Journal of Experimental Botany, Vol. 51, No. 353, pp. 2053-2066,
December 2000
© 2000 Oxford University Press
Transport and metabolic degradation of hydrogen peroxide in Chara corallina: model calculations and measurements with the pressure probe suggest transport of H2O2 across water channels
Tobias Henzler1 and
Ernst Steudle
Lehrstuhl Pflanzenökologie, Universität Bayreuth, D-95440 Bayreuth, Germany
Received 19 January 2000;
Accepted 24 July 2000
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Abstract
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A mathematical model is presented that describes permeation
of hydrogen peroxide across a cell membrane and the implications
of solute decomposition by catalase inside the cell. The model
was checked and analysed by means of a numerical calculation
that raised predictions for measured osmotic pressure relaxation
curves. Predictions were tested with isolated internodal cells
of
Chara corallina, a model system for investigating interactions
between water and solute transport in plant cells. Series of
biphasic osmotic pressure relaxation curves with different concentrations
of H
2O
2 of up to 350 mol m
-3 are presented. A detailed description
of determination of permeability (
Ps) and reflection coefficients
(
s) for H
2O
2 is given in the presence of the chemical reaction
in the cell. Mean values were
Ps=(3.6±1.0) 10
-6 m s
-1 and
s=(0.33±0.12) (±SD,
N=6 cells). Besides transport
properties, coefficients for the catalase reaction following
a Michaelis-Menten type of kinetics were determined. Mean values
of the Michaelis constant (
kM) and the maximum rate of decompositon
(
vmax) were
kM=(85±55) mol m
-3 and
vmax=(49±40)
nmol (s cell)
-1, respectively. The absolute values of
Ps and
s of H
2O
2 indicated that hydrogen peroxide, a molecule with
chemical properties close to that of water, uses water channels
(aquaporins) to cross the cell membrane rapidly. When water
channels were inhibited with the blocker mercuric chloride (HgCl
2),
the permeabilities of both water and H
2O
2 were substantially
reduced. In fact, for the latter, it was not measurable. It
is suggested that some of the water channels in
Chara (and,
perhaps, in other species) serve as ‘peroxoporins’
rather than as ‘aquaporins’.
Key words:
Catalase, Chara corallina, hydrogen peroxide, permeability coefficient, reflection coefficient, water channel.
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Introduction
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Hydrogen peroxide occurs in important metabolic reactions such
as during the action of oxygenases in glyoxysomes and peroxisomes,
during photosynthesis in choloplasts, and during the synthesis
of lignin in the apoplast (Asada, 1992
; Ishikawa
et al., 1993
;
Schopfer, 1996
). The metabolite is usually considered to be
toxic either by itself or by the fact that it is a precursor
of the even more toxic hydroxyl radical. Plants use H
2O
2 as
a signal and a chemical for defending against attacks by pathogens
(‘oxidative burst’; Wojtaszek, 1997
; Apostol
et al., 1989
; Peng and Kuc, 1992
). In peroxisomes, H
2O
2 is produced
at high rates. The organelles contain catalase at high concentrations
which splits H
2O
2 into water and oxygen. It has been found that
chloroplasts lack catalase, and H
2O
2 produced during photorespiration
is eliminated by reduction to water via the ascorbate/glutathione
cycle (Asada, 1992
). Although there are, as far as is known,
no quantitative data, hydrogen peroxide is usually thought to
move rapidly across the membranes of cells and organelles. If
the solute was that mobile, the diffusion out of compartments
such as peroxisomes could be a problem. The escape of H
2O
2 from
peroxisomes (where it is produced) could be favoured above its
degradation because of the small size of the organelles (high
surface area to volume ratio). Although this could be compensated
for by a high concentration of catalase (as found in peroxisomes),
there could be a serious problem depending on the absolute value
of the permeability of the membrane for H
2O
2. Despite the general
assumption that H
2O
2 rapidly crosses membranes, it is nevertheless
thought that it may be concentrated in certain tissues during
oxidative burst at a level which is sufficient to cause an oxidative
stress to pathogens (Apostol
et al., 1989
; Peng and Kuc, 1992
).
Obviously, different situations require some regulation of the
permeability of membranes to H
2O
2. The lack of data of the membrane
permeability of H
2O
2 is due to the fact that it is difficult
to measure H
2O
2 fluxes in the presence of substantial activities
of catalase and peroxidase, i.e. to separate membrane permeation
from reaction flows experimentally. The problem is that of measuring
the diffusional permeability of a substrate which takes part
in a chemical reaction. Provided that concentrations of H
2O
2 and its reflection coefficient are rather large, the permeation/decomposition
of H
2O
2 should also affect water flows and cell turgor pressure
and should be measurable using the pressure probe technique
(Steudle and Tyerman, 1983
; Rüdinger
et al., 1992
; Steudle,
1993
; Henzler and Steudle, 1995
). Since there is no direct coupling
between the decomposition of H
2O
2 and the transfer of water
across the membranes, interactions between the chemical reaction
and water flow should be indirect, i.e. mediated by changes
of the internal concentration of H
2O
2.
