Role of cation-chloride cotransporters, Na/K-pump, and channels in cell water/ionic balance regulation under hyperosmolar conditions: in silico and experimental studies of opposite RVI and AVD responses of U937 cells to hyperosmolar media

Abstract

The work provides a modern mathematical description of animal cell electrochemical system under a balanced state and during the transition caused by an increase in external osmolarity, considering all the main ionic pathways in the cell membrane: the sodium pump, K+, Na+, Cl- electroconductive channels and cotransporters NC, KC, and NKCC. The description is applied to experimental data obtained on U937 cells cultured in suspension, which allows the required assays to be performed, including determination of cell water content using buoyant density, cell ion content using flame photometry, and optical methods using flow cytometry. The study of these cells can serve as a useful model for understanding the general mechanisms of regulation of cellular water and ionic balance, which cannot be properly analyzed in many important practical cases, such as ischemic disturbance of cellular ionic and water balance, when cells cannot be isolated. An essential part of the results is the developed software supplied with an executable file, which allows researchers with no programming experience to calculate unidirectional fluxes of monovalent ions through separate pathways and ion-electrochemical gradients that move ions through them, which is important for studying the functional expression of channels and transporters. It is shown how the developed approach is used to reveal changes in channels and transporters underlying the RVI and AVD responses to the hyperosmolar medium in the studied living U937 cells.

Full text

Role of cation-chloride cotransporters, Na/K-pump, and channels in cell
water/ionic balance regulation under hyperosmolar conditions: in silico and
experimental studies of opposite RVI and AVD responses of U937 cells to
hyperosmolar media
Valentina E. Yurinskaya, and Alexey A. Vereninov*
Laboratory of Cell Physiology, Institute of Cytology, Russian Academy of Sciences, St-
Petersburg, Russia
Short: Cation-chloride cotransporters in RVI and AVD
Abstract
The work provides a modern mathematical description of animal cell electrochemical system
under a balanced state and during the transition caused by an increase in external osmolarity,
considering all the main ionic pathways in the cell membrane: the sodium pump, K+, Na+, Cl-
electroconductive channels and cotransporters NC, KC, and NKCC. The description is applied to
experimental data obtained on U937 cells cultured in suspension, which allows the required
assays to be performed, including determination of cell water content using buoyant density, cell
ion content using flame photometry, and optical methods using flow cytometry. The study of
these cells can serve as a useful model for understanding the general mechanisms of regulation
of cellular water and ionic balance, which cannot be properly analyzed in many important
practical cases, such as ischemic disturbance of cellular ionic and water balance, when cells
cannot be isolated. An essential part of the results is the developed software supplied with an
executable file, which allows researchers with no programming experience to calculate
unidirectional fluxes of monovalent ions through separate pathways and ion-electrochemical
gradients that move ions through them, which is important for studying the functional expression
of channels and transporters. It is shown how the developed approach is used to reveal changes
in channels and transporters underlying the RVI and AVD responses to the hyperosmolar
medium in the studied living U937 cells.
Keywords: cell ion homeostasis computation, cotransporters, ion channels, sodium pump, cell
volume regulation, regulatory volume increase, sodium potassium chloride fluxes
Introduction
Many processes at the physiological, proteomic, and genomic levels are triggered in cells already in the
first hour after the increase in the osmolarity of the external environment, which is often called "osmotic
stress" (Burg et al., 2007; Lambert et al., 2008; Hoffmann et al., 2009; Koivusalo et al., 2009; Wang et
al., 2014). Rapid osmotic shrinkage of cells is usually accompanied by a regulatory increase in volume,
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RVI, and, with some delay, an oppositely directed decrease in volume, AVD, which is associated with the
initiation of apoptosis (Yurinskaya et al., 2012). Monovalent ions redistribution mechanisms which cause
RVI and AVD remain insufficiently studied. There is no quantitative description of transient processes in
the cell electrochemical system caused by replacing the isoosmolar medium with a hyperosmolar
medium, which would consider, in addition to the sodium pump and electrically conductive channels, all
the main types of cation-chloride cotransporters. We tried to fill this gap using a mathematical analysis of
the complex interdependence of ion fluxes via the main pathways across the cell membrane and an
experimental study of living U937 cells included determination of cell water content by buoyant density,
cell ion content using flame photometry, and optical methods using flow cytometry. It is found by this
way that in U937 cells studied as example: (1) an effect like RVI can take place in hyperosmolar media
with addition of NaCl without changes in the membrane channels and transporters if certain cation-
chloride cotransporters present in the cell membrane, (2) time-dependent decrease in cell volume, such as
AVD, can occur in the hyperosmolar medium of sucrose without changes in membrane ion channels and
transporters; (3) the response of living cells to a hypoosmolar challenge is more complex than the
response of their electrochemical model due to regulation of transporters by intracellular signaling
mechanisms and due to changes in the content of intracellular impermeable osmolytes. These specific
effects are identified by eliminating the "physical" effects found by mathematical analysis of the entire
electrochemical system of the cell.
Materials and methods
Reagents
RPMI 1640 medium and fetal bovine serum (FBS, HyClone Standard) were purchased from
Biolot (Russia). Ouabain was from Sigma-Aldrich (Germany), Percoll was purchased from
Pharmacia (Sweden). The isotope 36Cl‾ was from “Isotope” (Russia). Salts and sucrose were of
analytical grade and were from Reachem (Russia).
Cell cultures and solutions
Lymphoid cell lines U937, K562, and Jurkat from the Russian Cell Culture Collection (Institute
of Cytology, Russian Academy of Sciences) were studied. The cells were cultured in RPMI 1640
medium supplemented with 10% FBS at 37 °C and 5% CO2 and subcultured every 2-3 days.
Cells with a culture density of approximately 1×106cells per ml were transferred to hyperosmolar
rmedium with addition of 100 mM NaCl or 150-300 mM sucrose for 0-4 h. A stock solution of 1
mM NaCl or 2 mM sucrose in PBS was used to add to the standard RPMI medium to prepare a
hyperosmolar medium. The osmolarity of solutions was checked with the Micro-osmometer
Model 3320 (Advanced Instruments, USA). All the incubations were done at 37 °C.
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Determination of cell water and ion content
Details of the experimental methods used were described in our previous study (Yurinskaya et
al., 2019-2021). Briefly, cell water content was estimated by the buoyant density of the cells in
continuous Percoll gradient, intracellular K+, Na+ and Rb+ content was determined by flame
emission on a Perkin-Elmer AA 306 spectrophotometer, the intracellular Cl‾ was measured using
a radiotracer 36Cl. The cell water content was calculated in ml per gram of protein as vprot = (1 −
ρ/ρdry)/[0.72(ρ − 1)], where ρ is the measured buoyant density of the cells and ρdry is the density
of the cell dry mass, the latter taken as 1.38 g/ml. The ratio of protein to dry mass was taken as
0.72. The cellular ion content was calculated in micromoles per gram of protein
Statistical analysis
Experimental data are presented as the mean ± SEM. P < 0.05 (Student’s t test) was considered
statistically significant. Statistical analysis for calculated data is not applicable.
