Journal of Experimental Botany, Vol. 51, No. 353, pp. 2053±2066, December 2000
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 PflanzenoÈkologie, UniversitaÈt Bayreuth, D-95440 Bayreuth, Germany
Received 19 January 2000; Accepted 24 July 2000
Abstract
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 H2O2 of up to 350 mol m 3 are
presented. A detailed description of determination of
permeability (Ps) and reflection coefficients (ss) for
H2O2 is given in the presence of the chemical reaction
in the cell. Mean values were Ps ˆ (3.6"1.0) 10 6 m s 1
and ss ˆ (0.33"0.12) ("SD, N ˆ 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 ˆ (85"55) mol m 3 and vmax ˆ (49"40)
nmol (s cell) 1, respectively. The absolute values of Ps
and ss of H2O2 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 (HgCl2),
1
the permeabilities of both water and H2O2 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.
Introduction
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 H2O2 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, H2O2
is produced at high rates. The organelles contain catalase
at high concentrations which splits H2O2 into water and
oxygen. It has been found that chloroplasts lack catalase,
and H2O2 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
To whom correspondence should be addressed. Fax: q49 921 552564. E-mail: [email protected]
Abbreviations: A, surface area; Ci/o, internal/external concentration; Ci`, internal concentration at steady-state; JV/s, volume/solute flow; kM, Michaelis
constant; ks, rate constant of permeation; ks, overall rate constant; ks, normalized rate constant; kcat, rate constant of decomposition; Lp, hydraulic
conductivity; dni(s/cat), change of moles inside (due to permeation/decomposition); P(0/`/min), cell turgor pressure (at time ˆ 0/steady-state/pressure
minimum); DP`/max, steady-state/maximal pressure difference; Ps, permeability coefficient; ss, reflection coefficient; t(min), time (at pressure minimum);
t, normalized time; vmax, maximal velocity of decomposition; V, volume; VÅw, molar volume of water; x(o), normalized (external) concentration of solute.
ß Society for Experimental Biology 2000
2054
Henzler and Steudle
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 H2O2 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 H2O2. Despite the general assumption
that H2O2 rapidly crosses membranes, it is nevertheless
thought that it may be concentrated in certain tissues
during oxidative burst at a level which is suf®cient 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 H2O2. The lack of data of the membrane
permeability of H2O2 is due to the fact that it is dif®cult to
measure H2O2 ¯uxes in the presence of substantial
activities of catalase and peroxidase, i.e. to separate
membrane permeation from reaction ¯ows experimentally. The problem is that of measuring the diffusional
permeability of a substrate which takes part in a chemical
reaction. Provided that concentrations of H2O2 and its
re¯ection coef®cient are rather large, the permeation/
decomposition of H2O2 should also affect water ¯ows and
cell turgor pressure and should be measurable using the
pressure probe technique (Steudle and Tyerman, 1983;
RuÈdinger et al., 1992; Steudle, 1993; Henzler and Steudle,
1995). Since there is no direct coupling between the
decomposition of H2O2 and the transfer of water across
the membranes, interactions between the chemical reaction and water ¯ow should be indirect, i.e. mediated by
changes of the internal concentration of H2O2.
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
re¯ection coef®cients 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 ¯ow (degradation of H2O2 in the cell) and due to solute ¯ow across
the membranes, a physical/mathematical model was
established which predicted the osmotic reactions of internodes (water and solute ¯ows in the presence of catalase
action), when H2O2 was added to the external medium.
Predictions from the model were tested experimentally.
Permeability and re¯ection coef®cients 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.
Theory
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 (C o ˆ constant).
A cell membrane separates the medium inside the cell
(superscript `i') with concentration C i(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 ˆ P(t ˆ 0)). The membrane has a permeability
for water (Lp, hydraulic conductivity) and for the solute
(permeability, Ps, and a re¯ection, ss, coef®cient). 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 ˆ 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 ¯ow 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, m3 m 2 s 1) and solute ¯ow (Js, mol m 2 s 1)
are given by equations 1 and 2 (RuÈdinger et al., 1992):
1 dV
ˆ Lp (P P0 ) Lpss RT (C i C o ) (1)
JV ˆ
A dt
Js ˆ
1 dnis
V dC i
ˆ
ˆ Ps (C i
A dt
A dt
(C i qC o )
JV
q(1 ss )
2
Co)
(2)
The symbol P denotes cell turgor pressure and R and T
are the gas constant and absolute temperature, respectively. dnis 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 ¯ow out of the cell has a positive sign. Since the
cell wall is assumed to be rigid, volume changes (dV ) are
less than 1% (dVHVfconstant). Therefore, the assumption holds that dnis ˆ V dC i (equation 2), i.e. the solute ¯ow
across the membrane is proportional to the change of
Transport of H2O2 across water channels
internal concentration. The ®rst term on the right side of
equation 1 describes the `hydraulic' and the second term
the `osmotic' water ¯ow. The ®rst 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 ¯ow (solvent drag).
This latter term is usually negligibly small even when ss
is substantially smaller than unity (ss-0.5; RuÈdinger
et al., 1992). One can calculate the ratio of diffusion to
solvent-drag at the beginning of an osmotic relaxation
(t ˆ 0) when JV and Js are at maximum. For a Chara internode, typical parameters of transport of water and H2O2
are: Lp ˆ 1.7 3 10 6 m (s MPa) 1, Ps ˆ 3.6 3 10 6 m s 1,
and ss ˆ 0.33 (Table 1). Assuming an initial concentration
gradient of C o C i(tˆ 0) ˆ C o ˆ 100 mol m 3, the solvent
drag component comprises always less than 2% of the
total solute ¯ow. Therefore, the solvent drag will be
neglected in further calculations.
