THE ACCUMULATION OF ELECTROLYTES : VIII. THE ACCUMULATION OF KCl IN MODELS

Models are described in which KCl enters until its chemical potential becomes much greater inside than outside. The energy needed to accomplish this comes from the chemical reactions occurring in the system and the continual supply of certain materials. An important factor is the maintenance of a lower pH value inside by means of CO₂. This may be analogous to what happens in some living cells. The concentration of K⁺ becomes higher inside, as happens in many living cells, but the concentration of Cl^- does not and in this respect the model differs from many living cells. As in Valonia, potassium tends to go out as KCl when the ionic activity product (K)(Cl) is greater inside but at the same time it tends to enter as KOH since the activity product (K)(OH) is greater outside. The net result is entrance of potassium presumably because the latter process is the more rapid.     

THE ACCUMULATION OF ELECTROLYTES : II. SUGGESTIONS AS TO THE NATURE OF ACCUMULATION IN VALONIA

It is suggested that K enters chiefly as KOH, whose thermodynamic potential (proportional to the ionic activity product (a _K) (a _OH)) is greater outside than within. As this difference is maintained by the production of acid in the cell K continues to enter, and reaches a greater concentration inside than outside. KOH combines with a weak organic acid which is exchanged for HCl entering from the sea water (or its anion is exchanged for Cl^-), so that KCl accumulates in the sap. Na enters more slowly and its internal concentration remains below that of K. The facts indicate that penetration is chiefly in molecular form. As the system is not in equilibrium the suggestion is not susceptible of thermodynamic proof but it is useful in predicting the behavior of K, Na, and NH₄.     

THE KINETICS OF PENETRATION : XIV. THE PENETRATION OF IODIDE INTO VALONIA

When 0.1 M NaI is added to the sea water surrounding Valonia iodide appears in the sap, presumably entering as NaI, KI, and HI. As the rate of entrance is not affected by changes in the external pH we conclude that the rate of entrance of HI is negligible in comparison with that of NaI, whose concentration is about 10⁷ times that of HI (the entrance of KI may be neglected for reasons stated). This is in marked contrast with the behavior of sulfide which enters chiefly as H₂S. It would seem that permeability to H₂S is enormously greater than to Na₂S. Similar considerations apply to CO₂. In this respect the situation differs greatly from that found with iodide. NaI enters because its activity is greater outside than inside so that no energy need be supplied by the cell. The rate of entrance (i.e. the amount of iodide entering the sap in a given time) is proportional to the external concentration of iodide, or to the external product [N⁺]_o [I^-l_o, after a certain external concentration of iodide has been reached. At lower concentrations the rate is relatively rapid. The reasons for this are discussed. The rate of passage of NaI through protoplasm is about a million times slower than through water. As the protoplasm is mostly water we may suppose that the delay is due chiefly to the non-aqueous protoplasmic surface layers. It would seem that these must be more than one molecule thick to bring this about. There is no great difference between the rate of entrance in the dark and in the light.     

THE KINETICS OF PENETRATION : V. THE KINETICS OF A MODEL AS RELATED TO THE STEADY STATE

An organic potassium salt, KG, passes from an aqueous phase, A, through a non-aqueous layer, B, into a watery solution, C. In C it reacts with CO₂ to form KHCO₃. The ionic activity product (K) (G) in C is thus kept at such a low level that KG continues to diffuse into C after the concentration of potassium becomes greater in C than in A. Hence potassium accumulates in C, the osmotic pressure rises, and water goes in. A steady state is eventually reached in which potassium and water enter C in a constant ratio. The rate of entrance of potassium (with no water penetrating into C) may fall off in a manner approximately exponential. But water enters and may produce an exponential decrease in concentration. This suggests that the kinetics may be treated like that of two consecutive monomolecular reactions. Calculations made on this basis agree very well with the observed values. The rate of penetration appears to be proportional to the concentration gradient of KG in the non-aqueous layer and in consequence depends upon the partition coefficients which determine this gradient. Exchange of ions (passing as such through the non-aqueous layer) does not seem to play an important rôle in the entrance of potassium. The kinetics of the model may be similar to that of living cells.     

