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1
* Université Libre de Bruxelles, Faculté des Sciences CP231, Brussels, Belgium;
Unité de Recherche U442, Institut National de la Santé et de la Recherche Médicale, Université de Paris sud, Orsay, France; and
Université Libre de Bruxelles, IRIBHN, Faculté de Médecine, Campus Erasme, Brussels, Belgium
1Correspondence: Unité de Recherche U442, Institut National de la Santé et de la Recherche Médicale, Université de Paris sud, bâ 443, 91405 Orsay, France. E-mail: laurent.combettes{at}ibaic.u-psud.fr
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSDESCRIPTION OF THE MODELRESULTS AND DISCUSSIONREFERENCES |
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Key Words: liver • phase wave • gap junctions • inositol 1,4,5-trisphosphate
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSDESCRIPTION OF THE MODELRESULTS AND DISCUSSIONREFERENCES |
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. These
Ca2+ signals can be elicited in isolated cells by
a large array of stimuli and often occur as repetitive
Ca2+ waves. The regenerative mechanism of these
Ca2+ waves is beginning to be well understood
(2)
. In isolated multicellular systems, or in intact
organs, Ca2+ waves are not restricted to the
cytosol of one cell but propagate toward other cells as intercellular
calcium waves (3
, 4)
. Theoretically, intercellular
Ca2+ signaling may occur through different
pathways, namely paracrine or junctional routes. Numerous studies have
reported that paracrine and/or junctional routes are involved in the
propagation of intercellular calcium waves in a large spectrum of cell
types including, for example, astrocytes (5
, 6)
,
chondrocytes (7)
, hepatocytes (8)
, pancreatic
acinar cells (9
, 10)
, or tracheal epithelial cells
(11
, 12)
. Most of these studies were performed under
particular experimental conditions, i.e., after mechanical stimulation
of a single cell from a cultured monolayer, which induces the
propagation of Ca2+ waves in the connected cells.
Such experimental studies on epithelial tracheal ciliated cells, glial
cells, and endothelial cells allowed Sneyd et al. (13
, 14)
to propose a theoretical model accounting for the propagation of
intercellular Ca2+ waves in these cell types.
This model is based on the passive diffusion of inositol
1,4,5-trisphosphate (InsP3) between adjacent
cells through gap junctions. InsP3 is produced in
the mechanically stimulated cell and provokes the release of
Ca2+ from internal stores, in the form of an
intracellular Ca2+ wave propagating via
Ca2+-induced Ca2+ release
(2)
. Because InsP3 is supposed to
move through gap junctions, similar Ca2+ waves
are initiated in adjacent cells. This phenomenon reproduces itself as
long as the amount of InsP3 entering a cell is
large enough to induce a Ca2+ wave. The model
thus accounts for the propagation of a restricted intercellular
Ca2+ wave after focal stimulation of one
individual cell, as well as for asynchronous Ca2+
oscillations that occur after the passage of the wave, as often
observed in glial cells (14
, 15)
.
In contrast to the studies that led to the model proposed by Sneyd et
al. (13)
, some experiments have been performed in freshly
isolated systems of connected cells that are globally stimulated by
hormones, or intact organs perfused with agonists (9
, 16
17
18
19)
. Especially in the liver, a striking feature of the
responses observed in the latter experimental conditions is the
sequential pattern of Ca2+ increases in the
different coupled cells, creating the appearance of intercellular
Ca2+ waves. This occurs both in hepatocyte
doublets and triplets and in liver cell plates from whole perfused
organs. The same sequence of Ca2+ responses is
observed for each spike for intermediate doses of agonists that cause
Ca2+ oscillations (17)
. This
sequence of cellular responses to a given agonist is maintained when
stimulation is repeated and does not depend on agonist concentration.
Thus, interhepatocyte Ca2+ waves, although
elicited by global agonist stimulation, appear to be oriented in a
specific direction in multiplets or in the perfused intact liver
(17
18
19)
.
