Solution of non-linear Poisson-Boltzmann equation for erythrocyte membrane

Cruz, Frederico Alan de Oliveira; Vilhena, Fernando S. D. S.; Cortez, Célia Martins

doi:10.1590/s0103-97332000000200023

Cited by 9 publications

(6 citation statements)

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“…Our results illustrate that the drop of the potential across the glycocalyx for the neuroblastoma cell is much smaller than for the spinal ganglion neuron, during both resting and AP states. This corroborates previous studies which show a smaller decay of the potential for the erythrocyte in the glycocalyx than for the neuron [2] , [4] , [5] . The different behavior of the potential across the glycocalyx, for the neuroblastoma and the spinal ganglion neuron, should indicate important differences among these cells, of the properties that enable the transmission of electric signals through the membrane.…”

Section: Discussionsupporting

confidence: 93%

“…In this work, we study the influence of surface electric charges on the stability of the cell membrane in the condition of equilibrium, by modeling the electric potential profile. The profile describes the behavior of the potential along the axis perpendicular to the cell membrane, from the outer bulk region to the inner cytoplasmic region [2] – [5] . We do not consider here dynamical phenomena in the structure of the membrane, and treat only the electrostatic situation, which occurs once the system has reached equilibrium.…”

Section: Introductionmentioning

confidence: 99%

“…We show a detailed and revised description of the model more briefly presented by Cortez and collaborators in [3] – [5] , which was originally used to simulate the squid giant axon. This model is based on the statistical mechanical theory of electrolyte solutions and electric double layers [12] – [15] .…”

Section: Introductionmentioning

confidence: 99%

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Modeling the Electric Potential across Neuronal Membranes: The Effect of Fixed Charges on Spinal Ganglion Neurons and Neuroblastoma Cells

2014

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We present a model for the electric potential profile across the membranes of neuronal cells. We considered the resting and action potential states, and analyzed the influence of fixed charges of the membrane on its electric potential, based on experimental values of membrane properties of the spinal ganglion neuron and the neuroblastoma cell. The spinal ganglion neuron represents a healthy neuron, and the neuroblastoma cell, which is tumorous, represents a pathological neuron. We numerically solved the non-linear Poisson-Boltzmann equation for the regions of the membrane model we have adopted, by considering the densities of charges dissolved in an electrolytic solution and fixed on both glycocalyx and cytoplasmic proteins. Our model predicts that there is a difference in the behavior of the electric potential profiles of the two types of cells, in response to changes in charge concentrations in the membrane. Our results also describe an insensitivity of the neuroblastoma cell membrane, as observed in some biological experiments. This electrical property may be responsible for the low pharmacological response of the neuroblastoma to certain chemotherapeutic treatments.

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Section: Discussionsupporting

confidence: 93%

Section: Introductionmentioning

confidence: 99%

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Modeling the Electric Potential across Neuronal Membranes: The Effect of Fixed Charges on Spinal Ganglion Neurons and Neuroblastoma Cells

2014

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“…Therefore, works of computer simulation are often based on subjective data from the literature [9]. In fact, more precise values of some characteristic parameters of biomembranes and neuronal interactions are not easily available in the literature [10], and we may be forced to use theoretical model estimates for these values [11,12,13]. In spite of the problems related to data defi ciency, system engineering has contributed to establishing theoretical models and to applying functional concepts of the nervous system at several levels of physiologic complexity [13,14].…”

Section: Introductionmentioning

confidence: 99%

Computer modeling of a spinal reflex circuit

Dalcin

Cruz²,

Cortez³

et al. 2005

Braz. J. Phys.

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We used a set of properties of the interactions among the spinal neurons in order to develop a computer model for a spinal reflex circuit. The model equations take into account the synaptic characteristics of the somatodendritic membrane of neurons in a morphofunctional unity of the spinal reflex activity. This model is based on the idea that the responses of spinal alpha-motoneurons to a sensorial stimulation can be modulated by the serial activation of a motor command chain. We developed a Fortran program for simulating a physiological situation. The results are discussed in terms of available experimental data for the motoneuron fi ring rate.

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“…Data obtained from experimental results [ 1 , 2 ] have been used to solve the first order ordinary differential Poisson-Boltzmann equations [ 3 , 4 ], which have been obtained for the regions of the membrane model we have adopted. Therefore, we have examined the influence of the electric parameters during resting and AP states, analyzing the differences between the healthy ganglion neuron and a neuroblastoma cell.…”

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confidence: 99%