On the Concept of Resting Potential—Pumping Ratio of the Na+/K+ Pump and Concentration Ratios of Potassium Ions Outside and Inside the Cell to Sodium Ions Inside and Outside the Cell

In animal cells, the resting potential is established by the concentration gradients of sodium and potassium ions and the different permeabilities of the cell membrane to them. The large concentration gradients of sodium and potassium ions are maintained by the Na⁺/K⁺ pump. Under physiological conditions, the pump transports three sodium ions out of and two potassium ions into the cell per ATP hydrolyzed. However, unlike other primary or secondary active transporters, the Na⁺/K⁺ pump does not work at the equilibrium state, so the pumping ratio is not a thermodynamic property of the pump. In this article, I propose a dipole-charging model of the Na⁺/K⁺ pump to prove that the three Na⁺ to two K⁺ pumping ratio of the Na⁺/K⁺ pump is determined by the ratio of the ionic mobilities of potassium to sodium ions, which is to ensure the time constant τ and the τ-dependent processes, such as the normal working state of the Na⁺/K⁺ pump and the propagation of an action potential. Further, the concentration ratios of potassium ions outside and inside the cell to sodium ions inside and outside the cell are 0.3027 and 0.9788, respectively, and the sum of the potassium and sodium equilibrium potentials is ?30.3 mV. A comparative study on these constants is made for some marine, freshwater and terrestrial animals. These findings suggest that the pumping ratio of the Na⁺/K⁺ pump and the ion concentration ratios play a role in the evolution of animal cells.     

THE ACCUMULATION OF ELECTROLYTES : I. THE ENTRANCE OF AMMONIA INTO VALONIA MACROPHYSA

When 0.005 M NH₄Cl is added to sea water containing cells of Valonia macrophysa ammonia soon appears in the sap and may reach a concentration inside over 40 times as great as outside. It appears to enter as undissociated NH₃ (or NH₄OH) and tends to reach a pseudoequilibrium in which the activity of undissociated NH₃ (or NH₄OH) is the same inside and outside. When ammonia first enters, the pH value of the sap rapidly rises but it soon reaches a maximum and subsequently falls off. At the same time there is an increase of halide in the sap which, however, does not run a parallel course to the ammonia accumulation, but it comes to a new equilibrium value and remains constant. The increase in NH₃ in the sap is accompanied by a decrease in the concentration of K. As NH₃ enters the specific gravity of the sap decreases and the cells rise to the surface and continue to grow as floating organisms. The growth of the cells is increased.     

THE ACCUMULATION OF ELECTROLYTES : III. BEHAVIOR OF SODIUM,POTASSIUM, AND AMMONIUM IN VALONIA

When 0.001 M NH₄Cl is added to sea water containing Valonia macrophysa there seems to be a rapid penetration of undissociated NH₃ (or NH₄OH) which raises the pH value of the sap so that the thermodynamic potential of KOH becomes greater inside than outside and in consequence K leaves the cell: NaOH continues to go in because its thermodynamic potential is greater outside than inside. NH₄Cl accumulates, reaching a much higher concentration inside than outside. This might be explained on the ground that NH₃, after entering, combines with a weak organic acid produced in the cell whose anion is exchanged for the Cl^- of the sea water, or (more probably) the organic acid is exchanged for HCl.     

SOME CHEMICAL ASPECTS OF THE POTASSIUM EFFECT

The ability of Nitella to distinguish electrically between Na⁺ and K⁺ (potassium effect) appears to depend on several organic substances (or groups of substances). Of these R_MK and R_SK determine the mobility and partition coefficient (S) respectively of K⁺ while R_MNa and R_SNa do the same for Na⁺. These substances can vary independently and this variation is susceptible to experimental control.     

Cell dualism: presence of cells with alternative membrane potentials in growing populations of bacteria and yeasts