Experimental results obtained in multiplets of connected hepatocytes
and in the perfused liver suggest that the mechanism for intercellular
calcium wave propagation in hepatocytes considerably differs from that
in tracheal epithelial cells or endothelial cells. First, in contrast
with the latter cell types in which only one Ca2+
wave propagates concentrically after focal stimulation, repetitive
Ca2+ waves propagate in multiplets of hepatocytes
(17
, 20
, 21)
or in the intact perfused liver (18
, 19)
. Second, each hepatocyte needs a stimulus (here in the form
of an agonist such as vasopressin or norepinephrine) to relay the
intercellular Ca2+ wave (20)
.
However, gap junction permeability is essential for coordinating
Ca2+ oscillations in the coupled cells (16
, 20)
. Coordinated intercellular Ca2+
signals in connected hepatocytes thus require both effective gap
junctions and global hormonal stimulation. Third, a crucial aspect of
interhepatocyte Ca2+ signals is the spatial
orientation of the Ca2+ wave, which is
unidirectional for a given agonist, as described above. We have
suggested that this oriented pattern relies on the observed gradient in
hepatocyte sensitivity to agonists along the liver cell plate
(21)
. The appearance of intercellular
Ca2+ waves could thus arise from the fact that
each individual hepatocyte in the liver cell plate (or in multiplets)
displays repetitive Ca2+ spikes with a slight
phase-shift with respect to neighboring cells.
The aim of this study is to develop a theoretical model for the
propagation of intercellular Ca2+ waves in
connected hepatocytes, which could account for this dual control by gap
junction permeability and hormonal stimulation. The model is based on
the observation that the number of external receptors on the membrane
of a hepatocyte depends on its location in the liver cell plate
(21)
. Thus, we assume in the model that a multiplet of
connected hepatocytes behaves as a set of individual
Ca2+ oscillators characterized by slightly
different periods, since the period of Ca2+
oscillations directly depends on the number of hormonal receptors that
have been stimulated (via intracellular InsP3).
These oscillators are in turn coupled by an intercellular messenger,
which may a priori be either Ca2+ or
InsP3 diffusing through gap junctions. Our
results suggest that there is a better agreement between the model and
the experimental data when InsP3 is considered as
the coordinating messenger. The model based on the hormonal sensitivity
gradient and the diffusion of InsP3 through gap
junctions leads to theoretical predictions that are confirmed
experimentally.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSDESCRIPTION OF THE MODELRESULTS AND DISCUSSIONREFERENCES |
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Preparation of hepatocytes
Single hepatocytes and multicellular systems were prepared from
fed female Wistar rats by limited collagenase digestion of the liver,
as described previously (17)
. After isolation, rat
hepatocytes were maintained (2 x 106
cells/ml) at 4°C in William’s medium E supplemented with 10% fetal
calf serum, penicillin (200,000 units/ml), and streptomycin (100
mg/ml). Cell viability, assessed by trypan blue exclusion, remained
greater than 96% for 4–5 h.
Loading of hepatocytes with Fura 2
Hepatocytes were loaded with Fura 2 either by injection (see
below) or by incubation with the dye, as described previously
(20)
. Small aliquots of the suspended hepatocytes (5 x 105 cells) were diluted in 2 ml of William’s
medium E modified as described above. The cells were then plated onto
dish glass coverslips coated with collagen I, and incubated for 60 min
at 37°C under an atmosphere containing 5% CO2.
After cell plating, the medium was removed and replaced with a
William’s medium E containing 3 µM Fura 2/AM. The hepatocytes were
then incubated for 30 min at 37°C under an atmosphere containing 5%
CO2. The coverslips were then washed twice with a
saline solution (10 mM HEPES, 116 mM NaCl, 5.4 mM KCl, 1.8 mM
CaCl2, 0.8 mM MgCl2, 0.96
mM NaH2PO4, 5 mM
NaHCO3, and 1 g/l glucose, pH 7.4). An Eppendorf
microinjector (5242) was used to microinject Fura 2 as described
previously (20)
. After microinjection, cells were allowed
to recover for at least 10 min. The success of microinjection was
assessed by monitoring the morphology of cells before and after
manipulation and checking the ability of the cell to retain injected
Fura 2 and low [Ca2+]i.
Freshly isolated doublets and triplets were distinguished from
aggregates of non-connected cells in conventional light microscopy by
screening for dilated bile canaliculi, which are indicators of
maintained functional polarity (22)
.
