Requirements on Models and Models of Active Transport of Ions in Biomembranes

Requirements on models of the active transport of ions in biomembranes have been formulated. The basic requirements include an explicit dependence of the resting potential and intracellular concentrations of ions on the difference of ATP-ADP chemical potentials, a consideration of the reversibility of the ionic pump operation, a correlation between theoretical and experimental data on the resting potential and intracellular concentrations of ions for different types of cells, the pump efficiency approaching 100%, and a tendency of the resting potential to the Donnan potential if the active transport is blocked. A model satisfying the aforementioned requirements has been proposed by the authors as an example.     

Model of Active Transport of Ions in Archaea Cells

A mathematical model of the active transport of main ions in cells of archaebacteria has been constructed. A set of equations has been developed and solved for ion fluxes through the bacterium membrane. The model is based on the principle “one ion—one transport system.” Considering experimental data, the major transport mechanism was determined for each ion and the balance equation was written on the basis of this mechanism in the stationary state. This allowed calculating values of the membrane potential and intracellular concentrations of the ions independently. The calculated values of the intracellular concentrations and resting potential are in qualitative agreement with the corresponding experimental values for cells of extremely halophilic archaea.     

Model of active transport of ions in biomembranes based on ATP-dependent change of height of diffusion barriers to ions

A closed model of the active transport was constructed taking into account ATP-dependent opening and closing of barriers to ions and the relationship between the membrane potential and the work of ionic pumps under the condition of electroneutrality inside the cell. The internal consistency of the model was verified by the fulfillment of Onsager's reciprocity relation. It was demonstrated that at the limit of large energy barriers the operation of the system of the active transport is equivalent to the "turning segment" model, which was proposed by the authors earlier. Values of the resting potential and the intracellular concentration of ions were obtained for different types of cells. These results were in qualitative agreement with relevant experimental data.     

On the mechanism of generation of electrical potential differences in cell biomembranes]

A statistical model of active ion transport in biomembranes was developed. The model makes it possible to calculate both the value of membrane potential phi zero and the rate of ion concentrations inside and outside the cell. These values depend on the difference of chemical potentials of the ATP-ADP system and the permeability of the biomembrane for ions being transported. The calculated phi zero value approximately 200-250 mV is consistent with the data on proton pumps.     

A model of active transport of ions in hepatocytes

A mathematical model of the transport of basic ions (K⁺, Na⁺, Cl⁻) across the hepatocyte membrane has been created using the previously constructed models of active ion transport in biomembranes. The dependence of the resting potential on extracellular ion concentration has been established. Using the model, it is possible to independently calculate the resting potential at the biomembrane and the concentrations of sodium, potassium, and chlorine ions in the cell. The calculated internal concentrations of the ions are in good agreement with the corresponding experimental values.     

Nonequilibrium Statistical Model of Active Transport of Ions and ATP Production in Mitochondria

A model of the active transport of ions through internal membranes of mitochondria is proposed. If concentrations of ions in a cell are known, this model allows calculating concentrations of all main ions (H⁺, Ca⁺², K⁺, Mg²⁺, Na⁺, Cl⁻) in the mitochondrion matrix and the resting potential across the membrane. The theoretical values satisfactorily agree with available experimental data on the concentrations and the potentials, including different operating regimes of the adenosine triphosphate (ATP) synthetase (the main regime, short circuiting or ATP synthetase blocking). The active transport of Mg²⁺ ions in exchange for protons was assumed. In accordance with the model, the ATP synthetase operation is possible only if the stoichiometric coefficient of protons is 3.     

Model of active transport of ions in cardiac cell

A model of the active transport of ions in a cardiac muscle cell, which takes into account the active transport of Na⁺, K⁺, Ca²⁺, Mg²⁺, HCO₃⁻ and Cl⁻ ions, has been constructed. The model allows independent calculations of the resting potential at the biomembrane and concentrations of basic ions (sodium, potassium, chlorine, magnesium and calcium) in a cell. For the analysis of transport processes in cardiac cell hierarchical algorithm “one ion-one transport system” was offered. The dependence of the resting potential on concentrations of the ions outside a cell has been established. It was shown, that ions of calcium and magnesium, despite their rather small concentration, play an essential role in maintenance of resting potential in cardiac cell. The calculated internal concentrations of ions are in good agreement with the corresponding experimental values.     