Preliminary observations showed that isolated internodes of Chara corallina could tolerate concentrations of more than 100 mM H2O2. From the osmotic responses measured with the cell pressure probe it was obvious that reflection coefficients were substantially larger than zero. Measurements of steady-state turgor in the presence of hydrogen peroxide indicated that there was a considerable degradation of H2O2 in the cells which was attributed to the action of catalase and peroxidases. In this paper, the permeability and decomposition of H2O2 of these cells is analysed in more detail. By means of the cell pressure probe, osmotic responses of the permeating solute H2O2 have been measured. In order to separate kinetics into components due to reaction flow (degradation of H2O2 in the cell) and due to solute flow across the membranes, a physical/mathematical model was established which predicted the osmotic reactions of internodes (water and solute flows in the presence of catalase action), when H2O2 was added to the external medium. Predictions from the model were tested experimentally. Permeability and reflection coefficients of H2O2 have been worked out as well as kM and vmax of the catalase activity of internodes. The facts that (i) the diffusional permeability of H2O2 (Ps) was smaller by only a factor of two than that of water (Pd) and that (ii) treatment with the channel blocker HgCl2 reduced both Ps and Pd, indicated that H2O2 used water channels on its passage across the plasma membrane. It is suggested that at least some of the water channels present in the cell membrane are H2O2 channels or ‘peroxoporins’ rather than aquaporins.
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Theory
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The system under investigation is a single cell sitting in a
big reservoir of a medium with a constant external concentration
of a permeating solute (
Co=constant). A cell membrane separates
the medium inside the cell (superscript ‘i’) with
concentration
Ci(
t) from the surrounding medium outside (superscript
‘o’). Osmotic pressures of all non-permeating solutes
can be comprised into the steady-state turgor pressure to a
good approximation (
P0=
P(
t=0)). The membrane has a permeability
for water (
Lp, hydraulic conductivity) and for the solute (permeability,
Ps, and a reflection,
s, coefficient). Any active transport
across the membrane is neglected since the time scales of such
processes are in ranges which are usually much larger than the
rapid processes considered here. At time
t=0, step-changes of
external concentrations are performed. In the following, an
experiment is called ‘exosmotic’ when the external
concentration is increased (positive step-change). This induces
a water flow out of the cell. An experiment is called ‘endosmotic’
when the external concentration is decreased (negative step-change,
and water uptake by the cell). In the system described, water
(
JV, m
3 m
-2 s
-1) and solute flow (
Js, mol m
-2 s
-1) are given
by
equations 1 and
2 (Rüdinger
et al., 1992
):
 | (1) |
 | (2) |
The symbol P denotes cell turgor pressure and R and T are the gas constant and absolute temperature, respectively. 
is the amount of moles of solute crossing the cell membrane during a time interval dt. A and V are the cell surface area and the cell volume, respectively. By convention, a flow out of the cell has a positive sign. Since the cell wall is assumed to be rigid, volume changes (dV) are less than 1% (dV<<V
constant). Therefore, the assumption holds that 
(equation 2
), i.e. the solute flow across the membrane is proportional to the change of internal concentration. The first term on the right side of equation 1 describes the ‘hydraulic’ and the second term the ‘osmotic’ water flow. The first term on the right side of equation 2 represents the diffusion of the solute along the concentration gradient. The second term expresses the coupling between water and solute flow (solvent drag). This latter term is usually negligibly small even when s is substantially smaller than unity (s<0.5; Rüdinger et al., 1992). One can calculate the ratio of diffusion to solvent-drag at the beginning of an osmotic relaxation (t=0) when JV and Js are at maximum. For a Chara internode, typical parameters of transport of water and H2O2 are: Lp=1.7x10-6 m (s MPa)-1, Ps=3.6x10-6 m s-1, and s=0.33 (Table 1). Assuming an initial concentration gradient of Co-Ci(t=0)=Co=100 mol m-3, the solvent drag component comprises always less than 2% of the total solute flow. Therefore, the solvent drag will be neglected in further calculations.
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Table 1. Summary of parameters for cell geometry, solute transport and enzyme kinetics
A summary of parameters for geometry (A and V: cell surface-area and volume), solute transport (Ps, permeability coefficient; s, reflection coefficient), and Michaelis-Menten kinetics (vmax; kM) is given for six different internodes of Chara corallina. Parameters of solute transport are mean values of five to six osmotic pressure relaxations (±SD: standard deviation; N=5–6 experiments). Parameters for Michaelis-Menten kinetics are obtained by a fitting procedure as described above (±SE: asymptotic standard error). Mean values are given as well in the bottom rows (relative error in %; N=6 cells). In the second last column, vmax per unit cell volume is given which shows a smaller relative error than vmax itself. In the last row, the ratio ß (=vmax/(kMPsA)=kcat/ks) is calculated that is a parameter used in the numerical analysis.