It is considered that all growing cells, for exception of acidophilic bacteria, have negatively charged inside cytoplasmic membrane (Δψ^? - cells). Here we show that growing populations of microbial cells contain a small portion of cells with positively charged inside cytoplasmic membrane (Δψ⁺ - cells). These cells were detected after simultaneous application of the fluorescent probes for positive membrane potential (anionic dye DIBAC^-) and membrane integrity (propidium iodide, PI). We found in exponentially growing cell populations of Escherichia coli and Saccharomyces cerevisiae that the content of live Δψ^- - cells was 93.6?±?1.8 % for bacteria and 90.4?±?4.0 % for yeasts and the content of live Δψ⁺ - cells was 0.9?±?0.3 % for bacteria and 2.4?±?0.7 % for yeasts. Hypothetically, existence of Δψ⁺ - cells could be due to short-term, about 1 min for bacteria and 5 min for yeasts, change of membrane potential from negative to positive value during the cell cycle. This change has been shown by the reversions of K⁺, Na⁺, and Ca²⁺ ions fluxes across the cell membrane during synchronous yeast culture. The transformation of Δψ^-- cells to Δψ⁺ - cells can be explained by slow influx of K⁺ ions into Δψ^-- cell to the trigger level of K⁺ concentration (“compression of potassium spring”), which is forming “alternative” Δψ⁺-cell for a short period, following with fast efflux of K⁺ ions out of Δψ⁺-cell (“release of potassium spring”) returning cell to normal Δψ^- state. We anticipate our results to be a starting point to reveal the biological role of cell dualism in form of Δψ^- - and Δψ⁺ - cells.     

Multi-ion distributions in the cytoplasmic domain of inward rectifier potassium channels

Inward rectifier potassium (Kir) channels act as cellular diodes, allowing unrestricted flow of potassium (K⁺) into the cell while preventing currents of large magnitude in the outward direction. The rectification mechanism by which this occurs involves a coupling between K⁺ and intracellular blockers—magnesium (Mg²⁺) or polyamines—that simultaneously occupy the permeation pathway. In addition to the transmembrane pore, Kirs possess a large cytoplasmic domain (CD) that provides a favorable electronegative environment for cations. Electrophysiological experiments have shown that the CD is a key regulator of both conductance and rectification. In this study, we calculate and compare averaged equilibrium probability densities of K⁺ and Cl⁻ in open-pore models of the CDs of a weak (Kir1.1-ROMK) and a strong (Kir2.1-IRK) rectifier through explicit-solvent molecular-dynamics simulations in ∼1 M KCl. The CD of both channels concentrates K⁺ ions greater than threefold inside the cytoplasmic pore while IRK shows an additional K⁺ accumulation region near the cytoplasmic entrance. Simulations carried out with Mg²⁺ or spermine (SPM⁴⁺) show that these ions interact with pore-lining residues, shielding the surface charge and reducing K⁺ in both channels. The results also show that SPM⁴⁺ behaves differently inside these two channels. Although SPM⁴⁺ remains inside the CD of ROMK, it diffuses around the entire volume of the pore. In contrast, this polyatomic cation finds long-lived conformational states inside the IRK pore, interacting with residues E224, D259, and E299. The strong rectifier CD is also capable of sequestering an additional SPM⁴⁺ at the cytoplasmic entrance near a cluster of negative residues D249, D274, E275, and D276. Although understanding the actual mechanism of rectification blockade will require high-resolution structural information of the blocked state, these simulations provide insight into how sequence variation in the CD can affect the multi-ion distributions that underlie the mechanisms of conduction, rectification affinity, and kinetics.     

Potassium and its role in cesium transport in plants

In plant cells, potassium (K⁺) is abundantly present and is dominant cation plays a vital role in maintaining physiological and morphological characteristics of plants. Many membrane integrated channels and transporters specific to K⁺ are involved in maintaining the potassium concentration within plants via membrane electrical activities. Elemental homologues to K⁺ compete with it for entry inside plants; among those, cesium is very common radionuclide. Once cesium enters into the plant cell, it can cause phytotoxicity. Therefore, it is desirable to understand complete pathway and mechanisms of cesium uptake in the plants, in order to assess consequences from accidental release of radioactive substance. This review focuses on mechanism of K⁺ ion uptake through channels/transporter and involvement of these channels/transporter in cesium uptake in plant cells.     

THE KINETICS OF PENETRATION : XII. HYDROGEN SULFIDE

The rate of entrance of H₂S into cells of Valonia macrophysa has been studied and it has been shown that at any given time up to 5 minutes the rate of entrance of total sulfide (H₂S + S^-) into the sap is proportional to the concentration of molecular H₂S in the external solution. This is in marked contrast with the entrance of ammonia, where Osterhout has shown that the rate of entrance of total ammonia (NH₃ + NR₄ ⁺) does not increase in a linear way with the increase in the external concentration of NH₃, but falls off. The strong base guanidine also acts thus. It has been shown that the rate of entrance of H₂S is best explained by assuming that it enters by diffusion of molecular H₂S through the non-aqueous protoplasmic surface. It has been pointed out that the simple diffusion requires that the rate of entrance might be expected to be monomolecular. Possible causes of the failure of H₂S to follow this relationship have been discussed.     

