This work presents a model for the simulation of plasmatic transmembrane ionic transport that may be exposed to a static gradient magnetic field. The simulation was carried out using the Monte Carlo method to simulate the transmembrane cell transport of five types of ions and obtain observables such as membrane potential, ionic current, and osmotic pressure. To implement the Monte Carlo method, a Hamiltonian was used that includes the contributions of the energy due to the cellular electric field, the electrostatic interaction between the ions, the friction force generated by moving the ion in the center and the contribution given by subduing a cell to a magnetic field gradient. The input parameters to carry out a simulation are the intra and extracellular concentrations of each ionic species, the length of the extracellular medium, the number of Monte Carlo steps (MCS) and the value of the magnetic gradient. The model was validated contrasting it with Gillespie’s algorithm to obtain variations less than 3 % in terms of membrane potential. The Monte Carlo Method combined with the Metropolis algorithm were considered for recreating the stochastic behavior of ion movement.
FertigD.MádaiE.ValiskóM. and BodaD., Simulating ion transport with the NP LEMC Method. applications to ion channels and nanopores, Hungarian Journal of Industry and Chemistry45 (2017), 73–84.
2.
GallandP. and PazurA., Magnetoreception in plants, Journal of Plant Research118 (2005), 371–389.
3.
QuinckeG., Ueber periodische Ausbreitung an Flüssigkeitsoberflächen und dadurch hervorgerufene Bewegungserscheinungen, Annalen Der Physik Und Chemie271 (1888), 580–642.
4.
DavenportC.B., The Cell Outlines of general anatomy and physiology, Science5 (1897), 111–113.
5.
GorterE. and GrendelF., On bimolecular layers of lipoids on the chromocytes of the blood, J Exp Med41 (1925), 439–443.
6.
BrooksS.C., The permeability of living cells, Science100 (1944), 30–31.
7.
GeislerM.WangB. and ZhuJ., Auxin transport during root gravitropism: transporters and techniques, Plant Biol16(Suppl 1) (2014), 50–57.
8.
McCormickD.A., Membrane potential and action potential, Fundamental Neuroscience (2013), 93–116. doi: 101016.
9.
KlepeisJ.L.Lindorff-LarsenK.DrorR.O. and ShawD.E., Long-timescale molecular dynamics simulations of protein structure and function, Current Opinion in Structural Biology, 19 (2009), 120–127.
10.
ImW. and RouxB., Brownian dynamics simulations of ions channels: A general treatment of electrostatic reaction fields for molecular pores of arbitrary geometry, The Journal of Chemical Physics115 (2001), 4850–4861.
11.
ImW.SeefeldS. and RouxB., A grand canonical monte carlo-brownian dynamics algorithm for simulating ion channels, Biophysical Journal79 (2000), 788–801.
12.
BoW.GuoL.YangY.MaJ.WangK.TangJ.WuZ.ZengB. and GongY., Numerical study of voltage-gated ca2 transport irradiated by terahertz electromagnetic wave, IEEE Access8 (2020), 10305–10315.
13.
ZhaoX.XiaC.Van DoorsselaereT.KeppensR. and GanW., Forward Modeling of SDO/AIA and X-Ray Emission from a Simulated Flux Rope Ejection, The Astrophysical Journal872 (2019), 190.
14.
BodaD.BusathD.D.EisenbergB.HendersonD. and NonnerW., Monte Carlo simulations of ion selectivity in a biological Na channel: Charge-space competition, Phys Chem Chem Phys4 (2002), 5154–5160.
15.
Monte-Carlo Simulation of the Ionic Transport of Electrolyte Solutions at High Concentrations Based on the Pseudo-Lattice Model, ECS Meeting Abstracts, (2016).
16.
MorganB.J., Lattice-geometry effects in garnet solid electrolytes: A lattice-gas Monte Carlo simulation study, R Soc Open Sci4 (2017), 170824.
17.
ReinaF.G.PascualL.A. and FundoraI.A., Influence of a stationary magnetic field on water relations in lettuce seeds. Part II: Experimental results, Bioelectromagnetics22 (2001), 596–602.
18.
SocorroA. and GarcíaF., Simulation of magnetic field effect on a seed embryo cell, International Agrophysics26 (2012), 167–173.
19.
RodiP.M.CabezaM.S. and GennaroA.M., Detergent solubilization of bovine erythrocytes. Comparison between the insoluble material and the intact membrane, Biophys Chem122 (2006), 114–122.
20.
AzanzaM.J.BlottB.H.del MoralA. and PegM.T., Measurement of the red blood cell membrane magnetic susceptibility, Bioelectrochemistry and Bioenergetics30 (1993), 43–53.
21.
FengZ.-G., A correlation of the drag force coefficient on a sphere with interface slip at low and intermediate reynolds numbers, Journal of Dispersion Science and Technology31 (2010), 968–974.
22.
RodiP.M.TruccoV.M. and GennaroA.M., Factors determining detergent resistance of erythrocyte membranes, Biophys Chem135 (2008), 14–18.
23.
MaffeoC.BhattacharyaS.YooJ.WellsD. and AksimentievA., Modeling and simulation of ion channels, Chem Rev112 (2012), 6250–6284.
24.
CorralJ.M.F.y. de Loma-OsorioJ.M.F.RodríguezJ.S. and VivesA.A., BIOELECTRÓNICA. SEÑALES BIOELÉCTRICAS, Ed. Univ. Politéc. Valencia, 1994.
25.
AponteC.A.MunozJ.D. and FayadR., Simulación por dinámica browniana del transporte ionico a través del canal gramicidina a, Revista Colombiana de Física, 38 (2006).
26.
MujumdarM.P., Monte Carlo simulations of ionic channel selectivity, Comput Appl Biosci7 (1991), 359–364.
27.
PangT.D., The Metropolis algorithm, An Introduction to Quantum Monte Carlo Methods, (2016).
28.
YatesC.A. and KlingbeilG., Recycling random numbers in the stochastic simulation algorithm, The Journal of Chemical Physics138 (2013), 094103, doi: 10.1063/1.4792207.
29.
General Biophysics, (1983).
30.
ZablotskiiV.PolyakovaT.LunovO. and DejnekaA., How a high-gradient magnetic field could affect cell life, Sci Rep6 (2016), 37407.
31.
TorresJ.HincapieE. and GilartF., Characterization of magnetic flux density in passive sources used in magnetic stimulation, J Magn Magn Mater449 (2018), 366–371.
32.
RamirezP.GomezV.AliM.EnsingerW. and MafeS., Net currents obtained from zero-average potentials in single amphoteric nanopores, Electrochem Commun31 (2013), 137–140.
