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Ion balance disturbance caused by turning off the pump at various pCl. A model without cotransporters was used. The parameters were chosen as follows: na0 140, k0 5.8, cl0 116, B0 48.2, kv 1, na 52.6, k 144.2, cl 11.9, beta 0 (at the initial balanced value of 0.039), gamma 1.5, pna 0.006, pk 0.06, pcl 0.1 (triangles), or 0.001 (circles), or 0.0001 (solid lines), hp 10000, inc = ikc = inkcc = 0.
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![Figure 2: Effect of cotransporters on [Cl] i, cell water (V/A) and ΔµCl...](profile/Alexey-Vereninov/publication/269716705/figure/fig3/AS:271519515410451@1441746705932/Effect-of-cotransporters-on-Cl-i-cell-water-V-A-and-DmCl-for-various-cell-types-and_Q320.jpg)
Many vital processes in animal cells depend on monovalent ion transport across the plasma membrane via specific pathways. Their operation is described by a set of nonlinear and transcendental equations that cannot be solved analytically. Previous computations had been optimized for certain cell types and included parameters whose experimental deter...
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... cells following pump inhibition by ouabain often do not swell for a long time. Low permeability of Cl -channels as well as the involvement of the Ca-ATPase pump, Na-Ca antiporter and NKCC cotransport have been listed as possible reasons for the delay in swelling [19][20][21]. Fig. 3 illustrates the development of a disturbance caused by stopping the pump in the simplest cell model with Na + , K + and Cl -channels and no symports. One can see that substantial water accumulation starts only when the K + /Na + inversion is almost complete. Thus, the simple model, which only assumes low permeability for Cl -, is ...
Context 2
... caused by ouabain. No significant changes in the rate of K + -Na + redistribution occur when p Cl is varied by as much as three orders of magnitude, and only water and Cl -dynamics are affected. It should be noted that the prompt shift in the MP due to pump blocking, i.e. the "electrogenic" effect of the pump, is sensitive to p Cl (see insert in Fig. 3). This is because the contribution of the pump to the total transmembrane current depends on all ion channels, including those for Cl -. Fig. 4A-4C compares the observed and predicted time courses of ion and water changes caused by ouabain. The parameters used for calculations were derived from the analysis of the balanced state of ...
Similar publications
The balance of K+, Na+ and Cl- fluxes through cell membrane with the Na+/K+ pump, ion channels and NKCC and NC cotransporters is considered. It is shown that all unidirectional K+, Na+ and Cl- fluxes through cell membrane, permeability coefficients of ion channels and membrane potential can be computed for balanced ion distribution between cell and...
Studying the transport of monovalent ions across the cell membrane in living cells is complicated by the strong interdependence of fluxes through parallel pathways and requires therefore computational analysis of the entire electrochemical system of the cell. Current paper shows how to calculate changes in the cell water balance and ion fluxes caus...
Fluxes of monovalent ions through the multiple pathways of the plasma membrane are highly interdependent, and their assessment by direct measurement is difficult or even impossible. Computation of the entire flux balance helps to identify partial flows and study the functional expression of individual transporters. Our previous computation of unidi...
Recently, we have developed software that allows, using a minimum of required experimental data, to find the characteristics of ion homeostasis and a list of all unidirectional fluxes of monovalent ions through the main pathways in the cell membrane both in a balanced state and during the transient processes. Our approach has been successfully vali...
Citations
... In subsequent studies, it was used to characterize osmotically induced changes [39,40]. To demonstrate the role of k v in the changes of TP caused by the addition of 100 mM KCl to the medium, its value was set either to 1 or 1.8 and the calculations were carried out using a program for the computation of pump-leak flux balance in animal cells [41]. The rate of TP changes at k v = 1.8 is slower than at k v = 1.0 for all three permeability ratios (Fig. 1). ...