Model for the cell biomembrane electric potential during active transport of various ions

A model of a stationary electrical potential on biomembrane was created. This model takes into account conformational changes in transport ATPase. N positive ions are transported simultaneously by the system of active transport. The model allows one to determine independently ion concentrations inside the cell and membrane electrical potential. It is shown that, to obtain the electrical potential, it is necessary to take into account organic negative intracellular ions. The effect of positive ions that are not transported by active transport systems on the potential value is discussed. The results obtained are in a good agreement with experimental data for various cells.     

Models of active transport of neurotransmitters in synaptic vesicles

Models of the active transport of neurotransmitters in synaptic vesicles were constructed. The models were used to determine the resting potential at membranes of synaptic vesicles: 40mV (monoamines and acetylcholine) and -40mV (glutamate). The potential at the membrane of a synaptic vesicle was almost absent for the transport of GABA and glycine. The neurotransmitter concentration of a cell was 0.1-18mM at the concentration of neurotransmitters in a vesicle equal to 0.5M. This result is in qualitative agreement with the relevant experimental data.     

Effects of sodium ions on the electrical and pH gradients across the membrane of streptococcus lactis cells

Energized cells of Streptococcus lactis conserve and transduce energy at the plasma membrane in the form of an electrochemical gradient of hydrogen ions (Δp). An increase in energy-consuming processes, such as cation transport, would be expected to result in a change in the steady state Δp. We determined the electrical gradient (ΔΨ) from the fluorescence of a membrane potential-sensitive cyanine dye, and the chemical H⁺ gradient (ΔpH) from the distribution of a weak acid. In glycolyzing cells incubated at pH 5 the addition of NaCl to 200 mM partially dissipated the Δp by decreasing ΔΨ, while the ΔpH was constant. The Δp was also determined independently from the accumulation levels of thiomethyl-β-galactoside. The Δp values decreased in cell fermenting glucose at pH 5 or pH 7 when NaCl was added, while the ΔpH values were unaffected; cells fermenting arginine at pH 7 showed similar effects. Thus, these nongrowing cells cannot fully compensate for the energy demand of cation transport.     

A metabolic osmotic model of human erythrocytes

A metabolic osmotic model of red blood cells is presented which takes into account the main reaction steps of glycolysis and the passive and active fluxes of ions across the cell membrane. Cellular energy metabolism and osmotic behaviour are linked by the ATP consumption for the active transport of cations as well as by the osmotic action of the glycolytic intermediate 2,3-diphosphoglycerate (2,3-DPG). The model is based on a system of differential equations describing the metabolic reactions and transport processes. Further, two algebraic conditions for the osmotic equilibrium and the electroneutrality of the cell are considered. Using realistic system parameters the model allows the calculation of a great number of dependent variables, among them the cell volume, the concentrations of metabolites and ions and the transmembrane potential. Only stationary states are considered.The parameter dependence of important model variables is characterized by control coefficients. The main results are: (a) The volume of erythrocytes is mainly determined by the permeabilities of the leak fluxes of cations, the content of hemoglobin and the activity of the hexokinase-phosphofructokinase system of glycolysis; (b) Changes of volume affect the glycolytic rate mainly by changing the concentration of ATP which is a regulator of glycolysis; (c) A change in the membrane area may affect the other cell properties only if it is connected with variations of the number of active and leak sites of the membrane.     

Model of Active Transport of Ions Through Diatom Cell Biomembrane

A model of the active transport of ions in the Cascinodiscus wailesii diatom cell is constructed taking into account the transport of H⁺, Na⁺, K⁺, Ca⁺², NO₃^-\mathrm{NO}_{3}^{-}, Cl⁻, and NH₄⁺\mathrm{NH}_{4}^{+} ions. This model allows calculating intracellular concentrations of basic ions and the biomembrane resting potential. A hierarchical algorithm “one ion—one transport system” is used in the model. The dependence of the resting potential on the extracellular concentration of potassium is plotted in terms of the model. The calculated values are in good agreement with the corresponding experimental data.     

Studies of energy transport in heart cells. The functional coupling between mitochondrial creatine phosphokinase and ATP ADP translocase: kinetic evidence.