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Equations 1
and 2
are valid only if the permeating solute remains
unchanged inside the cell, i.e. when it is not taking part in
metabolic processes. When the permeating solute is decomposed
inside the cell, this should be taken into account, i.e. equation
2
has to be extended by a term which incorporates the chemical
reaction. The most simple case of such a chemical reaction is
the decomposition of hydrogen peroxide in the presence of the
enzyme catalase inside the cell:
 | (3) |
Of course, there could be also other enzymes such as different peroxidases which would degrade H2O2, but their specific activities are usually smaller than that of catalase (see Discussion). The products of the degradation of H2O2 in the presence of catalase (H2O; O2) are not osmotically active. The enzymatic degradation reduces the internal concentration of H2O2 which is osmotically active. In other words, an additional ‘virtual’ flow of solute is produced (‘reaction flow’ of H2O2). The rate of decomposition (dnicat/dt) should follow a Michaelis-Menten type of kinetics (vmax: maximum rate, in mol (s cell)-1; kM: Michaelis constant, mol m-3). Equation 4 describes the reduction of the inner concentration due to enzymatic reaction according to a Michaelis-Menten equation:
 | (4) |
Equation 2 can be modified by adding the Michaelis-Menten term from equation 4 expressed per unit area:
 | (5) |
Equation 5 implies that the simple two-compartment model is still valid despite the fact that catalase is compartmented in peroxisomes where the splitting of H2O2 takes place. However, the assumption is reasonable, because of the small size of peroxisomes which provides a rapid equilibration of H2O2 in peroxisomes with its surroundings even if the permeabilities of the membranes of organelles were low. There is evidence from earlier data that the permeability of the tonoplast for uncharged small molecules is high which justifies the assumption of a two-compartment model (for a detailed consideration of compartmentation, see Discussion). Equation 5 describes the solute transport across a membrane when a chemical reaction following a Michaelis-Menten type of kinetics decomposes the solute inside the cell. By contrast with the situation in the absence of a chemical reaction, a simple analytical solution for the time-course of the inner concentration Ci(t) after changing the concentration of solute outside at t=0 is not available. It may be possible to calculate a complex formula for Ci(t) involving several substitutions, integrations and solving of a third order polynomial equation (not shown). However, such a complex formula would hardly be of practical use for analysing measured pressure relaxation curves. Nevertheless, three special cases should be discussed which are important in the context of this paper. For these cases, analytical solutions are given in the following paragraphs. Solutions are analysed for an exosmotic experiment, but the procedure for the endosmotic case is similar.
Case I (t
)
After changing the osmotic gradient between inside and outside at t=0, a new steady-state will be reached when water and solute flow have vanished again (JV, Js=0 at t). For the new steady-state, it follows from equation 5:
 | (6) |
where
is the final steady-state concentration inside. According to equation 6
, the substrate moves into the
cell at a rate which is just balanced by enzymatic degradation.
Equation 6
shows that, in the presence of a chemical reaction,
the internal concentration is always lower than the external.
From equation 1
it follows that the final steady-state pressure
(
P=
P(
t)) would also then be lower than the initial (
P0), i.e.:
 | (7) |
The value of
is difficult to measure. However, equation 6
can be used to
express
as a function of
Co. Substituting
into equation 7
leads to a relation between
P and
Co that can be measured:
 | (8) |
Figure 1
shows plots of
P as a function of either
(equation 7
) or
Co (equation 8
) which have been generated by
a computer. The figure illustrates that
P is a measure of the
rate of decomposition by the enzyme, and therefore, follows
a Michaelis-Menten type of kinetics. By definition, a Lineweaver-Burk
plot of 1/
P as a function of
yields a straight line (see inset of Fig. 1
). However, the inset also shows that
this type of plot is of no use for evaluating
vmax and
kM when
1/
P is plotted as a function of 1/
Co. At saturating concentrations
of substrate, the pressure difference approaches a maximum value
proportional to
vmax:
 | (9) |
Half of the maximum pressure difference is reached when the
concentration inside the cell equals
kM. Since the concentration
outside is always higher than inside, a plot of
P versus
Co is shifted to the right as compared with that of
P versus
. The difference between the two plots depends on
the ratio of the rates of decomposition to permeation of substrate
(
vmax/(
kMPs)). When treating a cell with a series of solutions
with different concentrations, the corresponding
P can be obtained
(see Results). From these data, it is then possible to evaluate
vmax and
kM using equation 8
.