... Changes of TP in a membrane Donnan system caused by the addition of 100 mM KCl to an external medium. Calculations were performed using the Web version of the program for the computation of pump-leak flux balance in animal cells[41]. The following initial parameters were used (in mM):[K] i =139, [Na] i =23.6, [Cl] i =3.8, [K] o =102, [Na] o =120, [Cl] o =221, P K was set to 0.002 min -1 (solid line), 0.01 min -1 (dashed line), or 0.06 min -1 (dotted line) while P Cl was kept constant at 0.01 min -1 . ...
The review is devoted to Alexey Vereninov's research in the field of cell permeability and ion homeostasis. Particular attention is paid to the modeling approach developed in the study of frog striated muscles and subsequently applied to other cell types. Biologically relevant ways by which the muscles were studied and the model that was constructed determines the overall nonreductionist approach of the research. In the first study of excitability in invertebrate tissues and organs Vereninov used techniques and methods derived from his teacher Dmitry Nasonov. From 1963 to 1971, he tested membrane and phase concepts of bioelectrogenesis using isolated fibers and whole sartorius muscles. Both mechanistic and theoretical models have been used in the study of “salt potentials”. The properties of muscles considered in these models are relevant to both the phase and membrane models. Vereninov’s work, therefore, led to reconciliation between the two theories. In studies performed in 1971 and 1976 Vereninov presented a nonreductionist approach to the study of ion and osmotic balance in animal cells. Using the concept of cell permeability, he developed a method to analyze potassium permeability by combining electrophysiological and ionic data. In 1980-1983 Vereninov applied Ussing's criterion to study the role of passive permeability in the ion balance of muscles in a bi-ionic system. These studies were carried out under specific ionic conditions that allow the distinction between passive and active components of ion transport. Under these conditions, sodium was actively transported, and potassium exhibited both active and passive transport. Moreover, in a bi-ionic system with rubidium and potassium, some unidentified transport component was also present. Therefore, instead of Ussing's criterion, the application of which is restricted to specific experimental conditions, the analysis of ion fluxes was carried out using mathematical modeling.
... These equations describe the dynamics on Na + , K + , and Cl − , the cell volume, and the membrane potential (see Results for more details). The PLEs were first proposed by Tosteson and Hoffman in 1960 and have been employed and extended by others to understand cell volume control in single cells (Jakobsson, 1980;Hernández, 2007;Vereninov et al., 2014) and epithelial (Lew et al., 1979;Sharp et al., 2015). Keener and Sneyd (2009) derived a very useful analytic solution to the PLEs. ...
The presence of impermeant molecules within a cell can lead to an increase in cell volume through the influx of water driven by osmosis. This phenomenon is known as the Donnan (or Gibbs–Donnan) effect. Animal cells actively transport ions to counteract the Donnan effect and regulate their volume, actively pumping Na⁺ out and K⁺ into their cytosol using the Na⁺/K⁺ ATPase (NKA) pump. The pump-leak equations (PLEs) are a system of algebraic-differential equations to model the membrane potential, ion (Na⁺, K⁺, and Cl⁻), and water flux across the cell membrane, which provide insight into how the combination of passive ions fluxes and active transport contribute to stabilizing cell volume. Our broad objective is to provide analytical insight into the PLEs through three lines of investigation: (1) we show that the provision of impermeant extracellular molecules can stabilize the volume of a passive cell; (2) we demonstrate that the mathematical form of the NKA pump is not as important as the stoichiometry for cell stabilization; and (3) we investigate the interaction between the NKA pump and cation–chloride co-transporters (CCCs) on cell stabilization, showing that NCC can destabilize a cell while NKCC and KCC can stabilize it. We incorporate extracellular impermeant molecules, NKA pump, and CCCs into the PLEs and derive the exact formula for the steady states in terms of all the parameters. This analytical expression enables us to easily explore the effect of each of the system parameters on the existence and stability of the steady states.
... From the "pump-leak" theory of monovalent ion distribution between animal cells and the medium, it follows that the amount of K + in a cell essentially depends on the amount of "impermeant" (through cell membrane) anions "sequestered" in the cell. It is the amount of these anions in combination with the Na/K pump that determines the water balance of the cell and the accumulation of K + inside the cell [24,[57][58][59][60]. In quiescent cells (such as human HBLs) that are stimulated to begin the division cycle, during the G0/G1/S progression, the increase in protein mass and volume is accompanied by an increase in the quantity of impermeable anions, which inevitably leads to an increase in the influx of water to restore the osmotic balance between the cell and the environment. ...