The mathematical background of the modeling
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, Bookchin, 1986; Lew et
al. 1991; Lew, 2000), as well as in our previous works (Vereninov et al., 2014, 2016; Yurinskaya
et al., 2019, 2020, 2021). It accounts for the Na/K pump, electroconductive channels,
cotransporters NC, KC, and NKCC. NKCC indicates the known cotransporters of the SLC12
family carrying monovalent ions with stoichiometry 1Na+:1K+:2Cl‾ and KC and NC stand for
cotransporters with stoichiometry 1K+:1Cl‾ or 1Na+:1Cl‾. The latter can be represented by a
single protein, the thiazide-sensitive Na-Cl cotransporter (SLC12 family), or by coordinated
operation of the exchangers Na/H, SLC9, and Cl/HCO3, SLC26 (Garcia-Soto and Grinstein,
1990). In the considered approach, the entire set of ion transport systems is replaced by a
reduced number of ion pathways, determined thermodynamically, but not by their molecular
structure. All the major pathways are subdivided into five subtypes by ion-driving force: ion
channels, where the driving force is the transmembrane electrochemical potential difference for a
single ion species; NKCC, NC, and KC cotransporters, where the driving force is the sum of the
electrochemical potential differences for all partners; and the Na/K ATPase pump, where ion
movement against electrochemical gradient is energized by ATP hydrolysis. This makes it
possible to characterize the intrinsic properties of each pathway using a single rate coefficient.
The using the model with single parameters for characterization of each ion pathways is quite
sufficient for successful description of the homeostasis in real cells at a real accuracy of the
current experimental data.
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The basic equations are presented below. Symbols and definitions used are shown in Table 1.
Two mandatory conditions of macroscopic electroneutrality and osmotic balance:
0][][][  V
zA
ClKNa iii
ooooiii BClKNa
V
A
ClKNa ][][][][][][][ 
The flux equations:
}][/)][)exp(]([{( NKCCNCioiNa
iJJNagNauNaupV
dt
dNa 

}/][/)][)exp(]([{( KCNKCCioiK
iJJNagKuKupV
dt
dK 

}2/)][)exp(]([{( NKCCKCNCioCl
iJJJgCluClupV
dt
dCl 
The left-hand sides of these three equations represent the rates of change of cell ion content. The
right-hand sides express fluxes, where u is the dimensionless membrane potential related to the
absolute values of membrane potential U (mV), as U = uRT/F = 26.7u for 37 °C and
)exp(1 ug 
. The rate coefficients pNa, pK, pCl characterizing channel ion transfer are similar to
the Goldman’s coefficients. Fluxes JNC, JKC, JNKCC depend on internal and external ion
concentrations as
JNC= inc·([Na]o[Cl]o − [Na]i[Cl]i)
JKC = ikc·([K]o[Cl]o − [K]i[Cl]i)
JNKCC = inkcc·([Na]o[K]o[Cl]o[Cl]o − [Na]i[K]i[Cl]i[Cl]i)
Here inc, ikc, and inkcc are the rate coefficients for cotransporters.
The rate coefficient of the sodium pump (beta) was calculated as the ratio of the Na+
pump efflux to the cell Na+ content where the Na+ pump efflux was estimated by ouabain-
sensitive (OS) K+(Rb+) influx assuming proportions of [Rb]o and [K]o, respectively, and Na/K
pump flux stoichiometry of 3:2.
Transmembrane electrochemical potential differences for Na+, K+, and Cl– were calculated as:
ΔμNa =26.7·ln([Na]i /[Na]o)+U, ΔμK =26.7·ln([K]i /[K]o)+U, and ΔμCl =26.7·ln([Cl]i /[Cl]o)-U,
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, 2020). Some readers of our previous publications have expressed doubt
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that using our tool it is possible to obtain a unique set of parameters that provide an agreement
between experimental and calculated data. Our mathematical comments on this matter can be
found in Yurinskaya et al., 2019 (Notes Added in Response to SomeReaders).
The executable file of the BEZ02BC program used in this study with two auxiliary files is
presented in the Supplement. It differs slightly from our previous executable file BEZ01B by
replacing in the output table the columns prn, prk, prcl (time derivatives of concentrations) with
the columns naC, kC, and clC representing intracellular content of Na+, K+, and Cl‾.
Results
1. Rearrangement of cell ionic homeostasis in hyperosmolar media, calculated for a system
with different, but invariable in time, membrane parameters.
Earlier it was shown that the same balanced intracellular concentrations of Na+, K+, Cl-, the
content of cell water, and the coefficient of the pumping rate, as in the experiment, can be
obtained in model with several sets of cotransporters (Yurinskaya and Vereninov, 2021). Despite
the difficulties with increasing the number of parameters, the use of additional data on the action
of specific inhibitors allows one to determine the required parameters (Yurinskaya et al., 2019,
2020). It was found also that the living U937 cells of the same established line can differ in real
physiological experiment by the functional expression of cotransporters. For these reasons, in
studying cell response to an increase in external osmolarity several sets of cotransporters are
considered some of which have analogs among the living cells. The values of the permeability
coefficients of the Na+, K+, and Cl- channels corresponding to the balanced distribution of ions
inevitably differ depending on the chosen cotransporters. The electrical, electrochemical
potential differences and their derivatives also significantly differ depending on the specified
cotransporters (Table 2). This is an example of when cotransporters with electrically neutral ion
transport significantly affect the membrane potential in the system due to changes in the
intracellular ion concentration (see difference between “voltagenic” and “amperogenic“ ion
transfers in Stanton, 1983).
Figure 1 shows calculated transition to hyperosmolar media in cells with the identical
initial intracellular Na+, K+ , Cl- concentrations (38, 147, 45 mM, respectively), cell water
content, and the same sodium pump rate coefficient (0.039 min-1) but with different set of the
assigned cotransporters. Computation shows the new ionic homeostasis is established with time
both in sucrose (Figure 1A-D) and in NaCl hyperosmolar media (Figure 1G-J).
Mathematically, this follows from the feedback between the intracellular concentration of Na+
and the efflux of Na+ through the pump. The higher the intracellular Na+ concentration, the
greater the outflow of the pump with the same pumping rate beta, that is, with the same intrinsic
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pump properties. As soon as a new water balance is established, the volume of cells in a
hyperosmolar medium with additional 180 mM sucrose or 100 mM NaCl should be 0.63
(310/490) or 0.61 (310/510) of the volume in a medium with a normal osmolarity 310 mOsm.
This follows simply from the equation of osmotic balance, which is achieved much faster than
the ionic balance.
Computation shows how the transition to new cell water and ionic homeostasis can differ
in NaCl and sucrose hyperosmolar media, and how this difference can depend on the
cotransporters in the cell membrane (Figure 1A, G, Table 3). A time-dependent increase in cell
volume, like RVI in living cells, occurs in a hyperosmolar medium supplemented with NaCl
under appropriate conditions (V/Vinitial>1, marked in yellow in Table 3), while, in contrast, a
decrease in cell volume increase, AVD (RVD), occurs in sucrose hyperosmolar medium
(V/Vinitial<1, marked in blue in Table 3). Changes in cell volume are associated in all cases with
changes in the K+, Na+ and Cl- content of the corresponding sign. A new balanced state in the
hyperosmolar medium with sucrose is achieved due to the approximately equal exit of K+ and
Na+ from the cell. In the medium with 100 mM NaCl, changes in K+ and Na+, which underlie
RVI, differ significantly depending on the set cotransporters. In the NC model, K+ uptake plays a
major role in RVI, while in the NC+KC model, Na+ uptake dominates. When NKCC is present
in the membrane, RVI is associated with Na+ uptake and small K+ release (Table 3). It is
essential that in all cases the RVI-like effect in the hyperosmolar NaCl medium and the AVD-
like effect in the hyperosmolar sucrose medium do not require any “regulatory” changes in the
parameters of membrane channels and transporters. It is noteworthy that a significant RVI effect
in the hyperosmolar NaCl medium is observed only in the system without the NKCC
cotransporter (Table 3, Figure 1G). The difference in behavior of the cell ionic system in the
sucrose and NaCl hyperosmolar solutions occurs because we are dealing with charged but not
with electrically neutral osmolytes. Consideration of the model with the unchanged in time cell
membrane parameters shows that the changes in the electrochemical potential difference moving
K+, Na+ and Cl- via corresponding pathways can be a solely determinant of the kinetics of the ion
homeostasis rearrangement. The electrochemical potential differences for each of the ions, K+,
Na+ and Cl-, in cells placed into sucrose and into NaCl hypertonic media can change by different
way and even in the opposite directions as well as the magnitudes and signs of the forces driving
ions via the NC, KC and NKCC cotransporters (Figure 1E, F, K, L).
