Balance of Na, K, and Cl Unidirectional Fluxes in Normal and Apoptotic U937 Cells Computed With All Main Types of Cotransporters

Abstract

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 unidirectional fluxes in real cells ignored the ubiquitous cotransporters NKCC and KCC. Here, we present an analysis of the entire balance of unidirectional Na⁺, K⁺, and Cl– fluxes through the plasma membrane in human lymphoid U937 cells, taking into account not only the Na/K pump and electroconductive channels but all major types of cotransporters NC, NKCC, and KCC. Our calculations use flux equations based on the fundamental principles of macroscopic electroneutrality of the system, water balance, and the generally accepted thermodynamic dependence of ion fluxes on the driving force, and they do not depend on hypotheses about the molecular structure of the channel and transporters. A complete list of the major inward and outward Na⁺, K⁺, and Cl– fluxes is obtained for human lymphoid U937 cells at rest and during changes in the ion and water balance for the first 4 h of staurosporine-induced apoptosis. It is shown how the problem of the inevitable multiplicity of solutions to the flux equations, which arises with an increase in the number of ion pathways, can be solved in real cases by analyzing the ratio of ouabain-sensitive and ouabain-resistant parts of K⁺ (Rb⁺) influx (OSOR) and using additional experimental data on the effects of specific inhibitors. It is found that dynamics of changes in the membrane channels and transporters underlying apoptotic changes in the content of ions and water in cells, calculated without taking into account the KCC and NKCC cotransporters, differs only in details from that calculated for cells with KCC and NKCC. The developed approach to the assessment of unidirectional fluxes may be useful for understanding functional expression of ion channels and transporters in other cells under various conditions. Attached software allows reproduction of all calculated data under presented conditions and to study the effects of the condition variation.

Full text

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ORIGINAL RESEARCH
published: 06 November 2020
doi: 10.3389/fcell.2020.591872
Edited by:
Markus Ritter,
Paracelsus Medical University, Austria
Reviewed by:
Silvia Dossena,
Paracelsus Medical University, Austria
Dandan Sun,
University of Pittsburgh, United States
*Correspondence:
Alexey A. Vereninov
verenino@gmail.com
Specialty section:
This article was submitted to
Cell Death and Survival,
a section of the journal
Frontiers in Cell and Developmental
Biology
Received: 05 August 2020
Accepted: 30 September 2020
Published: 06 November 2020
Citation:
Yurinskaya VE, Vereninov IA and
Vereninov AA (2020) Balance of Na+,
K+, and Cl−Unidirectional Fluxes
in Normal and Apoptotic U937 Cells
Computed With All Main Types
of Cotransporters.
Front. Cell Dev. Biol. 8:591872.
doi: 10.3389/fcell.2020.591872
Balance of Na+, K+, and Cl−
Unidirectional Fluxes in Normal and
Apoptotic U937 Cells Computed With
All Main Types of Cotransporters
Valentina E. Yurinskaya1, Igor A. Vereninov2and Alexey A. Vereninov1*
1Laboratory of Cell Physiology, Institute of Cytology, Russian Academy of Sciences, St-Petersburg, Russia, 2Peter the Great
St-Petersburg Polytechnic University, St-Petersburg, Russia
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 unidirectional fluxes in real cells ignored the ubiquitous cotransporters NKCC and
KCC. Here, we present an analysis of the entire balance of unidirectional Na+, K+, and
Cl−fluxes through the plasma membrane in human lymphoid U937 cells, taking into
account not only the Na/K pump and electroconductive channels but all major types of
cotransporters NC, NKCC, and KCC. Our calculations use flux equations based on the
fundamental principles of macroscopic electroneutrality of the system, water balance,
and the generally accepted thermodynamic dependence of ion fluxes on the driving
force, and they do not depend on hypotheses about the molecular structure of the
channel and transporters. A complete list of the major inward and outward Na+, K+,
and Cl−fluxes is obtained for human lymphoid U937 cells at rest and during changes
in the ion and water balance for the first 4 h of staurosporine-induced apoptosis. It is
shown how the problem of the inevitable multiplicity of solutions to the flux equations,
which arises with an increase in the number of ion pathways, can be solved in real
cases by analyzing the ratio of ouabain-sensitive and ouabain-resistant parts of K+(Rb+)
influx (OSOR) and using additional experimental data on the effects of specific inhibitors.
It is found that dynamics of changes in the membrane channels and transporters
underlying apoptotic changes in the content of ions and water in cells, calculated without
taking into account the KCC and NKCC cotransporters, differs only in details from that
calculated for cells with KCC and NKCC. The developed approach to the assessment
of unidirectional fluxes may be useful for understanding functional expression of ion
channels and transporters in other cells under various conditions. Attached software
allows reproduction of all calculated data under presented conditions and to study the
effects of the condition variation.
Keywords: cell ion homeostasis, membrane transport, ion channels, sodium pump, cotransporters, ion fluxes
calculation, apoptosis
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INTRODUCTION
Apoptosis is one of the three main types of cell death, along with
autophagy and necrosis itself (Galluzzi et al., 2018). A hallmark
of apoptosis is a specific cell shrinkage or, at least, the absence of
swelling and rupture of the plasma membrane (Yurinskaya et al.,
2005). This is due to specific apoptotic changes in monovalent
ion homeostasis, which is closely related to cell water balance
regulation (Maeno et al., 2000, 2012;Okada et al., 2001;Lang
et al., 2005;Lang and Hoffmann, 2012, 2013). Until now,
the quantitative study of changes in channels and transporters
responsible for specific apoptotic changes in the balance of Na+,
K+, and Cl−has been based on the use of staurosporine-treated
U937 cells and computer modeling without considering KCC
and NKCC cotransporters (Yurinskaya et al., 2019). However,
these cation-coupled Cl−cotransporters of the gene family
SLC12 attract much attention in the recent decade (Gagnon
and Delpire, 2013;Jentsch, 2016;Delpire and Gagnon, 2018).