The effect of ultraviolet light on the sodium and potassium composition of resting yeast cells

The Na⁺ and K⁺ content of non-metabolizing yeast cells was determined before and after monochromatic ultraviolet (UV) irradiation. UV facilitated the uptake of Na⁺ into and the loss of K⁺ from the cells (net ion flux); the effect is greatest for the shortest wavelength employed (239 mµ) and is partly dependent upon the presence of oxygen. The UV effect on net ion flux persists for at least 90 minutes during which tests were made and it occurs following dosages which are without measurable effect on colony formation. The UV effect on net ion flux is decreased by acidity and promoted by alkalinity. Addition of calcium ions in sufficient amount prevents the usual net ion flux changes observed in irradiated yeast. Increase in concentration gradient between the inside and the outside of the cell increases the net ion flux of irradiated yeast, Na⁺ uptake leading K⁺ loss in all cases. UV appears to act by disorganizing the constituents of the cell surface, permitting K⁺ to leave the cell in exchange for Na⁺. At low intensities of UV this ionic exchange approaches equivalence, but at higher intensities more Na⁺ is taken up than K⁺ is lost. Some evidence suggests that the Na⁺ in excess over that exchanged for K⁺ is adsorbed to charged groups produced by the photochemical effect of UV on the cell surface.     

Uptake and Concentration of Alkylamines by a Marine Diatom: EFFECTS OF H AND K AND IMPLICATIONS FOR THE TRANSPORT AND ACCUMULATION OF WEAK BASES

Methylamine, ethylamine, and dimethylamine (10 micromolar) are taken up and concentrated 600 to 6,000-fold by Cyclotella cryptica. Methylamine is concentrated most strongly, and its accumulation and retention are relatively insensitive to external pH but strongly inhibited by 30 millimolar external K⁺. Accumulation and retention of ethyl- and dimethylamine, on the other hand, are strongly affected by external pH and less sensitive to external [K⁺]. Intracellular pH, as estimated from neutral red staining and quenching of 9-aminoacridine fluorescence, was between 4 and 5, with the central vacuole being the major acidic compartment. The accumulation of ethyl- and dimethylamine could result from diffusion of the uncharged amine across the membrane(s) and passive equilibration of the charged form (R-NH₃⁺) inside and outside the cell. Differences in the accumulation ratio and the ion dependence for methylamine uptake relative to ethyl- and dimethylamine uptake suggests that a different mechanism is responsible for the concentration of the simpler amine.     

THE CONCENTRATION EFFECT WITH VALONIA: POTENTIAL DIFFERENCES WITH DILUTED POTASSIUM-RICH SEA WATERS

The concentration effect with sea waters containing more than the normal amount of potassium has been studied in Valonia macrophysa. This was done by comparing the initial changes in P.D. across the protoplasm when natural sea water bathing the cell was replaced by various isotonic dilutions of KCl-rich sea waters. With small dilutions of KCl-rich sea waters, the P.D.-time curves are of the same form as with the undiluted solution, exhibiting the fluctuations characteristic of KCl-rich solutions. This indicates that with these solutions K⁺ enters Valonia protoplasm and plays an important part in the P.D. The value of the initial rise in P.D. decreases with increasing dilution. With high dilutions of KCl-rich sea waters, the P.D.-time curves are of quite different shape, resembling the curves with diluted natural sea water; the P.D. is practically independent of small changes in the concentration of potassium, and increases with increasing dilution. That is, with these higher dilutions, the sign of the concentration effect is reversed, becoming the same as with diluted natural sea water. The greater the concentration of KCl in the undiluted sea water, the higher is the critical dilution at which K⁺ ceases to influence the P.D. For a wide range of sea waters containing both KCl and NaCl, it is shown that the concentration effect above the critical dilution is determined solely by the activity of NaCl in the external solution. It is concluded that with dilute natural sea water and with high dilutions of KCl-rich sea waters we have to do with a diffusion potential, involving only the Na⁺ and Cl^- ions, which are diffusing out from the vacuole. A quantitative relation between the composition of the sea water and the critical dilution has been deduced from the classical theory of the diffusion of electrolytes. It is shown that with dilutions less than this critical value the diffusion of K⁺ in the outer non-aqueous layer of the protoplasm is directed inward; hence K⁺ enters the protoplasm from these solutions. With dilutions greater than the critical value, the diffusion of K⁺ in this layer is directed outward; hence K⁺ does not enter the protoplasm. Since the P.D. shows no evidence of this outward diffusion of K⁺, it is concluded that the amount of K⁺ ordinarily present in the protoplasm is too small to produce any lasting electrical effect, and that the outward diffusion of K⁺ from the vacuole is prevented by the mechanism responsible for the accumulation of KCl in the cell sap.     