Case II (kM>>Co, Ci)
When the external (and therefore also the internal) concentration is much lower than the Michaelis constant kM, the rate of decomposition is proportional to the inner concentration to a good approximation (linear range of Michaelis-Menten kinetics). Equation 5 reduces to:
 | (10) |
Equation 10
can be integrated
using standard procedures. This yields the following time-course
for
Ci(
t):
 | (11) |
where
ks=(
APs)/
V,
kcat=
vmax/(
VkM), and
ks*=
ks+
kcat. Equation 11
describes an exponential
increase of
Ci(
t) up to a steady-state concentration lower than
Co. The rate constant of the process (
ks*) is higher than that
in the absence of a chemical reaction (i.e.
vmax=0,
kcat=0).
In this latter case, equation 11
reduces to:
 | (12) |
Permeation and decomposition of H
2O
2 take place simultaneously
and the overall rate constant (
ks*) in equation 11
reflects
the sum of the two single processes (see Discussion). In the
presence of a chemical reaction, the final pressure difference
is:
 | (13) |
It is easily verified from
equation 13
that the absolute value of
P depends on the relative
contribution of the rate of degradation (
kcat) to the overall
rate (
ks*). For example, when, transport dominates, i.e. when
vmax>>(
PsAkM),
P0 is obtained. This has been often verified
in the absence of a chemical reaction. On the other hand, if
vmax>>(
PsAkM) holds, the solute entering the cell is rapidly
degraded. At an extreme, this should result in a
P=
sCoRT. In
this case, the second solute phase would be completely missing.
This result has been obtained in this paper when the transport
of H
2O
2 was blocked in the presence of HgCl
2.
Case III (kM<<Ci, Co)
Under these conditions, maximum rates of decomposition of substrate should be attained. The second term on the right side of equation 5 reduces to the constant factor vmax/A. The integration of equation 5 then yields:
 | (14) |
It can be seen that the kinetics is independent of kM. The rate constant of the exponential process 
is that of the solute permeation only. This is so because, at high concentrations, membrane permeation is the limiting step (see Discussion). The final pressure difference is then P=Pmax (equation 9) which can be directly approximated from equation 8.
Cases II and III show that, in both extremes, time-courses of inner concentrations Ci(t) can be approximated by single exponential functions. Exponential curves just differ in their rate constants (ks+kcat and ks, respectively). This leads to the idea that, in general, the main part of a solution for equation 5 is a single exponential function, and its rate constant decreases with increasing concentrations outside (Co). To test this idea, a numerical solution of equation 5 must be found and analysed.
Basis of numerical simulation
In order to simplify expressions, it is useful to rewrite equation 5 by substituting time and concentration in terms of dimensionless variables (
=kst and x()=1+Ci()/kM), i.e.:
 | (15) |
Here,
xo=1+
Co/
kM and ß=
kcat/
ks=
vmax/(
PsAkM) which are
dimensionless, too. Equation 15
is therefore normalized. In
an exosmotic experiment, the external concentration changes
from
xo=1 to a constant
xo>1 at
=0. Boundary conditions for
a numerical solution are:
and
 | (16) |
In the case of an endosmotic experiment, step changes of concentration are in the opposite direction, i.e. at =0, the external concentration is changed from a constant xo>1 to xo=1. The differential equation is modified since the actual value of xo is xo=1:
 | (17) |
Boundary conditions are opposite as compared to the exosmotic
case, i.e.:
and
 | (18) |
where
xo=constant>1 is the initial external concentration
before changing back to the original medium. In order to find
an exponential kinetics for
x(
t), it is useful to also define
a dimensionless overall rate constant (
s*=
ks*/
ks). When the
process is dominated by permeation it follows that
ks*
ks and
s*
1.
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Materials and methods
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Plant material
Chara corallina was grown in artificial pond water (APW; composition
in mol m
-3: 1 NaCl, 0.1 KCl, 0.1 CaCl
2, 0.1 MgCl
2) in tanks
which contained a layer of natural pond mud (Henzler and Steudle,
1995
). Tanks were placed in a greenhouse without additional
illumination. Internodes used in pressure probe experiments
were 50–100 mm in length and 0.8–1.0 mm in diameter.