They can transport Cl−against an electrochemical gradient
and create a non-equilibrium distribution of Cl−across the
membrane. This is what makes Cl−an active player in various
physiological processes (Jentsch, 2016) since the permeability
of the Cl−channels can affect the entire homeostasis of
monovalent ions only when Cl−is in a non-equilibrium
state. The interplay of various Cl−coupled cotransporters
and Cl−channels has been particularly intensively studied in
connection with signal transmission in neurons (Kaila et al.,
2014;Doyon et al., 2016;Currin et al., 2020;Wilke et al., 2020).
Progress in the molecular biology of the cation-coupled Cl−
cotransporters is exciting; however, their functional expression
and role in maintaining Cl−homeostasis in non-polarized cells
is investigated much worse because electrophysiological methods
cannot be applied here, and possible tools are rather limited.
It was said: “Electrical activity in neurons requires a seamless
functional coupling between plasmalemmal ion channels and
ion transporters. Although ion channels have been studied
intensively for several decades, research on ion transporters is in
its infancy” (Kaila et al., 2014).
In our previous study, the cells with the sodium pump,
electroconductive Na+, K+, and Cl−channels and only one
cotransporter NC were considered (Yurinskaya et al., 2019). It
was found that the permeability of Cl−channels significantly
changes at the early stage of apoptosis. How the presence of
KCC and NKCC will affect the behavior of cells and how the
parameters of the main ion pathways obtained by calculations
will change were unknown. An increase in the number of
considered ionic paths significantly increases the difficulties of
finding the parameters, and these problems are also the subject
of the current study. We believe that the developed approach is a
useful tool for studying the fluxes of monovalent ions across the
plasma membrane with all major ion pathways.
MATERIALS AND METHODS
Cell Cultures
U937 human histiocytic lymphoma cells were obtained from the
Russian Cell Culture Collection (Institute of Cytology, Russian
Academy of Sciences, cat. number 160B2). The cells were cultured
in RPMI 1640 medium supplemented with 10% fetal bovine
serum (FBS) at 37◦C and 5% CO2. For the induction of apoptosis,
the cells, at a density of 1 ×106cells/ml, were exposed to 1 µM
staurosporine (STS) for 0.5–4 h. All the incubations were done
at 37◦C.
Reagents
RPMI 1640 medium and FBS (HyClone Standard) were
purchased from Biolot (Russia). STS and ouabain were from
Sigma-Aldrich (Germany), and Percoll was purchased from
Pharmacia (Sweden). The isotope 36Cl−was from “Isotope”
(Russia). Salts were of analytical grade and were from
Reachem (Russia).
Experimental Procedures
Details of the experimental methods used were described in
our previous study (Yurinskaya et al., 2019). Intracellular K+,
Na+, and Rb+contents were determined by flame emission on
a Perkin-Elmer AA 306 spectrophotometer, and the intracellular
Cl−was measured using a radiotracer 36Cl−. Cell water
content was estimated by the buoyant density of the cells in
continuous Percoll gradient, and it was calculated as vprot.= (1
-ρ/ρdry)/[0.72(ρ- 1)], where ρis the measured buoyant density
of the cells and ρdry is the cell dry mass density, which was given
as 1.38 g ml−1. The share of protein in dry mass was given as 72%.
The cell ion and water content were calculated in micromoles per
gram of protein.
Statistical Analysis
Statistical analysis of experimental data was carried out using
Student’s t-test and is presented in our original publications
(Vereninov et al., 2008;Yurinskaya et al., 2011).
Computation
Computation of the monovalent ion flux balance, membrane
potential, and ion electrochemical gradients was performed
using the computational program and appropriate executable
file BEZ01B as earlier (Vereninov et al., 2014;Yurinskaya
et al., 2019). Basic symbols and definitions used are shown in
Table 1. The input data (file DataB.txt, in supplement) are the
following: extracellular and intracellular concentrations (na0,
k0,cl0, and B0;na,k, and cl); kv; the pump rate coefficient
(β); the pump Na/K stoichiometric coefficient (γ); parameter
kb; channel permeability coefficients (pna,pk, and pcl); and the
rate coefficients for the NC, KC, and NKCC cotransporters (inc,
ikc, and inkcc). The terms NC, NKCC, and KC, cotransport, or
cotransporter, depending on the context, reflect the way these
carriers work, but not their genetic identity, which is irrelevant
in our study. Therefore, the abbreviations NC and KC are used,
but not NCC and KCC. It is known that unidirectional Na+–Cl−
coupled cotransport with 1:1 stoichiometry may be performed
both by a single transport protein, like thiazide-sensitive Na+–
Cl−cotransporter (Gamba, 2005), and by two functionally
coupled exchangers, NHE and Cl−/HCO3−(Garcia-Soto and
Grinstein, 1990;Hoffmann et al., 2009). The genetically identified
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cotransporters NKCC1 (SLC12A2) and KCC1 (SLC12A4) are
expressed in U937 cells1,2.
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]oand [K]o,
respectively, and Na/K pump flux stoichiometry of 3:2. kb is a
parameter of a linear decrease of beta over time. Coefficients
of ion channel permeability were selected by trial and error,
and rate coefficients of cotransporters, inc,ikc, and inkcc, were
selected in view of the effects of inhibitors (see text below).
Electrochemical gradients for Na+, K+, or Cl−,mun,muk, or
mucl, respectively, were calculated by the following equations:
mun = 26.7·ln([Na]i/[Na]o)+U,muk = 26.7·ln([K]i/[K]o)+U,
and mucl = 26.7·ln([Cl]i/[Cl]o) - Uand given in mV. The
results of computations appear in the file RESB.txt (its example
is given in the supplement). Equivalent exchange fluxes 1:1 are
1https://www.proteinatlas.org/ENSG00000064651-SLC12A2/blood
2https://www.proteinatlas.org/ENSG00000124067-SLC12A4/blood
TABLE 1 | Basic symbols and definitions.