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:
H2 O2
1
! H2 Oq O2
2
catalase
(3)
Of course, there could be also other enzymes such as
different peroxidases which would degrade H2O2, but
their speci®c 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
2055
reduces the internal concentration of H2O2 which is
osmotically active. In other words, an additional `virtual'
¯ow of solute is produced (`reaction ¯ow' 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:
dnicat
Ci
ˆ vmax
dt
kM qC i
(4)
Equation 2 can be modi®ed by adding the MichaelisMenten term from equation 4 expressed per unit area:
1 dni
1 dnis dnicat
ˆ
q
Js ˆ
A dt
A dt
dt
ˆ
V dC i
ˆ Ps (C i
A dt
C o )q
vmax
Ci
A kM qC i
(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 justi®es the assumption of a twocompartment 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
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 coef®cient; ss, re¯ection coef®cient),
and Michaelis-Menten kinetics (vmax; kM) is given for six different internodes of Chara corallina. Parameters of solute transport are mean values of ®ve
to six osmotic pressure relaxations ("SD: standard deviation; N ˆ 5±6 experiments). Parameters for Michaelis-Menten kinetics are obtained by a ®tting
procedure as described above ("SE: asymptotic standard error). Mean values are given as well in the bottom rows (relative error in %; N ˆ 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
b ( ˆ vmax/(kMPsA) ˆ kcat/ks) is calculated that is a parameter used in the numerical analysis.
Cell no.
Geometry
Solute transport
A
(mm2)
V
(mm3)
1
2
3
4
5
6
166
195
191
184
122
277
35
43
38
40
25
62
Mean
SD
(%)
189
51
27
40
12
30
Ps"SD
(mm s 1)
4.1"0.2
1.8"0.2
4.2"0.2
3.6"0.2
3.2"0.1
4.4"0.6
3.6
1.0
27
Michaelis-Menten kinetics
ss"SD
(1)
0.28"0.02
0.46"0.01
0.32"0.01
0.18"0.02
0.47"0.02
0.25"0.02
0.33
0.12
33
vmax"SE
(nmol s 1 cell 1)
kM"SE
(mol m 3)
71"4
20"2
42"1
42"11
3.2"0.2
115"12
153"19
51"19
43"5
149"72
28"6
88"23
49
40
81
85
55
64
vmax/V
(mmol s
1
m 3)
b
(%)
2.03
0.47
1.10
1.05
0.13
1.42
68
112
122
43
29
107
1.03
0.68
65
80
39
49
2056
Henzler and Steudle
analytical solution for the time-course of the inner
concentration C i(t) after changing the concentration of
solute outside at tˆ 0 is not available. It may be possible
to calculate a complex formula for C i(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 tˆ 0, a new steady-state will be reached
when water and solute ¯ow have vanished again (JV, Js ˆ 0
at t £`). For the new steady-state, it follows from
equation 5:
Ps (C`i
Co) ˆ
vmax
C i`
A kM q C i`
(6)
where C i` ˆ C i (t £` ) is the ®nal 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 ®nal steady-state pressure (P` ˆ P(t £`)) would also
then be lower than the initial (P0), i.e.:
DP` ^P0
P` ˆ ss RT(C o
ˆ s s RT
Fig. 1). However, the inset also shows that this type of
plot is of no use for evaluating vmax and kM when 1/DP`
is plotted as a function of 1/C o. At saturating concentrations of substrate, the pressure difference approaches
a maximum value proportional to vmax:
v
(9)
DPmax ˆ ss RT max
Ps A
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 DP` versus C o is shifted to the right as compared
with that of DP` versus C i` . 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 DP` can be obtained
(see Results). From these data, it is then possible to
evaluate vmax and kM using equation 8.
Case II (kMIC o, C i)
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:
Js ˆ
V dC i
ˆ Ps (C i
A dt
C o )q
vmax i
C
AkM
(10)
Equation 10 can be integrated using standard procedures.
C`i )
vmax
C i`
Ps A kM q C i`
(7)
The value of C i` is dif®cult to measure. However,
equation 6 can be used to express C i` as a function of
C o. Substituting C i` ˆ f (C o ) into equation 7 leads to
a relation between DP` and C o that can be measured:
2
ss RT 4vmax
qkM qC o
DP` ˆ
2
Ps A
s 3
2
vmax
o
qkM C
q4kM C o 5
Ps A
(8)
Figure 1 shows plots of DP` as a function of either
C i` (equation 7) or C o (equation 8) which have been generated by a computer. The ®gure illustrates that DP` is
a measure of the rate of decomposition by the enzyme,
and therefore, follows a Michaelis-Menten type of
kinetics. By de®nition, a Lineweaver-Burk plot of 1/DP`
as a function of 1/C i` yields a straight line (see inset of
Fig. 1. Calculation of the effects of external and internal concentrations
of H2O2 on steady-state pressure difference. The graph shows a plot
of the steady-state pressure difference DP` at t £` resulting from
a decomposition of solute inside the cell due to enzyme reaction
following a Michaelis-Menten type of kinetics. DP` is calculated either
as a function of the external concentration of H2O2 (C o, closed symbols,
equation 8) or as a function of the corresponding steady-state concentration inside the cell (C i`, open symbols, equation 7). Dashed-dotted
horizontal lines denote maximal or half-maximal pressure differences
(DPmax; equation 9), i.e. when vmax or 0.5vmax is reached. The dotted
vertical lines represent: (left) the exact value of kM ˆ 50 mol m 3 used for
the calculation; (right) the external concentration of C o ˆ 134 mol m 3
where 0.5vmax is reached. In the inset, a double-reciprocal plot
(Lineweaver-Burk type) for the same data is given as well (dotted
line: 1/kM; dashed-dotted line: 1/vmax).
