of the calcium set-point (concentration of calcium in cytosis below which calcium stops entering the mitochondrion).

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

“…The NPP model has been used to simulate the electrodiffusion of calcium ions through the mitochondrial membrane [143]. In this approach, the mitochondrial mem- Presented NPP results show the dependence of the potential profile on the concentration of the negative charges (anionic sites) inside the lipid bilayer.…”

“…The NPP model has been used to simulate the electrodiffusion of calcium ions through the mitochondrial membrane [143]. In this approach, the mitochondrial membrane is represented by a one-dimensional continuous element where only the maximum inward/outward flux of ions is limited by the channel density.…”

“…The inclusion of the reaction, occurring inside the mitochondrial matrix in the transport model, allows us to explain the difference between the total matrix concentration of calcium (established to be in the range of 0.5 M to 0.8 M [144][145][146][147][148]) and the free calcium concentration (in the range of 0.17 to 5 µM [149][150][151][152][153][154][155][156]), reported by numerous studies using fluorescent Ca 2+ indicators. The presented model [143] can be used as an efficient alternative for single-channel modeling. Despite its simplicity, the model has successfully described the existence of calcium set-point, i.e., the concentration of calcium in cytosis below which calcium stops entering the mitochondrion.…”

Description of ionophore-doped membranes with a blocked interface

“…The model is implemented in MATLAB using the numerical method of lines (MOL) based on published work [18,19,24]. The discretisation scheme and algorithm used is identical to the MATLAB implementation by Grysakowski et al in [18], but additionally incorporates information on ionionophore complexation following the work of Jasielec et al [22,27]. The model utilises MATLAB's inbuilt stiff integrator, ode15s, for solving the resulting system of spatially discretised ODEs in time.…”

Modeling of Electrodiffusion Processes from Nano to Macro Scale

“…22. Each layer has its own thickness d, is flat and isotropic, so it can be assumed as a continuous environment, inside which the change of the components concentration in space and time takes place.…”