This brief review explores the role of intracellular K+ during the transition of cells from quiescence to proliferation and the induction of apoptosis. We focus on the relationship between intracellular K+ and the growth and proliferation rates of different cells, including transformed cells in culture as well as human quiescent T cells and mesenchymal stem cells, and analyze the concomitant changes in K+ and water content in both proliferating and apoptotic cells. Evidence is discussed indicating that during the initiation of cell proliferation and apoptosis changes in the K+ content in cells occur in parallel with changes in water content and therefore do not lead to significant changes in the intracellular K+ concentration. We conclude that K+, as a dominant intracellular ion, is involved in the regulation of cell volume during the transit from quiescence, and the content of K+ and water in dividing cells is higher than in quiescent or differentiated cells, which can be considered to be a hallmark of cell proliferation and transformation.
... Our approach is based on the use of the thermodynamic classification of ion transport systems through the cell membrane and does not depend on the mechanism of ion movement. It takes into account all the main types of ion-conducting pathways through the plasma membrane: sodium pump, electrically conductive channels, and all main types of cation-chloride cotransporters [10][11][12][13][14][15]. Until now, the reliability of the proposed description has been successfully shown for transient processes such as Na/K pump blockage by ouabain or replacing extracellular Na + with Li + , as well as in staurosporine-induced apoptosis in proliferating lymphoid U937 cells [10][11][12][13][14]. ...
... It takes into account all the main types of ion-conducting pathways through the plasma membrane: sodium pump, electrically conductive channels, and all main types of cation-chloride cotransporters [10][11][12][13][14][15]. Until now, the reliability of the proposed description has been successfully shown for transient processes such as Na/K pump blockage by ouabain or replacing extracellular Na + with Li + , as well as in staurosporine-induced apoptosis in proliferating lymphoid U937 cells [10][11][12][13][14]. ...
... The mathematical background of the modeling has been described in details earlier [9][10][11][12][13][14]. The mathematical model of the movement of monovalent ions across the cell membrane is like that used by Jakobsson [9] and Lew with colleagues [1,3]. ...
Recently, we have developed software that allows, using a minimum of required experimental data, to find the characteristics of ion homeostasis and a list of all unidirectional fluxes of monovalent ions through the main pathways in the cell membrane both in a balanced state and during the transient processes. Our approach has been successfully validated in human proliferating lymphoid U937 cells during transient processes after stopping the Na/K pump by ouabain and for staurosporine-induced apoptosis. In present study, we used this approach to find the characteristics of ion homeostasis and the monovalent ion fluxes through the cell membrane of human erythrocytes in a resting state and during the transient processes after stopping the Na/K pump with ouabain and in response to osmotic challenge. Due to their physiological significance, erythrocytes remain the object of numerous studies, both experimental and computational methods. Calculations showed that, under physiological conditions, the K⁺ fluxes through electrodiffusion channels in the entire erythrocyte ion balance is small compared to the fluxes through the Na/K pump and cation–chloride cotransporters. The proposed computer program well predicts the dynamics of the erythrocyte ion balance disorders after stopping the Na/K pump with ouabain. In full accordance with predictions, transient processes in human erythrocytes are much slower than in proliferating cells such as lymphoid U937 cells. Comparison of real changes in the distribution of monovalent ions under osmotic challenge with the calculated ones indicates a change in the parameters of the ion transport pathways through the plasma membrane of erythrocytes in this case. The proposed approach may be useful in studying the mechanisms of various erythrocyte dysfunctions.
... Various aspects concerning the internal impermeant osmolyte were touched on the previous publications [1][2][3][4][5][6], but the present work is entirely focused on computational investigation of the consequences that changes in the amount of X and its net valence z have on other ionic concentrations, the membrane potential, and the cell volume. The practically important questions about the composition of the ultracomplex item which is called "internal impermeant anion" and how changes of its components result in changes of its concentration and its mean valence is outside of the scope of this paper. ...