Symbol Definitions and units
NC, NKCC, KC Types of cotransporters
[Na]i, [K]i, [Cl]i,na,k,cl Concentration of ions in cell water, mM
[Na]o, [K]o, [Cl]o,na0,k0,cl0 Concentration of ions in external medium, mM
B0 External concentrations of
membrane-impermeant non-electrolytes, mM
A Intracellular content of membrane-impermeant
osmolytes, mmol, may be related to g cell
protein or cell number
V Cell water volume, mL, may be related to g cell
protein or cell number
V/A Cell water content per unit of A
zMean valence of membrane-impermeant
osmolytes, A
OSOR Ratio of ouabain-sensitive to ouabain-resistant
Rb+(K+) influx
pNa, pK, pCl, pna,pk,pcl Permeability coefficients, min−1
Beta,βPump rate coefficient, min−1
Gamma,γNa/K pump flux stoichiometry, dimensionless
kv Ratio of “new” to “old” media osmolarity when
the external osmolarity is changed
UMembrane potential, MP, mV
PUMP K+influx or Na+efflux via the pump,
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,inkcc Cotransport rate coefficients, ml·µmol−1·min−1
for inc and ikc, and ml3·µmol−3·min−1for inkcc
mun,muk,mucl Transmembrane electrochemical potential
difference for Na+, K+, or Cl−, mV
kb Parameter of linear decrease of beta over time
not considered when calculating the ionic homeostasis of the cell,
since they do not change the concentration of Na+and Cl−in
the cell. Their calculation is considered in our previous study
(Vereninov et al., 2016).
RESULTS
Normal U937 Cells
Measured and Computed Characteristics of the Ion
Homeostasis in Cell With NKCC and KC
Cotransporters
The measured and computed data obtained for the cell with
the NC cotransport only and for the cell with the NKCC and
KC cotransports are presented in Table 2. The experimental
data are taken from our previous studies (Vereninov et al.,
2008;Yurinskaya et al., 2011, and yet unpublished materials).
Two variants of normal U937 cells with different measured
characteristics, Cells Aand B, are considered to show how
computed characteristics depend on the inevitable variability
of the real cells. The intracellular concentration of ions; the
ratio of ouabain-sensitive to ouabain-resistant influx of Rb+(K+),
OSOR, and their derivatives; the concentration and charge
of “impermeable” intracellular anions, Az, and the pump rate
coefficient beta belong to the group of “measured” characteristics.
The coefficient beta is easily and reliably calculated from
the measured ouabain-sensitive influx of Rb+, the known
relationship between the external concentrations of Rb+and K+,
and the known stoichiometry of the pump, i.e., ratio of the pump
K+influx to the pump Na+efflux. Intracellular Na+and Rb+
are analyzed in the same sample, and this reduces possible errors.
Determination of kinetic parameters characterizing channels
and transporters, unidirectional and total fluxes, and membrane
potential Urequires solving differential equations. For this, the
original computer program is used (Vereninov et al., 2016;
Yurinskaya et al., 2019). The data obtained in this way form a
group of “computed” characteristics.
The “computed” characteristics depend not only on the
experimental data used but also on the chosen list of ion pathways
and on the relationship between the parameters characterizing
the properties of the pathways. Shown are two different sets of
parameters, Xand Y, for two different cell variants, Aand B. Both
sets of Xand Ygive cells with almost the same characteristics,
like those measured in real cells. Thus, it can be assumed that
real cells can also achieve the same monovalent ion homeostasis
in different ways. The number of solutions to the flux balance
equations in a cell with only NC cotransport was discussed
earlier (Yurinskaya et al., 2019). The introduction of the NKCC
and KC cotransporters into consideration increases the number
of possible solutions to the system of equations describing cell
ion homeostasis. Parameters Xand Yare chosen as examples
of possible differences that result in unidirectional NKCC and
NC fluxes in the range possible for real U937 cells, as follows
from the data on the effects of NKCC and KC inhibitors. We
are currently unable to determine which of the Xor Yoptions
is more appropriate for real cells. However, the computation
can show what additional measured characteristics can help to
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TABLE 2 | Basic characteristics of ion distribution, measured in two variants of normal resting U937 cells (cells Aand B) and computed for schemes with and without
NKCC and KC cotransporters at two chosen sets of NKCC and KC parameters (Xand Y).
Characteristics Cells ACells B
Measured
[K]i, [Na]i, [Cl]i, mM 117, 32, 40 147, 38, 45
Cell density, g/ml 1.054 1.053
Az, mM 121 80
z−0.90 −1.75
beta 0.029 0.039
OSOR 5.61 3.89
Chosen NC only +(NKCC and KC) NC only +(NKCC and KC)
X Y X Y
inc 3E-5 1E-5 2.8E-5 3E-5 2.5E-5 7E-5
ikc – 2.4E-5 8.8E-5 – 1E-5 8E-5
inkcc – 4E-10 8E-10 – 11.4E-9 8E-9
Computed
U, mV −29.9 −30.8 −34.7 −44.7 −29.4 −45.0
mucl +1.5 +2.3 +6.3 +19.4 +4.1 +19.8
mun −69.3 −70.2 −74.1 −79.5 −64.2 −79.9
muk +50.3 +49.4 +45.5 +41.6 +56.9 +41.3
pna 0.0041 0.00355 0.00215 0.00382 0.00535 0.0017
pk 0.0115 0.01 0.0058 0.022 0.013 0.0115
pcl 0.0125 0.0102 0.005 0.0091 0.028 0.011
Partial influxes,% of total influx
INa Channels 95.1 83.4 53.7 69.3 69.9 28.7
INa NC 4.9 16.2 45.4 30.7 23.0 66.2
INa NKCC – 0.4 0.9 – 7.1 5.1
IK pump 84.8 84.0 82.8 79.0 79.0 78.0
IK Channels 15.2 13.3 8.0 21.0 9.9 10.9
IK KC – 2.2 7.9 – 0.5 4.2
IK NKCC – 0.6 1.2 – 10.5 6.9
The concentration of ions, impermeant intracellular anions A, their charge z, pump rate coefficient beta, and OSOR—ratio of ouabain-sensitive to ouabain-resistant
components of K+(Rb+) influx—are determined as described in section “Materials and Methods.” Symbols, definitions, and units are given in Table 1. Partial fluxes are
given in% to the sum of fluxes, excluding a 1:1 exchange flux. Cell variants A and B differ due to the use of different subline U937 cells studied in different years. The
experimental data are taken from our previous study (Vereninov et al., 2008;Yurinskaya et al., 2011, and yet unpublished materials).