Determination of transport parameters
Transport parameters were measured and calculated from ‘hydrostatic’ (Lp: hydraulic conductivity in m s-1 MPa-1) and ‘osmotic’ (Ps: permeability coefficient in m s-1; s: reflection coefficient) pressure relaxations. Relaxation curves have been measured using a conventional cell pressure probe as previously described (Henzler and Steudle, 1995). Numerical analysis of the time-course of solute concentration inside the cell indicated that kinetics can be described by single exponential functions to a good approximation (see Results). Therefore, overall rate constants (ks*) were evaluated from the second part of exosmotic pressure relaxations, i.e. from the ‘solute phase’. Rate constants ks used to calculate the solute permeability (Ps=ksV/A) were extrapolated from a series of exosmotic relaxations with different external concentrations of hydrogen peroxide to Co. In some cases, only a small if any correlation between ks* and Co could be detected. Hence, ks was calculated as a mean of ks*. In other cases, ks* decreased with increasing Co, and ks was determined from the extrapolated value of a single exponential fit of ks* as a function of Co.
The definiton for calcluation of reflection coefficients is derived from equation 1. Since JV vanishes at the minimum of the curve (JV(t=tmin)=0) it holds that:
 | (19) |
Assuming an exponential increase of the inner concentration
to a value
(equation 7
), the time-course
of
Ci(
t) can be espressed as:
 | (20) |
Combining equations 19
and 20
at
t=
tmin, yields an expression
which was used to calculate reflection coefficients from exosmotic
relaxation curves:
 | (21) |
Here,
Pmin denotes the pressure at
t=
tmin where the minimum of the curve
was reached. The exponential factor in equation 21
corrects
for the change of the initial osmotic pressure gradient (
RTCo)
caused by permeation and degradation of solute. Different from
earlier formulae used to estimate
s, the overall rate constant
ks*, and not
ks, had to be used for the correction, because
ks* describes the change of the concentration gradient (equations
11
and 14
). It can be seen from equation 21
that, in the absence
of a chemical reaction (
ks*=
ks and
P0=
P), equation 21
is identical
with the equation used earlier to evaluate reflection coefficients
from osmotic pressure relaxations (Steudle and Tyerman, 1983
).
Analysis of enzyme kinetics
To determine parameters for enzyme kinetics, a concentration series of osmotic experiments was performed with each of six different internodes. Starting with low concentrations of hydrogen peroxide, several subsequent exosmotic and endosmotic pressure relaxations with four to five different concentrations were performed (Fig. 3). Using equation 8, final steady-state pressure differences of the exosmotic experiments (P) were fitted to the corresponding concentrations of H2O2 in the medium (Co). Michaelis constants (kM) and maximum rates of decomposition (vmax
Pmax) were obtained from the fitted parameters either directly (kM) or using equation 9 (vmax). Since the external concentrations of substrate (Co) which could be measured here, were higher than internal concentrations at steady-state (Ci), a double reciprocal plot (Lineweaver-Burk type) was of no use (see inset of Fig. 1and equations 7 and 8).
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Fig. 3. Concentration series of osmotic pressure relaxation as measured subsequently with a cell pressure probe. A typical experiment of a series of five different osmotic pressure relaxations with one Chara internode is shown (cell no. 2 from Table 1). Arrows denote the time when the medium outside was quickly replaced by a solution containing denoted concentrations of hydrogen peroxide up to 265 mM (H2O2). Due to decomposition of H2O2 inside the cell, turgor pressure does not re-attain the initial value after adding a hypotonic solution (dotted arrows; dotted lines denote initial (P0) and end pressure (P) for each concentration). Steady-state cell turgor pressure P0 of about 0.7 MPa (=7 bar) remained nearly constant during 2 h of experiment with fairly high concentrations of H2O2.
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Numerical simulation
A numerical calculation of the solute concentration inside a
cell during an exosmotic or endosmotic pressure relaxation was
provided by solving the normalized equations 15
and 17
by means
of a computer (PC, Pentium-II, 300 MHz). Since start values
were known (equations 16
and 18
), time-courses were calculated
by stepwise iteration. During exosmotic water flow, values of
x(
+
) were calculated from previous values
x(
) using equation
15
:
x(
+
)=
x(
)+
[
x(
)-
xo+ß-ß/
x(
)]. Commercial data processing
software was employed in the simulations (Transform-tool of
SigmaPlot 2.01, Jandel Scientific, Erkrath, Germany). Time-steps
of
=5
x10
-5 were used that corresponded to 1–5 ms in ‘real’
time. Maximum changes of
x(
+
)-
x(
) occurred at the beginning
of calculations (
0) for the high values of
xo. These changes
corresponded to changes in ‘real’ concentration
of smaller than 0.05 mol m
-3 (50 µM) at external concentrations
of 7–1000 mol m
-3 (7 mM to 1 M). Therefore, a sufficient
resolution of time for numerical calculations and the linearity
of step-changes of
x(
) was guaranteed. Numerical calculations
of time-courses of
x(
) for 30 different values of
xo took about
3 h.
Fitting of curves
In the context of this paper, fitting of curves just means to determine numerically the optimal parameters of a pre-selected function for the measured data points by means of a least-square algorithm (Marquardt-Levenberg). No searches for appropriate mathematical functions were performed. Commercial software for data processing was employed for the fits (Curve-fit-tool of SigmaPlot 2.01) which also provided asymptotic standard errors for the parameters determined.