The dependence of the rate of creatine phosphate synthesis in the mitochondrial creatine phosphokinase reaction upon the rate of oxidative phosphorylation and ATP translocation from the matrix to outside of the mitochondria has been studied. It has been experimentally shown that mitochondrial creatine phosphokinase reacts slowly with ATP in the medium but is very active in utilization of ATP synthesized by the oxidative phosphorylation process. From these data, it is postulated, therefore, that the ATP-ADP translocase transports ATP molecules directly to the active site of creatine phosphokinase localized on the outer site of the inner membrane. This results in an increase in the effective concentration of ATP in the vinicity of the active sites of creatine kinase and in acceleration of the forward reaction (creatine phosphate synthesis). The kinetic theory based on this assumption allows a quantitative explanation of the observed dependences. These data indicate the tight functional coupling between ATP-ADP translocase and creatine phosphokinase in heart mitochondria. It is concluded that in heart cells energy can be transported by creatine phosphate molecules only.     

Transport and accumulation of nickel ions in the cyanobacterium Anabaena cylindrica

The uptake of nickel ions by the cyanobacterium Anabaena cylindrica was studied. Nickel transport was dependent on the membrane potential of the cells and the rate of uptake was decreased in the dark or by the addition of inhibitors, including uncouplers and electron transport inhibitors, which decreased or abolished the membrane potential of cells. The transport process obeyed hyperbolic kinetics, with a high affinity (apparent Km = 17 +/- 11 (SEM) nM) and low turnover number (maximum velocity = 22.3 +/- 5.4 (SEM) pmol h-1 mg dry wt-1 of cells or flux rate of 3.1 nmol h-1 m-2 of plasma membrane surface area). The process was also apparently specific for Ni2+, the rate being unaffected by the presence of a range of other metal ions in large excess. Equilibrium experiments showed that, over a range of nickel ion concentrations, the cells concentrated Ni2+ by a factor of 2700 +/- 240 (SEM)-fold, corresponding to a chemical diffusion potential for Ni2+ of 101 mV. It was concluded that the cells transport nickel ions by a carrier-facilitated transport process with the concentration factor for the ions being determined by the cell membrane potential according to the Nernst equation.     

Inhibitors of the Na+ K+-atpase

1. The major ionmotive ATPase, in animal cells, is the Na⁺, K⁺-ATPase or sodium pump.2. This membrane bound enzyme is responsible for the translocation of Na⁺ ions and K⁺ ions across the plasma membrane, an active transport mechanism that requires the expenditure of the metabolic energy stored within the ATP molecule.3. This ubiquitous enzyme controls directly or indirectly many essential cellular functions, such as, cell volume, free calcium concentration and membrane potential.4. It is, therefore, apparent that alterations in its regulation may play key roles in pathological processes.     

Analytical model of ion transport and conversion of light energy in chloroplasts

An analytical model, which describes the stationary transformation of light energy to the energy of pigment electronic excitation, has been constructed. A proton pump of the thylakoid membrane has been considered as a two-level conformon. The difference between the energies of the excited and ground states of both the pigment and the protein complex is assumed to be the energy of an absorbed photon. It has been found how the concentration of ions in a lumen and the potential across the thylakoid membrane depend on the concentration of ions in the stroma and the brightness temperature of absorbed radiation. Conditions for the maximum efficiency of the photosynthesis process have been analyzed. This model has been used to determine the electric potential (φ≈6.7 mV) at the chloroplast thylakoid membrane. The calculated value of the electric potential is in good agreement with the experimental data. A limitation on the stoichiometric coefficient of the proton transport through ATP-synthase, m>3, has been found theoretically.     

Mechanisms of ammonia and ammonium ion toxicity in animal cells: Transport across cell membranes

