The effect of (15)N to (14)N ratio on nitrification, denitrification and dissimilatory nitrate reduction.
ABSTRACT Earlier experiments demonstrated that isotopic effects during nitrification, denitrification and dissimilatory nitrate reduction can be affected by high (15) N contents. These findings call into question whether the reaction parameters (rate constants and MichaelisMenten concentrations) are function of δ(15) N values, and if these can also lead to significant effects on the bulk reaction rate.
Five experiments at initial δ(15) NNO(3) () values ranging from 0‰ to 1700‰ were carried out in a recent study using elemental analyser, gas chromatography, and mass spectrometry techniques coupled at various levels. These data were combined here with kinetic equations of isotopologue speciation and fractionation. Our approach specifically addressed the combinatorial nature of reactions involving labeled atoms and explicitly described substrate competition and timedependent isotopic effects.
With the method presented here, we determined with relatively high accuracy that the reaction rate constants increased linearly up to 270% and the MichaelisMenten concentrations decreased linearly by about 30% over the tested δ(15) NNO(3) () values. Because the parameters were found to depend on the (15) N enrichment level, we could determine that increasing δ(15) NNO(3) () values caused a decrease in bulk nitrification, denitrification and dissimilatory nitrate reduction rates by 50% to 60%.
We addressed a method that allowed us to quantify the effect of substrate isotopic enrichment on the reaction kinetics. Our results enable us to reject the assumption of constant reaction parameters. The implications of δdependent (variable) reaction parameters extend beyond the studycase analysed here to all instances in which high and variable isotopic enrichments occur.

Article: Ignoring isotopic fractionation does not bias quantifications of gross nitrogen transformations.
Rapid Communications in Mass Spectrometry 07/2012; 26(14):163940. · 2.51 Impact Factor  [show abstract] [hide abstract]
ABSTRACT: System dynamics of nitritedependent anaerobic methane oxidation (NDAMO) in a "Candidatus Methylomirabilis oxyfera" culture are described using a mathematical model based on chemical kinetics, microbial growth dynamics and equations for (13)C and (2)H isotopic fractionation. Experimental data for the NDAMO model were taken from Rasigraf et al. (2012), who studied NDAMO in a batch culture of "Ca. M. oxyfera" started at two different conditions with varying methane, nitrite and biomass concentrations. In the model, instead of using concentrations of each isotopologue ((12)C and (13)C, (1)H and (2)H), total concentrations and respective isotope ratios were considered as variables. The empirical Monod equations, which included methane and nitrite as two ratelimiting substrates, a threshold methane concentration CH 4min below which there was no biomass growth, and the same kinetic coefficients for the separate batch experiments, fitted the experimental data much better than apparent firstorder kinetics that required rather different kinetic coefficients for the two experiments. Nonlinear dynamics of (13)C and (2)H isotopic signatures were obtained based on the NDAMO model. It was shown that rate limitation by methane or nitrite concentrations significantly affected the dynamics of carbon and hydrogen isotopic signatures. Fractionation rate increased at higher initial biomass concentration. The nonlinear NDAMO model satisfactorily described experimental data presented in the twodimensional plot of hydrogen versus carbon stable isotopic signatures.Antonie van Leeuwenhoek 09/2013; · 2.07 Impact Factor
Page 1
The effect of15N to14N ratio on nitrification, denitrification and
dissimilatory nitrate reduction
Fiona H. M. Tang and Federico Maggi*
School of Civil Engineering, The University of Sydney, 2006 Sydney, NSW, Australia
RATIONALE: Earlier experiments demonstrated that isotopic effects during nitrification, denitrification and
dissimilatory nitrate reduction can be affected by high15N contents. These findings call into question whether the
reaction parameters (rate constants and MichaelisMenten concentrations) are function of d15N values, and if these can
also lead to significant effects on the bulk reaction rate.
METHODS: Five experiments at initial d15NNO3?values ranging from 0% to 1700% were carried out in a recent study
using elemental analyser, gas chromatography, and mass spectrometry techniques coupled at various levels. These data
were combined here with kinetic equations of isotopologue speciation and fractionation. Our approach specifically
addressed the combinatorial nature of reactions involving labeled atoms and explicitly described substrate competition
and timedependent isotopic effects.
RESULTS: With the method presented here, we determined with relatively high accuracy that the reaction rate constants
increased linearly up to 270% and the MichaelisMenten concentrations decreased linearly by about 30% over the tested
d15NNO3?values. Because the parameters were found to depend on the15N enrichment level, we could determine that
increasing d15NNO3?values caused a decrease in bulk nitrification, denitrification and dissimilatory nitrate reduction
rates by 50% to 60%.
CONCLUSIONS: We addressed a method that allowed us to quantify the effect of substrate isotopic enrichment on
the reaction kinetics. Our results enable us to reject the assumption of constant reaction parameters. The implications
of ddependent (variable) reaction parameters extend beyond the studycase analysed here to all instances in which high
and variable isotopic enrichments occur. Copyright © 2012 John Wiley & Sons, Ltd.
