Download Physicochemical aspects of ion relations and pH

Journal of Experimental Botany, Vol. 50, No. 336, pp. 1101–1114, July 1999
REVIEW ARTICLE
Physicochemical aspects of ion relations and pH
regulation in plants—a quantitative approach1
Jóska Gerendás2,4 and Ulrich Schurr3
2 Institute for Plant Nutrition and Soil Science, University Kiel, Olshausenstr. 40, D-24118 Kiel, Germany
3 Botanical Institute, University Heidelberg, Im Neuenheimer Feld 360, D-69120 Heidelberg, Germany
Received 27 January 1999; Accepted 29 March 1999
Abstract
A quantitative physicochemical approach to ion relations of biological solutions is presented, which applies
fundamental laws of physical chemistry to these systems and allows analysis of dependent variables ([H+],
[OH−] and the dissociation state of partially dissociated
(‘weak’) ions including carbonate species) in relation to
independent variables (concentrations of strong and
weak ions, dissociation constants and CO partial pres2
sure). Within this concept the influence of strong (fully
dissociated) ions is confined to their net unbalanced
positive charge which is referred to as SID (strong ion
difference). The SID concept is then applied to membrane transport processes and ion relations of xylem
and phloem sap: simple transmembrane transport of
protons between compartments cannot affect pH on
either side of the membrane, because rather small deviations from electrical neutrality results in substantial
changes of the membrane potential under natural conditions. Thus the membrane ATPases as electrogenic
pumps cannot control the pH of adjacent compartments, but they energize secondary active transmembrane ion transport that results in pH changes. The SID
approach is shown to be valid by matching pH values
calculated from analysis of xylem and phloem saps with
actual measured values. Sensitivity analysis based on
the SID approach allows (1) to detect inconsistency in
determination of composition in the analysed solutions
and (2) quantitatively to analyse the influence of ion
export or import and variations of pCO on pH and
2
dissociation state of weak acids of complex biological
solutions. The SID concept thus allows the evaluation
of the contribution of a proposed pH-regulating or
pH-affecting mechanism on a quantitative physicochemical basis.
Key words: Electrical neutrality, membrane potential, pH
regulation, phloem sap, SID, xylem sap.
Introduction
The ionic composition of biological solutions, like cytosol,
xylem and phloem saps as well as apoplastic fluids is
determined by physical (e.g. gas exchange, transmembrane transport, membrane potential ) and chemical (e.g.
metabolic conversion, dissociation) processes. Individual
aspects have been described in detail (Raven and Smith,
1976; Gollan et al., 1992; Peuke et al., 1994), but an
integrated approach is required to assess the interaction
of the different processes involved. The SID concept
(Stewart, 1978, 1981) addresses simultaneous acid–base
relations of all substances present using physicochemical
relationships. It is based on conventional laws of chemistry and physics which can be adequately described
mathematically. The concerted combination of the underlying principles (ion dissociation, gas dissolution, ion
exchange, electrochemical laws) has already been applied
to acid–base control in human blood (Stewart, 1978).
His concept has found wide application in animal sciences
(Pieschl et al., 1992; Brechue et al., 1994; Whitehair et
al., 1995) and human physiology (Lindinger et al., 1992;
Fencl and Leith, 1993; Jennings, 1994), but attracted
only limited attention in the plant sciences ( Ullrich and
Novacky, 1990, 1992; Ratcliffe, 1994). The rigorous
quantitative analysis shows that pH is a dependent variable and is determined by the independent variables of
the system: (1) the strong ion difference (SID), which
represents the net positive charge on the fully dissociated
(strong) ions, (2) the total concentration of weak ions
(ionizable groups) and (3) the partial pressure of CO .
2
Thus experiments that measure intracellular or extracellu-
1 Dedicated to the late Peter A. Stewart who established the physicochemical concept of acid-base chemistry to biology and medicine.
4 To whom correspondence should be addressed. Fax: +49 431 880 1625. E-mail: [email protected]
© Oxford University Press 1999
1102 Gerendás and Schurr
lar pH changes require detailed information on the distribution of all independent variables before a sound
conclusion on the cause of pH changes can be drawn. In
plants, the chemi-osmotic gradient theory for photosynthetic ATP synthesis is well established, but in addition
to the original model (Mitchell, 1966) it was soon recognized that the substantial pH gradient across the thylakoid
membrane, as observed in illuminated chloroplasts, simultaneously requires ion fluxes for charge compensation
( Edwards and Walker, 1983). The SID concept was
successfully applied to this coupled system, and it was
concluded that K+, Mg2+ or Cl− fluxes almost fully
compensate for the charge separation due to H+ transport
and thus allow substantial pH gradients (Good, 1988;
Hangarter and Good, 1988; Ullrich and Novacky, 1992).
Furthermore, when evaluating the ‘influence’ of pH on
enzyme activities, it should be expressed more carefully
as the relationship between pH and enzyme activity,
considering the substantial changes in other dependent
variables, like the dissociation state of metabolites and
enzyme proteins (weak acids). Here the SID concept is
applied to proton transport across membranes in general
and to ion relations in the xylem and the phloem saps in
particular, as these are easily obtained, but nevertheless
relevant complex biological solutions.
Materials and methods
Plant material
Seedlings of Populus tremula×Populus alba were grown as
described previously (Schurr and Schulze, 1995). In short,
saplings were transplanted to soil-filled planting pots topped
with an aluminium lid with a central bore. The plants were
grown for 6 weeks in a greenhouse before use. Seeds of Ricinus
communis var. Carmencita soaked in water overnight were
germinated in wet vermiculite (Heckenberger et al., 1998).
When the seminal root was 3–5 cm long, seedlings were planted
into the planting pots fitting into the root pressure chamber.
Plants were grown for 6 weeks at 12/12h light/dark period at
25 °C and 60% relative humidity in a walk-in growth cabinet
( Weiss, Reiskirchen) at a photon flux density of 300 mmol m−2
s−1 at the top of the plants.
For collection of xylem sap, root systems of plants were
introduced into a root pressure chamber (Schurr, 1998).
Pneumatic pressure was applied to the root system with the
oxygen partial pressure of the gas maintained at ambient partial
pressure by mixing pressed air with nitrogen gas. Populus
saplings were decapitated and root exudate sampled at different
flux rates by varying the overpressure at the root system. Xylem
sap from intact Ricinus plants was sampled as previously
described (Schurr and Schulze, 1995): When the pneumatic
pressure in the root chamber increased above compensation
pressure, xylem sap exuded at a cut in the midrib of a leaf.