A model for transport of ammonia and ammonium ions across cell membranes is presented. The model suggests that ammonium ions compete with potassium ions for inward transport, over the cytoplasmic membrane, via potassium transport proteins like the Na⁺/K⁺-ATPase and the Na⁺K⁺2Cl⁻-cotransporter. It also explains the difference between the ammonia/ammonium that is added to the cells and which is formed by the cells during metabolism of amino acids, especially glutamine and glutamate. The ammonium transport and subsequent events lead to predictable intracellular and extracellular pH (pH_e) changes. Experiments which verified the model and the predicted consequences were performed by measurements of the pH_e in concentrated cell suspensions. Addition of ammonium ions caused a time-dependent pH_e increase which was inhibited by potassium ions. The test system is not per se specific for transport measurements but the effect of potassium ions on the pH_e strongly favors our suggested model. Simple diffusion of ammonium ions would not be counteracted by potassium ions. The results show that ammonium ion transport in the murine myeloma cell line (Sp2/0-Ag14) used is inhibited by an excess of potassium ions. Results from experiments with specific inhibitors of suggested transport proteins were not conclusive. It is postulated that one important toxic effect of ammonia/ammonium is an increased demand for maintenance energy, caused by the need to maintain ion gradients over the cytoplasmic membrane. The results also suggest that potassium ions can be used to detoxify ammonia/ammonium in animal cell cultivations.     

A network model for biofilm development in Escherichia coli K-12

Proteins in any solution with a pH value that differs from their isoelectric point exert both an electric Donnan effect (DE) and colloid osmotic pressure. While the former alters the distribution of ions, the latter forces water diffusion. In cells with highly Cl^--permeable membranes, the resting potential is more dependent on the cytoplasmic pH value, which alters the Donnan effect of cell proteins, than on the current action of Na/K pumps. Any weak (positive or negative) electric disturbances of their resting potential are quickly corrected by chloride shifts. In many excitable cells, the spreading of action potentials is mediated through fast, voltage-gated sodium channels. Tissue cells share similar concentrations of cytoplasmic proteins and almost the same exposure to the interstitial fluid (IF) chloride concentration. The consequence is that similar intra- and extra-cellular chloride concentrations make these cells share the same Nernst value for Cl^-. Further extrapolation indicates that cells with the same chloride Nernst value and high chloride permeability should have similar resting membrane potentials, more negative than -80 mV. Fast sodium channels require potassium levels >20 times higher inside the cell than around it, while the concentration of Cl^- ions needs to be >20 times higher outside the cell. When osmotic forces, electroneutrality and other ions are all taken into account, the overall osmolarity needs to be near 280 to 300 mosm/L to reach the required resting potential in excitable cells. High plasma protein concentrations keep the IF chloride concentration stable, which is important in keeping the resting membrane potential similar in all chloride-permeable cells. Probable consequences of this concept for neuron excitability, erythrocyte membrane permeability and several features of circulation design are briefly discussed.     

Solute transport process in intestinal epithelial cells

In rat small intestine, the active transport of organic solutes results in significant depolarization of the membrane potential measured in an epithelial cell with respect to a grounded mucosal solution and in an increase in the transepithelial potential difference. According to the analysis with an equivalent circuit model for the epithelium, the changes in emf's of mucosal and serosal membranes induced by active solute transport were calculated using the measured conductive parameters. The result indicates that the mucosal cell membrane depolarizes while the serosal cell membrane remarkably hyperpolarizes on the active solute transport. Corresponding results are derived from the calculations of emf's in a variety of intestines, using the data that have hitherto been reported. The hyperpolarization of serosal membrane induced by the active solute transport might be ascribed to activation of the serosal electrogenic sodium pump. In an attempt to determine the causative factors in mucosal membrane depolarization during active solute transport, cell water contents and ion concentrations were measured. The cell water content remarkably increased and, at the same time, intracellular monovalent ion concentrations significantly decreased with glucose transport. Net gain of glucose within the cell was estimated from the restraint of osmotic balance between intracellular and extracellular fluids. In contrast to the apparent decreases in intracellular Na+ and K+ concentrations, significant gains of Na+ and K+ occurred with glucose transport. The quantitative relationships among net gains of Na+, K+ and glucose during active glucose transport suggest that the coupling ratio between glucose and Na+ entry by the carrier mechanism on the mucosal membrane is approximately 1:1 and the coupling ratio between Na+-efflux and K+-influx of the serosal electrogenic sodium pump is approximately 4:3 in rat small intestine. In addition to the electrogenic ternary complex inflow across the mucosal cell membrane, the decreases in intracellular monovalent ion concentrations, the temporary formation of an osmotic pressure gradient across the cell membrane and the streaming potential induced by water inflow through negatively charged pores of the cell membrane in the course of an active solute transport in intestinal epithelial cells are apparently all possible causes of mucosal membrane depolarization.