Transport of H2O2 across water channels
i
This yields the following time-course for C (t):
ks
C i (t)ˆ C o
(1 e (ks qkcat )t )
ks qkcat
ks
ˆ C o (1 eks t )
ks
(11)
where ks ˆ (APs)/V, kcat ˆ vmax/(VkM), and ks ˆ ksqkcat.
Equation 11 describes an exponential increase of C i(t) up
to a steady-state concentration lower than C o. The rate
constant of the process (ks ) is higher than that in the
absence of a chemical reaction (i.e. vmax ˆ 0, kcat ˆ 0). In
this latter case, equation 11 reduces to:
C i (t)ˆ C o (1
e
ks t
)
(12)
Permeation and decomposition of H2O2 take place
simultaneously and the overall rate constant (ks ) in
equation 11 re¯ects the sum of the two single processes
(see Discussion). In the presence of a chemical reaction,
the ®nal pressure difference is:
kcat
DP` ˆ ss RTC o
ks qkcat
vmax
o
(13)
ˆ ss RTC
vmax qPs AkM
It is easily veri®ed from equation 13 that the absolute
value of DP` depends on the relative contribution of
the rate of degradation (kcat) to the overall rate (ks ).
For example, when, transport dominates, i.e. when
vmaxI(PsAkM), DP`f0 is obtained. This has been often
veri®ed in the absence of a chemical reaction. On the
other hand, if vmaxI(PsAkM) holds, the solute entering
the cell is rapidly degraded. At an extreme, this should
result in a DP` ˆ ssC oRT. In this case, the second solute
phase would be completely missing. This result has been
obtained in this paper when the transport of H2O2 was
blocked in the presence of HgCl2.
Case III (kMHC i, C o)
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:
vmax
C i (t) ˆ C o
(14)
(1 e ks t )
Ps A
It can be seen that the kinetics is independent of kM.
The rate constant of the exponential process ( ks ˆ ks ) is
that of the solute permeation only. This is so because, at
high concentrations, membrane permeation is the limiting
step (see Discussion). The ®nal pressure difference is
then DP` ˆ DPmax (equation 9) which can be directly
approximated from equation 8.
Cases II and III show that, in both extremes, timecourses of inner concentrations C i(t) can be approximated
2057
by single exponential functions. Exponential curves just
differ in their rate constants (ksqkcat 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 (C o). 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 (t ˆ ks t and
x(t)ˆ 1qC i(t)/kM), i.e.:
dx(t )
b
(15)
ˆ x(t )qb xo
dt
x(t )
Here, xo ˆ 1qC o/kM and b ˆ kcat/ks ˆ vmax/(PsAkM) which
are dimensionless, too. Equation 15 is therefore normalized. In an exosmotic experiment, the external concentration changes from xo ˆ 1 to a constant xo)1 at t ˆ 0.
Boundary conditions for a numerical solution are:
x(t ˆ 0)ˆ 1
and
q 1 o
bq (xo b)2 q4b
x(t £` ) x
(16)
2
In the case of an endosmotic experiment, step changes
of concentration are in the opposite direction, i.e. at t ˆ 0,
the external concentration is changed from a constant
xo)1 to xo ˆ 1. The differential equation is modi®ed since
the actual value of xo is xo ˆ 1:
dx(t )
b
(17)
ˆ x(t )qb 1
dt
x(t )
Boundary conditions are opposite as compared to the
exosmotic case, i.e.:
q 1
x(t ˆ 0) ˆ xo bq (xo b)2 q4b
2
and
(18)
x(t £` )ˆ 1
where xo ˆ constant)1 is the initial external concentration before changing back to the original medium. In
order to ®nd an exponential kinetics for x(t), it is useful
to also de®ne a dimensionless overall rate constant
(ks ˆ ks /ks). When the process is dominated by permeation it follows that ks fks and ks f1.
Materials and methods
Plant material
Chara corallina was grown in arti®cial pond water (APW;
composition in mol m 3: 1 NaCl, 0.1 KCl, 0.1 CaCl2, 0.1
MgCl2) in tanks which contained a layer of natural pond mud
(Henzler and Steudle, 1995). Tanks were placed in a greenhouse
2058
Henzler and Steudle
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 coef®cient in m s 1; ss: re¯ection
coef®cient) 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 ˆ ksV/A) were
extrapolated from a series of exosmotic relaxations with
different external concentrations of hydrogen peroxide to
C o £`. In some cases, only a small if any correlation between
ks and C o could be detected. Hence, ks was calculated as a mean
of ks . In other cases, ks decreased with increasing C o, and ks
was determined from the extrapolated value of a single
exponential ®t of ks as a function of C o.
The de®niton for calcluation of re¯ection coef®cients is
derived from equation 1. Since JV vanishes at the minimum
of the curve (JV(t ˆ tmin) ˆ 0) it holds that:
1 P0 P(tmin )
(19)
ss ˆ
RT C o C i (tmin )
Assuming an exponential increase of the inner concentration
to a value C i` (equation 7), the time-course of C i(t) can be
espressed as:
P0 P`
(1 e ks t )
C i (t) ˆ C`i (1 e ks t ) ˆ C o
(20)
ss RT
Combining equations 19 and 20 at t ˆ tmin, yields an expression
which was used to calculate re¯ection coef®cients from
exosmotic relaxation curves:
ss ˆ
(P`
Pmin )eks tmin q(P0
RTC o
P` )
(21)
Here, Pmin denotes the pressure at t ˆ 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
(RTC o) caused by permeation and degradation of solute.