The direction of the force driving ions through the pathways of cotransporters determines
their role in the regulation of the ionic and water balance of the cell. 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
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and decrease the membrane potential. They are antagonists of the pump (Vereninov et al., 2014;
Dmitriev et al., 2021). 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. In cells such as U937, as well as in many other cells, when they are balanced
with the normal medium, the relationship between concentration ratio for K+, Na+ and Cl- on the
membrane correspond to zero driving force for the transport of ions through the NKCC (Figire
1). In this case NKCC cotransporter stabilizes the normal state of a cell. Variation in the rate
coefficient inkcc has no effect on the state of the electrochemical system of a normal cell. The
deviation of ion distribution from the standard generates non-zero NKCC which declines with
time to zero in the sucrose hyperosmolar medium but not in the NaCl hyperosmolar medium
(Figure 1). An increase in NKCC gradient generates the net fluxes of Na+, K+, and Cl– via
NKCC pathway. It looks like “activation” of NKCC transporter although the intrinsic properties
of cotransporter, i.e., rate coefficient in the model is not changed. The increase in the net fluxes
of K+, Na+ and Cl- via NKCC caused by an increase in the NKCC gradient is clearly seen if the
dynamic of the unidirectional and net fluxes is considered which is shown in Table 4. The
considered examples show that specific NKCC blockers like bumetanide and its analogues can
have no effect on the entire ion homeostasis in normal cells. However, it would be mistaken to
say that the NKCC is absent or “not-activated” and “silent”. The unidirectional fluxes via NKCC
pathway can be significant and presence of this cotransporter can be revealed for example by
measurement of the bumetanide-inhibitable Rb+ influx. The situation changes when a normal
medium is replaced with the hyperosmolar one, especially with the NaCl hyperosmolar medium.
The impact of the net fluxes of Na+, K+ and Cl- via NKCC in the total flux balance increases
significantly and inhibitors become effective.
Alteration of ionic homeostasis in hyperosmolar media is fully restored after the return of
cells into the medium of normal osmolarity. (Figures 1 and 2). The kinetics of the Iso-Hyper-Iso
transition, both direct and reverse, significantly depends on the set of cotransporters in the case
of a NaCl hyperosmolar solution. This occurs mostly because of the different basic pCl at
different cotransporters. At low pCl, the new balance is reached more slowly. We observed a
similar effect when modeling changes in ionic homeostasis due to blockage of the sodium pump
(Yurinskaya et al., 2019). The kinetics of the reverse Hyper-Iso transition for both sucrose and
NaCl cases is at first glance similar and copies that of the direct Iso-Hyper transition. However, a
more detailed analysis shows that there are certain differences between changes in the direct and
reverse direction, and between the cases of sucrose and NaCl hyperosmolar solutions (Figure 2).
As mentioned above, NKCC cotransport attenuates changes in homeostasis both in the
hyperosmolar medium with sucrose and with additional NaCl.
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2. Rearrangement of ionic homeostasis in hyperosmolar media at the simultaneous
alteration of channels and transportersin cell model like U937.
It is believed that specific changes in channels and transporters of the cell membrane are
responsible for the regulation of cell volume under anisosmolar conditions, which are triggered
by osmotic stress and can differ depending on the cell type (Hoffmann et al., 2009; Koivusalo et
al., 2009; Hoffmann and Pedersen, 2010; Lang and Hoffmann, 2012; Jentsch, 2016; Pasantes-
Morales, 2016; Delpire and Gagnon, 2018; Larsen and Hoffmann, 2020). This concept is based
mostly on the studies of the effects of inhibitors and genetic cell modifications. Calculation of
ionic homeostasis can provide a rational and more rigorous solution to the question of what
changes in channels and transporters could underly the observed changes in ionic homeostasis
under anisosmolar conditions. The parameters considered below as significant for RVI or AVD
were determined in the simulation itself and taking into account opinions in the literature.
2.1. Effect of NC cotransporter and Cl- channels.
Lew and Bookchin studying human reticulocytes were the first who showed that Na+ and Cl-
coupled transport across the cell membrane (NC) is an indispensable in quantitative description
of the monovalent ion flux balance in cell (Lew et al., 1991). Analysis of the balance of ion
fluxes in the main types of animal cells: the cells with low and high membrane potential and with
high and low potassium content, led us to the conclusion that the K+/Na+ ratio and membrane
potential depend primarily on the ratio of the Na+ and K+ channels permeability to the rate
coefficient of the sodium pump, while the water content in the cell and intracellular Cl- is mainly
determined by the cotransporters and the permeability of the Cl- channels (Vereninov et al.,
2014; Yurinskaya et al., 2019; see also Jentsch, 2016; Dmitriev et al., 2019). NC cotransport in
ionic homeostasis in U937 cells and, as we believe, in proliferating cells of a similar type, is the
most important driver for active transport of Cl– into cells and generation of a difference in
electrochemical potential of Cl– on the plasma membrane. A 3-fold increase in inc in the U937
cell model under standard isosmolar conditions increases the water content in cells from 12.5 to
19.64 ml/mmol A, and a 0.2-fold decrease decreases to 10.2 ml/mmol A (Figure 3A).
Small RVI occurs in a hyperosmolar NaCl medium even without any changes in inc or
other membrane parameters. An increase in inc increases the RVI, while a decrease, on the
contrary, causes a decrease in volume, like AVD. An increase in inc by about 5 times returns cell
volume in the NaCl hyperosmolar medium to its level in the standard medium (Figure 3E). The
effect of increasing inc in the sucrose hyperosmolar medium differs significantly from that in the
NaCl hyperosmolar medium. A decrease in cell volume instead of an increase occurs in the
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sucrose hyperosmolar medium without changing inc (Figure 3I, Table 6). RVI can be obtained
in the sucrose hyperosmolar only at a very significant increasing inc of about 10-50 times
(Figure 3I, Table 6). The difference in the effects of inc in the hyperosmolar media with
addition of sucrose and NaCl is due to the difference in changes of the electrochemical potential
difference driving ions via NC pathway in the compared cases (Figure 1F, L).
The Cl- channels and KC cotransporter in cells like U937 are the main antagonists of NC
cotransporterbecause this is a significant pathway for the net Cl- flux down electrochemical
gradient (Table 4, yellow lines “Before”). The pair NC cotransporter-Cl- channels is a powerful
regulator of the cell water balance. This is since active transport of Cl- into the cell via NC,
which increases its intracellular concentration above the equilibrium level, is equivalent to an
increase in the amount of internally sequestered Donnan anions which causes an increase in the
water content in the cell. In the considered U937 cell model the effect of pCl variation on ion
homeostasis is less significant than the effect of NC. For example, the 10-fold decrease of pCl
causes an increase in cell volume by a factor 1.18 (from 12.5 to 14.83 ml/mmol A, Figure 3M)
in the standard medium and, respectively, 1.09 (from 7.6 to 8.32 ml/mmol A) in hyperosmolar
medium with the addition of 100 mM NaCl (Figure 3Q). The 3-fold increase in NC rate
coefficient turns out to be stronger than 10-fold decrease in the permeability of Cl- channels.