Determination of [Ca2+]i changes in
hepatocytes
Dish coverslips were put onto a thermostated holder (34°C) on
the stage of a Zeiss Axiovert 35 microscope set up for epifluorescence
microscopy. The excitation light was supplied by a high-pressure xenon
arc lamp (75 W), and the excitation wavelengths were selected by 340
and 380 nm filters (10-nm bandwidth) mounted in a processor-controlled
rotating filter wheel (Sutter) between the ultraviolet lamp and the
microscope. Ca2+ imaging was performed as
described by Combettes et al. (17)
. Briefly, fluorescence
images were collected by a low-light-level ISIT camera (Lhesa, France),
digitized, and integrated in real time by an image processor
(Metafluor, Princeton, NJ).
Superfusion
Cells were continuously superfused with control or test
solutions (at 34°C) by six inlet tubes converging on the coverslip
chamber. The perfusion rate was 1.5 to 2 ml/min and the chamber volume
was ~0.2 ml. The medium was continuously renewed by aspiration.
Agonists were rapidly removed during the Ca2+
response with this superfusion system, by increasing the perfusion rate
to 4 ml/min to improve the washing efficiency.
Microperfusion
As described previously (20)
, agents were applied
locally by positioning a micropipette (Femtotips, Eppendorf) close to
the cell of interest and applying a constant pressure (120 hPa) via the
Eppendorf injector. This allowed the delivery of picoliter quantities
of agonist-containing solution. To monitor the extent of
microperfusion, fluorescein (30 µM) was included in the micropipette
and the fluorescein image was monitored at 510 nm using an excitation
wavelength of 480 nm.
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DESCRIPTION OF THE MODEL |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSDESCRIPTION OF THE MODELRESULTS AND DISCUSSIONREFERENCES |
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, 24)
. It is assumed
that InsP3- and
Ca2+-mediated activation are instantaneous,
whereas Ca2+-induced inactivation develops
slowly; if activation and inhibition are considered as cooperative
processes, the change in the fraction of inactive
InsP3 receptors
(Rdes) obeys the following equation
(see references for a detailed description of the equations):
 |
 |
 |
 |
, 26)
. Catot represents the total
intracellular Ca2+ concentration. If
Clum represents the intraluminal
Ca2+ concentration, Catot =
Clum +
Ccyto where is the ratio
between the volume of the InsP3-sensitive
Ca2+ pool and the volume of the cytosol. No
equation explicitly describes the change in the intraluminal
Ca2+ concentration
(Clum) over time, as the total
intracellular Ca2+ concentration remains constant
and equal to Catot. Note that this assumption
does not hold if it is assumed that Ca2+ diffuses
through gap junctions, in which case another equation for the change in
Clum needs to be considered. As shown
previously (24)
, the model defined by Eqs.
1 and 2 accounts for intracellular
Ca2+ oscillations resembling those observed
experimentally. By incorporating diffusion of cytosolic
Ca2+ in Eq. 2, the model also accounts
for the propagation of intracellular Ca2+ waves.
Here, we focus on multiplets of connected hepatocytes (doublets or
triplets), which allows us to look at our system in one dimension.
It should be pointed out, however, that our results describing a
possible mechanism for intercellular Ca2+ wave
propagation do not depend on the precise model used to describe the
intracellular Ca2+ dynamics. We have verified
that the outcome remains qualitatively unchanged when the intracellular
Ca2+ dynamics are described by the model
developed by Atri et al. (27)
, instead of Eqs. 1 and 2 above. Other models for intracellular
Ca2+ oscillations and waves, also involving the
stimulation of the InsP3R activity by
Ca2+, could also have been used
(28
29
30)
. Moreover, we neglect any possible spatial
inhomogeneity in the intracellular distribution of
InsP3 receptors because the main rate-limiting
processes are related to InsP3 synthesis,
degradation, and passage through gap junctions; the characteristic time
for InsP3 diffusion through a hepatocyte is
indeed on the order of 100 ms, whereas the characteristic times for the
other processes are at least on the order of a few seconds.
In view of the fact that in the model InsP3 can
diffuse through gap junctions (Fig. 1
), its progression over time needs to be considered in the description
of the Ca2+ dynamics in each individual cell. To
this end, we have incorporated in the model a general equation
describing synthesis of InsP3 by phospholipase C
(PLC) and InsP3 metabolism by
InsP3 3-kinase and 5-phosphatase (see ref. 31
).