Different from earlier formulae used to estimate ss, 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 ˆ ks and P0 ˆ P`), equation
21 is identical with the equation used earlier to evaluate re¯ection
coef®cients 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 ®ve different concentrations
were performed (Fig. 3). Using equation 8, ®nal steady-state
pressure differences of the exosmotic experiments (DP`) were
®tted to the corresponding concentrations of H2O2 in the
medium (C o). Michaelis constants (kM) and maximum rates of
decomposition (vmax;DPmax) were obtained from the ®tted
parameters either directly (kM) or using equation 9 (vmax). Since
the external concentrations of substrate (C o) which could be
measured here, were higher than internal concentrations at
steady-state (C`i ), a double reciprocal plot (Lineweaver-Burk
type) was of no use (see inset of Fig. 1 and equations 7 and 8).
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 ¯ow,
values of x(tqDt) were calculated from previous values x(t)
using equation 15: x(tqDt)ˆx(t)qDt[x(t) xoqb b/x(t)].
Commercial data processing software was employed in the
simulations (Transform-tool of SigmaPlot 2.01, Jandel Scienti®c,
Erkrath, Germany). Time-steps of Dt ˆ 5 3 10 5 were used that
corresponded to 1±5 ms in `real' time. Maximum changes of
x(tqDt) x(t) occurred at the beginning of calculations (tf0)
for the high values of xo. These changes corresponded to
changes in `real' concentration of smaller than 0.05 mol m 3
(50 mM) at external concentrations of 7±1000 mol m 3 (7 mM
to 1 M). Therefore, a suf®cient resolution of time for numerical
calculations and the linearity of step-changes of x(t) was
guaranteed. Numerical calculations of time-courses of x(t)
for 30 different values of xo took about 3 h.
Fitting of curves
In the context of this paper, ®tting 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 ®ts (Curve-®t-tool of
SigmaPlot 2.01) which also provided asymptotic standard errors
for the parameters determined.
Results
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 ˆ 1±12;
xo;C o), x(t) 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 (t ˆ 6±7),
initial slopes were smaller than mean slopes. Towards
the end of relaxations (t)10), slopes became bigger.
Transport of H2O2 across water channels
The asymmetry between exosmotic and endosmotic
experiments originated from either increasing (exosmotic)
or decreasing (endosmotic) internal concentrations.
Therefore, the two processes (permeation and degradation) in¯uenced the curves differently during different
time intervals. This resulted in a more complex behaviour
in the case of an endosmotic experiment. Hence, for the
2059
sake of simplicity, only the exosmotic case was investigated further.
Figure 2C shows a plot of the normalized overall rate
constant (ks ˆ ks /ks) as a function of xo. Data were
determined from the ®ts in Fig. 2A. It can be seen that ks
decreased with increasing xo. For the exosmotic experiment, values varied from 1qb (low xo;1) 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 ks were, in general,
larger in endosmotic than in exosomotic relaxations. The
functional relation between ks and the external concentration was exponential in nature (exponential ®ts in
Fig. 2C). The numerical analysis veri®ed that the rate
constant of the sum of the processes (permeation and
degradation of H2O2) 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 H2O2, 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 ®ve different concentrations of hydrogen peroxide (40±265 mM). After quickly
replacing the medium with a solution containing a certain
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(t)) 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 ˆ 3.6 3 10 6 m s 1; A ˆ 1.9 3 10 4 m2;
vmax ˆ 4.5 3 10 8 mol s 1; kM ˆ 91 mol m 3; b ˆ 0.723; time-step of
numerical calculation: Dt ˆ 5 3 10 5). Only every 5000th calculated
value is shown. Curves were ®tted assuming an exponential kinetics
(solid line). The only parameter to be ®tted was the rate constant (ks ; see
C). Dotted lines at the exosmotic side represent theoretically predicted
values for x(t £`) (equation 16). In (B), a semi-logarithmic plot of the
data of (A) is given using the value of x(t £`) 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
coef®cients 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 (ks , (k): endosmotic; (m): exosmotic) and
external concentrations is analysed. Data were taken from ®ts of the
numerical calculations in (A). The value of ks decreased with increasing
concentration outside. Data were ®tted to one (dashed line) or two
exponentials (solid line). At low xo, ks is close to 1qb ˆ 1qkcat/ks, at
high xo, ks reached unity (dotted horizontal lines). In the endosmotic
experiment, values were, in general, higher. The dotted vertical line
denotes xo ˆ 1 (C o ˆ 0).
Fig. 3. Concentration series of osmotic pressure relaxation as measured
subsequently with a cell pressure probe. A typical experiment of a series
of ®ve 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 ( ˆ 7 bar) remained
nearly constant during 2 h of experiment with fairly high concentrations
of H2O2.