This is because there are other pathways for downhill movement of Cl- besides channels in the
cells like U937. The channel part of the Cl- downhill net flux is only about half; the other half is
the flux through the KC pathway and about 0.6 % is the flux through the NKCC cotransporter
(Table 4, yellow lines “Before”).
2.2. Effect of NKCC and KC cotransporters (ikc, inkcc).
The specifically weak effect of NKCC on ion homeostasis of cells balanced with the normal
medium was discussed in the previous section.This is due to a small integral electrochemical
difference driving ions via NKCC under normal conditions. Accordingly, the net fluxes of K+,
Na+ and Cl- via NKCC in cells like U937 balanced with normal isosmolar medium are small and
increase when cells are transferred into the hyperosmolar medium (Table 4, compare the lines
“Before” marked in yellow with lines marked in green). Changes in inkcc, simultaneously with
an increase in external osmolarity, change both the dynamics of the transition and homeostasis in
a new state of balance in a hyperosmolar medium with the addition of NaCl, but not in a sucrose
medium (Figure 4). However, even in the NaCl hyperosmolar medium, a 10-fold increasing or
decreasing inkcc affects the new balanced cell volume by no more than 1.16 times. A decrease in
inkcc by a factor 0.1 causes RVI in the NaCl hyperosmolar medium, while its increase causes
volume decrease like AVD. A decrease in the KC rate coefficient, ikc, affects the water balance
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in NaCl hyperosmotic medium in a similar way as NKCC, but its effect on membrane potential
is stronger than that of NKCC (Figure 4I, J).
2.3. Effect of Na+ channels and non-selective hypertonicity-induced cation channels, HICC.
In view of the experimental data indicating that Na+ channels and the channels known as HICC
(Wehner et al., 2003, 2006; Plettenberg et al., 2008) in some cell types can play a role in RVI
(Hoffmann et al., 2009) the possible effects of these channels were examined in U937 cell
model. The Na+, K+ non-selective channels HICC were mimicked by increasing pNa 10 times
with simultaneous increasing pK 1.6 times. This is equivalent to the addition of the HICC in an
amount 1.6 times higher than the standard number of K+ channels. It turned out that an increase
in pNa upon transition to a hyperosmolar medium causes RVI in the considered system, but only
in a hyperosmolar medium with the addition of NaCl (Figure 5). No RVI occurs in case of the
medium with 180 mM sucrose. An increase in pNa in cells placed in a standard 310 mOsm
medium causes a much greater increase in cell volume than in a hyperosmolar medium with
additional NaCl under the same conditions. The effect of increasing pNa alone is attenuated in
case of HICC which include increasing pK. This is due to the opposite effect of changes in pNa
and pK on ionic homeostasis.
The examples in Figures 3-5 demonstrate which changes in membrane channels and
transporters of the cell in a hyperosmolar medium can be associated with RVI, and which, on the
contrary, with AVD. Table 5 summarizes the main differences associated with changes in the
new balanced state in hyperosmolar media under various conditions. One of the intuitively
unpredictable points is that the same changes in channels and transporters, for example, a
decrease in ikc or pCl, can cause RVI (marked in yellow in Table 5) in a hyperosmolar medium
with added NaCl and oppositely directed AVD (marked in blue) in a hyperosmolar medium with
sucrose. It turned out that in cells such as U937, there is only one way to obtain RVI in the
hyperosmolar medium with sucrose by changing the membrane parameters. This is an increase
in parameter inc. There are more variants in the hyperosmolar medium with added NaCl. One of
the intuitively unpredicted points is that the balanced state in hyperosmolar medium with added
NaCl is associated mostly with an increase in cell Na+ content whereas K+ content decreases.
The only exception is when the RVI is caused by a strong decrease in the rate coefficient ikc. In
the hyperosmolar sucrose medium, the balanced state of cells is characterized, for the most part,
by a stronger decrease in the Na+ content than in K+. Only an increase in inc, HICC and a
decrease in Pump beta cause a stronger decrease in K+ and an increase in the Na+ content in the
balanced state.
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3. Changes in water and ionic balance in living cells such as U937 in a hyperosmolar media.
Dual responseoflivingcellsto hyperosmolar challenge.
The response of living cells to transfer in hyperosmolar medium is more complicated than in the
electrochemical model since the properties of membrane channels and transporters can be
changed by physically unpredictable way through the intracellular signaling network. Cell
shrinkage in hyperosmolar medium triggers two complex general cellular responses, which are
characterized by the opposite direction of volume change and develop with a shift in time
(Yurinskaya et al., 2011, 2012, 2017). This is the AVD associated with apoptosis (Okada et al.,
2001), and the oppositely directed RVI, which precedes the AVD (Yurinskaya et al., 2012). In
our experience, the analysis of the distribution of cells in the density gradient is the best method
for separating the primary rapid physical decrease in the volume of cells in the hyperosmolar
environment and the specific processes of RVI and AVD (Figure 6). Due to the time shift, RVI
and AVD can be observed on the same sample of cells. An essential detail is that the transition
from RVI to AVD in the cell population manifests itself as a change in the ratio between the
number of cells in the RVI and AVD stages. The number of RVI cells decreases over time and
the number of AVD cells increases (Figure 6M). This indicates that the transition from RVI to
AVD in each cell is fast. Ionic changes underlying RVI and AVD in hyperosmolar media,
obtained on K562, Jurkat, and U937 cells in another separate series of experiments, where all
these cell types were studied simultaneously, are presented in Figure 7 and Table 6.
The RVI and AVD mechanisms are discussed in more detail below, considering
computer simulations of the system and data related to U937 cells (Yurinskaya et al., 2011,
2012, 2017). In the experiments shown in Figure 6, the mean values of ions and water during the
first 2 hours characterize mainly cells at the RVI stage. At the time point 4 h the light, RVI, and
heavy, AVD, subpopulations could be analyzed separately. According to modeling in a
hyperosmolar medium with sucrose, RVI in U937 cells is possible only with an increase in the
coefficient inc (Table 5). This should be associated with an increase in the intracellular content
of Na+ and Cl- and a slight change in the content of K+. It is these changes in the content of Na+
and K+ that were observed in experiments with U937 cells for a light subpopulation of RVI in a
hyperosmolar medium with sucrose (Figure 6E, Table 6). The key role of the NC cotransporter
in RVI is independently confirmed by the blocking effect of the combination of
dimethylamiloride, a known inhibitor of Na/H exchanger, and DIDS, which inhibits the Cl/HCO3
exchanger (Figure 6N, O). In hyperosmolar medium with addition NaCl an increase in inc or a
decrease in ikc, inkcc, pCl or appearance of channels HICC increases RVI (Figures 3E, O, 4A,
I, Table 5). In all these cases, RVI is associated with an increase in the total content of K+ and
Na+, but the relative changes in the content of K+ and Na+ depend on which parameter changes.
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In living U937 cells, RVI in a hyperosmolar medium with the addition of NaCl is small, the
content of K+ and Na+ changes insignificantly (Figure 6A, D). However, the available data are
insufficient to differentiate the mechanism of RVI in these cases in more detail.
In experiments where cells U937, K562, and Jurkat were studied in parallel in
hyperosmolar medium with 200 mM sucrose for 4 h the certain differences between cell species
were revealed (Table 6, Figure 7). RVI at the time point 4 h was rather small but differences in
K+ and Na+ content in K562, Jurkat and U937 cells were significant. Further research is needed
to better understand these cell-species differences.
