Models of active transport of ions in biomembranes of various types of cells

Nonequilibrium statistical models of the active transport of ions in biomembranes have been constructed. Differences of chemical potentials of the ATP-ADP reaction and the electrochemical potential of ions were taken as the thermodynamic forces responsible for the flow of ions through the membrane. The active transport of ions was viewed as a cross phenomenon arising from the chemical reaction of the ATP hydrolysis. These models provide independent calculations of the resting potential at the biomembrane and concentrations of ions in a cell on the assumption the free energy of the ATP-ADP reaction is fully (without the dissipation loss) converted to the free energy of transported ions. They take into account the presence of nonpenetrating ions in a cell. It was shown that different concentrations of nonpenetrating ions have a considerable effect on the resting potential. The proposed models were compared with experimental data obtained for different types of cells including neurons, muscular cells, bacteria, plants, and mitochondria. Calculated values of the membrane potential and ion concentrations were in good qualitative agreement with experimental data.     

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 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.     

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.     

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.     

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.     

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.     

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.     

Effect of the medium composition on the resting membrane potential in the earthworm longitudinal somatic muscle fibers

Norepinephrine or increased extracellular K+ hyperpolarize the membrane of the earthworm somatic muscle fibre, whereas removal of Cl- from external solution or a hypotonic solution depolarize the membrane. The dependence of the membrane resting potential on the extracellular K+ is quite characteristic against the background of ouabain action. A preliminary membrane depolarisation by ouabain eliminates the above effects on the membrane resting potential. The data obtained suggest that the ouabain-sensitive active ion pump directly contributes to the membrane resting potential value. This hypothesis is discussed with respect to existence of active Cl- transport combined with Na+, K(+)-pump which presumably takes part in the intracellular osmotic pressure regulation in the earthworm somatic muscle.     

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.     

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.     

Regulation of the electrogenic (Na+ + K+)-pump of Ehrlich cells by intracellular cation levels

Ehrlich cells actively accumulate neutral amino acids even if both the Na⁺ and K⁺ gradients are inverted. The seeming contradiction of this observation to the gradient hypothesis is, however, explained by the presence of a powerful electrogenic Na⁺ pump, which stongly raises the electrochemical potential gradient of Na⁺ under these conditions. Since the evidence of this pump has so far been found only during abnormal concentrations of alkali ions (low K⁺, high Na⁺) in these cells, the question arises whether the pump is equally powerful with completely normal cells, when the pump is not ‘needed’ for amino acid transport. Using the initial rate of uptake of the test amino acid (2-aminoisobutyrate) as a sensitive monitor of the electrical potential at constant cation distribution between cell and medium, a procedure has been devised to split the overall electrical potential into the diffusional and the pump component. With this procedure it could be shown that the electrogenic pump per se is most powerful in K⁺-depleted and Na⁺-rich cells but declines to a lower ‘resting’ value according as the electrolyte content of the cell approaches normality. A strong positive correlation between cellular Na⁺ content and the electrogenic pumping activity suggests that the intracellular activity of this ion regulates the rate of the electrogenic pump. The low activity of the pump under normal conditions may explain why the existance of this pump has rarely come to attention previously.     

Sodium and potassium content and membrane transport properties in red blood cells from newborn puppies

The intracellular sodium and potassium concentrations and membrane transport properties for these ions were investigated in red blood cells from newborn puppies and adult dogs. At birth the intracellular concentrations of sodium and potassium are much higher than those found in adult dog red cells. During the first few weeks of life the intracellular concentrations of these ions gradually decrease until the adult level is reached. Changes in the membrane transport properties develop concurrently. The rate of active potassium influx, as measured by ouabain-sensitivity, and the pump to leak ratio are greater in red cells from newborn puppies than in those from adult animals. No ouabain-sensitive sodium efflux could be demonstrated in red cells from older puppies or adult dogs. When either puppy or adult dog red cells are depleted of ATP (by incubation at 37°C with no substrate), potassium permeability increases, and the permeability of the membrane to sodium decreases. The addition of adenosine reverses the effect of depletion.     