select the best option. For example, variants B–Xand B–Ydiffer
significantly in the resting membrane potential, in the K+(Rb+)
influx sensitive to inhibitors, in the electrochemical Cl−gradient,
and, consequently, in the effect of changes in the Cl−channel
permeability on the entire ionic homeostasis. Variants A–X and
A–Y differ significantly in K+(Rb+) influx sensitive to the specific
NKCC and KC inhibitors, bumetanide, and DIOA, respectively.
The difficulty here lies in the low values of the partial fluxes
NKCC and KC in U937 cells (see below). The parameters of the
main ion pathways computed at different variants of the NKCC
and KC rate coefficients are different. However, the range of their
variation can be estimated by computing the desired options.
Ion Fluxes
Figure 1 shows the relationship between all quantitatively
significant components of the unidirectional fluxes of Na+, K+,
and Cl−in U937 cells (B–Y) calculated on the assumption that
seven types of ionic pathways exist in their plasma membrane
in a balanced cell state: the Na/K ATPase pump; the Na+,
K+, and Cl−electroconductive channels; the NC, NKCC, and
KC cotransporters; and the coupled ion exchange with a 1:1
stoichiometry, which is especially important in consideration
of Na+and Cl−unidirectional fluxes. The equivalent exchange
Na/Na and Cl/Cl constitutes the dominant part of the entire
unidirectional flux of these ions through the cell membrane.
These exchange fluxes are not associated with changes in
intracellular ion concentrations and differences in electrical
potentials in the cell membrane or with its conductivity and
cannot be measured by electrophysiological methods. However,
they are extremely significant when the transport of ions across
the membrane is studied by measuring fluxes using radioisotopes.
These measurements show that the fluxes underlying the 1:1
exchange of ions across the membrane can be significantly higher
in real cells than those considered in a simple pump-leak model.
The presented data on the overall exchange fluxes of Na+and Cl−
in the normal U937 cells have been obtained using radiotracers
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FIGURE 1 | Ion distribution and unidirectional K+, Na+, and Cl-fluxes in normal U937 cells under the balanced state. Cells B–Yfrom Table 2 are given as an
example. Other details are on the plot.
22Na+and 36Cl−or low concentrations of Li+as an analog of
Na+for most of the Na+pathways except the pump (Vereninov
et al., 2007, 2016;Yurinskaya et al., 2011). The dominance of
the 1:1 exchange flux in the entire Cl−flux across the plasma
membrane is known for other cells (Hoffmann et al., 1979;
Hoffmann, 1982, 2001). Fluxes related to the Na/Na and Cl/Cl
equivalent exchange are not considered further in the calculation
of the flux balance.
Computation shows that the effect of the NKCC cotransport
on the asymmetry in the balanced distribution of K+, Na+,
and Cl−in U937 cells is small, because the influx and efflux
of ions mediated by NKCC differ insignificantly and the net
NKCC flux is small in comparison with other net fluxes (Table 3).
Importantly, the unidirectional NKCC influx accounts for 0.4
and 0.9% of the total Na+influx in cells Abut 7.1 and 5.1%
in cells Bin variants Xand Y, respectively (Table 2). Detection
of such a small bumetanide-inhibitable NKCC influx in the
presence of a large background Na/Na equivalent exchange
is impossible. The Na+net flux via NKCC is small as the
driving force for NKCC is small. The driving force for NKCC
cotransport is mun +muk +2mucl =−16.2 ÷ −16 mV in cells
Aand +0.9 ÷+1 mV in cells B(Table 2).
The balanced unequilibrium distribution of Na+(mun
is −64 ÷-80 mV depending on variants) is determined mostly
by the relationship between the Na+pump flux uphill and
Na+flux downhill through not only the channels but also
via the NC pathway. This means that the Na+flux through
the NC route significantly “loads” the pump in the studied
U937 cells. Computation shows that NC cotransport is a
strong regulator of intracellular Na+concentration with all the
ensuing consequences.
A small share of KC influx in the entire K+influx in the
considered cells (0.5–7.9% depending on the options) (Table 2)
makes it difficult to study KC fluxes with inhibitors. At the same
time, the net K+flux via KC can be comparable with the net K+
flux through the channels (see examples A–Yand B–Y,Table 3).
Therefore, the effect of KC cotransporter on the entire cell ion
homeostasis can be significant.
Computation makes it possible to quantify the effect of the
NC, NKCC, and KC cotransporters on generation of the Cl−
electrochemical gradient across the cell membrane. The NC
cotransport is the most important here, at least in U937 cells. KC
and NC cotransports are antagonists as the net Cl−flux due to
the KC cotransport is directed out of the cell whereas that due to
the NC cotransport, in contrast, is directed into the cell (Table 3).