Pressure in the root chamber was controlled to keep the
hydraulic pressure in the xylem sap at this cut at atmospheric
pressure (Schurr et al., unpublished results). The xylem was
opened at a second site below. This caused a constant exudation
of xylem sap, which was sampled by a fraction collector.
Phloem sap was sampled from incisions in the cortex of
Ricinus communis plants yielding pure phloem sap collected
directly into a glass capillary to prevent significant evaporation
( Komor et al., 1989; Baker, 1988).
Analytical procedures
Concentrations of cations and organic and inorganic anions in
the xylem sap samples were analysed by capillary electrophoresis
on a Spectra Phoresis 1000 (TSP, Darmstadt) according to
Bazzanella et al. (Bazzanella et al., 1997). The electrolyte for
cation determination contained 6 mM imidazol (pH 4.5) and
2 mM 18-Krone-6. Separation was performed in a 43 cm long
capillary (75 mm diameter) at 20 kV at a capillary temperature
of 20 °C with 3–5 s injection time. Electropherograms obtained
by indirect UV detection at 214 nm were analysed by the TSP
data system.
The electrolyte for anion determination contained 7.5 mM
salicylic acid, 15 mM TRIS, 500 mM DoTAOH, and 600 mM
Ca(OH ) . Separation was done on a 76 cm long capillary (inner
diameter2 75 mm) at −28 kV and a capillary temperature of
25 °C with 3–5 min injection time.
Concentrations of amino acids were determined by HPLC
after derivation of primary amino acids with o-phthalic acid
dialdehyde (OPA). The derivatization reagent contained 25 mg
OPA in 500 ml methanol, 4.5 ml 0.8 M borate buffer (pH 10.4),
and 50 ml mercaptopropionic acid. Derivation of 35 ml of diluted
xylem sap was performed automatically by the autosampler
( Kontron 465, Kontron, Eching). Separation was done after
injection of 20 ml on a Hypersil ODSII column ( Knauer, Berlin)
at a flux rate of 0.8 ml min−1 with a step mixing gradient.
Detection of separated derivated amino acids was done
fluorometrically (SFM 25, Kontron, Eching) with 330 nm
excitation at 450 nm (emission wavelength). Chromatograms
were quantitatively evaluated by a data system ( Kontron,
Eching).
Calculations
The chemical equilibria for particular data sets were calculated
using the program GEOCHEM-PC ( Version 2.0), kindly
provided by Professor Dr D Parker ( University of California,
Riverside, California). The program itself has been described
elsewhere (Sposito and Mattigod, 1980; Parker et al., 1987,
1995). The original database was extended to data for glutamine,
asparagine, c-butyric, and lactic acid ( Table 1). Stability
constants of fixed ionic strength (Martell and Smith, 1976–1989)
were extrapolated to infinite dilution using the Davies equation
(Davies, 1962) as used by GEOCHEM-PC. Values refer to the
following equilibria (M=metal, L=ligand, k=stability constant):
a×M+b×t<c×ML k=
[ML]c
[M ]a×[L]b
Values of dependent variables were calculated from independent
variables using the spreadsheet programme (LotusTM Version
5.0). The stability constants were taken from GEOCHEM-PC
calculations, where the conditional stability constants are
corrected for ionic strength. An algorithm searching the
minimum of the absolute electrical charge of a solution was
used to calculate the equilibrium pH and based on this pH all
other variables were determined. Formation of complexes was
not taken into account.
Results and discussion
Theoretical considerations
The ion relations of complex ‘systems’, like biological
solutions, is influenced by several mechanisms (ion disso-
Physicochemical aspects of ion relations
1103
Table 1. Stability constants (log(k) at infinite dilution) of glutamine, asparagine, c-butyric and lactic acid
Constants for fixed ionic strength taken from Martell and Smith (1976–1989) were corrected to infinite dilution using the Davies equation as used
by GEOCHEM-PC. Complex stoichiometry indicated by number of metal5number of ligands5number of protons.
Ligand
Ligand
charge
Metal
log(k)
Complex
log(k)
Complex
Glutamine
Asparagine
c-aminobutyric acid
Lactic acid
Lactic acid
Lactic acid
−1
−1
−1
−1
−1
−1
H+
H+
H+
Ca2+
Mg2+
H+
9.23
8.95
10.51
1.46
1.44
3.89
05151
05151
05151
15150
15150
05151
11.4
11.09
14.56
2.48
2.49
05152
05152
05152
15250
ciation, dissolution of CO etc.). Only the simultaneous
2
consideration of all mechanism can quantitatively explain
the hydrogen ion behaviour (see Appendix for details).
In this context, it is necessary to differentiate between
‘dependent’ and ‘independent variables’ (Baxley and
Moorhouse, 1984; Haimovici, 1979). The values of the
independent variables are imposed on the system from
the outside (ion dissociation equilibria, conservation of
mass etc) and determine the internal relations within the
system. Dependent variables (dissociation state of buffers,
pH, dissolved CO ) are internal to a system, depend on
2
the independent variables and can not be set arbitrarily.
The correlation between the individual dependent parameters originates from the simultaneous determination
by the independent variables, while the independent variables do not affect each other.
In pure water, the proton concentration is defined by
its own dissociation constant (the ion product of water)
in combination with the requirement for electrical neutrality (see Appendix for details). In an aqueous solution
containing fully dissociated ions (e.g. K+, NO−) the
3
requirement for electrical neutrality has to be fulfilled for
these ions as well as for water. The net positive charge is
called the strong ion difference [SID] which also lent its
name to the concept in general. Put simply, whenever
[SID] is positive, i.e. the strong cations exceed strong
anions, the solution is alkaline (Fig. 1). The proton
concentration is hence given by
[H+]=
S A
k∞ +
w
B
[SID]
([SID])
2−
2
2
and determined by [SID] and k∞ .
w
Close to [SID]=0 there is a smooth transition from
the linear to the non-linear part of the relation between
[H+] and [SID], where the proton concentration approximates the square root of the ion product of water. In this
[SID] range the pH scale exhibits a substantial change
(Fig. 1B), which does not reflect the actually gentle change
of proton concentration. The symmetry of the pH titration curve suggests that the proton concentration behaves
in much the same way in either acid or alkaline solutions,
which is clearly not the case (Fig. 1A). In contrast, [ H+]
Fig. 1. Hydrogen ion [ H+], hydroxyl ion [OH−] concentrations (A),
and pH and pOH (B) plotted against strong ion difference [SID], over
the [SID] range from −0.02 to +0.02 mmol l−1.
and [OH−] are linearly related to [SID] in acid and
alkaline solutions, respectively. Protons seem to behave
like strong ions in acidic solutions. However, the quantitatively identical increase of [ H+] in a solution when x
moles of HNO are added are due to the addition of the
3
otherwise unbalanced addition of x moles of an anion,
rather than to the addition of available protons. The
corresponding increase in proton concentration is due to
the recruitment of protons from water to maintain electrical neutrality. This means that in alkaline solutions
(e.g. cytosol ) the changes in [SID] and [OH−] are several
orders of magnitude larger than changes of [ H+] (Figs 5,
6, 8).