AVD in living U937 cells incubated in a hyperosmolar sucrose medium is slightly
stronger than in a medium with additional NaCl of almost the same osmolarity. In both cases,
AVD is associated with a significant decrease in the K+ content in cells, while the Na+ content in
cells increases in a hyperosmolar NaCl medium and changes insignificantly in a sucrose
medium. This agrees with the model prediction. It was shown earlier that a decline in ouabain-
inhibitable Rb+ (K+) influx due to a decrease in the pump rate coefficient, beta, plays significant
role in AVD during apoptosis of U937 cells induced with staurosporine (Yurinskaya et al., 2019,
2020). AVD in U937 in hyperosmolar media in experiment described in the present article is
also associated with a decrease in the OS Rb+ influx whereas the decline in OR influx is much
less (Figure 6G-L, H-AVD subpopulation). Comparison of the changes in OS Rb+ influx with
the changes in concentration of Na+ in cell water indicates that a decline in the pump Rb+ influx
manifests mostly the changes in the pump rate coefficient, i.e., in intrinsic pump properties.
There are no significant changes in the in OS Rb+ influx and the pump rate coefficient in cells of
the light subpopulations in 100 mM NaCl and 200 mM sucrose hyperosmolar media (Figure 6G,
H, J, K; L-RVI subpopulation).
Discussion
This work continues our studies aimed at developing a modern mathematical description of a
complex interrelationship of monovalent ion fluxes via all main parallel pathways across the cell
membrane, including all cation-chloride cotransporters, which all together determine the entire
water and ion balance in animal cell. Earlier this mathematical description was applied to cases
of blockage of the Na/K pump (Vereninov et al., 2014, 2016; Yurinskaya et al., 2019,
Yurinskaya and Vereninov, 2021), apoptosis (Yurinskaya et al., 2019, 2020), and the response to
hypoosmolar stress (Yurinskaya and Vereninov, 2021). Now it is used to analyze the cellular
response to hyperosmolar stress, during which two opposite effects of this stress on water
balance, RVI and AVD, occur in the same cells, following each other with a delay.
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As in the pioneering fundamental works (Jakobsson, 1981; Lew, Bookchin 1986; Lew et
al., 1991; Lew, 2000), our description is based on the classification of ion transport pathways
according to the acting driving forces and the type of coupling of the fluxes of various ions and
on characterization of the kinetics of ion transfer using a single rate coefficient. This makes the
description independent of the specific molecular mechanism of ion movement via channels and
transporters. Only such a holistic approach enables quantitative analysis and allows to predict
real changes in cell ion and water balance and electrochemical ion gradients on the cell
membrane. Due to complex interdependence of ion fluxes related to parallel pathways the
individual unidirectional fluxes along the separate channels or transporter usually cannot be
measured directly. They must be calculated considering all fluxes in the cell. Since we cannot
measure individual fluxes, we had to use alternative approach to validateof the mathematical
description. The validation was based on the analysis of the cell system dynamics by stopping
sodium pump. Calculation of the unidirectional fluxes is important for studying the functional
expression of separate channels and transporters using specific inhibitors because enables to
determine when the use of inhibitors can reveal fluxes related to specific channels or
transporters, and when not, due to masking by fluxes across parallel pathways.
Our description is applied to experimental data obtained from U937 cells cultured in
suspension, which allows a wide range of assays to be used without cell change caused by
isolation, and includes cell water determination using buoyant density, cell ions using flame
photometry, and optical methods using flow cytometry. In recent years, in neurobiology and
other fields, there has been a growing interest in disorders of ionic and water homeostasis of cells
(Dijkstra et al.., 2016; Pasantes-Morales, 2016; Casula et al., 2017; Wilson and Mongin, 2018;
Bortner and Cidlowski, 2020; Van Putten et al., 2021). However, in many cases of practical
importance cells cannot be isolated for proper assays. Therefore, U937 cells can serve a useful
model for understanding the general mechanisms of cell water and ionic balance regulation.
An essential part of the results is a developed software supplied with executable file that
allows one to determine the role of each type of cotransporters or channel in the regulation of the
ionic and water balance of cells in the context of the cell type and actual conditions. The variety
of the effects caused by changing channels and transporters is vast, even for one type of cells, as
shown by the example of U937 cells demonstrated in previous and present studies.Even the
limited number of examples selected to illustrate our approach took up a lot of space.It is clear
that serious research in this area is impossible without calculating a specific system.
Computation of the possible changes in ionic and water balance in the U937 cell model
specifically in hyperosmolar media has revealed many interesting and, at first glance, unexpected
things. (1) An AVD-like effect can occur in a sucrose-supplemented hyperosmolar medium and an RVI-
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like effect in a NaCl-supplemented hyperosmolar medium without altering membrane channels and
transporters due to time-dependent changes in the forces moving monovalent ions across the cell
membrane. It is noteworthy that this is observed only with some types of cotransporters. (2) Changes in
the cell membrane potential in hyperosmolar media of both types significantly depend on the set of
cotransporters, despite their "electroneutrality", as predicted by more general considerations (Stanton,
1983). (3) The sign of the forces driving ions through the NC, KC, and NKCC cotransporters under
certain conditions is of paramount importance for the role of these cotransporters in the regulation of the
ionic and water balance of the cell during RVI and AVD. Simulation draws attention to the analysis of
changes in driving forces in addition to changes in channel and transporters properties.
Study of living U937 cells shows that RVI and AVD responses to the hyperosmolar
medium are caused not only by changes in ion channels and transporters but, in addition, by the
redistribution of organic osmolytes, regulated by signals from the intracellular signaling network.
A similar redistribution of organic osmolytes has been shown for many other cells (see reviews:
Kirk, 1997; Lambert et al., 2008; Hoffmann et al., 2009; Koivusalo et al., 2009; Pasantes-
Morales, 2016). Modeling can tell nothing about which intracellular signals change channels and
transporters or change the intracellular content of impermeant osmolytes or their
charge.However, it is possible to recognize and estimate quantitatively the alteration of
executing mechanisms regulating cell ion and water balance.
In the case of living cells, such as U937, when the required minimum of experimental
data for calculations is available, our results show that RVI in a hyperosmolar medium with
sucrose is possible only due to an increase in the coefficient inc. In this case, RVI should be
associated with an increase in the intracellular content of Na+ and Cl- and a slight change in the
content of K+. It is these changes in the content of Na+ and K+ that were observed in experiments
with U937 cells for a light subpopulation of RVI in a hyperosmolar medium with 200 mM
sucrose. The key role of the NC cotransporter in RVI is independently confirmed by the blocking
effect of the combination of dimethylamiloride, a known inhibitor of Na/H exchange, and DIDS,
which inhibits the Cl/HCO3 exchange.
In a hyperosmolar medium with the addition of NaCl, a slight increase in cell volume
with time, like RVI, can occur in accordance with modeling even without changing the
membrane parameters in a cell with NC or NC+KC cotransporters, but without NKCC. In this
medium, an increase in inc or a decrease in ikc, inkcc, pCl or appearance of channels HICC
increases RVI.In all these cases, RVI is associated with an increase in the total content of K+ and
Na+, but the relative changes in the content of K+ and Na+ depend on which parameter
changes.Living U937 cells in a hyperosmolar medium supplemented with NaCl show a small
RVI and insignificant changes in the content of K+ and Na+. However, the available data are
insufficient to differentiate in more detail the mechanism of RVI in these cases.
