The Boyle-Conway model including the effect of an electrogenic pump for nonexcitable cells

A mathematical model which enables a quantitative interpretation of the results of electrophysiological, morphometric, and bioenergetic measurements within the framework of a homogeneous cell is proposed. Using the model one can calculate the membrane potential, ionic fluxes, intracellular ionic concentrations, cell volume, and the rate of ATP hydrolysis with an ionic pump. Comparison between model predictions and experimental results is carried out. It is shown that the model allows correlation of the results of numerous independent experiments.     

Simulation of developmental changes in action potentials with ventricular cell models

During cardiomyocyte development, early embryonic ventricular cells show spontaneous activity that disappears at a later stage. Dramatic changes in action potential are mediated by developmental changes in individual ionic currents. Hence, reconstruction of the individual ionic currents into an integrated mathematical model would lead to a better understanding of cardiomyocyte development. To simulate the action potential of the rodent ventricular cell at three representative developmental stages, quantitative changes in the ionic currents, pumps, exchangers, and sarcoplasmic reticulum (SR) Ca²⁺ kinetics were represented as relative activities, which were multiplied by conductance or conversion factors for individual ionic systems. The simulated action potential of the early embryonic ventricular cell model exhibited spontaneous activity, which ceased in the simulated action potential of the late embryonic and neonatal ventricular cell models. The simulations with our models were able to reproduce action potentials that were consistent with the reported characteristics of the cells in vitro. The action potential of rodent ventricular cells at different developmental stages can be reproduced with common sets of mathematical equations by multiplying conductance or conversion factors for ionic currents, pumps, exchangers, and SR Ca²⁺ kinetics by relative activities.     

Beating irregularity of single pacemaker cells isolated from the rabbit sinoatrial node.

Single pacemaker heart cells discharge irregularly. Data on fluctuations in interbeat interval of single pacemaker cells isolated from the rabbit sinoatrial node are presented. The coefficient of variation of the interbeat interval is quite small, approximately 2%, even though the coefficient of variation of diastolic depolarization rate is approximately 15%. It has been hypothesized that random fluctuations in interbeat interval arise from the stochastic behavior of the membrane ionic channels. To test this hypothesis, we constructed a single channel model of a single pacemaker cell isolated from the rabbit sinoatrial node, i.e., a model into which the stochastic open-close kinetics of the individual membrane ionic channels are incorporated. Single channel conductances as well as single channel open and closed lifetimes are based on experimental data from whole cell and single channel experiments that have been published in the past decade. Fluctuations in action potential parameters of the model cell are compared with those observed experimentally. It is concluded that fluctuations in interbeat interval of single sinoatrial node pacemaker cells indeed are due to the stochastic open-close kinetics of the membrane ionic channels.     

稳定表达hHCN2基因 HEK293细胞系的建立

目的：培育稳定表达hHCN2基因的细胞系,建立一种表达研究心肌离子通道的有效模型。方法：通过脂质体转染的方法,将重组pcDNA3-hHCN2真核表达载体导入人胚肾细胞（HEK293细胞）,以G418压力筛选转染细胞,并对其进行全细胞膜片钳记录。结果：经600μg／ml压力筛选后,获得抗性细胞克隆,并用全细胞膜片钳技术记录到克隆hHCN2通道编码电流。结论：本实验采用脂质体转染法成功地培育出G418抗性HEK293细胞。为进一步研究克隆离子通道结构和功能的关系奠定基础。     

Membrane potential and active transport--an information theory approach

A membrane potential stabilizing mechanism is proposed. Permeability is portrayed as controlled by a potential sensor. The active transport system is suggested to be a Maxwell demon able to recognize different ions, and modulate their passage into and out of the cell, without apparent reliance on energy. The idea that information is equivalent to entropy is used to resolve that paradox and construct a model of the active transport system. The non-steady ionic state of muscle cell is deduced; that ionic concentration may determine the condition of muscle is also suggested.     