1104 Gerendás and Schurr
Weak electrolytes are important for all biological solutions and are traditionally referred to as ‘buffers’. These
introduce another set of variables (total weak acid concentration, A ) and parameters (weak acid dissociation
tot
constant) that need to be considered. Including weak
electrolytes results in a fourth order polynomial (see
Appendix), which relates the proton concentration to the
ion species in the solution (Fig. 2).
The pH-scale can be misleading as well. Adding a weak
acid to a solution of [SID]=0 results in a much lower
pH than in simple strong ion solutions (compare Fig. 1).
Increasing [SID], e.g. by adding NaOH, to half the
concentration of the weak acid added ([A ]/2), results
tot
in a pH at the maximal buffering capacity (indicated by
the low slope of the pH curve in Fig. 2). Adding more
NaOH results in a substantial pH increase when [SID]
approaches [A ]. However, the actual proton concentratot
tion, when [SID] equals [A ]/2 changes only gradually
tot
and the [ H+] approaches the abscissa asymptotically at
[SID]=[A ], which contrasts with the strong increase in
tot
the pH value.
Any one of the dependent variables can be changed
exclusively by changing the independent ones, and this
will always affect all dependent variables to some degree.
The dependent variables are thus correlated to each other,
but they never determine each other. For example, it is
not appropriate to say that changes of [ H+] cause changes
of the dissociation of weak acids ( [A−] and [ HA]), these
changes only accompany each other. The Henderson–
Hasselbalch equation represents only one of the four
equations necessary for quantitative analysis. Of course,
even in a quantitative physicochemical analysis the buffer
equation is used to calculate the concentration of individual ion species after the equilibrium [H+] has been
determined by considering all equilibria simultaneously.
CO is a major determinant of pH in biological solu2
tions and forms dissolved CO (d ), free carbonic acid
2
(H CO ), bicarbonate (HCO−), and carbonate (CO2−).
2 3
3
3
The concentration of CO (d) is governed by the partial
2
pressure of CO ( pCO ), which is the independent vari2
2
able. For simplicity, dissolved CO and free carbonic acid
2
are combined as H CO*. After combining these CO
2 3
2
equilibria with the water and the weak acid dissociation
equilibrium, the conservation of the total mass of the
weak acid and the electrical neutrality, the behaviour of
dependent variables in a system containing strong ions
[SID], and a single weak acid [A ], and which is in
tot
equilibrium with CO (the independent variables) can be
2
quantitatively analysed. Seven dependent variables,
namely
[HA][A−][H CO*][HCO−][CO2−][H+][OH−]
2 3
3
3
are determined by the independent parameters:
k∞ k k
k
k
[SID] [A ] p(CO )
w a CO2 HCO3 CO3
tot
2
The correct proton concentration can only be calculated
by taking into account all relationships simultaneously.
The SID concept will now be applied to a number of
biologically important situations and the determinants of
proton concentration in these solutions quantitatively
evaluated. In order to cope with more complex biological
solutions (xylem and phloem saps, cytosolic fluids) the
contribution of all individual constituents has to be taken
into account resulting in a large set of equations (25
amino acids, 10 organic acids and phosphate), solved
numerically using GEOCHEM and a spreadsheet
program.
Membrane potential and pH regulation
Electrical neutrality implies an isolated system like a
beaker or pot. However, living plant cells typically have
a electrical potential difference across the plasma membrane of −50 to −150 mV (Nobel, 1991; Ullrich and
Novacky, 1990), reflecting the fact that the negative
charges inside plant cells exceed the positive ones.
Nevertheless, this surplus of negative charge is minute
both in absolute terms and in relation to the overall
charges present in plant cells (Allen and Raven, 1987;
Nobel, 1991). The membrane potential can be incorporated into the SID concept considering appropriate pCO
2
and intracellular metabolite concentrations. The relationship between the membrane potential and the extra
negative charge is given by
DE=
Fig. 2. Relationship between [H+] and [OH−] versus [SID] for a weak
acid solution with [A ]=0.02 mol l−1 and k =3×10−7 mol l−1. The
tot
A
vertical dashed lines are at [SID]=A and at [SID]=[A ]/2 (=
tot
tot
0.01 mol l−1).
(r×c×F )
3C∞
with DE=membrane potential, r=cell radius, c=uncompensated charge, F=Faraday constant, and C∞=membrane capacitance per unit area (10−2 C V−1 m−2; Nobel,
1991). For calculation, three weak acids were considered
Physicochemical aspects of ion relations
as specified Table 2, which results in a buffering capacity
of 24 mmol H+ l−1 pH−1 at pH 7.26. As the three buffers
differ in pK and concentration the buffering capacity
a
was obtained by determining the change of SID required
to alter the original cytoplasmic pH by only 0.1 unit. As
opposed to the conventional approach, where the
buffering capacity is pre-set ( Walker and Smith, 1977;
Guern et al., 1982), the SID concept allows the consideration of a large number of ‘buffers’ of different pK and
a
concentration, which ultimately results in the familiar,
pH-dependent buffering capacity of xylem sap (Gollan et
al., 1992), cytoplasmic and vacuolar fluid (Takeshige and
Tazawa, 1988) by evaluating all dissociation equilibria
simultaneously (see Figs 3, 4). The buffering capacity of
24 mmol H+ l−1 pH−1 represents the low end of the
range observed ( Kurkdjian and Guern, 1989) in order
not to underestimate the impact of the membrane potential on intracellular pH. For the same reason a small cell
diameter was chosen, since the impact of the membrane
potential on the intracellular pH is higher in small cells
( Walker and Smith, 1977; Guern et al., 1982). The
calculated charge distribution and the corresponding pH
for a model plant cell is presented in Table 2.