The change in InsP3 over time is therefore
determined by:
 |
, the rate of
InsP3 synthesis is assumed to be independent of
the level of cytosolic Ca2+ (32
, 33)
. Stimulation of InsP3 3-kinase
activity by Ca2+ (in reality through
Ca2+/calmodulin) is reflected in Eq. 3
by Kd, which is the threshold constant for
activation, and nd, the Hill
coefficient characterizing the latter process. In fact, as emphasized
in a previous study (31)
, InsP3
metabolism is dominated by InsP3 5-phosphatase.
In the model, oscillations of InsP3 due to the
stimulation of 3-kinase activity by Ca2+ are
negligible.
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As previously reported (34)
, in the simulations of the
model defined by Eqs. 1
,2
,3, the latency (that is, the time
interval between the onset of stimulation and the peak of the first
Ca2+ spike) directly depends on the rate of
InsP3 synthesis,
VPLC. The first
Ca2+ spike indeed occurs when the concentration
of InsP3 reaches a threshold value. Thus, to
approximately match the theoretical latencies with experimental
observations, we have chosen parameter values characterizing
InsP3 synthesis and metabolism such as to get a
half-time for an increase in InsP3 of ~45 s at
low levels of stimulation which, in the model, leads to a latency of
~70 s.
Incorporation of gap junctions
In the liver or in freshly isolated multicellular systems of rat
hepatocytes, cells are tightly coupled by gap junctions
(35)
. The latter allow the diffusion of diverse
small-sized molecules between adjacent cells. We have attempted to
incorporate InsP3 diffusion through gap junctions
in our model. If Ca2+ was the messenger, the same
equation would hold after changing Ip into
Ccyto (see below). Thus, in the model
we assume that at each cell boundary the flux is dependent on both the
concentration difference across the membrane and on the permeability of
the gap junction to InsP3. We have therefore used
the same mathematical formulation as Sneyd et al. (14)
. At
each boundary between two cells:
 |
reduces to no flux boundary conditions; infinitely
large values for FIP correspond to the
absence of any cell membrane (Fig. 1)
.
The model Eqs. 1
,2
,3
,4 were solved by the finite difference
method on an array of two or three cells, each containing 20 grid
points. Each cell was assumed to be 20 µm long. Integration was
performed numerically using a fourth-order, variable time-step
Runge-Kutta method. Parameter values are listed in Table 1
, except for the rate of InsP3 synthesis
(VPLC) and the junctional permeability
to InsP3 (FIP),
whose value is discussed below.
|
Gradient of hormonal sensitivity among connected hepatocytes
It is well known that hepatocytes contribute differently to a
large number of biological processes depending on their location in the
portocentrilobular axis of the liver acinus (36)
. In the
same manner, there is morphological evidence for a gradient of
vasopressin receptors along the liver cell plate (18
, 37)
.
This increasing density of hormonal receptors from the periportal to
the perivenous zones of the liver cell plate may account for a gradient
of sensitivity to vasopressin that we have observed recently
(21)
. Indirect evidence suggesting the existence of a
similar gradient for -adrenoceptors has been reported previously
(21
, 38)
. In this experiment, global perfusion of
norepinephrine elicited a sequential Ca2+
response in a hepatocyte triplet (Fig. 2
, left). When the agonist was quickly removed from the medium,
immediately after Ca2+ levels increased in the
second cell, the third cell did not respond (Fig. 2
, middle).
Similarly, when the agonist was removed by rapidly washing the medium
immediately after Ca2+ levels increased in the
first cell, the second and the third cells did not respond (Fig. 2
,
right). Thus, in conditions where cells are uniformly perfused with
norepinephrine, the time of contact between the agonist and the cell
necessary to induce a Ca2+ response is largest in
the last and shortest in the first responding hepatocyte. This
experiment thus argues for a gradual change in hepatocyte sensitivity
to norepinephrine in multiplets.
|
Such sensitivity gradients are taken into account in the model
(illustrated in Fig. 1
) by assuming that each cell has a different
velocity of InsP3 synthesis by phospholipase C
(VPLC). It has been estimated that the
mean number of V1a vasopressin binding sites in the perivenous zone of
the cell plate exceeds by 40% the mean number of the same binding
sites in the periportal zone (21)
. Thus, assuming that the
average number of cells in a cell plate is ~20, then the model
presumes that VPLC differs by 5%
between two neighboring hepatocytes. In the model, for the parameter
values listed in Table 1
, a 5% difference in
VPLC leads to variations of ~20% in
the period of Ca2+ oscillations.