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Results
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Numerical simulation
A stepwise numerical solution of
equations 15 and
17 for 30
different values of the normalized external concentration (
xo)
is shown in Fig. 2
. Exosmotic as well as endosmotic experiments
were simulated (Fig. 2A
). For the exosmotic case, a semi-logarithmic
plot showed that, for the whole range of external concentrations
(
xo=1–12;
xoCo),
x(
) can be described by a single exponential
function to a good approximation (Fig. 2B
, left). This has already
been proposed in the theoretical section. Deviations from a
single exponential could be seen only in endosmotic experiments
(Fig. 2B
, right). In this case, deviations increased with increasing
external concentrations. At the beginning of the endosmotic
curves (
=6–7), initial slopes were smaller than mean slopes.
Towards the end of relaxations (
>10), slopes became bigger.
The asymmetry between exosmotic and endosmotic experiments originated
from either increasing (exosmotic) or decreasing (endosmotic)
internal concentrations. Therefore, the two processes (permeation
and degradation) influenced the curves differently during different
time intervals. This resulted in a more complex behaviour in
the case of an endosmotic experiment. Hence, for the sake of
simplicity, only the exosmotic case was investigated further.
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Fig. 2. Numerical solution and analysis of equations 15 and 17. In (A), the numerically determined time-course of the normalized internal concentration of H2O2 (x()) is shown (different symbols denote different values for external concentration (xo)). For each value of xo, an exosmotic as well as an endosmotic relaxation is calculated. For the numerical calculation, a set of parameters was used similar to those measured in experiments (Ps=3.6x10-6 m s-1; A=1.9x10-4 m2; vmax=4.5x10-8 mol s-1; kM=91 mol m-3; ß=0.723; time-step of numerical calculation: =5x10-5). Only every 5000th calculated value is shown. Curves were fitted assuming an exponential kinetics (solid line). The only parameter to be fitted was the rate constant (s*; see C). Dotted lines at the exosmotic side represent theoretically predicted values for x() (equation 16). In (B), a semi-logarithmic plot of the data of (A) is given using the value of x() from equations 16 and 18. For each value of xo, a different constant term was added to the logarithm to broaden the distances between curves. Correlation coefficients of linear regressions were close to unity (r2>0.99) showing that simulated curves were single exponentials to a good approximation. Only at high concentrations in the endosmotic case, deviations of the straight line can be seen. In (C), the functional relation between normalized rate constants (s*, ( ): endosmotic; (•): exosmotic) and external concentrations is analysed. Data were taken from fits of the numerical calculations in (A). The value of s* decreased with increasing concentration outside. Data were fitted to one (dashed line) or two exponentials (solid line). At low xo, s* is close to 1+ß=1+kcat/ks, at high xo, s* reached unity (dotted horizontal lines). In the endosmotic experiment, values were, in general, higher. The dotted vertical line denotes xo=1 (Co=0).
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Figure 2C
shows a plot of the normalized overall rate constant
(
s*=
ks*/
ks) as a function of
xo. Data were determined from the
fits in Fig. 2A
. It can be seen that
s* decreased with increasing
xo. For the exosmotic experiment, values varied from 1+ß
(low
xo1) to unity (high
xo) as was expected before (Cases II
and III in the Theory section). Due to the bigger slopes at
the end of the curves (see above), values for
s* were, in general,
larger in endosmotic than in exosomotic relaxations. The functional
relation between
s* and the external concentration was exponential
in nature (exponential fits in Fig. 2C
). The numerical analysis
verified that the rate constant of the sum of the processes
(permeation and degradation of H
2O
2) was bigger than that of
permeation only. Absolute values depended on the actual concentration
of hydrogen peroxide in the medium. Only at high concentrations
of H
2O
2, measured rate constants could be regarded solely as
those of the process of permeation only.
Pressure probe experiments
In Fig. 3, a typical series of time-courses of osmotic pressure relaxations is shown for five different concentrations of hydrogen peroxide (40–265 mM). After quickly replacing the medium with a solution containing a certain amount of H2O2, cell turgor pressure decreased due to a flow of water out of the cell. After reaching a horizontal tangent at the minimum of the curve (P(tmin)=Pmin and JV=0), pressure increased again due to permeation of hydrogen peroxide into the cell. However, turgor pressure did not come back to its initial value. Since H2O2 was decomposed inside the cell, a final steady-state pressure difference (P) was maintained. Changing the medium back to a solution containing no H2O2 resulted in a response curve which was symmetrical to the exosmotic one, but was in the opposite direction.