The movement of Cl−into the cell due to NC or from the cell due
to KC leads to a non-equilibrium distribution of Cl−across the
membrane in a balanced state and changes the apparent content
of “impermeant” anions in the cell. According to the theory of the
double Donnan system, the amount of “impermeant” anions in a
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TABLE 3 | Net and unidirectional K+, Na+, and Cl−fluxes in normal resting U937 cells calculated for two variants of cells and for two different sets of cotransport
parameters, Xand Y.
Ion Net fluxes Influx Efflux
Cells A–X:pna 0.00355, pk 0.01, pcl 0.0102, inc 1E-5, ikc 2.4E-5, and inkcc 4E-10
K+Channel PUMP NKCC KC IChannel PUMP INKCC IKC EChannel PUMP ENKCC EKC
−0.5248 0.6189 0.002 −0.0961 0.0977 0.6189 0.0044 0.0161 −0.6225 – −0.0024 −0.1123
Na+Channel NC NKCC PUMP IChannel INC INKCC PUMP EChannel ENC ENKCC PUMP
0.7767 0.1496 0.002 −0.9283 0.8372 0.1624 0.0044 – −0.0605 −0.0128 −0.0024 −0.9283
Cl−Channel NC NKCC KC IChannel INC INKCC IKC EChannel ENC ENKCC EKC
−0.0575 0.1496 0.004 −0.0961 0.6296 0.1624 0.0087 0.0161 −0.6870 −0.0128 −0.0048 −0.1123
Cells A–Y:pna 0.00215, pk 0.0058, pcl 0.005, inc 2.8E-5, ikc 8.8E-5, and inkcc 8E-10
K+Channel PUMP NKCC KC IChannel PUMP INKCC IKC EChannel PUMP ENKCC EKC
−0.2702 0.6184 0.0041 −0.3523 0.0601 0.6184 0.009 0.0592 −0.3304 – −0.0049 −0.4115
Na+Channel NC NKCC PUMP IChannel INC INKCC PUMP EChannel ENC ENKCC PUMP
0.5046 0.4189 0.0041 −0.9276 0.5381 0.4547 0.009 – −0.0335 −0.0358 −0.0049 −0.9276
Cl−Channel NC NKCC KC IChannel INC INKCC IKC EChannel ENC ENKCC EKC
−0.0748 0.4189 0.0081 −0.3523 0.2823 0.4547 0.0179 0.0592 −0.3572 −0.0358 −0.0098 −0.4115
Cells B–X:pna 0.00535, pk 0.013, pcl 0.028, inc 2.5E-5, ikc 1E-5, and inkcc 11.4E-9
K+Channel PUMP NKCC KC IChannel PUMP INKCC IKC EChannel PUMP ENKCC EKC
−0.9244 0.9882 −0.0044 −0.0594 0.1243 0.9882 0.1246 0.0067 −1.0487 – −0.1290 −0.0661
Na+Channel NC NKCC PUMP IChannel INC INKCC PUMP EChannel ENC ENKCC PUMP
1.1235 0.3632 −0.0044 −1.4823 1.2351 0.406 0.1246 – −0.1116 −0.0428 −0.1290 −1.4823
Cl−Channel NC NKCC KC IChannel INC INKCC IKC EChannel ENC ENKCC EKC
−0.2950 0.3632 −0.0088 −0.0594 1.7825 0.406 0.2491 0.0067 −2.0776 −0.0428 −0.2579 −0.0661
Cells B–Y:pna 0.0017, pk 0.0115, pcl 0.011, inc 7E-5, ikc 8E-5, and inkcc 8E-9
K+Channel PUMP NKCC KC IChannel PUMP INKCC IKC EChannel PUMP ENKCC EKC
−0.5096 0.988 −0.0031 −0.4753 0.1381 0.988 0.0874 0.0538 −0.6477 – −0.0905 −0.5291
Na+Channel NC NKCC PUMP IChannel INC INKCC PUMP EChannel ENC ENKCC PUMP
0.4679 1.0171 −0.0031 −1.4820 0.4927 1.1368 0.0874 – −0.0248 −0.1197 −0.0905 −1.4820
Cl−Channel NC NKCC KC IChannel INC INKCC IKC EChannel ENC ENKCC EKC
−0.5357 1.0171 −0.0061 −0.4753 0.4889 1.1368 0.1748 0.0538 −1.0246 −0.1197 −0.1809 −0.5291
Basic ionic characteristics of cells A and B and parameters X and Y are given in Table 2. Parameters in computation: Cells A, na 32, k 117, cl 40, and beta 0.029; Cells B,
na 38, k 147, cl 45, and beta 0.039. The following parameters are the same for both variants: na0 140, k0 5.8, cl0 116, B0 48.2, gamma 1.5, kv 1.0, hp 240, and kb = 0.
Specific sets of channel permeability coefficients and cotransporter parameters are shown in the table. Fluxes are given in µmol·min−1·(ml cell water)−1. Calculation
performed as described in section “Materials and Methods.” Cells under the balanced state and Cl−and Na+fluxes via exchangers 1:1 are omitted.
cell is a basic factor creating the asymmetry in distribution of ions
across the cell membrane and the electrical potential difference at
the membrane. Thus, NC and KC cotransporters turn out to be
important regulators of the ionic, electrical, and water balance of
the cell as a whole due to their influence on the unequilibrium
distribution of Cl−. The Cl−unequilibrium distribution also
makes the Cl−channel permeability an important regulator of
the entire ionic homeostasis of the cell. The interaction of the NC,
NKCC, and KC cotransporters and Cl−channels is well tested
using our computational program.