The causal theory of the resting potential of cells

In this pedagogical article the causal theory of the resting potential of cells is presented, which for given extracellular ion concentrations predicts the intracellular ones simultaneously with the resting potential. In addition to the Na, K-pump, fixed charges on the membrane surfaces are taken into account. The equation determining the resting potential in the causal theory suggests a new explanation of the genesis of the resting potential. The usual criterion for an ion pump to be electrogenic is not relevant for the whole of the resting potential, and may therefore be misleading. The physical meaning of the Goldman-Hodgkin-Katz formula for the membrane potential as a diffusion potential is also explained and tested with numbers for the giant axon of the squid. A significant discrepancy between theory and experiment is found which calls for an experimental re-examination of the constitutive equations for passive potassium and sodium currents.     

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.     

Resolution of Pump and Leak Components of Sodium and Potassium Ion Transport in Human Erythrocytes

Further support for the pump-leak concept was obtained. Net transport was resolved into pump and leak components with the cardiac glycoside, ouabain. The specificity of ouabain as a pump inhibitor was demonstrated by its ineffectiveness when the pump was already inhibited by lack of one of the three pump substrates, sodium ion, potassium ion, or adenosine triphosphate. In the presence of ouabain the rates of passive transport of sodium and potassium ions changed almost in proportion to changes in their extracellular concentrations when one ion was exchanged for the other. In the presence of ouabain and at the extracellular concentrations which produced zero net transport, the ratio of potassium ions to sodium ions was 1.2-fold higher inside the cells than outside. This finding was attributed to a residual pump activity of less than 2% of capacity. The permeability to potassium ions was 10% greater than the permeability to sodium ions. A test was made of the independence of pump and leak. Conditions were chosen to change the rate through each pathway separately or in combination. When both pathways were active, net transport was the sum of the rates observed when each acted separately. A ratio of three sodium ions pumped outward per two potassium ions pumped inward was confirmed.     

A model study of the contribution of active Na-K transport to membrane repolarization in cardiac cells

A biochemical model of active Na-K transport in cardiac cells was studied in conjunction with a representation of the passive membrane currents and ion concentration changes. The active transport model is based on the thermodynamic and kinetic properties of a six-step reaction scheme for the Na,K-ATPase. It has a fixed Na:K stoechiometry of 3:2, and its activation is governed by three parameters: membrane potential intracellular Na+ concentration, and interstitial K+ concentration. The Na-K pump current is directly proportional to the density of Na,K-ATPase molecules. The passive membrane currents and ion concentration changes involve only Na+ and K+ ions, and no attempt was made to provide a precise representation of Ca2+ currents or Ca2+ concentration changes. The surface-to-volume ratio of the interstitial compartment is 55 times larger than that of the intracellular compartment. The flux balance conditions are such that the original equilibrium concentration values are re-established at each stimulation cycle. The underlying assumptions of the model were checked against experimental measurements on Na-K pump activity in a variety of preparations. In addition, the qualitative validation of the model was carried out by comparing its behavior following sudden frequency shifts to corresponding experimental observations. The overall behavior of the model is quite satisfactory and it is used to provide the following indications: (1) when the intracellular and interstitial volumes are relatively large, the ion concentration transients are small and the pumping rate depends essentially on average concentration levels. (2) An increase in internal Na+ concentration potentiates the response of the Na-K pump to rapid membrane depolarizations. (3) When the internal Na+ concentration is large enough, the Na-K pump current transient plays an important role in shaping the plateau and repolarization phase of the action potential. (4) A rapid increase in external K+ concentration during voltage clamp in multicellular preparations could saturate the Na-K pump response and lead to a fairly linear dependence of the pump activity on the internal Na+ concentration.     

AmtB-mediated NH3 transport in prokaryotes must be active and as a consequence regulation of transport by GlnK is mandatory to limit futile cycling of NH4(+)/NH3

The nature of the ammonium import into prokaryotes has been controversial. A systems biological approach makes us hypothesize that AmtB-mediated import must be active for intracellular NH(4)(+) concentrations to sustain growth. Revisiting experimental evidence, we find the permeability assays reporting passive NH(3) import inconclusive. As an inevitable consequence of the proposed NH(4)(+) transport, outward permeation of NH(3) constitutes a futile cycle. We hypothesize that the regulatory protein GlnK is required to fine-tune the active transport of ammonium in order to limit futile cycling whilst enabling an intracellular ammonium level sufficient for the cell's nitrogen requirements.