Cellular heterogeneity is clearly dominated by these variations in the
rate of InsP3 synthesis; indeed, when caged
InsP3 is microinjected into one cell of
Fluo3-loaded doublets and triplets of hepatocytes, the
Ca2+ increases observed after flash photolysis
appear to be nearly identical and simultaneous in the connected cells
(21)
. This strongly suggests that the behavior of distinct
hepatocytes, which were originally closely located in the cell plate,
is nearly identical when the steps responsible for
InsP3 synthesis are bypassed.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSDESCRIPTION OF THE MODELRESULTS AND DISCUSSIONREFERENCES |
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, 19)
, mainly because the
microinjection of large amounts of Ca2+ or
InsP3 in one cell of a doublet increases
Ca2+ in the connected cell (39)
. It
has also been reported that gap junctional permeability is essential
for coordination of Ca2+ signaling in coupled
hepatocytes (16
, 20)
. However, little is known about the
extent of InsP3 intercellular diffusion during
agonist stimulation. We have shown recently that when one cell within a
doublet is stimulated by submaximal doses of norepinephrine, the amount
of messenger diffusing through the gap junctions is insufficient on its
own to induce a Ca2+ response in the adjacent
cell (20)
. Similarly, as shown in Fig. 3A
, focal vasopressin stimulation of a single cell in a
doublet induces Ca2+ oscillations that are
limited to the stimulated hepatocyte and do not show up in the
connected cell. At the end of the experiment, when the doublet is
globally superfused with vasopressin (0.1 nM), both cells exhibit
Ca2+ oscillations that are sequential and well
coordinated (Fig. 3B
).
|
We have used this experiment to evaluate the permeability coefficient
(FIP), to be incorporated in the model. To
this end, we considered a theoretical doublet, consisting of two
Ca2+ oscillators whose values for
VPLC, the parameter reflecting the
rate of InsP3 synthesis, differ by 5%. We then
performed successive trials to determine a value for
FIP that allows for both coordination of
Ca2+ spiking when the whole doublet is stimulated
(lower limit for FIP), and for the absence
of Ca2+ variations in an unstimulated cell
connected to an oscillating one (upper limit for
FIP). In Fig. 3C
, D
,
each color represents the change in Ca2+
concentration in a given cell. For a value of the permeability
coefficient (FIP) equal to 0.88 µm/s,
Ca2+ oscillations were restricted to the
stimulated cell (in blue), as shown in Fig. 3C
; on global
stimulation both cells oscillated, with a slight phase-shift (Fig. 3D
). A similar result was obtained for other
FIP values differing by ~10%. This
value for the permeability coefficient
FIP, which is close to the one predicted
in previous theoretical studies (13
, 14
, 40)
, was thus
used for the remaining simulations.
Phase waves of Ca2+ increases among connected
hepatocytes
We have simulated the behavior of three hepatocytes whose values
for VPLC differ by 5%. These cells
were assumed to be connected by gap junctions allowing the diffusion of
InsP3, by considering the boundary conditions
given in Eq. 4 and the permeability coefficient estimated
above. As shown in Fig. 4A
, the Ca2+ oscillations generated by
the model were tightly coordinated among the three cells. The change in
cytosolic Ca2+ in the most sensitive cell, i.e.,
the one with the largest value for
VPLC, is shown in red; less-sensitive
cells are shown in blue and green, respectively. As previously observed
experimentally (17
, 21)
, peaks of cytosolic
Ca2+ appeared sequentially in cells 1 (red), 2
(blue), and 3 (green), giving the appearance of an intercellular
Ca2+ wave. Because we assumed in the model that
no Ca2+ is transported from one cell to another,
this wave is in fact a "phase wave" (41)
. This means
that the appearance of a wave propagation phenomenon comes from the
slight phase-shift between the individual oscillators. This phase-shift
originates because the three cells of the triplet do not simultaneously
enter into the oscillatory domain because of their different values for
VPLC.