Background/Aims: For many years experimental and theoretical studies of the processes controlling the transmembrane potential of living cells and their volume were focused on ions, first of all Na+, K+, and Cl-, that can be moved in and out of the cell by various active and passive mechanisms. But recently more and more attention has been directed toward the internal impermeant anion (Xz-) – a complex entity that is comprised of many very different molecules. The most intriguing feature of the internal impermeant anion is that its amount and, importantly, its mean valence can be changed during the metabolic activity of the cell. The aim of this paper is to computationally investigate how changes in the amount and the mean valence of the internalimpermeant anion influence the concentration of the main ions, the membrane potential, and the cell volume. Methods: The computational analyses were performed using our charge-difference model describe earlier. Results and Conclusion: The results of computational simulations confirm previous results that changes in the amount of Xz- influence nothing but the cell volume if z remains constant, although transient disturbances of concentrations and Em happen and their extent depends on the speed of Xz- changes. Changes of z have more serious consequences. A decrease of |z| leads to a decrease of concentrations of cations ([K+]i and [Na+]i), to an increase of the concentrations of anions ([Cl-]I and [Xz-]i), and to depolarization of the cell membrane; an increase of |z| leads to changes in the opposite directions. Interestingly, even in conditions when Xz- remains unchanged, the normal electrophysiological activity expressed in changes of Em will affect [Cl-]i and consequently [Xz-]i (due to volume changes), inducing feedback effects on the cation concentrations and Em. Accordingly, Xz- is viewed as an important but not the only component of a broader concept of osmolarity-charge asymmetry. The basic physical reasons that determine the interrelations between Xz- on one hand and ionic concentrations, Em, and the cell volume on the other hand are discussed.
... In 3D eMSCs, ouabain-inhibited Rb + influx accounts for a significant part of the total Rb + uptake and somewhat higher than that in 2D eMSCs ( Figure 1C). To determine whether the increased ouabain-inhibitable Rb influx in 3D eMSCs is proportional to changes in intracellular Na + content, we compared pump rate coefficients calculated as the ratio of ouabain-inhibitable Rb + uptake to intracellular Na + content in 2D and 3D cultures [38,39]. It turned out that the pump rate coefficients are close in value both in eMSCs spheroids (0.021 ± 0.002 min −1 ) and in preconfluent eMSCs monolayer culture (0.025 ± 0.002 min −1 ), which indicates that the increased ouabain-inhibitable Rb + transport in spheroids is not associated with a change in the intrinsic properties of the Na/K pump, but is a consequence of flux concentration relations in existing ion pumps. ...
This study describes the changes in ion homeostasis of human endometrial mesenchymal stem/stromal cells (eMSCs) during the formation of three-dimensional (3D) cell structures (spheroids) and investigates the conditions for apoptosis induction in 3D eMSCs. Detached from the monolayer culture, (2D) eMSCs accumulate Na+ and have dissipated transmembrane ion gradients, while in compact spheroids, eMSCs restore the lower Na+ content and the high K/Na ratio characteristic of functionally active cells. Organized as spheroids, eMSCs are non-proliferating cells with an active Na/K pump and a lower K+ content per g cell protein, which is typical for quiescent cells and a mean lower water content (lower hydration) in 3D eMSCs. Further, eMSCs in spheroids were used to evaluate the role of K+ depletion and cellular signaling context in the induction of apoptosis. In both 2D and 3D eMSCs, treatment with ouabain (1 µM) results in inhibition of pump-mediated K+ uptake and severe K+ depletion as well as disruption of the mitochondrial membrane potential. In 3D eMSCs (but not in 2D eMSCs), ouabain initiates apoptosis via the mitochondrial pathway. It is concluded that, when blocking the Na/K pump, cardiac glycosides prime mitochondria to apoptosis, and whether a cell enters the apoptotic pathway depends on the cell-specific signaling context, which includes the type of apoptotic protein expressed.