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The AVD response demonstrated by a heavy subpopulation of living U937 cells
incubated in a hyperosmolar medium with sucrose is slightly stronger than in a medium
supplemented with NaCl of almost the same osmolarity.In both cases, AVD is associated with a
significant decrease in the K+ content in cells, while the Na+ content in cells increases in a
hyperosmotic NaCl medium and changes insignificantly in a sucrose-containing medium. This is
consistent with the prediction of the model.It was shown earlier that a decrease in the ouabain-
inhibited Rb+ (K+) influx due to a decrease in the pumping rate coefficient beta plays an
important role in AVD during apoptosis of U937 cells induced by staurosporine (Yurinskaya et
al., 2019, 2020). AVD in U937 in hyperosmolar media in the experiments described in the
present article is also associated with a decline in the pump Rb+ influx due to mostly the changes
in the pump rate coefficient, i.e., in intrinsic pump properties. No significant changes in the OS
Rb+ influx and the pump rate coefficient were observed in cells of the light subpopulations in
100 mM NaCl and 200 mM sucrose hyperosmolar media demonstrating the RVI response.
The main conclusion of this study, which demonstrates an example of analysis of the
mechanism of the RVI and AVD responses to hyperosmolar stress of cells such as U937, is that
computer calculations are an indispensable tool for studying mechanisms not only of RVI and
AVD, but all phenomena associated with the regulation of the entire electrochemical system of
the cell.
DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article/Supplementary
Material, further inquiries can be directed to the corresponding author.
AUTHOR CONTRIBUTIONS
Both authors contributed to the design of the experiments, performed the experiments, analyzed
the data, and approved the final version of the manuscript and agreed to be accountable for all
aspects of the work. Both persons designated as authors qualify for authorship.
FUNDING
The research was supported by the State assignment of Russian Federation No. 0124-2019-0003
and by a grant from the Director of the Institute of Cytology of RAS. The cells for this study
were obtained from the shared research facility “Vertebrate cell culture collection” supported by
the Ministry of Science and Higher Education of the Russian Federation (Agreement №075-15-
2021-683).
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ACKNOWLEDGMENTS
We are grateful to Dr. Igor A. Vereninov for correcting the manuscript and suggestions for
improvement. Our thanks to Igor Raikov, a student of the Alferov Federal State Academic
University RAS, Russia, for checking the use of the BEZ02BC file on a 32-bit computer.
SUPPLEMENTARY MATERIAL
Executable file to the programme code BEZ02BC and Instruction: How to use programme code
BEZ02BC.doc are attached to the article electronic version.
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Conflict of Interest: The authors declare that the research was conducted in the absence of any
commercial or financial relationships that could be construed as a potential conflict of interest.
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Table 1. Symbols and definitions
Symbols in software
Symbols in text
Definitions and units
Na, K, Cl
Na+, K+, Cl–, Rb+
Ion species
NC, NKCC, KC
Types of cotransporters
na, k, cl, na0, k0, cl0
[Na]i , [K]i , [Cl]i
[Na]o , [K]o , [Cl]o
Concentration of ions in cell water or external medium, mM
naC, kC, clC
Nai, Ki , Cli
Content of ions in cell per unit of A, mmolmol-1
B0
[B]0
External concentrations of membrane-impermeant non-electrolytes
such as mannitol introduced sometimes in artificial media, mM
A
A
Intracellular content of membrane-impermeant osmolytes, mmol,
may be related to g cell protein or cell number, etc.
V
V
Cell water volume, ml, may be related to g cell protein or cell
number, etc.
A/V*1000
Membrane-impermeant osmolyte concentration in cell water, mM
V/A
Cell water content per unit of A, mlmmol-1
z
z
Mean valence of membrane-impermeant osmolytes A,
dimensionless
pna, pk, pcl
pNa, pK, pCl; pNa,
pK, pCl
Permeability coefficients, min-1
beta
β
Pump rate coefficient, min-1
gamma
γ
Na/K pump flux stoichiometry, dimensionless
U
U
Membrane potential, MP, mV
u
Dimensionless membrane potential U = uRT/F, dimensionless
NC, KC, NKCC
JNC, JNKCC, JKC
Net fluxes mediated by cotransport, µmolmin-1 (ml cell water)-1
PUMP
-β[Na]i
Na efflux via the pump, µmolmin-1 (ml cell water)-1
PUMP
β[Na]i/γ
K influx via the pump, µmolmin-1 (ml cell water)-1
Channel
Net fluxes mediated by channels, µmolmin-1 (ml cell water)-1
IChannel, INC, IKC,
INKCC
Unidirectional influxes of Na, K or Cl via channels or cotransport,
µmolmin-1 (ml cell water)-1
EChannel, ENC,
EKC, ENKCC
Unidirectional effluxes of Na, K, or Cl via channels, or
cotransport, µmolmin-1 (ml cell water)-1
inc, ikc
inc, ikc
NC, KC cotransport rate coefficients, mlµmol-1min-1
inkcc
inkcc
NKCC cotransport rate coefficients, ml3µmol-3min-1
kv
Ratio of “new” to “old” media osmolarity when the external
osmolarity is changed, dimensionless
hp
Number of time points between output of results, dimensionless
mun, muk, mucl
ΔμNa, ΔμK, ΔμCl
Transmembrane electrochemical potential difference for Na+, K+,
or Cl–, mV
OSOR
OSOR
Ratio of ouabain-sensitive to ouabain-resistant Rb+ (K+) influx,
dimensionless
kb
Parameter characterizing a linear decrease of the pump rate
coefficient β with time, min-1
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Table 2. Basic characteristics of ion distribution, measured in living U937 cells equilibrated with
a normal isotonic medium RPMI, and computed for models with different sets of parameters.
Measured characteristics in normal RPMI medium
[K]i 147, [Na]i 38, [Cl]i 45, Az 80 mM,
V/A 12.5 ml/mmol, Beta 0.039 min-1, OSOR 3.89, z -1.75
Cotransporters assigned for balanced state in normal medium
NC
NC+KC
NC+NKCC
NC+KC+NKCC
inc
3E-5
4.87E-5
3E-5
7E-5
ikc
–
6E-5
–
8E-5
inkcc
–
–
7E-9
8E-9
Parameters computed for balanced state in normal medium
pna
0.00382
0.00263
0.0043
0.0017
pk
0.02200
0.0165
0.0175
0.0115
pcl
0.00910
0.006
0.0139
0.011
Computed characteristics in normal medium, mV
U
-44.7
-49.3
-37.6
-45.0
mucl
+19.4
+24.0
+12.3
+19.8
mun
-79.5
-84.1
-72.4
-79.9
muk
+41.6
+37.0
+48.7
+41.3
Data related to the sample of the living cells U937 described in our 2021 article as Cells B are
used as an example in this study.
Table 3. Changes in ionic homeostasis under new balanced state in hyperosmolar media with
100 mM NaCl or 180 mM sucrose, calculated for the U937 cell model with different sets of
cotransporters and parameters corresponding to cells balanced with normal 310 mOsm medium.