|
Variations in VPLC also cause the
period of Ca2+ oscillations to be different in
the three cells, resulting in a progressive loss of coordination. Figs. 3D
and 4A
show that, in the model, the delay
between Ca2+ spiking in adjacent cells increased
with time. Thus, the model predicts that after a sufficient number of
apparent intercellular Ca2+ waves the hepatocytes
will oscillate in a less synchronous manner. This is because in each
cell the frequency of Ca2+ oscillations is
imposed by the level of InsP3, whose value
depends on both hormonal sensitivity
(VPLC) and diffusion through gap
junctions (FIP). The delay between
Ca2+ spiking, and thus the velocity of the
apparent intercellular Ca2+ wave, is then fixed
by these differences in the levels of InsP3,
which themselves depend on the parameters affecting synthesis,
metabolism, and diffusion of this messenger. In particular, as expected
intuitively, coordination was enhanced when the permeability
coefficient was increased or when the sensitivity gradient was
decreased (data not shown). Also, coordination increased with the level
of stimulation, a property that is reflected by the fact that the
velocity of the intercellular Ca2+ wave rises
with agonist concentration, as shown in the experiments
(17
18
19)
.
That the level of synchronization is better for the first few spikes
after stimulation is indeed experimentally observed in most cases; one
example is shown in Fig. 4B
. The loss of coordination among
this triplet of connected hepatocytes was not due to a time-dependent
alteration of the cells. Indeed, resynchronization could be achieved by
washing and restimulation of the same triplet by an identical
concentration of vasopressin (Fig. 4B
, right).
In the model, the gradual loss in coordination can be explained by the fact that the apparent intercellular Ca2+ waves are actually the result of uncoupled oscillators because InsP3 does not oscillate significantly during the course of Ca2+ oscillations. Thus, initial coordination arises because of the initial conditions and the proximal levels of InsP3 prevailing during the evolution of the three cells toward their steady state situations. However, because the oscillators are basically uncoupled, they do not remain coordinated for long time periods.
On the basis of estimates of the mean numbers of V1a vasopressin
binding sites in the perivenous and periportal zones along the liver
cell plate, we assumed in the model a well-organized gradient of
VPLC within a triplet. This assumption
allowed us to mimic experimental observations as well as to make
appropriate theoretical predictions (see below). However, if this
organization is not respected, e.g., if the least or the most sensitive
cell of a triplet is the central one, the model predicted that the
coordination of Ca2+ oscillations would be
maintained, but the appearance of a unidirectional
Ca2+ wave would be lost (data not shown). Such a
coordinated Ca2+ response, in which the
Ca2+ spike first occurs in the intermediate cell,
has been reported experimentally (17)
and could be the
result of the three-dimensional network of liver cell plates that
branch and bend back onto themselves (42)
.
Theoretical predictions
A peculiar feature of intercellular Ca2+
waves in hepatocytes, compared with other cell types, is that they
require the continuous presence of an agonist (20)
. Thus,
we compared the results of the model with that of the real cells when
the agonist is removed. In Fig. 5A
, norepinephrine was used to stimulate a triplet and then,
during oscillations, the agonist was rapidly washed out. Spiking did
not occur in cell 3 after washing, probably because the level of
InsP3 in this cell was too low due to the absence
of the agonist. Simulation of this experiment, with the same parameter
values as in Figs. 3
and 4
, is shown in Fig. 5B
. A sudden
decrease of VPLC to its basal value in
the three connected cells (at t = 275 s) prevented
Ca2+ spiking in cell 3. When
VPLC was returned to its stimulated
value in all three cells, coordinated Ca2+
spiking recovered, similar to that observed in the experiments (Fig. 5B
). However, in contrast to the situation before washing,
cell 3 (green line) spiked first after the agonist was reapplied. This
was due to the fact that the fraction of activable
InsP3 receptors was slightly higher in this cell
because the levels of InsP3 and
Ca2+ were already raised before washing (see Fig. 5B
).