Apoptotic Changes in the Net and
Unidirectional Fluxes of Na+, K+, and
Cl−, Underlying the Change in Ionic and
Water Balance in U937 Cells Treated
With STS
The dynamics of apoptotic changes in the measured
characteristics of ionic balance in U937 cells treated with STS,
and changes in the rate coefficients for the main transporters
and channels, calculated for the cell with the NKCC and KC
cotransporters are shown in Figure 2. The measured linear
decrease in the rate coefficient of the Na/K pump remains
an important factor in the apoptotic alteration of cell ionic
balance in the cell with NKCC and KC like in the cell with NC
only. It should be noted that the pump K+and Na+fluxes in
apoptotic cells decrease with time more slowly than the pump
rate coefficient beta due to an increase in intracellular Na+
during apoptosis (Table 4). This is a good example that the
pump coefficient beta is a more adequate characteristic of the
intrinsic properties of the pump. The data in Figure 2A show
that a decrease in pump activity gives good agreement between
calculated and experimental results for K+and Na+, but not
for Cl−, cell water, and OSOR (Figures 2C,D). Changes in the
permeability coefficients of ion channels are required.
Changes in pCl, pK, and pNa, which give good agreement
between the calculated and observed dynamics of the ion and
water content during apoptosis, turn out to be practically
the same (qualitatively) as in the cell without NKCC and
KC in A–Xcells, but with more significant changes in pCl
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FIGURE 2 | Apoptotic changes in measured and calculated intracellular concentrations of Na+, K+, and Cl-(A,B), cell water Vol/A (C), OSOR (D), and calculated
membrane potential U(E) in U937 cells. Cells A–Yfrom Table 2 are given as an example of apoptotic cells treated with STS. Experimental data are shown by
symbols; calculated, by lines. (A) Only a linear decrease of the pump rate coefficient beta from an initial 0.029–0.013 at 4 h (coefficient kb = 0.000068 t>0).
(B) Additional changes in channel permeability shown on the top graphs: pna 0.00215t=0→0.0015t>0;pcl 0.005t=0→0.09t>0;pk 0.0058t=0→0.0174t>0;inc,
ikc, and inkcc rate coefficients remain constant throughout. Initial parameters: na0 140; k0 5.8; cl0 116; B0 48.2; kv 1.0; na 32; k117; cl 40; beta 0.029; gamma
1.50; pna 0.00215; pk 0.0058; pcl 0.005; inc 2.8E-5; ikc 8.8E-5; and inkcc 8E-10.
in A–Ycells (Table 5). The experimental data obtained
for the studied U937 cells do not allow one to accurately
determine the changes in parameter values but are sufficient
to determine the extent of possible parameter changes. Our
conclusion is that apoptotic changes in unidirectional and net
fluxes of Na+, K+, and Cl−in the studied U937 cells are
caused by a gradual decrease in the pumping coefficient by
about a factor of 2 in 4 h, steep increase in the integral
permeability of the Cl−channel by 6–18 times (depending on
the selected cell), increase in the permeability of the integral
K+channel by about 3 times, and decrease in the permeability
of the integral Na+channel by 30%. The introduction of
the KC and NKCC cotransporters into the calculations did
not change the general mechanism of apoptotic changes in
ionic homeostasis.
DISCUSSION
The importance of cotransporters in maintaining cellular ion
homeostasis and active Cl−transport against an electrochemical
gradient is generally known (Russell, 2000;Hoffmann et al., 2009;
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TABLE 4 | Dynamics of the net and unidirectional K+, Na+, and Cl−fluxes during apoptosis of U937 cells.
Ion Time, min Net flux total Pump beta Influx Efflux
K+PUMP IChannel IKC INKCC EChannel PUMP EKC ENKCC
0 0.0000 0.029 0.6184 0.0601 0.0592 0.0090 −0.3304 – −0.4115 −0.0049
30 −0.2829 0.027 0.5801 0.1985 0.0592 0.0087 −0.8442 – −0.2829 −0.0023
60 −0.0732 0.025 0.5562 0.2121 0.0592 0.0087 −0.7443 – −0.2284 −0.0016
240 −0.1330 0.013 0.4386 0.2077 0.0592 0.0087 −0.6484 – −0.1967 −0.0022
Na+IChannel INC PUMP INKCC PUMP ENC EChannel ENKCC
0 0.0000 0.029 0.5381 0.4547 – 0.0090 −0.9276 −0.0358 −0.0335 −0.0049
30 −0.0412 0.027 0.4130 0.4547 – 0.0087 −0.8701 −0.0250 −0.0202 −0.0023
60 +0.0290 0.025 0.4413 0.4547 – 0.0087 −0.8343 −0.0212 −0.0187 −0.0016
240 +0.1717 0.013 0.4321 0.4547 – 0.0087 −0.6579 −0.0337 −0.0301 −0.0022
Cl−IChannel INC IKC INKCC EChannel ENC EKC ENKCC
0 0.0000 0.029 0.2823 0.4547 0.0592 0.0179 −0.3572 −0.0358 −0.4115 −0.0098
30 −0.3194 0.027 4.3633 0.4547 0.0592 0.0175 −4.9016 −0.0250 −0.2829 −0.0046
60 −0.1075 0.025 3.8964 0.4547 0.0592 0.0175 −4.2824 −0.0212 −0.2284 −0.0031
240 −0.0379 0.013 4.0421 0.4547 0.0592 0.0175 −4.3010 −0.0337 −0.1967 −0.0043
Cells A and set of parameters Y are shown as an example. STS is introduced in the media at t = 0. Fluxes are given in µmol·min−1·(ml cell water)−1. Calculation is
performed as described in section “Materials and Methods.” Basic characteristics of cells and parameters are given in Table 2. Parameters change at t >0: pna 0.00215
to 0.0015; pk 0.0058 to 0.0174; pcl 0.005 to 0.09; kb 0t=0to 0.000068t>0; inc, ikc, and inkcc remain unchanged; see Figure 2. Cl−and Na+fluxes through 1:1
exchangers are not included in the calculation.