Cotransporter
UIso
UHyper
V/A
V/Vinitial
Ion concentration, mM
Content, mol/mol A
Difference in content
for 4 h and initial
mV
ml/mmol
RVI, AVD
[Na+]i
[K+]i
[Cl–]i
Na+
K+
Cl–
Na+
K+
Cl–
In normal 310 mOsm medium, experimental data for U937 cells
45.0
12.5
38
147
45
0.48
1.84
0.56
Initial in hyperosmolar medium with 100 mM NaCl, by basic osmotic equations
-47.0
7.60
62
242
74
0.47
1.84
0.56
Balanced in hyperosmolar medium with 100 mM NaCl, by computation
(K, Na, Cl uptake, exit)
NC
44.7
-39.5
9.98
1.31
74
218
117
0.74
2.18
1.17
+0.27
+0.34
+0.61
NC+KC
49.3
-48.3
8.99
1.18
87
210
102
0.77
1.89
0.92
+0.30
+0.05
+0.36
NC+ NKCC
37.6
-38.3
7.87
1.03
74
229
80.4
0.58
1.80
0.63
+0.11
-0.04
+0.07
NC+KC+NKCC
45.0
-49.0
7.78
1.02
91
212
78.3
0.71
1.65
0.61
+0.24
-0.04
+0.07
Initial in hyperosmolar medium with180 mM sucrose:
NC+KC+NKCC
-46.3
7.90
0.63
60
232
71
0.47
1.83
0.56
Balanced in hyperosmolar medium with 180 mM sucrose, by computation
(K, Na, Cl exit)
NC
44.7
-60.1
6.46
0.82
45
258
32
0.29
1.67
0.21
-0.18
-0.16
-0.35
NC+KC
49.3
-66.1
6.37
0.81
44
260
29
0.28
1.66
0.19
-0.19
-0.17
-0.37
NC+NKCC
37.6
-53.1
6.39
0.81
46
258
30
0.29
1.65
0.19
-0.18
-0.18
-0.37
NC+KC+NKCC
45.0
-62.9
6.36
0.81
43
261
29
0.27
1.66
0.19
-0.20
-0.17
-0.37
UIso and UHyper are membrane potentials of U937 cells balanced with iso- and hypertonic media,
respectively. V/Vinitial is the ratio of balanced V to the initial in a hyperosmolar medium. Other
symbols and definitions are given in Table 1. The columns "Difference in content for 4 h and
initial" show changes in the content of Na+, K+ and Cl- in cells, balanced in a hyperosmolar
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medium, compared with the initial in hyperosmolar media. RVI and ion uptake are marked in
yellow, AVD and ion exit are marked in blue.
Table 4. Dynamics of the net and unidirectional K+, Na+, and Cl– fluxes in U937 cells during
transition Iso-Hyper (+100 NaCl) calculated for the modelwith all main cotransporters and
parameters like in cells U937 equilibrated with standard 310 mOsm medium.
Ion
Incubation
time
in +NaCl
medium, min

mV
Net
fluxes,
total
Unidirectional fluxes
Net fluxes
Influxes
Effluxes
K+
PUMP
IChannel
IKC
INKCC
EChannel
PUMP
EKC
ENKCC
PUMP
Channel
KC
NKCC
Before
41.3
0.0000
0.9880
0.1381
0.0538
0.0874
-0.6477
--
-0.5291
-0.0905
0.9880
-0.5096
-0.4653
-0.0031
10
51.3
-0.5606
1.8993
0.1418
0.1002
0.5196
-0.9682
--
-1.4357
-0.8176
1.8993
-0.8264
-1.3355
-0.2980
30
49.4
-0.3087
2.1698
0.1430
0.1002
0.5196
-0.9084
--
-1.4002
-0.9327
2.1698
-0.7654
-1.3000
-0.4131
48
48.4
-0.1688
2.2717
0.1440
0.1002
0.5196
-0.8810
--
-1.3708
-0.9526
2.2717
-0.7370
-1.2706
-0.4330
120
47.3
-0.0117
2.3565
0.1455
0.1002
0.5196
-0.8537
--
-1.3328
-0.9470
2.3565
-0.7082
-1.2326
-0.4274
240
47.2
-0.0002
2.3613
0.1456
0.1002
0.5196
-0.8518
--
-1.3297
-0.9453
2.3613
-0.7062
-1.2295
-0.4257
Na+
IChannel
INC
PUMP
INKCC
PUMP
ENC
EChannel
ENKCC
PUMP
Channel
NC
NKCC
Before
-79.9
0.0000
0.4927
1.1368
--
0.0874
-1.4820
-0.1197
-0.0248
-0.0905
-1.4820
0.4679
1.0171
-0.0031
10
-78.8
0.9052
0.8673
3.6288
--
0.5196
-2.8489
-0.3986
-0.0454
-0.8176
-2.8489
0.8219
3.2302
-0.2980
30
-75.8
0.3138
0.8747
3.6288
--
0.5196
-3.2547
-0.4663
-0.0511
-0.9327
-3.2547
0.8236
3.1625
-0.4131
48
-75.1
0.1300
0.8811
3.6288
--
0.5196
-3.4076
-0.4864
-0.0528
-0.9526
-3.4076
0.8283
3.1424
-0.4330
120
-74.9
0.0050
0.8897
3.6288
--
0.5196
-3.5348
-0.4974
-0.0538
-0.9470
-3.5348
0.8359
3.1314
-0.4274
240
-74.9
0.0001
0.8904
3.6288
--
0.5196
-3.5420
-0.4976
-0.0539
-0.9453
-3.5420
0.8365
3.1312
-0.4257
Cl-
IChannel
INC
IKC
INKCC
EChannel
ENC
EKC
ENKCC
Channel
KC
NC
NKCC
Before
19.8
0.0000
0.4889
1.1368
0.0538
0.1748
-1.0246
-0.1197
-0.5291
-0.1809
-0.5357
-0.4653
1.0171
-0.0062
10
19.8
0.3446
0.8689
3.6288
0.1002
1.0391
-1.8229
-0.3986
-1.4357
-1.6352
-0.9540
-1.3355
3.2302
-0.5960
30
21.0
0.0099
0.8559
3.6288
0.1002
1.0391
-1.8823
-0.4663
-1.4002
-1.8653
-1.0264
-1.3000
3.1625
-0.8262
48
21.5
-0.0387
0.8448
3.6288
0.1002
1.0391
-1.8892
-0.4864
-1.3708
-1.9052
-1.0444
-1.2706
3.1424
-0.8560
120
21.8
-0.0067
0.8300
3.6288
0.1002
1.0391
-1.8806
-0.4974
-1.3328
-1.8940
-1.0506
-1.2326
3.1314
-0.8548
240
21.9
0.0000
0.8288
3.6288
0.1002
1.0391
-1.8791
-0.4976
-1.3297
-1.8906
-1.0503
-1.2295
3.1312
-0.8514
The “Before” lines, marked in yellow, represent the balance state in a normal medium. The lines
marked in green represent the initial values in the hyperosmolar medium. Parameters for the
hypertonic medium are as follows, in mM: na0 240, k0 5.8, cl0 216, B0 48.2; kv 1.645. Other
parameters remain unchanged and given in Table 2.
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Table 5. Dependence of RVI and AVD in the U937 cell model on the rate coefficients inc, ikc,
inkcc, pCl, the permeability coefficient of the HICC channel (pNa+pK), and pump

rate
coefficient

changing simultaneously with an increase in external osmolarity. Other parameters
remain unchanged. The calculation was carried out for a model with all cotransporters. hp = 240
in all cases except hp=800 for Pump

The RVI effect is marked in yellow, the AVD effect is
marked in blue.