2060
Henzler and Steudle
amount of H2O2, cell turgor pressure decreased due to
a ¯ow of water out of the cell. After reaching a horizontal
tangent at the minimum of the curve (P(tmin)ˆ Pmin and
JV ˆ 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 ®nal steady-state
pressure difference (DP`) 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 ®t procedure was used to determine
®t
the optimal values for P®t(tˆ 0), P®t
` ˆ P (t £`), and ks
of a single exponential curve. In Fig. 4B, a semilogarithmic plot of the data of Fig. 4A is given which
shows that curves were single exponentials to a good
approximation (correlation coef®cient r2)0.97). At the
end of relaxations, differences between P and P®t
` were
small which resulted in a marked scatter of the semilogarithmic 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 H2O2 is shown. The extrapolated value of
P®t(tˆ 0) is a theoretical value that would be attained in an
experiment if the half-time of water exchange was close to
zero (T w
1/2f0) and therefore tminf0. Then from equation
21, it follows that (P®t(tˆ 0) ˆ P(tˆ tmin ˆ 0) ˆ Pmin):
ss ˆ
(P0 Pmin ) (P0 Pfit (tˆ 0))
ˆ
RTC o
RTC o
(22)
The high correlation (r2 ˆ 0.999) indicated that ®tting
the curves yielded consistent results. The slope of the
regression line is a measure for the re¯ection coef®cient
(ss; 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
Fig. 4. Analysis of solute permeation from measured osmotic pressure relaxations. In (A), a summary of six subsequently measured pressure relaxation
curves for one cell of Chara corallina is shown (cell no. 5; different symbols denote different external concentrations of H2O2). Solute phases of each
curve (positive slope, open symbols) were ®tted to single exponential functions (solid lines). In (B), a semi-log plot of the curves from (A) is given using
®t
parameters determined from the ®t (P®t
` ˆ P (t £`)). Regression lines are plotted for each curve (dotted lines) omitting data scattering due to small
numeric differences (systematic errors, open symbols). To a good approximation, relaxation curves were single exponentials (r2G0.974). In (C),
the extrapolated hydrostatic pressure difference at t ˆ 0 (from ®t in A) is plotted versus the osmotic pressure of the medium (RTC o) that caused the
response in cell pressure. The very good correlation of the linear regression shows the consistency of results determined with a ®t procedure for
different concentrations (r2 ˆ 0.999; solid line; dotted lines: prediction interval at 95% level). The slope of the regression line is a measure of the
re¯ection coef®cient (ss ˆ 0.52; compare value in Table 1). In (D), rate constants (ks ) are plotted versus the osmotic pressure of the medium. Values for
ks were determined either from a ®t in (A) (®lled triangles) or from the slope of the semi-logarithmic plot in (B) (open triangles). Also an exponential ®t
for the data from (A) is given (solid line) that approaches a value of ks ˆ ks ˆ 0.0157 s 1 (dotted line) used to calculate the permeability coef®cient (Ps).
Transport of H2O2 across water channels
Fig. 5. Dependence of rate constants of solute kinetics (ks ) on the
external concentration of H2O2. Graphs for each of six measured Chara
internodes are shown where rate constants (ks ) are plotted versus the
medium concentration (C o). Values were determined by ®tting the solute
phase of a series of osmotic pressure relaxation curves (Fig. 4A) to a
single exponential curve. In four cases (cells 1, 2, 4, 5), a marked decrease
of ks with increasing C o was found. Analogous to (D), data were ®tted
to single exponential curves (solid lines). End values (dashed horizontal
line) were used to calculate Ps (;ks; Table 1). Dotted parallel lines
represent the theoretical maximal value of ks ˆ ksqkcat (kcat calculated
from parameters determined analogous to the procedure in Fig. 6B). For
cells 3 and 6, rate constants did not depend on the external
concentration. Therefore, only mean values ("SD; dashed-dotted
horizontal lines) were used for calculating permeability coef®cients (Ps).
2061
®tting 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 ®gure 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 ®ts (see Materials and
methods). The mean value for six internodal cells was
Ps ˆ (3.6"1.0) 3 10 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
®tting the steady-state pressure differences (DP` ˆ P0 P`)
to the external concentrations used (C o), according
to equation 8. Mean values for six cells were:
kM ˆ (85"55) mol m 3 and vmax ˆ 49"40 nmol (s cell) 1
Table 2. Comparison of transport properties of different solutes and water
Permeability and re¯ection coef®cients (ss) for water (H2O) and four osmotically active solutes (HDO: heavy water; H2O2: hydrogen peroxide;
acetone; ethanol) are listed ("SD: standard deviation; N: number of cells). Data were taken from: (a) this paper and (b) Henzler and Steudle (1995).
w (molar volume
For water, a permeability coef®cient of bulk ¯ow of water (Pf) was calculated from the hydraulic conductivity (Lp): Pf ˆ LpRT=V
W ˆ 18 3 10 6 m3 mol 1). The diffusional permeability of water (Pd) denotes the permeability of HDO (Pd ˆ Ps(H2O)). By de®nition, ss is
of water: V
zero for water.
Solute
Permeability coef®cient
(10 6 m s 1)
Re¯ection coef®cient
ss"SD (1)
N
Refs.
H2O (bulk; Pf)
HDO (Pd)
H2O2 (Ps)
Acetone (Ps)
Ethanol (Ps)
230"90
7.7"3.0
3.6"1.0
4.1"0.2
2.7"1.0
0.0
0.0034"0.0007
0.33"0.12
0.13"0.04
0.28"0.06
6
4
6
3
9
a
b
a
b
b
Fig. 6. Determination of parameters of enzyme kinetics: (A) summarizes a typical experiment with a series of different concentrations analogous to
Fig. 4 (cell no. 3). To compare differences between initial (P0) and ®nal pressure (P`; dotted lines), curves were calibrated to a uniform steady-state
pressure P0 ˆ 0.7 MPa. In (B), the ®nal steady-state pressure difference (DP` ˆ P0 P`) is plotted against the external concentration of H2O2
(C o in mol m 3). Fitting the data points according to equation 8 (dashed line) yielded a kM ˆ (43"5) mol m 3 and a vmax ˆ (42"1) nmol (s cell) 1
(dashed-dotted vertical and horizontal lines, respectively). The dotted vertical line represents the external concentration outside at which half of the
maximal pressure difference (0.5 DPmax; dotted horizontal line) is reached.
2062
Henzler and Steudle
(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 Lpˆ 1.7"0.7 3 10 6 m
(s MPa) 1. This value can be converted to an osmotic
ˆ 2.3"0.9 3 10 4 m s 1
water permeability Pf ˆ LpRT/V
6
3
1
V w ˆ 18 3 10 m mol , 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 ®le 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 ˆ 7.7 3 10 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 re¯ection coef®cient could
be evaluated (equation 21; ks f0) 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 re¯ection
coef®cient of the bilayer of H2O2 is smaller than that of
the water channel array (see Discussion). The half-time of
water exchange (®rst 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 ®nding 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 ®gure also indicates that in
the presence of two stresses (mercury and high hydrogen
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 mM
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 halftimes (T w
1/2) were assigned to water ¯ow. They were of an order similar to
those measured during hydrostatic pressure relaxations (T w
1/2 ˆ 15"4 s;
"SD, n ˆ 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.