Isotopologue molecules in nature include both naturally
abundant and rare isotopic expressions (heavier or lighter)
of the constituting atoms. Any variations in the ratio between
the concentrations of rare over abundant isotopologues are
relatively small but can precisely be measured with mass
spectrometry techniques. Under typical conditions, heavier
isotopologue reactants take part in a reaction more slowly
than lighter isotopologue reactants regardless of the nature
of the reaction (i.e., physical, chemical or biochemical) and
regardless of whether this is an equilibrium or a kinetic
reaction. This feature results in isotopic effects on reactants
and products that eventually ascribe to a mass difference
between light and heavy isotopes.[4]Although the difference
in atomic mass has only a minor impact on the molecular
mass, the differing affinity of light and heavy isotopologues
to a reaction is significant.
The reaction sensitivity to isotopologues can be exploited to
determine the origin, reaction rate, and turnover time of
chemicals in a broad sense including in biogeochemical,
environmental and ecological studies.[5–8]
stable
determine C fixation rates in plants,[9]microbial respiration
rates,[8,10]organic matter accumulation and decomposition
For example,
13C and radioactive
14C isotopes have been used to
rates in soils,[11–13]
atmosphere.[14]
have been instrumental to detect sinks and sources of NO
and N2O in terrestrial and aquatic systems,[15]
exchange rate with the atmosphere,[16]the relative contri
bution of nitrification and denitrification to N2O production
and emission from soils,[14,17,18]and the pathway of NO3?
dissimilatory reduction.[19]
Highly enriched labeled substrates can be used to produce
a sharp peak in isotopic composition and track its pro
pagation throughout single or multiple reactions.[20,21]The
sampling technique and measuring principle for naturally
and highly enriched substances are analogous, but highly
enriched substrates can have major effects on the bulk
reaction rates and can therefore lead to a systematic under
estimation or overestimation of the isotopic effects of a
reaction. These effects can be attributed to isotopically heavier
reactants, which would presumably slow down the bulk
reaction rate. Experimental evidence of these effects was
reported in regards to nitrification, denitrification and dissim
ilatory nitrate reduction by Mathieu and colleagues.[1]They
observed that substantial decreases in the kinetic isotope
fractionation resulted from d15N values ranging from 0%
to 1700%, and that isotopic effects became insensitive to
any further enrichment only beyond about d15N = 1000%.
The effect of substrate isotopic enrichment on the bulk reac
tion rate has not received enough attention yet. For exam
ple, in a broad sense, how does an increasing concentration
and CO2 exchange rate with the
Similarly,
14N and
15N stable isotopes
their
* Correspondence to: F. Maggi, School of Civil Engineering,
The University of Sydney, 2006 Sydney, NSW, Australia.
Email: federico.maggi@sydney.edu.au
Copyright © 2012 John Wiley & Sons, Ltd.Rapid Commun. Mass Spectrom. 2012, 26, 430–442
Research Article
Received: 16 October 2011Revised: 28 November 2011 Accepted: 29 November 2011Published online in Wiley Online Library
Rapid Commun. Mass Spectrom. 2012, 26, 430–442
(wileyonlinelibrary.com) DOI: 10.1002/rcm.6119
430
Page 2
of heavy isotopes affect the reaction velocity? To answer
this question, we must clarify the implications of increasing
relative concentration of heavy isotopes on the reaction
parameters, be these within zero, first or MichaelisMenten
order frameworks.
The aim of this paper is to quantify the effects of substrate
enrichment level on the rate and isotopic effects of bio
chemical reactions performed by microorganisms in soils.
Based upon earlier results in Mathieu et al.,[1]we hypothesize
that the reaction rate constants and MichaelisMenten concen
trations are not independent from the substrate enrichment
level, but are instead a function of the enrichment itself.
Finding a parametric dependence on the enrichment level
implies that the reaction velocity is also a function of the
enrichment level.
To demonstrate our hypothesis, the experiments carried
out by Mathieu et al.[1]were combined with the mathemati
cal framework developed by Maggi and Riley.[3]The
experiments reported by Mathieu et al. allowed to detect
the effect of increasing substrate isotopic ratio on the
reaction’s isotopic effects and bulk concentrations over
time. The mathematical framework in Maggi and Riley[3]
complements the experiments by introducing a mechanistic
description of each isotopologue and isotopomer reaction
under competitive MichaelisMentenMonod kinetics. This
mathematical framework overcomes the Rayleigh equation,
which uses firstorder kinetics and does not include compe
titive isotopologue substrate consumption.[22]Determining
the reaction rate constants and MichaelisMenten concen
trations for each isotopologue competitive reaction can pro
vide us with an explicit accounting of the effects of differing
isotopic ratios on the reaction rates, and can enable us to
understand a posteriori the scaling laws linking the reaction
parameters to the substrate isotopic ratio.