Parameters
Concentration, mM
Content, mmol/mol A
V/A,
ml/mmol
V/Vinitial
RVI, AVD
Ion content ratio for RVI, AVD
Na
K
Cl
Na
K
Cl
Na+K
NaH/NaIso
KH/KIso
ClH/ClIso
Standard
Balanced in standard 310 mOsm medium
38
147
45
475
1837
562
2312
12.5
Initial in hyperosmolar medium with addition of 100 mM NaCl
63
242
75
475
1837
562
2312
7.60
0.61
No
1
1
1
Balanced in hyperosmolarmedium with addition of 100 mM NaCl
Standard
91
212
78
707
1652
609
2359
7.78
1.02
Weak RVI
1.49
0.90
1.08
inc x3
148
143
122
1536
1483
1269
3019
10.4
1.37
RVI
3.23
0.81
2.26
Incx0.2
50
263
45
326
1720
296
2046
6.55
0.86
AVD
1.43
0.94
0.53
Ikc x0.01
74
222
105
679
2035
964
2714
9.17
1.21
RVI
1.43
1.11
1.71
Ikcx10
127
190
30
771
1158
180
1929
6.10
0.80
AVD
1.62
0.63
0.32
inkcc x0.1
93
204
99
824
1803
878
2627
8.83
1.16
RVI
1.74
0.98
1.56
inkcc x10
89
219
62
629
1559
438
2188
7.11
1.01
Weak RVI
1.32
0.85
0.78
pClx0.1
91
209
90
754
1742
747
2496
8.32
1.23
RVI
1.59
0.95
1.31
pClx10
92
213
69
682
1576
509
2258
7.39
0.97
AVD
1.44
0.86
0.91
+HICC
146
154
91
1224
1289
762
2513
8.38
1.10
RVI
2.58
0.70
1.36
Pump

x0.2
238
60
98
2031
550
832
2581
8.77
1.15
RVI
4.28
0.30
1.48
Pump

x5
23
275
97
197
2399
847
2596
8.71
1.15
RVI
0.41
1.30
1.51
Initial in hyperosmolar medium with addition of 180 mM sucrose
Standard
60
232
71
475
1837
562
2312
7.91
0.63
No
1
1
1
Balanced in hyperosmolar medium with addition of 180 mM sucrose
Standard
43
261
29
271
1661
185
1932
6.36
0.81
AVD
0.57
0.90
0.33
Incx10
109
180
85
937
1547
737
2484
8.61
1.09
RVI
1.97
0.84
1.31
Incx0.1
22
287
11
130
1680
63
1810
5.86
0.71
AVD
0.27
0.91
0.11
Ikc x0.01
37
262
49
257
1838
347
2095
7.02
0.89
AVD
0.54
1.0
0.62
Ikcx10
50
259
8
290
1505
48
1795
5.80
0.73
AVD
0.61
0.82
0.09
Inkccx0.1
43
261
29
270
1659
182
1929
6.35
0.80
AVD
0.57
0.90
0.33
inkcc x50
43
260
31
278
1669
199
1946
6.42
0.81
AVD
0.58
0.91
0.35
pClx0.1
43
258
41
290
1730
272
2020
6.72
0.85
AVD
0.61
0.94
0.48
pClx10
43
264
19
259
1606
117
1865
6.08
0.77
AVD
0.55
0.87
0.21
+HICC
98
203
38
651
1350
254
2001
6.64
0.84
AVD
1.37
0.74
0.45
Pump

x0.2
153
161
30
977
963
193
1940
6.39
0.81
AVD
1.94
0.55
034
Pump

x5
9.3
294
30
60
1882
194
1942
6.40
0.81
AVD
0.13
1.02
0.35
V/Vinitial is the ratio of the cell volume, balanced in a hyperosmolar medium, to the initial one.
The columns "Ion content ratio for RVI, AVD" show the ratio of the content of Na+, K+ and Cl-
in cells balanced in a hyperosmolar medium to the initial content in a hyperosmolar medium.
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Table 6. Changes in the buoyant density, K+ and Na+ content in living K562, Jurkat, and U937
cells transferred to a hyperosmolar medium with adding 200 mM sucrose.
Medium,
mOsm
Incubation
time
Cells
Density,
g/ml
Water,
ml/g pr.
K+ ,
µmol/g pr.
Na+ ,
µmol/g pr.
n
K562 cells
310
4 h
1.045± 0.001
7.49
1031± 53
281± 25
17 (15)
510
15 min
1.051± 0.002
6.49
834± 19
194± 44
3 (2)
4 h
L
1.049± 0.001
6.80
1107± 85
211 ± 20
13 (12)
H
1.062± 0.002
5.16
709± 143
247± 40
8
Jurkat cells
310
4 h
1.048± 0.001
6.96
973± 64
326± 34
9
510
15 min
1.057± 0.001
5.70
837± 31
236± 98
2
4 h
L
1.055± 0.001
5.95
485± 110
629± 196
6
H
1.066± 0.003
4.79
207± 44
578± 45
5 (4)
U937 cells
310
4 h
1.046± 0.001
7.31
861± 122
307± 58
5 (4)
510
15 min
nd
672
134
1
4 h
L
1.053± 0.004
6.21
863± 65
371± 5
2
H
1.062± 0.002
5.16
485± 91
281± 28
3
L and H – light and heavy cell populations separated in a Percoll density gradient. Means ± SE
of n density measurements are given; the number of measurements of ion content is the same or
as indicated in parentheses. Water is calculated as indicated in the Methods section.
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Figure 1. Rearrangement of ionic homeostasis following an increase in external osmolarity due
to addition of 180 mM sucrose (A-F) or 100 mM NaCl (G-L) and a reverse transition to the
normal medium, calculated for a model of U937 cells with different cotransporters and
invariable in time parameters of channels and transporters like in U937 cells, equilibrated with
the standard RPMI medium.
Figure 2. Rearrangement of ionic homeostasis caused by an increase in external osmolarity in
the U937 cell model with different cotransporters and parameters like in cells balanced with the
standard medium. Direct Iso-Hyper (A-D) and reverse Hyper-Iso (E-H) transitions.
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Figure 3. The effects of NC rate coefficient (A-L) and permeability coefficient of Cl- channels
(M-R) on the ionic homeostasis in U937 cell model under standard conditions and after
transition to hyperosmolar medium with 180 mM sucrose or 100 mM NaCl. The calculation was
carried out for a model with a full set of cotransporters. Changes in NC rate coefficient (inc) and
in permeability coefficient of Cl- channels (pCl) are shown in the graphs, other parameters
remained unchanged and are shown in Table 2.
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Figure 4. Dependence of ionic homeostasis in U937 cell model during transition to hypertonic
medium with 100 mM NaCl (A-D, I-L) or 180 mM sucrose (E-H) on the rate coefficients inkcc
(A-H) and ikc (I-L), changing simultaneously with external osmolarity. The calculation was
carried out for a model with a full set of cotransporters. Changes in NKCC and KC rate
coefficients are shown in the graphs, other parameters remain unchanged and are shown in Table
2.
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Figure 5. The effect of changes in the Na+ and HICC channel permeability coefficients on ion
homeostasis in the U937 cell model under standard conditions (A, B) and in a hyperosmolar
medium with 100 mM NaCl (C, D) or 180 mM sucrose (E, F). The calculation was carried out
for a model with a full set of cotransporters. Changes in pNa, and HICC (pNa+pK) are shown in
the graphs, other parameters remained unchanged and are shown in Table 2.
Figure 6. Effect of hyperosmolar medium on living U937 cell. (A-C) cell water content, (D-
F) intracellular K+, Na+ content, (G-I) ouabain-sensitive (OR) and –resistant (OR) Rb+ influxes,
(J -L) Na+ concentrations and beta, (M) the percentage of cells with RVI (fraction L) after 2-
hour and 4-hour incubation in a hypertonic medium assessed by protein, (N, O) DMA+DIDS
(DD) effect on RVI in hyperosmolar medium with 150 mM sucrose. Solid lines with open
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symbols indicate light (L) cell subpopulation going RVI stage; dotted lines with filled symbols
indicate heavy (H) cell subpopulation going AVD stage. Data at time zero represent cells in
normal RPMI medium. Mean ± SEM values were calculated from at least 3 independent
experiments. (N, O) DMA (0.05 mM) and DIDS (0.5 mM) were added simultaneously with
addition of 150 mM sucrose. FromYurinskaya et al., 2012 modified.
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Figure 7. Cell water, K+, and Na+ content in living K562 (A, D), Jurkat (B, E), and U937 (C, F)
cells before and after 4 h incubation in hyperosmolar medium with 200 mM sucrose (510
mOsm). The broad gray lines show the level of the initial water and ion content in hyperosmolar
medium (15 min incubation).
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