... These data indicate elevated pump-mediated K + transport in established senescent hMESCs. To determine whether the observed increase in pump activity is proportional to changes in intracellular Na + concentration, we compared pumping rate coefficients calculated as the ratio of ouabain-inhibitable Rb + uptake to intracellular Na + content during senescence development [35][36][37] . It turned out that the rate coefficients do not differ for early and late stressed cells. ...
... In the present study, by analogy with our previous experimental data when reliable measurements of K + , water and volume were carried out simultaneously on proliferating and resting cells in suspension 13,38,39 , relying on a theoretical analysis of ion and water balance in animal cells 5,35 , and also taking into account that K + is the main cation compensating intracellular anions we assume that the lower ratio of cell K + content to cell protein mass can be interpreted as lower water content in senescent hMESCs. To find out if this is really so, it is necessary to take reliable measurements of the volume of senescent cells. ...
Monovalent ions are involved in growth, proliferation, differentiation of cells as well as in their death. This work concerns the ion homeostasis during senescence induction in human mesenchymal endometrium stem/stromal cells (hMESCs): hMESCs subjected to oxidative stress (sublethal pulse of H2O2) enter the premature senescence accompanied by persistent DNA damage, irreversible cell cycle arrest, increased expression of the cell cycle inhibitors (p53, p21) cell hypertrophy, enhanced β-galactosidase activity. Using flame photometry to estimate K+, Na+ content and Rb+ (K+) fluxes we found that during the senescence development in stress-induced hMESCs, Na+/K+pump-mediated K+ fluxes are enhanced due to the increased Na+ content in senescent cells, while ouabain-resistant K+ fluxes remain unchanged. Senescence progression is accompanied by a peculiar decrease in the K+ content in cells from 800–900 to 500–600 µmol/g. Since cardiac glycosides are offered as selective agents for eliminating senescent cells, we investigated the effect of ouabain on ion homeostasis and viability of hMESCs and found that in both proliferating and senescent hMESCs, ouabain (1 nM–1 µM) inhibited pump-mediated K+ transport (ID50 5 × 10–8 M), decreased cell K+/Na+ ratio to 0.1–0.2, however did not induce apoptosis. Comparison of the effect of ouabain on hMESCs with the literature data on the selective cytotoxic effect of cardiac glycosides on senescent or cancer cells suggests the ion pump blockade and intracellular K+ depletion should be synergized with target apoptotic signal to induce the cell death.
... The mathematical model of the movement of monovalent ions across the cell membrane was like that used by Jakobsson [11], and Lew with colleagues [12][13][14], as well as in our previous works [8][9][10]15,16]. It accounts for the Na/K pump, electroconductive channels, cotransporters NC, KC, and NKCC. ...
... www.videleaf.com [15], the using of the executable file is illustrated more in [8]. The problems in determination of the multiple parameters in a system www.videleaf.com ...
... Changes in the rate coefficients inc and ikc have approximately the same effect as changes in pk, pna, and pcl, that is, they zero out the electrochemical gradients of monovalent ions generated by the sodium pump and decrease the membrane potential. They are antagonists of the pump [15,18]. This is not the case in an increase in inkcc rate coefficient which shifts the system to the ion distribution when the driving force for the transport of ions through the NKCC is close to zero. ...
... The mathematical model of the movement of monovalent ions across the cell membrane was like that used by Jakobsson (1980), and Lew with colleagues (Lew and Bookchin, 1986;Lew et al., 1991;Lew, 2000), as well as in our previous works (Vereninov et al., 2014;Vereninov et al., 2016;Yurinskaya et al., 2019;Yurinskaya et al., 2020;Yurinskaya and Vereninov, 2021a). It accounts for the Na/K pump, electroconductive channels, cotransporters NC, KC, and NKCC. ...
... Parameter characterizing a linear decrease of the pump rate coefficient β with time, min −1 respectively. The algorithm of the numerical solution of the system of these equations is considered in detail in (Vereninov et al., 2014), the using of the executable file is illustrated more in (Yurinskaya et al., 2019). The problems in determination of the multiple parameters in a system with multiple variables like cell ionic homeostasis are discussed in more detail in (Yurinskaya et al., 2019(Yurinskaya et al., , 2020. ...