|
Experimentally, such an inversion in the sequence of responses was also
observed. Fig. 5A
shows that when the washing time was short
(see below), the initial sequence (cell 1, 2, then 3) was modified
(cell 3, 1, then 2). In the model, the initial sequence (cell 1 to 3)
recovered after five coordinated spikes, whereas in the experiments,
recovery generally occurred sooner (see Fig. 5A
). A
straightforward prediction of the model is that when the time interval
during which no InsP3 synthesis occurs (i.e., the
washing time) becomes very large, the sequence of
Ca2+ spikes occurring in response to the second
addition of the hormone will be imposed by the hormonal sensitivity, as
it is for the first addition of agonist (data not shown). This
prediction is in good qualitative agreement with the experimental
results, although the time scales do not match the experimental
observations (i.e., the washing time needs to be longer in the model
than in reality). Analysis of 12 multiplets of connected hepatocytes (7
doublets and 5 triplets) showed that when the washing time was greater
than 50 s, no inversion was observed. In contrast, the cell that
had been prevented from responding was the first responding cell after
washing when the washing time was below 30 s.
Experimental observations have clearly shown that effective gap
junctions are necessary to coordinate Ca2+
spiking in connected hepatocytes. In the model, gap junctions reduced
the differences in the levels of InsP3 because of
the imposed gradient in the rates of InsP3
synthesis (VPLC). Because the gradient
in hormonal sensitivity is tenuous (a value of 5% between two adjacent
cells is used in the simulations), it is expected that some level of
coordination in Ca2+ spiking should be observed
in neighboring cells, even if the cells are not connected through gap
junctions. This point is illustrated by the results shown in Fig. 6A
; this simulation was performed under the same conditions as
Fig. 4A
, except that the permeability of the gap junctions
to InsP3 (FIP) was
set to zero. It is clearly visible that the first
Ca2+ spike is coordinated in the three cells.
This is due to the fact that, after the rise in
InsP3 resulting from the increase in
VPLC, the three cells enter the
oscillatory domain at about the same time. However, because the
stationary values of InsP3 concentrations are
significantly different, each cell oscillates afterward at its own
frequency and spiking occurs independently in the different cells. This
mechanism bears much similarity with that proposed by Jafri and Keizer
to account for intracellular Ca2+ waves in
Xenopus oocytes (43)
.
|
This property of the model is corroborated by the experiment shown in
Fig. 6B
. The first Ca2+ spike after
stimulation of a triplet of hepatocytes pretreated with AGA, a gap
junction inhibitor, occurred nearly at the same time in all three
cells, although thereafter there was no coordination of
Ca2+ spiking among the three cells. Then, if it
is possible in principle to coordinate the first few
Ca2+ spikes in the absence of gap junctions,
e.g., by adjusting the values of some parameters of the model such as
the intensity of the gradient in hormonal sensitivity, this mechanism
would not be in agreement with the experimental observation that
Ca2+ spikes are not coordinated if a triplet of
cells is treated with gap junction inhibitors (Fig. 6B
above, see also Fig. 4
in ref. 20
). Thus, if we assume in the model
differences in hormonal sensitivities matching reasonably well the
experimental observations, one has to incorporate
InsP3 diffusion through gap junctions to account
for the observed coordination in Ca2+ spiking
among neighboring cells.
The last prediction presented here pertains to the behavior of
connected hepatocytes stimulated by very low doses of agonist. Indeed,
in the model coordination of Ca2+ spikes relied
on close levels of InsP3. If the intensity of
stimulation is low, the relative differences between the concentrations
of InsP3 among the connected cells are more
important, although the gradient in the number of receptors remains the
same. As shown in Fig. 7A
, in the model, very low levels of stimulation led to
non-coordinated spiking among a triplet of connected cells. Similar
results were also found experimentally (Fig. 7B
); the same
triplet exhibited no coordination at low agonist levels (0.02 nM
vasopressin) and good coordination at higher agonist doses (0.2 nM
vasopressin).
|
Model in which Ca2+ is the coordinating messenger
We have also tested the hypothesis that
Ca2+, and not InsP3, could
diffuse through gap junctions. To this end, we have replaced the
boundary conditions given in Eq. 4 by a similar equation for
Ca2+; we have also added an equation for changes
in the concentration of luminal Ca2+
(Clum), because the total intracellular
Ca2+ concentration does not remain constant.
Because the release of Ca2+ through the
InsP3R is stimulated by both
Ca2+ and InsP3,
coordination of Ca2+ spikes throughout a group of
connected cells could in principle also be achieved in this way.