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).
Discussion
The mathematical model given in this paper describes the
combination of the permeation of a solute (H2O2) and of
its enzymatic decomposition. Experiments are presented
which are in line with the model. According to the results,
H2O2 permeates membranes at a rate which is comparable to that of diffusional water ¯ow. This and the fact
that the chemical structure of H2O2 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 ®rst rigorous theoretical
and experimental analyses of a permeation/reaction
Transport of H2O2 across water channels
system, which may be of some importance because, on
one hand, H2O2 is a precursor of other toxic oxygen
compounds. On the other hand, rapid membrane transport of H2O2 should affect the intracellular concentration
of H2O2 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 (H2O2), which is
osmotically active, is decomposed inside the cell by the
enzyme catalase into products (H2O and O2) 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 cells because it is a precursor of highly reactive oxygen
species such as the hydroxyl radical which attacks
proteins, lipids and nucleic acids (Foyer et al., 1994; van
Rensburg et al., 1992). Oxidative bursts caused by high
levels of H2O2 play a role during the defence of plants
against pathogens (Wojtaszek, 1997; Apostol et al., 1989;
Peng and Kuc, 1992). Hydrogen peroxide and other
reactive oxygen compounds have also been discussed in
relation to senescence and the development of cancer (van
Rensburg et al., 1992; Sinha et al., 1987). By means of the
enzymes superoxide dismutase, ascorbate peroxidase and
catalase, organisms keep the levels of toxic compounds
low. According to the literature, catalase (largely concentrated in peroxysomes) has the highest speci®c activity
(in U mg 1: catalase (EC 1.11.1.6): 7800±282 000; peroxidase (EC 1.11.1.7): 262±290; L-ascorbate peroxidase
(EC 1.11.1.11): 34±254; Schomburg et al., 1994).
These experiments show that Chara cells can tolerate
H2O2 at concentrations as high as 350 mol m 3, when
these concentrations are applied at time intervals of
5±10 min that are necessary to attain a steady-state
(DP`). Experiments with an individual cell treated repeatedly with H2O2 lasted for up to 3 h. During this period
of time, initial cell turgor (which is a good indicator
of membrane integrity) was lost by only a few per cent
if any. At ®rst sight, the ®nding that Chara internodes
can tolerate H2O2 at concentrations of a few hundred
millimoles may be astonishing. Although there are other
examples that plant cells can tolerate H2O2 in the range
of some millimoles (Baker and Orlandi, 1995; Schopfer,
1994, 1996), the very high concentrations found for
Chara may be exceptional. It was reported that, in
contrast to higher plants, the photosynthesis of algae is
2063
more resistant to H2O2 due to structural differences of
their thiol-mediated enzymes (Takeda et al., 1995). The
®ndings presented here indicate that H2O2 by itself is
not very toxic to Chara as long as the concentration of
OH radicals is kept low. This is in line with experiments
in which much lower concentrations of H2O2 were added
to the medium in the presence of Fe2q. This increased
the level of OH radicals and caused an immediate loss
of cell turgor and big changes in the permeabilty of
the internodes for water and solutes (Fenton reaction;
E Steudle and T Henzler, unpublished results). Eventually,
cells were irreversibly damaged.
In the calculations of transport coeffcients and of
kinetic parameters of the splitting of H2O2, it was
assumed that the cell interior and the medium can be
treated as a two compartment system. The assumption
may be questioned, because catalase is compartmented
in peroxisomes which would require that the substrate
has to cross another membrane. The tonoplast could
represent another substantial barrier for H2O2. Since the
surface area to volume ratio of cell organelles was bigger
by three orders of magnitude than that of the entire cell
(diameter of peroxisomesf1 mm), concentration differences of H2O2 between cytoplasm and organelles should
be rapidly equilibrated, although there may be differences
in the permeability between the plasma membrane
and that of peroxisomes. In Chara, there is experimental
evidence that, compared to the plasma membrane, the
permeability of the tonoplast for small uncharged solutes
such as H2O2 is high. When the solute permeability was
evaluated from the solute phase of biphasic pressure
relaxations, the `cytoplasmic' compartment may be overlooked, because it could be `buried' within the water
phase. For the experiments reported here, an appropriate
compartment analysis is, therefore, not possible. The
solute phase and the Ps derived from it would refer to the
sum of the permeation resistances of plasma membrane
and tonoplast. However, data of solute permeability
measured from the solute phase agreed quite well with
those obtained by the pressure minimum technique
which allowed the evaluation of Ps from the shape of
pressure/time-courses around the minimum, i.e. during
periods of time of about 20±30 s (Tyerman and Steudle,
1984). Values of Ps determined from the solute phase also
agreed with data which were obtained from measuring the
initial uptake of radioactive tracers (Dainty and Ginzburg,
1964). In both cases, permeabilities were measured during
periods of time, where the cytoplasmic compartment
(plasmalemma) should have dominated (initial uptake
of tracers) or should have contributed substantially to
the measured Ps (Tyerman and Steudle, 1984). These
results were obtained with solutes exhibiting a fairly
large range of permeability and different solubility
in lipids (Ps ˆ 0.1±3 3 10 7 m s 1). They strongly suggest
a large permeability of the tonoplast. The ®ndings are in
2064
Henzler and Steudle
line with other results (Kiyosawa and Tazawa, 1977;
Tazawa et al., 1996), where no change was found in
Lp(Pf), when removing the tonoplast of perfused internodes of Chara. These authors concluded that, in Chara,
the plasma membrane rather than the tonoplast is the
main barrier of water transport.