The membrane potential is energized by the plasma
membrane ATPase in plant cells (Spanswick, 1981;
Serrano, 1989). Occasionally it has been discussed in
terms of pH regulation itself (Bertl and Felle, 1985;
Mathieu et al., 1986; Marré et al., 1988). Although at
first glance it sounds convincing to assume that the
ATPase can excrete excess protons generated during meta-
1105
bolic activity, a closer look reveals that the capacity of
simple proton extrusion is minute: considering typical
cells (internal buffers, CO ) as specified in Table 2 the
2
extra negative charge generated by an enforced action of
the H+-ATPase (proton pump) would amount to about
2.4 mmol l−1 in order to change the cytoplasmic pH by
as little as 0.1 units. However, this would result in a
unrealistic membrane potential of several hundred V (not
mV ). Only cells deprived of their internal buffers and of
CO would change their pH within the normal membrane
2
potential range. Even very small deviations from electrical
neutrality have serious consequences for the membrane
potential ( Table 2), which means that within the membrane potential relevant for (plant) cells the translocation
of protons has no consequence for cytoplasmic (and
external ) pH. An earlier analysis using a more conventional approach ( Walker and Smith, 1977) reached the
same conclusion. In the context of the SID concept,
whenever pH changes are observed within or outside
living cells, independent variables like SID, pCO or A
2
tot
have changed. In most situations [SID] changes as a
result of strong ion movements across the plasma membrane (Stewart, 1983). Proton and strong ion movement
are strictly coupled via its impact on the membrane
potential (Nobel, 1991). It has been pointed out that
‘micromolar concentrations of K+ are high enough to
release the [proton] pump from voltage inhibition created
by its electrogenic activity’ ( Kurkdjian and Guern, 1989).
The SID concept provides a valuable tool for designing
experiments on the stoichiometry of ion uptake at the
Table 2. Relationship between the membrane potential, the calculated extra negative charge and the cytoplasmic pH
The following assumptions were made: Spherical cells, 10 mm cell diameter, 100 mmol l−1 cations, anions as required to start at pH 7.26 for the
individual data sets. Weak acids: 20 mmol l−1 phosphate (pK =7.2), 40 mmol l−1 histidine buffer (pK =6.5) and 50 mmol l−1 amino buffer (pK =
a
a
a
9.7) were applicable.
Membrane
potential
[mV ]
Calculated
buffering
capacity
[mmol H+ l−1 pH−1]
pCO
2
[Pa]
Internal
pH
Extra negative
charge in
mmol l−1
Extra negative charge
in relation to the total
internal negative
charges [in ppm]
Cells with internal buffers and in equilibrium with CO
2
0
24
−100
24
−200
24
−300
24
−50 000
24
30
30
30
30
30
7.2587
7.2588
7.2590
7.2591
7.3261
0.0000
−0.0031
−0.0062
−0.0093
−1.5544
0.0
−20.7
−41.5
−62.2
−10 270.7
Cells without internal buffers in equilibrium with CO
2
0
0
−100
0
−200
0
−300
0
−50 000
0
30
30
30
30
30
7.2586
7.2747
7.2903
7.3053
8.5448
0.0000
−0.0031
−0.0062
−0.0093
−1.5544
0.0
−31.1
−62.2
−93.3
−15 306.7
0
0
0
0
0
0
7.2581
8.2269
8.5103
8.8024
8.9756
11.1916
0.0000
−0.0016
−0.0031
−0.0062
−0.0093
−1.5544
0.0
−15.5
−31.1
−62.2
−93.3
−15 544.1
Cells without internal buffers in the absence of CO
2
0
0
−50
0
−100
0
−200
0
−300
0
−50 000
0
1106 Gerendás and Schurr
plasma membrane and the tonoplast and for putting their
quantitative interpretation on a sound physicochemical
basis ( Ullrich and Novacky, 1992).
Composition of xylem sap and sensitivity analysis using the
SID concept
Full coverage of all independent parameters is required
to apply the SID concept to complex solutions in a
quantitative way, but in many cases this is hardly possible
for technical reasons. Nonetheless, the SID concept may
contribute to the understanding of pH regulating and pH
changing processes by comparing a ‘control’ measurement
with a ‘treated’ system. By making reasonable assumptions and bringing the calculated pH for the ‘control’ in
agreement with its measured pH (in analogy to the
calculations presented in Table 2) it is possible to evaluate
to what extent the pH change observed in the ‘treated’
system agrees with the calculated pH. Fortunately, xylem
sap can be obtained in large enough quantities from
decapitated plants by applying pneumatic pressure to the
root system. pH values were determined and the samples
were subsequently analysed for all known major constituents. Variations of flux conditions caused considerable
alterations of exudate composition ( Table 3, Schurr and
Schulze, 1995). The calculated pH depends on the partial
pressure of CO , which has not been determined in the
2
xylem vessels in these experiments. However, in woody
stems concentration of CO has been reported to be
2
considerably higher than in ambient air ( Eklund, 1990):
0.2–1.8 vol-% CO , Macdougal and Working, 1933, cited
2
in Stiles, 1960: 1.25 vol-%). Occasionally even concentrations of 10 vol-% and higher have been reported
(Carrodus and Triffett, 1975; Eklund, 1990). Inside bulky
organs (potato tubers, carrot taproots and apples) stored
at low temperature, concentrations of 1.8–10 vol-% CO
2
have frequently been documented (Stiles, 1960).
Therefore, values of 0.32–3.2 vol-% CO ( pCO =320–
2
2
3200 Pa) were included, which correspond to
10–100-times the atmospheric CO level, in the calcula2
tions of xylem sap from stems of young Populus ( Table 3)
and Ricinus plants (see below). Table 3 shows that the
calculated pH (considering a 10-times ambient CO level )
2
for the xylem sap of Populus plants agrees well with the
measured pH ( Table 3), particularly at the beginning of
the experiment. The deviation at the end of the experiments might be due to as yet undetermined constituents
of the root exudate or to analytical error (see below).
Xylem sap from intact Ricinus plants was sampled with
a root pressure chamber (Schurr, 1998), and the calculated and measured pH values are included in Table 4.