... Changes in the rate coefficients inc and ikc have approximately the same effect as changes in pk, pna, and pcl, that is, they zero out the electrochemical gradients of monovalent ions generated by the sodium pump and decrease the membrane potential. They are antagonists of the pump (Vereninov et al., 2014;Dmitriev et al., 2019). This is not the case in an increase in inkcc rate coefficient which shifts the system to the ion distribution when the driving force for the transport of ions through the NKCC is close to zero. ...
Studying the transport of monovalent ions across the cell membrane in living cells is complicated by the strong interdependence of fluxes through parallel pathways and requires therefore computational analysis of the entire electrochemical system of the cell. Current paper shows how to calculate changes in the cell water balance and ion fluxes caused by changes in the membrane channels and transporters during a normal regulatory increase in cell volume in response to osmotic cell shrinkage (RVI) followed by a decrease in cell volume associated with apoptosis (AVD). Our recently developed software is used as a computational analysis tool and the established human lymphoid cells U937 are taken as an example of proliferating animal cells. It is found that, in contrast to countless statements in the literature that cell volume restoration requires the activation of certain ion channels and transporters, the cellular responses such as RVI and AVD can occur in an electrochemical system like U937 cells without any changes in the state of membrane channels or transporters. These responses depend on the types of chloride cotransporters in the membrane and differ in a hyperosmolar medium with additional sucrose and in a medium with additional NaCl. This finding is essential for the identification of the true changes in membrane channels and transporters responsible for RVI and AVD in living cells. It is determined which changes in membrane parameters predicted by computational analysis are consistent with experimental data obtained on living human lymphoid cells U937, Jurkat, and K562 and which are not. An essential part of the results is the developed software that allows researchers without programming experience to calculate the fluxes of monovalent ions via the main transmembrane pathways and electrochemical gradients that move ions across the membrane. The software is available for download. It is useful for studying the functional expression of the channels and transporters in living cells and understanding how the cell electrochemical system works.
... These data indicate elevated pump-mediated K + transport in established senescent hMESCs. To determine whether the observed increase in pump activity is proportional to changes in intracellular Na + concentration, we compared pumping rate coe cients calculated as the ratio of ouabain-inhibitable Rb + uptake to intracellular Na + content during senescence development [35][36][37] . It turned out that the rate coe cients do not differ for early and late stressed cells. ...
Monovalent ions are involved in growth, proliferation, differentiation of cells as well as in their death. This work concerns the ion homeostasis during senescence induction in human mesenchymal endometrium stem cells (hMESC): hMESCs subjected to oxidative stress (pulse H2O2 treatment) enter the premature senescence accompanied by persistent DNA damage, irreversible cell cycle arrest, cell hypertrophy, lipofuscin accumulation, enhanced β-galactosidase activity. Using flame photometry to estimate K+, Na+ content and Rb+ (K+) fluxes we found that during the senescence development in stress-induced hMESCs, Na+/K+pump-mediated K+ fluxes are enhanced due to the increased Na+ content in senescent cells, while ouabain-resistant K+ fluxes remain unchanged. Senescence progression is accompanied by a peculiar decrease in the K+ content in cells from 800-900 µmol/g to 500-600 µmol/g. Since cardiac glycosides are offered as selective agents for eliminating senescent cells, we investigated the effect of ouabain on ion homeostasis and viability of hMESCs and found that in both proliferating and senescent hMESCs, ouabain (1 nM-1 µM, 24-48 h) inhibited pump-mediated K+ transport (ID50 5x10-8 M), decreased cell K+/Na+ ratio to 0,1-0,2, however did not induce apoptosis. Comparison of the effect of ouabain on hMESCs with the literature data on the selective cytotoxic effect of cardiac glycosides on senescent or cancer cells suggests the ion pump blockade and intracellular K+ depletion should be synergized with target apoptotic signal to induce the cell death.