However, it should be kept in mind that Ca2+
buffering (here taken into account by using an appropriate
Ca2+ diffusion coefficient) and extrusion from
the cytosol are both very efficient and fast processes. Thus, small
amounts of Ca2+ diffusing through gap junctions
would probably not provoke a rise in cytosolic free
Ca2+ large enough to activate the
InsP3Rs and induce a Ca2+
wave. Although the model does not allow us to exclude the hypothesis
that intercellular Ca2+ waves in hepatocytes rely
on the passage of Ca2+ through gap junctions, the
following negative results suggest that InsP3 is
a more likely candidate for coordination.
First, in this model including Ca2+ diffusion through gap junctions, the spikes propagated intercellularly with decreasing amplitudes (data not shown). This behavior is due to the fact that spiking in cells 2 and 3 occurs sooner and with lower levels of InsP3 than Ca2+ spikes that occur without Ca2+ input from adjacent cells. Thus, the fraction of activable InsP3 receptors at the onset of the spikes is lower and the flux through the InsP3 receptor is of reduced amplitude, which is not observed experimentally.
Second, the results of the agonist removal experiment (see Fig. 5
)
cannot be accounted for by the model based on
Ca2+ diffusion through gap junctions. Indeed, in
this model, when the agonist is removed just after the
Ca2+ spike in cell 1, the amount of
Ca2+ transferred through the gap junctions is
sufficient to induce a Ca2+ spike in cells 2 and
3, even at the reduced levels of InsP3 generated
by the sudden return of VPLC to its
basal level. Given that InsP3 synthesis and
metabolism are relatively slow (to account for latencies on the order
of 1 min, see above), the decrease in the level of
InsP3 occurring in a few seconds is quite small;
as a consequence the level of InsP3 is still high
enough to allow the generation of a Ca2+ spike in
response to the Ca2+ input from the adjacent
cell. The model thus predicts that the Ca2+
permeability necessary to coordinate Ca2+ spikes
in hepatocytes, whose periods are intrinsically different due to
different hormonal sensitivities, is too high to prevent
Ca2+ spiking in a connected cell in which the
level of InsP3 has been decreasing for a few
seconds after washing.
Third, the model based on the diffusion of Ca2+
through gap junctions cannot account for the asynchronous spiking
observed at low levels of stimulation (see Fig. 7
). Because the
amplitude of the Ca2+ spike does not much depend
on the level of InsP3, the amount of
Ca2+ diffusing through gap junctions remains the
same for all values of VPLC. As a
consequence, spiking is either coordinated or does not occur at all in
the less sensitive cell(s), because the level of
InsP3 in these cells is too low.
Altogether, these comparisons between theoretical and experimental results led us to conclude that InsP3 diffusion through gap junctions must play a dominant role in the coordination of Ca2+ spikes among connected hepatocytes. However, it is possible that Ca2+ can also somewhat diffuse through gap junctions and thereby synchronize the Ca2+ responses in adjacent cells exhibiting small random variations in the different processes related to Ca2+ handling.
Conclusions
Based on the assumption that connected hepatocytes differ in their
sensitivity to an agonist, we have shown that coordinated
Ca2+ spiking can be ascribed to the diffusion of
small amounts of InsP3 through gap junctions. The
direction of the gradient of hormonal receptors determines the
direction of the wave, whereas its amplitude determines the propagation
velocity.
From a more general and physiological point of view, intercellular
Ca2+ waves in hepatocytes resemble the
propagation of signals in some other tissues. For example, the
propagation of the action potential in the cardiac sinoatrial node can
indeed be described as a phase wave propagating through large groups of
cells whose intrinsic periods are different (44)
. Although
there are noticeable differences in intercellular propagation of
signals in hepatocytes and cardiac pacemaker cells, in both cases the
coordination of the response among a large group of cells optimizes the
operation of the whole organ, and the direction of propagation is
determined by a gradual heterogeneity in cellular spiking. The
physiological impact of such an organization at the multicellular (or
tissue) level may be important for orienting cell-to-cell signals in
specific directions, not only in the heart but also in other tissues
such as the liver or colon (18
, 19
, 45)
.
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSDESCRIPTION OF THE MODELRESULTS AND DISCUSSIONREFERENCES |
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