TABLE 5 | Changes in the permeability coefficients of Na+, K+, and Cl−channels obtained for apoptotic U937 cells by computation at a different set of parameters of
NC, KC, and NKCC cotransporters (cells Ain Table 2).
Cotransporters Channel permeability Resting In apoptosis Apoptotic to resting
NC only pCl 0.0125 0.068 5.4
pNa 0.0041 0.003 0.73
pK 0.0115 0.030 2.6
NC, KC, and NKCC XpCl 0.0102 0.065 6.4
pNa 0.00355 0.0025 0.70
pK 0.010 0.033 3.3
YpCl 0.005 0.09 18
pNa 0.00215 0.0015 0.70
pK 0.0058 0.0174 3.0
Lang and Hoffmann, 2012, 2013;Jentsch, 2016;Delpire and
Gagnon, 2018;Dmitriev et al., 2019). However, only a few
studies have considered the cotransporters in the quantitative
description of the entire balance of ion fluxes across the cell
membrane. Lew was the first to find that the balance in human
reticulocytes with a non-equilibrium balanced distribution of Cl−
cannot be explained without NC (Lew et al., 1991). NC and KC
cotransporters were included in cellular ionic homeostasis model
by Hernández and Cristina (1998). The NKCC cotransport was
considered when modeling the ionic balance in cardiomyocytes
(Terashima et al., 2006). The balance of Cl−fluxes through
cotransporters and channels was not considered in the early
fundamental studies of cotransporters in erythrocytes because the
distribution of Cl−is determined in these cells by a powerful
Cl−/HCO3−exchanger, but not by Cl−channels.
Later, the interplay between various cation-coupled Cl−
cotransporters (SLC12 gene family) and Cl−channels has been
intensively studied in relation to signal transduction in neurons
(Kaila et al., 2014;Doyon et al., 2016;Currin et al., 2020;
Wilke et al., 2020), in astroglia physiology (Wilson and Mongin,
2018) and in phagocytosis (Wang, 2016;Perry et al., 2019).
Unfortunately, in all these cases, it was extremely difficult to
obtain a complete set of accurate and reliable experimental data
necessary for quantitative description of the entire flux balance
across the cell membrane. Computer calculations show that
small variations in the input data may produce substantially
different results.
The use of ion-sensitive dyes and calcein to determine the cell
water, Cl−, and Na+allows us to measure mainly the relative
changes in their values, but absolute value measurements may
not be reliable enough due to calibration difficulties. Recently,
we have found that measurements of Na+concentration in
U937 cells by the direct flame emission method and by
the ANG-2 dye method give substantially different results
(Yurinskaya et al., 2020b).
It is important that U937 cells cultured in suspension allow the
determination of the cell water content by measuring the buoyant
density without known problems in estimation of extracellular
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water in the sample. These cells also allow determining cell
ions both by direct flame emission and by ion-sensitive dyes
using flow cytometry. It is also important that cells cultured in
suspension remain intact during transfer to a flow cytometer or
to a density gradient. The detachment of cells from the substrate,
enzymatically or mechanically, when working with adherent cell
cultures, always affects their ionic composition. We use computer
calculations and cell experimental data to analyze the role of the
NKCC and KC cotransporters in the ionic balance of cells at
rest and in early apoptosis. Our program allows one to quickly
test various sets of parameters characterizing the kinetics of
ion transport through multiple pathways of the cell membrane.
By combining measured and computed data, we were able to
compare pathway behavior in normal and apoptotic cells.
One of the most important and difficult problems in this
area is the determination of the real values of the parameters
based on real experimental data, rather than searching additional
parameters characterizing all variety of channels or transporters.
To quantitatively analyze the relationships between fluxes
through multiple ionic pathways in the cell membrane, it is
sufficient to use the driving forces for each type of pathway
that are known and linear coefficients for each pathway and
each type of ion. The number of even simplified parameters
turns out to be rather large. In our case, it is impossible to
predict theoretically how many sets of parameters will give the
same result and how to obtain a unique set of parameters
that provide agreement between experimental and calculated
data (Yurinskaya et al., 2019). However, a unique set of
parameters can be obtained if auxiliary information from the
experiment is used in addition to mathematical solutions. In the
present study, the ratio of ouabain-sensitive to ouabain-resistant
components of rubidium influx (OSOR) helped to select the
right set of parameters. OSOR is easily and reliably obtained
from experimental data. Its value is included in the output table
calculated by our computing program. The use of bumetanide
and DIOA, specific blockers of NKCC and KC fluxes, gave an
upper limit for Rb+(K+) influxes mediated by these transporters
in our study. Calculations predict different membrane potential
for a different set of NKCC and KC parameters. Hence, the
measurement of membrane potential can determine which of
the Xor Yparameter sets in Table 2 is correct for the cells
in question. We suggest that reliable membrane potential data
can be obtained using voltage-sensitive dyes such as DiBaC4
rather than microelectrodes. An interesting comparison of the
two methods has been made recently (Bonzanni et al., 2020).
Measuring multiple cell characteristics can solve the problem of
multiple parameters.
U937 cells are an established model in the experimental study
of apoptosis. The calculation of apoptotic changes in cell ionic
homeostasis in our previous study concerned the interaction
between pump, channels, and NC cotransport without NKCC
and KC. The effects of the cotransporters NKCC and KC
on changes in the flux balance during apoptosis remained
unexplored. Calculation of the net and unidirectional Na+, K+,
and Cl−fluxes via KC and NKCC pathways in the studied cells
showed that the difference in the effects of the specific inhibitors
of KC and NKCC on the uptake Rb+(K+) as in conventional
methods of testing KC and NKCC cotransport does not reflect
their impact upon the entire ionic homeostasis. The effect of
the net KC flux on the entire ionic balance is higher than the
net NKCC flux because the driving force in the KC pathway
is higher than in the NKCC pathway. Whereas NC plays a
critical role in generating mucl, the driving force for the Cl−
net flux through channels with all its consequences, the NKCC
cotransport is practically ineffective in creating mucl, while KC
can only reduce it.