The measured pH is rather stable during the time-course,
while the calculated pH values tend to increase with time
(except for the 5th time interval ). The reason for this
behaviour could not be identified, but apparently the
Table 3. Composition of the xylem sap obtained from decapitated
Populus plants
During the experiment the pneumatic pressure at the root system was
stepwise increased to obtain differences in xylem flux rate. All values in
mmol l−1. Measured and calculated pH values at various CO partial
2
pressures are given. Calculations were carried out using GEOCHEM.
Constituent
Pressure in the root chamber [105 Pa]
4
3
2
1
Inorganic cations
NH
4
K
Na
Ca
Mg
288.0
1869.0
190.0
192.5
99.5
290.5
1868.0
416.5
176.0
107.5
348.0
2281.0
408.5
333.5
178.5
320.5
2767.5
803.0
349.0
218.5
Inorganic anion
NO
3
SO
4
PO
4
Cl
1890.9
136.7
240.7
45.9
1923.9
138.7
258.3
204.7
2195.5
196.7
321.0
245.4
2655.0
126.4
390.8
475.3
43.3
59.9
48.6
57.5
62.2
73.1
84.4
97.5
2.6
203.7
7.3
461.5
16.5
11.2
6.9
8.3
2.9
285.6
9.5
648.8
13.2
15.3
6.1
342.1
14.6
764.6
10.2
18.7
9.5
14.1
8.9
14.1
11.0
16.8
Organic anions
Citrate
Malate
Amino acids
Asp
Glu
Asn
Ser
Gln
Gly
Thr
His
Ala
Arg
GABA
Val
Met
Ile
Leu
Measured pH
Calculated pH at
pCO =32 Pa
2
pCO =320 Pa
2
pCO =3200 Pa
2
1.2
2.1
199.2
15.2
532.1
8.4
8.2
6.7
11.2
1.8
8.5
7.4
1.7
6.0
5.0
13.7
7.1
2.1
7.0
6.7
6.69
6.56
6.65
6.62
7.15
6.55
5.7
7.15
6.55
5.70
7.55
6.90
6.05
7.70
7.05
6.15
calculated pH, assuming a pCO of 320–3200 Pa (see
2
above), agrees well with the measured pH, again particularly at the beginning of the experiment.
The authors do not recommend calculating the pH of
xylem saps rather than measuring it, since the latter is
certainly much easier. However, the SID concept may be
used (1) to check the completeness of the analytical data
( Frischmeyer and Moon, 1994; Oster et al., 1988) and
(2) to quantify the sensitivity of concentrations of protons
and other ion species to variations of the solution—an
approach that can be used to evaluate the significance of
proposed mechanisms on a quantitative basis. For
example, starting from the given xylem sap composition
in Ricinus ( Table 4), it is possible to investigate how
sensitively the pH, the concentration of various carbonate
species and the dissociation state of various weak acids
Physicochemical aspects of ion relations
1107
Table 4. Composition of the xylem sap obtained from Ricinus communis in a time-course experiment and the modified ‘standard
xylem sap’ used for subsequent sensitivity analysis: all values in mmol l−1
Constituent
Inorganic cations
K
Ca
Mg
Na
NH
4
Inorganic anions
NO
3
PO
4
SO
4
Cl
Organic anions
Acetate
Citrate
Lactate
Amino acids
Asp
Glu
Asn
Ser
Gln
Gly
Thr
His
Ala
Arg
Val
Met
Phe
Ile
Leu
Lys
Measured pH
Calculated pH at
pCO =32 Pa
2
pCO =320 Pa
2
pCO =3200 Pa
2
Time interval
21.30–22.40
8.40–9.30
9.30–10.30
10.30–11.30
11.30–13.00
13.00–14.00
Standard
xylem
sap
6186
1600
619
574
1193
5316
1306
537
1244
810
5567
1101
401
736
781
5138
974
412
900
1903
6023
937
458
1161
1081
6761
989
500
1308
1198
6210
1680
650
480
1370
9002
1022
685
175
8297
672
483
223
7282
526
403
197
7322
451
212
179
9512
559
347
215
9974
607
291
9590
1020
720
184
22
10
24
52
8
63
23
21
35
29
31
60
22
28
47
15
24
35
34
27
10
9
3
24
42
2526
24
34
23
31
27
30
5
3
17
12
1246
30
25
21
11
27
22
3
2
13
18
1020
29
23
20
7
14
18
2
1
3
14
17
1307
21
16
16
9
17
18
1553
23
24
13
17
18
1875
22
25
13
19
1
3
14
23
16
27
3
21
52
2393
31
36
23
35
25
33
4
12
15
42
23
14
24
13
18
12
14
13
17
16
29
15
39
6.02
5.92
5.71
5.38
5.33
5.27
—
6.60
6.55
6.05
6.85
6.70
6.10
7.55
7.00
6.30
8.15
7.40
6.60
4.80
4.75
4.60
7.15
6.85
6.15
—
—
—
respond to changes of independent variables (SID, A )
tot
or pCO . (1) Selective ion transport into or out of the
2
xylem will affect ion relations inside the xylem sap. When
K+ is selectively removed, [SID] decreases, while removal
of NO− has the opposite effect. H+ concentration
3
increases rapidly as [SID] falls below 0.05 mmol l−1
(Fig. 3A), and changes in pCO affect pH less at high
2
[SID] values. The semi-log pH plot in Fig. 3B gives a
rather different impression and basically represents a
titration curve. Here the influence of pCO seems to be
2
larger at high [SID] values. At the measured [SID] of
0.14 mmol l−1 a 10-fold rise from the normal pCO level
2
lowers the pH from 6.5 to about 6.3.
The analysis using the SID approach makes it possible
to address the question of how the dependent variables
of the system respond to changes of [SID] on a quantitative physicochemical basis (Stewart, 1983; Ullrich and
Novacky, 1992): An increasing [SID] has no influence on
the uncharged H CO*, but raises the HCO− concentra2 3
3
tion ( Fig. 4). The response of the phosphate species
is particularly informative. In a more conventional
approach the addition of potassium (increases [SID])
would be discussed as a partial neutralization of the
H PO− ion, ignoring CO and the other 20 organic
2 4
2
compounds involved (Table 4). In order to maintain
electrical neutrality after an increase of [SID] by, for
example, selective import of K+ or removal of NO−, the
3
system adjusts by additional negative charges from
dependent variables like dissolved carbonate and the
dissociation state of water and weak acids. The actual
changes of H+ and OH− are minute (Fig. 4), and
HCO− is only of moderate importance. Phosphate ions
3
are quantitatively most significant, since their changes are
several orders of magnitude larger than those of H+.