A quantitative model of the cardiac ventricular cell incorporating the transverse-axial tubular system

The role of the transverse-axial tubular system (TATS) in electrical activity of cardiac cells has not been investigated quantitatively. In this study a mathematical model including the TATS and differential distribution of ionic transfer mechanisms in peripheral and tubular membranes was described. A model of ventricular cardiac cell described by Jafri et al. (1998) was adopted and slightly modified to describe ionic currents and Ca2+ handling. Changes of concentrations in the lumen of the TATS were computed from the total of transmembrane ionic fluxes and ionic exchanges with the pericellular medium. Long-term stability of the model was attained at rest and under regular stimulation. Depletion of Ca2+ by 12.8% and accumulation of K+ by 4.7% occurred in the TATS-lumen at physiological conditions and at a stimulation frequency of 1 Hz. The changes were transient and subsided on repolarization within 800 ms (Ca2+) and 300 ms (K+). Nevertheless, the course of action potentials remained virtually unaltered. Simulations of voltage clamp experiments demonstrated that variations in tubular ionic concentrations were detectable as modulation of the recorded membrane currents.     

A simulation study of the anomalous osmotic behavior of red cells

The factors responsible for movements of water across cell membranes were described mathematically and incorporated into a model which simulates water balance in the cell. Included in the model are a variable charge and osmotic coefficient of hemoglobin, a Na/K pump whose rate varies with ionic concentrations, and the standard electroneutrality and osmotic equilibrium assumptions. The model was used to investigate the phenomena whereby human red cells placed in media of varying tonicities exhibit steady state volume changes less than those predicted by van't Hoff's Law. The model results showed that this anomalous osmotic behavior was primarily due to changes in the osmotic coefficient of hemoglobin as its concentration in the cell varied. A second factor accounting for a part of this behavior was the alteration in the rate of the Na/K pump due to intracellular ionic concentration changes as cell volume varied. The effect of variable electrical charge on the hemoglobin molecule was found to be in the wrong direction to account for the observed osmotic behavior. Also, this effect was seen to produce relatively large changes in cell membrane potential, a result inconsistent with experimental data. It was concluded from the model results that the anomalous osmotic behavior of human red cells is primarily due to the variation in the osmotic coefficient of hemoglobin as the cell volume changes, and that the variable charge effect on the hemoglobin molecule, if it exists, does not play a role in this response.     

Ionic Partition between Surface and Bulk Water in a Silica Gel: A Biological Model

Distribution of the biologically important ions between two aqueous phases of different structure has been used as a model for ionic distribution in living tissue. When other sources of specificity had been eliminated or corrected for, surface-oriented water in a silica gel was found to have increased solvent power for water-structure-breaking ions and decreased solvent power for water-structure-making ions; and the relative solubility of an ion in the phase of enhanced structure increased regularly with the water-structure-breaking powers of the ion. The ionic selectivity was decreased in the presence of urea. The selectivity of the gel water for potassium relative to sodium increased to a maximum when the gel surface was partially ionized so that distribution of cations was not linked to distribution of anions, and then decreased as the surface changed from a hydrogen bonding to an ionic surface. It is pointed out that the distribution of ions across most living cell membranes is qualitatively the same as that found in this silica gel, and it is suggested that the membrane separates two aqueous phases of different structure, and that the enhanced structure of cell water contributes to the observed ionic distributions.     

Modeling electroporation in a single cell. II. Effects Of ionic concentrations.

This study expands a previously developed model of a single cell electroporated by an external electric field by explicitly accounting for the ionic composition of the electroporation current. The previous model with non-specific electroporation current predicts that both the transmembrane potential V(m) and the pore density N are symmetric about the equator, with the same values at either end of the cell. The new, ion-specific case predicts that V(m) is symmetric and almost identical to the profile from the non-specific case, but N has a profound asymmetry with the pore density at the hyperpolarized end of the cell twice the value at the depolarized end. These modeling results agree with the experimentally observed preferential uptake of marker molecules at the hyperpolarized end of the cell as reported in the literature. This study also investigates the changes in intracellular ionic concentrations induced around an electroporated single cell. For all ion species, the concentrations near the membrane vary significantly, which may explain the electrical disturbances observed experimentally after large electric shocks are delivered to excitable cells and tissues.     