THE KINETICS OF PENETRATION : I. EQUATIONS FOR THE ENTRANCE OF ELECTROLYTES

When the only solute present is a weak acid, HA, which penetrates as molecules only into a living cell according to a curve of the first order and eventually reaches a true equilibrium we may regard the rate of increase of molecules inside as See PDF for Equation where P_M is the permeability of the protoplasm to molecules, M_o, denotes the external and M_i the internal concentration of molecules, A_i denotes the internal concentration of the anion A^- and See PDF for Equation (It is assumed that the activity coefficients equal 1.) Putting P_MF_M = V_M, the apparent velocity constant of the process, we have See PDF for Equation where e denotes the concentration at equilibrium. Then See PDF for Equation where t is time. The corresponding equation when ions alone enter is See PDF for Equation. where K is the dissociation constant of HA, P_A is the permeability of the protoplasm to the ion pair H⁺ + A^-, and A_ie denotes the internal concentration of A_i at equilibrium. Putting P_AKF_M = V_A, the apparent velocity constant of the process, we have See PDF for Equation and See PDF for Equation When both ions and molecules of HA enter together we have See PDF for Equation where S_i = M_i + A_i and S_ie is the value of S_i at equilibrium. Then See PDF for Equation V_M, V_A, and V_MA depend on F_M and hence on the internal pH value but are independent of the external pH value except as it affects the internal pH value. When the ion pair Na⁺ + A^- penetrates and Na_i = BA_i, we have See PDF for Equation and See PDF for Equation where P _NaA is the permeability of the protoplasm to the ion pair Na⁺ + A^-, Na_o and Na_i are the external and internal concentrations of Na⁺, See PDF for Equation, and V _Na is the apparent velocity constant of the process. Equations are also given for the penetration of: (1) molecules of HA and the ion pair Na⁺ + A^-, (2) the ion pairs H⁺ + A^- and Na⁺ + A^-, (3) molecules of HA and the ion pairs Na⁺ + A^- and H⁺ + A^-. (4) The penetration of molecules of HA together with those of a weak base ZOH. (5) Exchange of ions of the same sign. When a weak electrolyte HA is the only solute present we cannot decide whether molecules alone or molecules and ions enter by comparing the velocity constants at different pH values, since in both cases they will behave alike, remaining constant if F_M is constant and falling off with increase of external pH value if F_M falls off. But if a salt (e.g., NaA) is the only substance penetrating the velocity constant will increase with increase of external pH value: if molecules of HA and the ions of a salt NaA. penetrate together the velocity constant may increase or decrease while the internal pH value rises. The initial rate See PDF for Equation (i.e., the rate when M_i = 0 and A_i = 0) falls off with increase of external pH value if HA alone is present and penetrates as molecules or as ions (or in both forms). But if a salt (e.g., NaA) penetrates the initial rate may in some cases decrease and then increase as the external pH value increases. At equilibrium the value of M_i equals that of M_o (no matter whether molecules alone penetrate, or ions alone, or both together). If the total external concentration (S_o = M_o + A_o) be kept constant a decrease in the external pH value will increase the value of M_o and make a corresponding increase in the rate of entrance and in the value at equilibrium no matter whether molecules alone penetrate, or ions alone, or both together. What is here said of weak acids holds with suitable modifications for weak bases and for amphoteric electrolytes and may also be applied to strong electrolytes.     