Increasing pCO raises the proton concentration, and
2
this effect is particularly strong at low [SID] values
1108 Gerendás and Schurr
Fig. 4. Concentration of carbonate and phosphate species plotted
against SID for the standard xylem model at pCO =320 Pa. The
2
vertical dashed line indicates the observed SID of 0.14 mmol l−1.
Fig. 3. Proton concentration (A) and pH (B) plotted against SID for
the standard xylem model at different pCO . The vertical dashed line
2
indicates the observed SID of 0.14 mmol l−1.
(Fig. 5A), while the semi-log pH scale gives a different
impression of the same process (Fig. 5B). Looking at the
concentration of carbonate and phosphate species
(Fig. 6), H CO* concentration increases linearly with
2 3
pCO (equation 6). Its dissociation into HCO− results in
2
3
extra negative charge (equation 7), which again is mainly
compensated for by the reduction of the double negatively
charged HPO2− at the expense of H PO− ( Fig. 6).
4
2 4
Significant variations of pH in the rooting media,
nutrient solutions and in the xylem sap have been reported
in response to the form of N nutrition. While ammonium
nutrition consistently caused a strong acidification and
nitrate nutrition a moderate alkalization in the rooting
media (Dijkshoorn, 1962; Kirkby and Mengel, 1967;
Raven and Smith, 1976; Marschner and Römheld, 1983),
considerable discrepancies were found in the effects on
xylem sap pH: Allen and Raven (1987) reported a lower
pH for the xylem sap of ammonium-grown Ricinus plants,
while in other studies (Allen and Smith, 1986; Zornoza
and Carpena, 1992) no substantial differences have been
found. Occasionally even higher pH values in the xylem
sap of ammonium-grown plants have been observed
(Römheld et al., personal communication). With the
background of the SID concept it is possible that these
discrepancies are due to differences in the [SID] in the
xylem, for example, due to variations in other nutritional aspects.
Analysis of the pH effects on the basis of the SID
concept have analytical limitations as (1) the data set
must be complete and (2) common analytical uncertainties can cause substantial changes of the calculated pH,
particularly in solutions of low buffering capacity as
xylem fluids ( Table 5). The xylem sap of Populus and
Ricinus plants was used as a reference model, and the
consequence of a 5% error in the analytical determinations
of anions, cations and amino acids was evaluated. As
indicated in Table 5, even these moderate analytical
errors, which are certainly within the limits of routine
analytical procedures, result in considerable deviations of
the calculated pH. Nevertheless, sensitivity analysis at a
given composition gives valid results.
Phloem
Phloem sap differs significantly from xylem fluids as (1)
it is a much more concentrated solution, (2) has a high
pH (often around 8) and (3) contains a large number of
important ionic metabolites (amino acids etc.) at high
concentration ( Table 6). Consequently phloem sap has a
much higher buffering capacity, which makes the calculations more stable against analytical errors. CO levels
2
Physicochemical aspects of ion relations
1109
Fig. 6. Concentration of carbonate, phosphate and glutamine species
plotted against pCO for the standard xylem model at SID=
2
0.14 mmol l−1.
Table 5. Impact of variations of independent parameters on the
calculated pH of the xylem sap of Populus and Ricinus plants
All values calculated using GEOCHEM ( pCO =300 Pa).
2
Calculated pH according to the
original data
Cations underestimated by 5%
Anions underestimated by 5%
Amino acids underestimated
by 5%
Phosphate and organic acids
underestimated by 5%
Fig. 5. Proton concentration (A) and pH (B) plotted against pCO for
2
the xylem model at different SID values.
Populusa
Ricinusb
Calculated pH
6.55
Calculated pH
6.55
6.20
6.70
6.55
6.15
6.70
6.55
6.60
6.55
Observed pH
6.56
Observed pH
6.00
a see Table 3, second column (pressure 3×105 Pa) for composition.
b see Table 4, first column (time interval 21.30–22.40) for composition.
bear significant consequences for the pH of the phloem
sap ( Fig. 9), since the dissolved carbonate species substantially contribute to the charge balance at alkaline pH
(Fig. 8B). A positive relationship between the calculated
and observed pH was obtained ( Fig. 7), and the r2
indicates that about 50% of the observed variation can
be explained by the variation of [SID]. The mean pH
calculated for 10 to 100-times atmospheric CO is 8.2 to
2
7.5 ( Table 6), and thus close to the actually measured pH
and in agreement with reported values ( Tammes and van
Die, 1964; Hall and Baker, 1972; Schurr et al., unpublished results).
Due to the high buffering capacity of the phloem sap
and the high concentration of physiologically important
metabolites, the consequences of selective ion removal
(variations of [SID]) and different pCO levels are particu2
larly rewarding. The change of [SID] has to be more
substantial to cause a certain change in phloem pH
( Fig. 8) than in the xylem sap ( Fig. 3), due to the higher
concentration of weak acids in the phloem sap ( Table 6).