Besides compartmentation, unstirred layers may contribute to the overall measured transport parameters
tending to reduce Lp, Ps(Pd), and ss. Two different types
of unstirred layers have to be distinguished, i.e. unstirred
layers of the diffusion versus convection type (`sweepaway' effects) and purely diffusive unstirred layers
(Dainty, 1963; Barry and Diamond, 1984). It has been
readily shown that, in the case of measurements of
isolated cells with the pressure probe, sweep-away effects
are small or negligible (Steudle and Tyerman, 1983;
Steudle et al., 1980; Steudle, 1993). This is so because the
amounts of water moved across the membrane are very
small (as discussed in detail for Chara by Hertel and
Steudle, 1997). External diffusive layers should also have
been small in the presence of a vigorously stirred medium
as in the present experiments. However, diffusional
unstirred layers inside the internodes could be as large
as a few hundred micrometers (at maximum) which is not
negligible. So, there may be a contribution of these
internal unstirred layers of the diffusive type to the overall
measured values of transport coef®cients (Ps and ss).
Cytoplasmic streaming, the cylindrical geometry, and
the fact that H2O2 is rapidly diffusing would reduce the
effects of internal unstirred layers. The diffusion coef®cient of H2O2 at 20 8C is D ˆ 1.3 3 10 9 m2 s 1 (see Meyer,
1966, and references therein). Assuming a permeability
of Ps ˆ 3.6 3 10 6 m s 1, the resistance of the membrane
to the solute ¯ow (i.e. 1/Ps) would be equivalent to
a diffusional resistance of a plane water layer of as large
as d ˆ 360 mm (1/Ps ˆ d/D). This is similar to the radius
of the internodes (f500 mm). Therefore, the internal
equilibration of H2O2 gradients should be fairly rapid as
compared with membrane permeation even for the giant
internodes of Chara. Accordingly, there are indications
from osmotic experiments with solutes having a diffusion
coef®cient similar to that of H2O2 (e.g. monohydric
alcohols, acetone, formamide), that membrane permeation rather than internal diffusion limits transport. First,
solute phases could be nicely ®tted by a single exponential
which would not be true in the presence of a limitation by
diffusion within the cell. During internal diffusion, the
thickness of the unstirred layer would increase with time
during the solute phase (see preceding paragraph).
Second, the Ps of different solutes used to date with
Chara internodes ranged over nearly two orders of magnitude. If uptake were controlled by diffusion, Ps values
should have been similar, because the diffusion coef®cients of these solutes are similar. So, for these reasons
it is safe to conclude that, although there may be some
in¯uence of internal unstirred layers on the absolute
values of the Ps and ss of H2O2, membrane permeation
and the subsequent degradation of the substrate in the
cell should have dominated the processes measured.
The numerical simulation yielded predictions which
were in line with the experimental results. When the effect
of the chemical reaction was taken into account, it
could be veri®ed that H2O2 rapidly permeated the cell
membrane. At high external concentrations, membrane
permeation dominated the overall rate of the process.
At low concentrations, the chemical reaction contributed
to as much as 44% to the overall rate (Table 1). The
latter case may be found in cells where concentrations
are barely millimolar. Hence, when H2O2 is going to
be exported from one cell compartment into another
(e.g. from the cytosol to the wall space) or is concentrated
in a tissue (as during oxidative bursts in the presence of
pathogens) this requires a balance between production
and degradation on one hand and transport on the other.
When H2O2 uses water channels (or when some of the
water channels are in fact H2O2 channels), the balance
could be affected on the transport side to allow either
rapid export (open H2O2 channels) or concentration of
hydrogen peroxide (closed H2O2 channels) in a given
compartment.
Other important predictions from the model and from
the numerical simulations are that the time-course of the
internal concentration can be ®tted by a single exponential
to a good approximation, and that the rate constant (ks ) of
this exponential curve is dependent on external concentration. Predictions have been veri®ed in experiments. Values
of rate constants decreased with increasing external
concentration and converged to the value that represents
the permeation of solute only. This means that in order to
separate the transport step from the chemical reaction, the
concentration dependence has to be analysed. The fact
that there is a simple exponential rate should not be
misunderstood in terms of either a simple diffusional
mechanism for the uptake or by a ®rst order chemical
reaction. The results show that even in the simplest
case of a decomposition and permeation process, a rather
complex type of kinetics may result. A numerical analysis, in combination with experimental results, provides
a powerful tool to get a deeper insight into the processes.
The absolute value for the permeability of hydrogen
peroxide (Ps) has been worked out from values of ks
extrapolated to high external concentrations. The value
of Ps was 3.6 3 10 6 m s 1, which is smaller by a factor
of two than the diffusional permeability of water (Pd)
for the same species and similar to that of rapidly
permeating small organic solutes (Henzler and Steudle,
1995; Table 2). The polarity of H2O2 is similar to that of
water and its van-der-Waals volume (a measure of the
volume required by a molecule) larger by about a factor
of about 1.5 (in 10 6 m3 mol 1: VH2O ˆ 15.5;VH2O2 ˆ 10.7;
Transport of H2O2 across water channels
calculated according to Bondi, 1964). Therefore, one
would expect that H2O2 is not able to permeate the
membrane rapidly. In order to move across the bilayer,
its polarity would be too high. The molecule would be
too big to move across highly selective water channels.