Macroscopic Na+ Currents in the “Nonconducting” Shaker Potassium Channel Mutant W434F

C-type inactivation in Shaker potassium channels inhibits K⁺ permeation. The associated structural changes appear to involve the outer region of the pore. Recently, we have shown that C-type inactivation involves a change in the selectivity of the Shaker channel, such that C-type inactivated channels show maintained voltage-sensitive activation and deactivation of Na⁺ and Li⁺ currents in K⁺-free solutions, although they show no measurable ionic currents in physiological solutions. In addition, it appears that the effective block of ion conduction produced by the mutation W434F in the pore region may be associated with permanent C-type inactivation of W434F channels. These conclusions predict that permanently C-type inactivated W434F channels would also show Na⁺ and Li⁺ currents (in K⁺-free solutions) with kinetics similar to those seen in C-type-inactivated Shaker channels. This paper confirms that prediction and demonstrates that activation and deactivation parameters for this mutant can be obtained from macroscopic ionic current measurements. We also show that the prolonged Na⁺ tail currents typical of C-type inactivated channels involve an equivalent prolongation of the return of gating charge, thus demonstrating that the kinetics of gating charge return in W434F channels can be markedly altered by changes in ionic conditions.     

THE KINETICS OF PENETRATION : VIII. TEMPORARY ACCUMULATION

A model is described which throws light on the mechanism of accumulation. In the model used an external aqueous phase A is separated by a non-aqueous phase B (representing the protoplasm) from the artificial sap in C. A contains KOH and C contains HCl: they tend to mix by passing through the non-aqueous layer but much more KOH moves so that most of the KCl is formed in C, where the concentration of potassium becomes much greater than in A. This accumulation is only temporary for as the system approaches equilibrium the composition of A approaches identity with that of C, since all the substances present can pass through the non-aqueous layer. Such an approach to equilibrium may be compared to the death of the cell as the result of which accumulation disappears. During the earlier stages of the experiment potassium tends to go in as KOH and at the same time to go out as KCl. These opposing tendencies do not balance until the concentration of potassium inside becomes much greater than outside (hence potassium accumulates). The reason is that KCl, although its driving force be great, moves very slowly in B because its partition coefficient is low and in consequence its concentration gradient in B is small. This illustrates the importance of partition coefficients for penetration in models and in living cells. It also indicates that accumulation depends on the fact that permeability is greater for the ingoing compound of the accumulating substance than for the outgoing compound. Other things being equal, accumulation is increased by maintaining a low pH in C. Hence we may infer that anything which checks the production of acid in the living cell may be expected to check accumulation and growth. This model recalls the situation in Valonia and in most living cells where potassium accumulates as KCl, perhaps because it enters as KOH and forms KA in the sap (where A is an organic anion). In some plants potassium accumulates as KA but when HCl exists in the external solution it will tend to enter and displace the weaker acid HA (if this be carbonic it can readily escape): hence potassium may accumulate to a greater or less extent as KCl. Injury of the cell may produce a twofold effect, (1) increase of permeability, (2) lessened accumulation. The total amount of electrolyte taken up in a given time will be influenced by these factors and may be greater than normal in the injured cell or less, depending somewhat on the length of the interval of time chosen.     

An analysis of conductance changes in squid axon

The membrane of the squid axon is considered on the basis of a pore model in which the distribution of the pore sizes strongly favors K⁺ transfer when there is no potential. Electrical asymmetry causes non-penetrating ions on the membrane capacitor to exert a mechanical force on both membrane surfaces and this force results in a deformation of the membrane pore system such that it assumes a distribution of sizes favoring the ions exerting mechanical force. The ions involved appear to be Ca⁺⁺ on the outside of the membrane and isethionate^-, (i^-) on the inside; as Ca⁺⁺ is equivalent in size to Na⁺, the charged membrane is potentially able to transfer Na⁺, when the ions deforming the membrane pore distribution are removed. A depolarization of the membrane leads to an opening of pores that will allow Na⁺ penetration and a release of the membrane from deformation. The pores revert to the zero-potential pore size distribution hence the Na permeability change is a transient. Calculation shows that the potassium conductance vs. displacement of membrane potential curve for the squid axon and the "inactivation" function, h, can be obtained directly from the assumed membrane distortion without the introduction of arbitrary parameters. The sodium conductance, because it is a transient, requires assumptions about the time constants with which ions unblock pores at the outside and the inside of the membrane.