When [SID] is varied around its original values
(72 mol l−1), the proton concentration is reduced with
increasing [SID] (e.g. K+ uptake) particularly at higher
CO concentrations (Fig. 8A). In order to maintain elec2
trical neutrality the phloem solution generates negative
charges in accordance with all dissociation equilibria
considered simultaneously (Fig. 8B). In contrast to the
xylem sap, this is hardly accomplished by changing the
dissociation state of phosphate, but merely by increasing
levels of bicarbonate, carbonate and by increasing the
dissociation of amino acids, among which glutamine is
the most important. As compared to the changes of these
ions the contribution of changes of the proton concentra-
1110 Gerendás and Schurr
Table 6. The ionic composition of the phloem sap obtained from Ricinus communis plants (all values in mmol l−1): pH calculated
using GEOCHEM-PC
Plant identification
Cations
NH
K
Na
Ca
Mg
Anions
Cl
SO
4
NO
3
PO
4
Organic acids
Citrate
Malate
Oxalate
Succinate
Pyruvate
Lactate
Amino acids
Asp
Glu
Asn
Ser
Gln
Gly
Thr
His
Ala
Arg
GABA
Val
Met
Try
Phe
Ile
Leu
Lys
Measured pH
Calculated pH at
pCO =32 Pa
2
pCO =320 Pa
2
pCO =3200 Pa
2
A
B
C
D
E
F
G
0.797
59.618
8.152
1.118
4.047
0.605
79.875
7.031
1.297
7.442
1.113
71.756
9.255
0.727
6.895
1.415
83.240
11.044
1.896
8.443
2.286
100.690
8.636
3.216
5.514
1.379
172.612
10.494
4.850
11.022
1.042
71.044
9.778
2.862
10.566
11.688
4.617
2.079
4.604
21.57
5.011
1.223
5.092
11.617
6.240
19.972
5.870
3.373
7.049
39.919
4.076
6.672
11.857
85.419
5.372
13.278
18.137
8.662
5.795
6.228
13.415
2.622
3.739
4.754
2.439
0.564
0.564
1.293
2.728
3.497
0.393
0.484
0.123
1.720
0.356
1.020
1.535
5.762
0.527
0.204
0.330
0.244
2.123
2.435
4.419
0.24
0.658
0.776
3.540
4.256
4.873
0.364
0.740
2.296
4.395
0.734
0.537
3.158
1.695
5.991
11.584
0.324
4.322
25.456
0.993
0.981
1.108
1.409
0.416
0.420
2.644
0.360
0.395
1.142
1.657
1.166
0.662
5.524
10.888
0.307
3.449
26.118
0.695
1.009
1.228
1.451
0.526
0.434
2.941
0.397
0.487
1.248
2.001
1.360
0.678
3.827
8.490
0.504
3.944
49.217
0.673
1.202
1.493
1.874
1.380
0.409
3.415
0.634
0.541
1.103
2.329
1.531
1.320
0.697
2.176
2.049
13.206
84.225
2.527
1.434
1.312
1.537
0.650
0.388
2.672
0.437
0.105
0.594
0.927
1.060
0.841
4.822
8.378
0.433
4.686
18.662
0.893
0.447
4.261
6.773
2.503
12.044
85.852
4.201
1.878
1.1945
2.449
0.397
2.506
3.866
0.776
0.175
1.346
1.822
1.405
0.8155
4.607
8.982
0.928
7.069
80.397
3.296
0.998
1.247
2.868
0.352
3.219
2.987
0.633
7.91
7.87
8.22
7.95
7.17
7.27
7.42
8.45
8.05
7.25
8.90
8.35
7.60
8.80
8.40
7.65
8.60
8.30
7.65
8.60
8.10
7.35
8.40
8.15
7.55
8.30
8.05
7.40
4.721
tion (Fig. 8A) is minute due to the high pH, and even
the increase of the hydroxide concentration (not shown)
does not significantly contribute to the charge balance.
Impact of pCO on the proton and ion species concen2
tration of phloem sap is significant, due to the high SID
values, pH and solubility of CO ( Fig. 9). At the actual
2
SID value found (72 mmol l−1) the calculated pH for
pCO =320 Pa is around 8.4, which is close to what has
2
been observed or reported in literature (8–8.2 Tammes
and van Die, 1964; Hall and Baker, 1972). The average
observed pH was only 7.7 (see Fig. 7), which agrees with
the reports of Allen and Smith (1986). Anions generated
by the system to maintain electrical neutrality in response
to rising CO levels are mostly bicarbonate and Gln−
2
0.740
0.073
3.062
0.765
0.186
0.186
1.065
0.989
0.756
( Fig. 9) as well as numerous other amino acids (not
shown) with pK values close to the pH of phloem saps
a
(Martell and Smith, 1976–1989).
Conclusions
The SID concept is based on fundamental laws of physical
chemistry and provides a quantitative approach to acidbase equilibria, which allows alterations of dependent variables (dissociation state of weak ions, carbonate species,
[H+], [OH−]) to be discussed in terms of changes of
independent variables ([SID], total concentration of weak
ions, pCO ). By incorporating the membrane potential in
2
this concept it could be illustrated that proton movement
Physicochemical aspects of ion relations
1111
Fig. 7. Relationship between calculated and observed pH of phloem
sap obtained from Ricinus communis plants.
Fig. 9. Concentration of protons (A) and carbonate, phosphate and
glutamine species at [SID]=72 mmol l−1 (B) plotted against pCO for
2
phloem sap obtained from Ricinus communis (sample C from Table 6).
mechanisms with respect to pH homeostasis even of complex solutions like xylem and phloem saps.
Acknowledgements
Fig. 8. Concentration of protons (A) and carbonate, phosphate and
glutamine species at pCO =320 Pa (B) plotted against SID for phloem
2
sap obtained from Ricinus communis (sample C from Table 6). The
vertical dashed line indicates the observed SID of 72 mmol l−1.
by itself cannot regulate intracellular pH. The SID concept
also provides a useful tool to assess the completeness of
data sets of solution composition and directs to critical
points requiring careful analysis. An analysis of the quantitative impact of variations of independent variables on the
pH (sensitivity analysis) allows to quantitatively assess the
capacity of any proposed pH disturbing and pH regulating
This work was supported by the Deutsche Forschungsgemeinschaft (SFB 199/C 1 and Schwerpunktprogramm 717
‘Apoplast’). The authors gratefully acknowledge stimulating
discussions with RG Ratcliffe ( University of Oxford), CI Ullrich
( University of Darmstadt) and W Hartung ( University of
Würzburg). DR Parker ( University of California) provided a
copy of GEOCHEM and helpful advice for using it. We thank K
Herdel and R Feil for technical support, S Siebrecht ( University
of Göttingen) for growing the Populus plants and H Rennenberg
( University of Freiburg) for supply of the saplings. We wish to
thank B Sattelmacher for his interest in this work and J Sauter
( University of Kiel ) for helpful suggestions concerning the CO
2
concentration within plant tissues.
Appendix
Concentrations versus activities
The dissociation equilibria are ultimately related to the activities
of the ions involved, while the equilibrium constants are either
based on ion concentrations for a given ionic strength or
activities (effective concentrations, corrected for ionic strength
by multiplying the concentration by the activity coefficient;
[A]×f ={A}). In the calculations presented here, concentraA
tions are considered and the concentration-based equilibrium
constants as taken from Martell and Smith (1976–1989), are
1112 Gerendás and Schurr
corrected for ionic strength using the Davies equation (Sigg
and Stumm, 1996).