Although high concentrations of hydrogen peroxide of up to 350 mol m-3 were used with some cells, there was a decrease of cell turgor of only 3–9% of the initial pressure during 1–2 h of experiment with a given cell. After one ex- and endosmotic experiment with a given concentration, a decrease of steady-state pressure of about 0.3–1% was found resulting in a slight ‘undershoot’ of the endosmotic curve (as compared with the initial pressure before the exosmotic experiment). Although this pointed to a stress of the cell caused by the treatment, its effect was fairly small. Therefore, it was concluded that the intregrity and stability of the cell membrane was maintained.
In Fig. 4, the evaluation of the rate constant of solute permeation is shown. Figure 4A summarizes biphasic exosmotic pressure relaxation curves for six different external concentrations of H2O2 as subsequently measured with a cell pressure probe. Fits for the second phase are plotted which represent the increase of concentration inside the cell. The fit procedure was used to determine the optimal values for Pfit(t=0), Pfit=Pfit(t), and ks* of a single exponential curve. In Fig. 4B, a semi-logarithmic plot of the data of Fig. 4A is given which shows that curves were single exponentials to a good approximation (correlation coefficient r2>0.97). At the end of relaxations, differences between P and Pfit were small which resulted in a marked scatter of the semi-logarithmic plot. This systematic error at the end of the curves was cut off for evaluation.
In Fig. 4C
, a plot of the extrapolated initial pressure differences
caused by the different osmotic pressure gradients of H
2O
2 is
shown. The extrapolated value of
Pfit(
t=0) is a theoretical
value that would be attained in an experiment if the half-time
of water exchange was close to zero (
Tw1/20) and therefore
tmin0.
Then from equation 21
, it follows that (
Pfit(
t=0)=
P(
t=tmin=0)=
Pmin):
 | (22) |
The high correlation (r2=0.999) indicated that fitting the curves yielded consistent results. The slope of the regression line is a measure for the reflection coefficient (s; equation 22). Alternatively, this parameter was determined from the pressure minimum of the curve (equation 21). A similar value was obtained (cell no. 5 in Table 1). Figure 4D presents values for the rate constant (ks*) of the change of the internal concentration of H2O2 determined by two slightly different procedures. Both fitting the curve and regressions of a semi-logarithmic plot yielded nearly the same values of the overall rate constant (ks*).
In Fig. 5, a summary of the dependence of ks* on the concentration of H2O2 in the medium is given for all measured cells. It can be seen form the figure that with four cells (1, 2, 4, 5), ks* decreased with increasing concentration. This can be attributed to the fact that, at high concentrations, substrate permeation became limiting (see Discussion). Values for ks used to calculate Ps were obtained by extrapolating ks* to high concentrations of hydrogen peroxide in the medium, either from mean values or from exponential fits (see Materials and methods). The mean value for six internodal cells was Ps=(3.6±1.0)x10-6 m s-1 which is high compared with other permeating solutes, including the diffusional permeability of water (Pd) as measured with isotopic water (HDO; Tables 1, 2).
In Fig. 6
, the analysis of enzyme kinetics from a typical plot
of a series of exosmotic pressure relaxations is shown. Values
for
kM and
vmax were evaluated by fitting the steady-state pressure
differences (
P=
P0-
P) to the external concentrations used (
Co),
according to equation 8
. Mean values for six cells were:
kM=(85±55)
mol m
-3 and
vmax=49±40 nmol (s cell)
-1 (Table 1
). Values
are in line with data for other species reported in literature
(see Discussion).
The hydraulic conductivity was measured from hydrostatic pressure
relaxation curves (not shown). The mean value for six internodes
was
Lp=1.7±0.7
x10
-6 m (s MPa)
-1. This value can be converted
to an osmotic water permeability
Pf=
LpRT/
m s
-1 
m
3 mol
-1, molar volume of water;
Table 2
). It should be noted that
Pf was larger by a factor
of 30 than
Pd. The ratio of
Pf/
Pd has been used as a measure
for the number of water molecules aligned in a single file in
water channels (Steudle and Henzler, 1995
; Hertel and Steudle,
1997
).