Monolayer and interfacial permeation

Transport across physical-chemical interfaces is considered in connection with three particular problems of biological interfaces: the structure and properties of cell membranes, the properties of the lung surfactant, and the effects of ionic currents across excitable membranes. With regard to cell membranes, studies of monolayer permeation suggest that permselectivity on the basis of size is a property of bilayer structure and probably gives rise to the observed dependence of the permeability on partition coefficients. The permeabilities of lipid and protein monolayers are consistent with the bimolecular leaflet (BML) model of the membrane and not with mosaic models. Experiments with the lung surfactant indicate that, in addition to its surface tension-lowering properties, it is unusual in its ability to form a strong two-dimensional network, which probably contributes to alveolar stability. Finally, the results of studies of interfacial ionic transference suggest a new way of accounting for the ionic fluxes in excitable membranes during an action potential without assuming ion-selective pores or carriers. In the suggested mechanism, it is possible to account for the change in ionic selectivity and the proper phasing of the fluxes, as well as other aspects of excitation in natural membranes.     

Multiple-state model of ionic channel in reproducing the time course of electrophysiological events.

BACKGROUND: The predictions of the Hodgkin-Huxley model do not accurately fit all the measurements of voltage-clamp currents, gating charge and single-channel currents. There are many quantitative differences between the predicted and measured characteristics of the sodium and potassium channels. For example, the two-state gate model has exponential onset kinetics, whereas the sodium and potassium conductances show S-shaped activation and the sodium conductance shows an exponential inactivation. In this paper we shall examine a more general channel model that can more faithfully represent the measured properties of ionic channels in the membrane of the excitable cell. METHODS: The model is based on the generalisation of the notion of a channel with a discrete set of states. Each state has state attributes such as the state conductance, state ionic current and state gating charge. These variables can have quite different waveforms in time, in contrast with a two-state gate channel model, in which all have the same waveforms. RESULTS: The kinetics of all variables are equivalent: gating and ionic currents give equivalent information about channel kinetics; both the equilibrium values of the current and the time constants are functions of membrane potential. The results are in almost perfect concordance with the experimental data regarding the characteristics of nerve impulse. CONCLUSIONS: The expected values of the gating charge and the ionic conductance are weighted sums of the state occupancy probabilities, but the weights differ: for the expected value of the gating charge the weights are the state gating charges and for the expected value of the ionic conductance the weights are the state conductances. Since these weights are different, the expected values of the gating charge and the ionic conductance will differ.     

Membrane currents in the oocyte of the toad Bufo arenarum

The amphibian oocyte cell model is widely used for heterologous expression of ionic channels and receptors. Little is known, however, about the physiology of oocyte cell models other than Xenopus laevis. In this study, the two-electrode voltage clamp technique was used to assess the most common electrical patterns of oocytes of the South American toad Bufo arenarum. Basal membrane resistance, resting potential, and ionic currents were determined in this cell model. The oocyte transmembrane resistance was 0.35 M(Omega), and the resting potential in normal saline was about -33 mV with a range between -20 mV and -50 mV. This is, to our knowledge, the first attempt to begin an understanding of the ion transport mechanisms of Bufo arenarum oocytes. This cell model may provide a viable alternative to the expression of ion channels, in particular those endogenously observed in Xenopus laevis oocytes.     

Analysis of electrophoretic mobility data for human erythrocytes according to sublayer models

An attempt was made to analyze the electrophoretic mobility data of human erythrocytes in media of different pH values and ionic strengths through cell surface models in which the surface charge layer consists of several ion-penetrable sublayers with a uniform charge distribution in each sublayer. As a result, the three-sublayer model was found to explain the mobility data much better than the two-sublayer model in a wide range of ionic strength at all pH values studied.     

Reduction of a channel-based model for a stomatogastric ganglion LP neuron

Buchholtz et al. constructed a detailed conductance-based model of the LP cell of the stomatogastric ganglion of crustacea based upon the experimental work of Golowasch. Their model incorporated seven ionic currents and had 13 dynamical variables. We have produced a simplification of this model that has a seven-dimensional phase space by using the method of equivalent potentials, suggested by Abbott and Kepler, to combine several dynamical variables with similar time scales. Analysis of the dynamics of the reference and reduced model reveals similar bifurcation diagrams and similar dynamical behavior of the individual ionic currents.     