A
B
√I
log f = −1.82×106(eT )−3/2×C2
−0.3×I
A
1+√I
with e=dielectric constant, T=absolute temperature, C=
charge of the ion, and I=ionic strength (1/2(C Z2). This
i i
approach eases the inclusion of a key boundary of the SID
concept, namely the electrical neutrality, which is based on
concentrations rather than activities
Theoretical considerations on the SID concept
In the quantitative acid-base chemistry of the SID concept as
developed by Stewart (1978) a solution behaves as a ‘system’,
whose internal relationships are based on fundamental laws of
physical chemistry. ‘Independent’ variables are imposed on the
system from the outside (e.g. concentration of fully dissociated
ion, the total concentration of partially dissociated ion,
dissociation constants). ‘Dependent’ variables are internal to a
system, depend on the independent variables and can not be
set arbitrarily. The functional relationships between the dependent and the independent variables are defined by elementary
laws of chemistry and physics (water and ion dissociation
equilibria, conservation of mass, etc.). In the following, two
systems of increasing complexity (aqueous solutions with strong
and weak ions in the absence and presence of CO ) are
2
characterized mathematically (see Stewart, 1978, for details).
Aqueous solutions with strong and weak ions in the absence of
CO : The proton concentration in pure water is determined by
2
the dissociation of water itself ([H+]×[OH−]=k ×[H O]),
w
2
and because the dissociation of water is only 1.8×10−16 mol l−1
and the molar concentration of water is high (about 55.5 mol
1−1), the term k ×[ H O] is usually combined to k∞ to give the
w
2
w
ion product of water (Sigg and Stumm, 1996)
[H+]×[OH−]=k∞
(1)
w
For the fully dissociated cations and anions the net charge
needs to be considered. This term is given in mol charges l−1,
which is the relevant SI unit. For consistency and clarity, the
authors discouraged the use of the so-called C–A value, often
cited in the plant science literature, as this term often includes
partially dissociated ions (phosphate, ammonium) at an assumed
charge, and since the term C–A has been used in the more
conventional approaches to pH regulation. The impact of
strong ions is confined to its charge and not to the substance
from which it originates. For convenience and generalization
the term ( [sum of cations]−[sum of anions]), the net positive
charge of the strong ions, is substituted by [SID], the strong
ion difference.
([sum
])−([sum
])=[SID]
(2)
cations
anions
All relevant biological solutions contain some ‘weak ions’
(referred to as ‘A’), which are only partially dissociated and are
traditionally referred to as buffers. The dissociation is given by
the weak acid dissociation equilibrium (e.g. k =
A
10−6.5 mmol l−1). To comply with SI nomenclature the concentration of A is not given in eq l−1, but in mol of ionizable
tot
groups l−1.
[H+]×[A−]=k ×[HA]
(3)
A
Irrespective of the actual dissociation state the total amount of
A needs to be conserved.
[A ]=[HA]+[A−]
(4)
tot
Electrical neutrality must be maintained in all solutions (for
inclusion of the membrane potential see Results and discussion section).
The electrical neutrality statement is thus given by the
following equation:
[H+]−[OH−]+[SID]−[A−]=0
(5)
This set of four independent equations contains at least two
independent variables ([A ] and [SID]), two constants (for a
tot
given temperature and ionic strength, k∞ and k ), and four
w
A
dependent variables ([H+], [OH−], [A−], [HA]). Each additional
weak acid has to be included analogously with a separate equation.
The values of these dependent variables depend only on the
independent variables and must meet all equations simultaneously.
These equations are combined to determine the [H+] of this
system. See Results and discussion section for typical relationships
between [SID] and [H+] based on equation (6).
[H+]3+(k +[SID])×[H+]2
(6)
A
+(k ×[SID]−[A ])−k∞ )×[H+]1−k ×k∞ =0
A
tot
w
A
w
Aqueous solutions with strong and weak ions in equilibrium with
carbon dioxide: All relevant biological solutions are exposed to
exogenous CO or generate it during respiration and fermenta2
tion, which introduces another four species in the system. CO
2
dissolves in solutions to form dissolved CO (d ), free carbonic
2
acid (H CO ), bicarbonate (HCO−) and carbonate (CO2−).
2 3
3
3
The concentration of CO (d) is determined by the partial
2
pressure of CO , with which the solution is in equilibrium
2
(Henry’s law). Dissolved CO combines with water to form
2
H CO , but the actual concentration of H CO is really small.
2 3
2 3
For simplicity, dissolved CO and the actual H CO formed are
2
2 3
combined to H CO*. The quantitative relationship is given by
2 3
equation [7].
[ H CO ]=k ∞×pCO
2 3
H
2
k =3×10−7 mol l−1 Pa−1
(7)
H∞
Carbonic acid dissociates to form bicarbonate, which itself
dissociates into carbonate and protons.
[H+]×[HCO−]=k ×[H CO*]
3
1
2 3
k =5×10−7 mol l−1
(8)
1
[H+]×[CO2−]=k ×[HCO−] k =5×10−11 mol l−1 (9)
3
2
3
2
These three equations together with the weak acid dissociation
equilibrium (3), the conservation of mass for A (4),
the water dissociation equilibrium (1) and the extended electrical
neutrality statement (10)
[H+]−[OH−]+[SID]−[A−]−[ HCO−]−[CO2−]=0 (10)
3
3
describe quantitatively the behaviour of dependent variables in
a system containing strong ions [SID] and a single weak acid
[A ], and which is in equilibrium with CO (the independent
tot
2
variables). In order to address the question what determines
the pH of this solution, all these equations are combined and
give a 6th order polynomial containing seven equations for
seven dependent variables, namely
[HA][A−][ H CO*][ HCO−][CO2−][H+][OH−]
2 3
3
3
which are determined by the independent parameters:
k∞ k k
k k [SID] [A ] p(CO )
w
a
H∞
1
2
tot
2
In order to cope with more complex biological solutions
(xylem and phloem saps, cytosolic fluids) the contribution of all individual constituents has to be taken into
account resulting in a set of equations (25 amino acids, 10
Physicochemical aspects of ion relations
organic acids and phosphate), solved numerically using
GEOCHEM and a spreadsheet program.
References
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communis grown with ammonium or nitrate as N source: the
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communis: its effect on plant growth and the chemical
composition of the whole plant, xylem and phloem saps.
Journal of Experimental Botany 37, 1599–1610.
Baker DA. 1988. Regulation of long-distance transport of
assimilates. In: Atkin RK, Clifford DR, eds. Mechanisms and
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