However, the data presented in this paper show that
permeability of H2O2 is high and similar to that of low
molecular weight solutes (monohydric alcohols, acetone)
which largely move across the bilayer by solubility
mechanism (Table 2). The permeability of H2O2 is also
somewhat lower than the diffusional permeability of
water (as measured in diffusion experiments with heavy
water; Henzler and Steudle, 1995; Table 2). Hence, it is
assumed that H2O2 crosses the membrane largely via
water channels (aquaporins). This assumption is based
on the fact that the conformation of H2O2 is that of
a stretched molecule with a mean diameter of about
0.25 nm and a mean length of about 0.28 nm (calculated
from geometrical data: wO±OH ˆ 94.88, wHO±OH ˆ 111.58,
dOH ˆ0.095 nm, dOO ˆ0.147 nm, dH ˆ0.12 nm; Hollemann
et al., 1995, p. 533). The H2O2 molecule may ®t into the
pores of water channels (width: 0.2±0.4 nm; Steudle
and Henzler, 1995). The assumption is supported by the
observation that the passage of H2O2 is strongly inhibited
by mercurials (see next paragraph).
At ®rst sight, the relatively high absolute value
of the re¯ection coef®cient of hydrogen peroxide
(ss ˆ 0.33"0.12; Table 2) seems to contradict the assumption that H2O2 crosses the membrane via water channels.
However, this ®nding can be explained when it is assumed
that the population of water channels in the Chara internode consists of some narrow individuals which allow
the passage of H2O2 and others which do not. According
to the composite transport model, the latter would then
cause the overall value of the re¯ection coef®cient to be
rather high, whereas the former would tend to keep it
low (Steudle and Henzler, 1995). Thus, the difference
in the transport pattern for heavy water (ss ˆ 0.0034
and Pd ˆ 7.7 3 10 6 m s 1) and for H2O2 (ss ˆ 0.33 and
Ps ˆ 3.6 3 10 6 m s 1) would be understandable. This
interpretation is in line with the experiments which show
that the channel blocker HgCl2 caused a decrease of
Lp(;Pd) and of Ps and a decrease of the overall re¯ection
coef®cient (Fig. 7). To date, these ®ndings can not
completely rule out the possibility that the channels
which permit the passage of H2O2 are highly selective for
this substrate and do not enable the passage of water.
However, considering the polarity and sizes of H2O2 and
H2O, this possibility seems to be unlikely. Alternatively,
the population of water channels could be fairly homogenous and HDO and H2O2 would just differ in their
re¯ection coef®cients because of the bigger size of the
H2O2 molecule. This latter explanation is also unlikely
because from the small differences in permeability coef®cients one would expect a much smaller difference in
2065
re¯ection coef®cients. More experiments are necessary
to answer the question as to whether there are two
functionally different types of channels present or just one
population of water channels with somewhat variable
diameters as the present results suggest. The problem can
be solved functionally by measuring Lp, Ps, and ss with a
pressure probe before and after closure of channels. This
approach is powerful because water and solute transport
and their coupling can be measured simultaneously in one
experiment which gives a much deeper insight into the
processes. A molecular characterization of water channels
versus H2O2 channels in Chara would be helpful as well,
but is not yet available. An extended functional analysis
requires an estimate of the contribution of the lipid array
to the overall transport and of the re¯ection coef®cient
of H2O2 for the lipid array. Because closure of water
channels (HgCl2, at external concentrations of some
10 mM) causes a stress to which the oxidative stress by
H2O2 is then added, these experiments are dif®cult to
perform. The use of less harmful treatments other than
HgCl2 would be helpful.
For the ®rst time, parameters of an enzyme kinetics
have been evaluated directly from a series of pressure
relaxation curves. The Michaelis constant (kM) obtained
from the effect of external concentration on DP` were
28±153 mM. This is of an order of magnitude which is
similar to that reported in the literature for other systems.
For example, the kM of catalase extracted from pea leaves
(Pisum sativum L.) was 190 mM (del Rio et al., 1976).
For Mycobacterium avium, Wayne and Diaz found two
different catalases which exhibited values of kM of about
5 mM and 150 mM, respectively (Wayne and Diaz, 1982).
The reason for the big relative errors in these parameters
found in this paper may be that different cells exhibited
different absolute amounts of catalase either due to size
or age of cells. It can be seen from Table 1 that referring
vmax to unit cell volume reduced the relative error by over
15%. It should be noted that the physiologically relevant
parameter b(;vmax/(kMPs)) which characterizes the relative contributions of solute degradation and permeation
to overall solute ¯ow has an even smaller relative error.
One may expect that the content of catalase in the
internodes would be dependent on age. Perhaps, older
cells have a lower capability to degrade hydrogen
peroxide than younger. However, to date, it has not yet
been possible to characterize the effect of age on the
catalase content of Chara internodes.
In conclusion, it has been shown that the measured
kinetics of a simple system where transport of a substrate
(H2O2) into a cell is followed by its chemical decomposition, quantitatively agrees with model predictions. From
the kinetics, transport properties of the solute have been
derived (permeability and re¯ection coef®cients of the
plasma membrane for H2O2) as well as the Michaelis
constant and the maximum rate of decomposition.
2066
Henzler and Steudle
Measured osmotic pressure relaxation curves quantitatively agreed with predictions derived from a twocompartment model. The two processes (permeation and
degradation) could be quantitatively separated. The
model may be used for other systems such as during
osmoregulation when osmotic processes (water relations)
interfere with metabolism. The permeability of the plasma
membrane for H2O2 was fairly high at relatively high
values of the re¯ection coef®cient for this solute. This and
the similarity of the chemical structure of the solute to
that of water suggested that H2O2 is transported across
water channels, but that the bigger solute uses somewhat
wider aquaporins of the water channel population.
To date, the data do not allow the conclusion that there
are special H2O2 channels which are not used by water.
Since water channels in Chara can be affected by different
triggers (temperature, high concentration, and heavy
metals), they may allow the regulation of H2O2 passage
depending on conditions. Currently, the role of water
channels during the permeation of hydrogen peroxide
is studied in greater detail to answer the question whether
or not some of the different water channels could be
`peroxoporins' rather than aquaporins.
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