A simple theoretical model of steady-state electrogenic transfer of reactive species across membranes. The case of Chara corallina

Transfer across membranes is treated for simultaneous active pumping and passive flow of the main ionic constituents of plant cells. The chemical equilibrium conditions for H2CO3 and H2O dissociation prevailing in the external and internal solutions are taken into account. Our model assumes steady-state conditions, zero electrical current, electroneutrality inside the membrane and, in both solutions, finite space charge densities in two diffuse regions in contact with both sides of the membrane. A computer program has been developed for the integration of a set of flux equations. The results are displayed in terms of ionic flux parameters, each proportional to the ionic pump flow and to the reciprocal of the passive ionic mobility. The discussion emphasizes the role of anion inward pumping and of non-diffusible anions. The cationic pumps serve to establish different ionic balances in the cell. Transmembrane (bulk to bulk) proton pumping affects essentially the pH regulation in the cell.     

A theory for the membrane potential of living cells

We give an explicit formula for the membrane potential of cells in terms of the intracellular and extracellular ionic concentrations, and derive equations for the ionic currents that flow through channels, exchangers and electrogenic pumps. We demonstrate that the work done by the pumps equals the change in potential energy of the cell, plus the energy lost in downhill ionic fluxes through the channels and exchangers. The theory is illustrated in a simple model of spontaneously active cells in the cardiac pacemaker. The model predicts the experimentally observed intracellular ionic concentration of potassium, calcium and sodium. Likewise, the shapes of the simulated action potential and five membrane currents are in good agreement with experiment. We do not see any drift in the values of the concentrations in a long time simulation, and we obtain the same asymptotic values when starting from the full equilibrium situation with equal intracellular and extracellular ionic concentrations. Received: 9 December 1998 / Revised version: 30 August 1999 / Accepted: 15 October 1999     

Parameter estimation in cardiac ionic models

We examine the problem of parameter estimation in mathematical models of excitable cell cardiac electrical activity using the well-known Beeler–Reuter (1977) ionic equations for the ventricular action potential. The estimation problem can be regarded as equivalent to the accurate reconstruction of ionic current kinetics and amplitudes in an excitable cell model, given only action potential experimental data. We show that in the Beeler–Reuter case, all ionic currents may be reasonably reconstructed using an experimental design consisting of action potential recordings perturbed by pseudo-random injection currents.

The Beeler–Reuter model was parameterised into 63 parameters completely defining all membrane current amplitudes and kinetics. Total membrane current was fitted to model-generated experimental data using a ‘data-clamp’ protocol. The experimental data consisted of a default action-potential waveform and an optional series of perturbed waveforms generated by current injections. Local parameter identifiability was ascertained from the reciprocal condition value (1/λ) of the Hessian at the known solution. When fitting to a single action potential waveform, the model was found to be over-determined, having a 1/λ value of 3.6e−14. This value improved slightly to 1.4e−10 when an additional 2 perturbed waveforms were included in the fitting process, suggesting that the additional data did not overly improve the identifiability problem. The additional data, however, did allow the accurate reconstruction of all ionic currents. This indicates that by appropriate experimental design, it may be possible to infer the properties of underlying membrane currents from observation of transmembrane potential waveforms perturbed by pseudo-random currents.     

Cell growth: how to grow and where to grow

Root hairs provide a model system for studying tip growth in plants. The recent cloning of genes required for tip growth has shed new light on the link between ionic regulation, cell wall assembly and the cytoskeleton in cell growth.     

Boron adsorption by maize cell walls

Boron adsorption by cell walls isolated from corn (Zea mays) roots was investigated as a function of solution pH and ionic strength. Adsorption increased with increasing solution pH from pH 4.5 to 10, exhibited an adsorption maximum at pH 10–10.5, and decreased with increases in pH above 10.5. Boron adsorption increased with increasing solution ionic strength indicating the formation of strong inner-sphere surface complexes. A surface complexation model, the constant capacitance model was well able to describe the B adsorption data, optimizing two B surface complexes and the dissociation constant for the surface functional group, XOH. The large absolute value of the dissociation constant is consistent with phenolic functional groups.