An increase in the permeability of Cl−channels at the
early stage of apoptosis, found by calculations, is in good
agreement with numerous electrophysiological data indicating
an increase in the integral conductance of chloride channels
VRAC during apoptosis (Hoffmann et al., 2015;Kondratskyi
et al., 2015;Jentsch, 2016;Pedersen et al., 2016;Wanitchakool
et al., 2016). We studied the expression of these channels
in U937 cells under our experimental conditions using an
antibody against the outer loop of the LRRC8A VRAC subunit
(Yurinskaya et al., 2020a). It was found that the number
of channels expressed in the membrane does not change
to the extent comparable with the changes in the integral
permeability of Cl−channels. This indicates a change in the
internal properties of the channels, but not their number
in the membrane.
Calculation shows that the net fluxes out of cells of all three
ions, K+, Na+, and Cl−, arise at the early stage of apoptosis
(Table 4). The K+net flux out of cells is the one of the most
significant causes of the known apoptotic decrease of K+content
in cells and their concomitant apoptotic shrinkage (Yurinskaya
et al., 2005). The significant K+net flux out of cells arises at
the early stage of apoptosis mostly due to an increase of the
channel K+efflux caused by an increase in channel permeability
and also due to a decrease of the pump K+influx. It should
be noted that the K+and Cl−channel fluxes increase in both
directions, but the increase in efflux exceeds the increase in
influxes. The net Cl−flux out of cells underlies the initial
drop in Cl−content and concentration observed in apoptotic
cells. It is caused not only by an increase of pCl from 0.005
to 0.09 but also by a shift in the membrane potential toward
hyperpolarization due to an increase in pK. The shift in the
membrane potential causes an increase in Cl−electrochemical
potential difference. The initially outward net Na+flux reverses
later to the inward net flux and Na+content, and concentration
in apoptotic cells begins to increase. This is because the apoptotic
decrease in the pump efflux outweighs the decrease in channel
Na+influx (Table 4). It has been shown earlier that pNa decrease
and pK increase alone without a pCl increase could also be
sufficient to get agreement between real and calculated chloride
concentrations for the first 30 min. However, this variant should
be rejected as the OSOR value becomes unrealistically low
(Yurinskaya et al., 2019).
Non-zero net fluxes of all three K+, Na+, and Cl−ions in
U937 cells during STS-induced apoptosis indicate that a balanced
ion distribution is not achieved within the first 4 h. In our
earlier study (Yurinskaya et al., 2011), it was hypothesized that
a balanced state takes place in apoptotic U937 cells under the
discussed conditions. At that time, data on the distribution
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Yurinskaya et al. Na+, K+, and Cl−flux computation
of Cl−were scarce, and the computational tool was not yet
sufficiently developed. Based on that hypothetical assumption it
was concluded that “A decrease in the channel permeability of the
plasma membrane for Na+is proved to be crucial for preventing
cell swelling due to the decrease in the Na+/K+pump activity in
cells undergoing apoptosis whereas opening of the K+and Cl−
channels is not required”. This conclusion should be considered
at present as incorrect.
It would be very interesting to learn about the role of
monovalent ions not only at the early 4 h stage of STS-induced
apoptosis in U937 cells, despite the fact that this model is
popular and that the developed approach to studying apoptosis
in other cells may have a more general significance. The role of
monovalent ions in the subsequent development of apoptosis is
no less interesting, since understanding apoptosis in its entirety
is necessary for solving many practical problems, for example,
searching for targets of anticancer drugs. Unfortunately, there
are still no necessary data on changes in the ion content, water
balance, and sodium pump fluxes at the late stages of apoptosis.
A quantitative description of ionic processes during late apoptosis
is a matter of the future.
CONCLUSION
A developed approach enables us to obtain a complete list of
the inward and outward Na+, K+, and Cl−fluxes via all major
pathways across the plasma membrane including NKCC and KC
cotransporters in U937 cells at rest and during the first 4 h of
apoptosis induced by staurosporine.
The problem of the inevitable multiplicity of solutions to the
flux equations arising with an increase in the number of paths for
ions can be solved in real cases if we take into account the ratio
of the ouabain-sensitive and ouabain-resistant parts of the influx
K+(Rb+) and use additional experimental data on the effects of
specific inhibitors or some other data.
The dynamics of changes in plasma membrane channels and
transporters, which underlie apoptotic changes in the content
of ions and water in cells, calculated earlier without taking
into account the KC and NKCC cotransporters, differs from
that calculated for cells with the KC and NKCC cotransporters
only in details.
The developed approach to determining unidirectional fluxes
can be useful for studying the functional expression of ion
channels and transporters in other cells.
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
AV wrote the manuscript with input from all authors. All 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. All persons designated as authors qualify for authorship,
and all those who qualify for authorship are listed.
FUNDING
The research was supported (VY and AV) 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.
ACKNOWLEDGMENTS
We thank Dr. Tatyana Goryachaya for excellent assistance in
the experiments with cells. We are grateful to Drs. AV and AA
Dmitriev (Department of Biomedical Engineering, Northwestern
University, Evanston, Illinois, United States) for correcting the
manuscript and suggestions for improvement.
SUPPLEMENTARY MATERIAL
The Supplementary Material for this article can be found
online at: https://www.frontiersin.org/articles/10.3389/fcell.2020.
591872/full#supplementary-material
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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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Frontiers in Cell and Developmental Biology | www.frontiersin.org 11 November 2020 | Volume 8 | Article 591872