The absolute value of the permeability of hydrogen peroxide was rather high. It was smaller by only a factor of two than that of heavy water (HDO: Pd=7.7x10-6 m s-1; Henzler and Steudle, 1995). This may suggest that, because of the similarity in the chemical structure, H2O2, uses water channels to cross the plasma membrane. In order to test this possibility, the channel blocker mercuric chloride (HgCl2) was used to inhibit water channels. If the permeability of H2O2 were affected, one should expect a decrease of the rate constant of the solute phase. Figure 7 shows that, upon treatment with mercuric chloride, the second (solute) phase was completely absent. This may indicate, that in the presence of the channel blocker, the rate of chemical degradation could compete with that of membrane permeation, i.e. the amount of H2O2 arriving in the cell was immediately degraded in the presence of the enzyme. Assuming that, under these conditions, the concentration of the substrate in the cell was close to zero, a reflection coefficient could be evaluated (equation 21; ks*0) which was smaller than that measured in the absence of the blocker. In terms of the composite transport model of the membrane (Steudle and Henzler, 1995), this may indicate that the reflection coefficient of the bilayer of H2O2 is smaller than that of the water channel array (see Discussion). The half-time of water exchange (first phase of biphasic pressure relaxations) increased indicating a decrease of Lp(Pf) besides the reduction of the rate of uptake of H2O2. To date, an inhibition of solute transport in the presence of the channel blocker HgCl2 has only been shown for heavy water (Henzler and Steudle, 1995; Steudle, 1993). An effect on the permeability of other small uncharged solutes such as monohydric alcohols, amides and acetone was not detectable, although there was some slippage of these solutes across water channels (Hertel and Steudle, 1997). The finding that transport of H2O2, HDO and water (Lp) were similarly affected by a closure of water channels, strongly suggests that there was a substantial movement of H2O2 across water channels. Figure 7C shows that the scavenger 2-mercaptoethanol reverted the effect of HgCl2. However, the figure also indicates that in the presence of two stresses (mercury and high hydrogen peroxide levels), cells tended to become leaky and turgor slowly but inexorably tended to decline. The combination of two stresses could only be tolerated over periods of time which were much shorter than that used during the application of high concentration of H2O2 (up to 3 h).
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Fig. 7. Effect of mercuric chloride (HgCl2) on solute permeability of hydrogen peroxide in a Chara internode. (A) A typical time-course during an osmotic pressure relaxation experiment with H2O2 as permeating solute is shown in the control. As in Fig. 3, H2O2 was permeating the cell membrane at a relatively high rate during the solute phase. (B) After treating the cell with a blocking agent for water channels (50 µM HgCl2; 35 min), the response of turgor to a similar concentration of H2O2 was lacking the solute phase. Either hydrogen peroxide was not permeating at all, or the substrate entering the cell at a low rate was completely degraded in the presence of catalase. The measured half-times (Tw1/2) were assigned to water flow. They were of an order similar to those measured during hydrostatic pressure relaxations (Tw1/2=15±4 s; ±SD, n=6, data not shown). (C) After removing the mercury from the membrane with 4 mM of the scavenger 2-mercaptoethanol, the solute phase appeared again, showing that permeation was re-attained. This panel also shows that the integrity of the cell membrane was affected by the combination of two different toxic stresses (HgCl2 and H2O2). Therefore, turgor pressure did not recover a stable steady value.
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Discussion
|
|---|
The mathematical model given in this paper describes the combination
of the permeation of a solute (H
2O
2) and of its enzymatic decomposition.
Experiments are presented which are in line with the model.
According to the results, H
2O
2 permeates membranes at a rate
which is comparable to that of diffusional water flow. This
and the fact that the chemical structure of H
2O
2 resembles that
of water suggests that hydrogen peroxide uses water channels
to cross membranes. To the best of the authors’ knowledge,
these data are the first rigorous theoretical and experimental
analyses of a permeation/reaction system, which may be of some
importance because, on one hand, H
2O
2 is a precursor of other
toxic oxygen compounds. On the other hand, rapid membrane transport
of H
2O
2 should affect the intracellular concentration of H
2O
2 and, hence, all metabolic reactions in which this compound is
involved. The most simple case of a transport combined with
a chemical reaction has been investigated. The permeating solute
(H
2O
2), which is osmotically active, is decomposed inside the
cell by the enzyme catalase into products (H
2O and O
2) which
are not osmotically active. However, even in this simple case,
a general simple analytical solution is not available. Therefore,
a numerical simulation is shown, that yields quantitative predictions
which were sucessfully tested in experiments. The experimental
results indicate that the model is adequate to describe the
system under investigation.
Hydrogen peroxide is produced during different metabolic processes such as during photorespiration in chloroplasts or during the formation of lignin in cell walls (Asada, 1992; Ishikawa et al., 1993; Takeda et al., 1995; Schopfer, 1996). Hydrogen peroxide affects the integrity of cell
Top
Abstract
Introduction
0.974). In (C), the extrapolated hydrostatic pressure difference at t=0 (from fit in A) is plotted versus the osmotic pressure of the medium (RTCo) that caused the response in cell pressure. The very good correlation of the linear regression shows the consistency of results determined with a fit procedure for different concentrations (r2=0.999; solid line; dotted lines: prediction interval at 95% level). The slope of the regression line is a measure of the reflection coefficient (
(molar volume of water: 
m3 mol-1). The diffusional permeability of water (Pd) denotes the permeability of HDO (Pd=Ps(H2O)). By definition, 