Here, modeling results, comparison with experiments,
parametric analyses, and analytical interpretations are pre
sented. These results are eventually discussed with suggestions
and recommendations on the interpretations of isotopic
signatures in a wide sense.
METHODS
Experiments
The biochemical reactions of NH4+nitrification to NO3?(NIT),
NO3?denitrification to N2O(aq)(DEN1), N2O(aq)denitrifica
tion to N2 (DEN2), and dissimilatory NO3?reduction to
NH4+(DNR) were experimentally reproduced in incubated
soils in laboratory conditions.[1]Five experiments, each with
three replicates, were carried out by amending soil samples
with a solution of potassium nitrate (KNO3) as the NO3?
source at15N concentrations of 0.37, 0.4, 0.5, 0.75 and 1.0%
atom (natural
corresponded to isotopic compositions d15N of about 0, 100,
350, 1000 and 1700%, respectively. The bulk concentration
of aqueous NH4+and NO3?ions were measured at t = 0 h
and t = 68 h during each test using colorimetric analyses
(indophenols for NH4+and sodium salicylate for NO3?).[1]
The15N enrichment values were determined with diffusion
method, while
an elemental analyser coupled with a mass spectrometer
15N abundance is 0.3663% atom[23]), which
15N isotopic analyses were carried out with
(see details in Mathieu et al.[1]). The N2O(g)bulk concentra
tionwasmeasuredfourtimesduringeachtestusingagaschro
matography analyzer, whereas the d15NN2O(g)values were
determined by mass spectrometry.[1]
Reaction network and model state variables
Figure 1 shows the chemical species tested in the experiments
in Mathieu et al.[1]and provides the conceptual reaction
network used for modeling. In this biochemical system, the
state variables were the bulk concentration and15N isotopic
composition of NH4+, NO3–, N2O(g), the
ratio, the
N2O(g)fractionation factor relative to NO3–.
Biological oxidation and reduction of these species along
NIT, DEN1, DEN2 and DNR reactions were modeled using
aqueous kinetics, whereas N2O(g)exsolution (EXS) was dealt
with as an equilibrium reaction. Note that some reactions in
Fig. 1 are a simplification of the actual reactions occurring in
soils (see Discussion section).
15NNO3–isotopic
15NN2O(g)instantaneous isotopic ratio, and the
Kinetic equations of aqueous reactions
The kinetic NIT, DEN1, DEN2 and DNR reactions occur
along multiple isotopologue pathways, each including the
two stable isotopes14N and15N as:
14NHþ
4!
NIT
14NO?
3
(1a)
15NHþ
4!
NIT
15NO?
3
(1b)
214NO?
3!
DEN114N2O(1c)
14NO?
3þ15NO?
3!
DEN114N15NO(1d)
14NO?
3þ15NO?
3!
DEN115N14NO (1e)
14NO?
3!
DNR
14NHþ
4
(1f)
15NO?
3!
DNR
15NHþ
4
(1g)
DEN 1
DEN 2
NIT
DNR
EXS
NH4
+(aq)
NO3
¯(aq)
N2O(aq)
N2(aq)
N2O(g)
Figure 1. Network of biochemical and physical reactions
of NH4+nitrification (NIT), NO3?denitrification to N2O(aq)
(DEN 1), N2O(aq) denitrification to N2(aq) (DEN 2), NO3?
dissimilatory reduction to NH4+(DNR), and N2O(g) gas
exsolution (EXS).
Effect of substrate enrichment level
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Copyright © 2012 John Wiley & Sons, Ltd.Rapid Commun. Mass Spectrom. 2012, 26, 430–442
431
Page 3
14N2OðaqÞ!
DEN214N2
(1h)
14N15NOðaqÞ!
DEN214N15N (1i)
15N14NOðaqÞ!
DEN214N15N (1j)
Note that Eqns. (1c)–(1e) describe three DEN1 isotopologue
reactions, each one relative to the14N2O isotopologue, and
the
15N2O isotopologue product was excluded from DEN1 as its
relative abundance is negligible compared with that of the
other N2O isotopologues. Similarly, N2O consumption along
the DEN2 pathway in Eqns. (1h)–(1j) accounted for the three
isotopologues mentioned above, but excluded15N2O.
The classical approach to describe these reactions and
quantify their isotopic effects is that of using firstorder
kinetics and expressing the isotope fractionation factor, a,
as the ratio between the rate constant of heavy and light
isotopologue substrate consumption (i.e., the Rayleigh
equation[22]). Within this approach, a is independent of
time and substrate concentration. Although accurate and
widely used, the Rayleigh equation prevents us from
clearly detecting the effect of competitive consumption of
isotopologue reactants. Because substrate competitive con
sumption is crucial to model timevarying isotopic effects
under variable substrate isotopic ratios, we instead use the
General Equations for Biochemical Isotope Kinetics and
Fractionation (GEBIK and GEBIF).[3]In their full form,
GEBIK and GEBIF couple MichaelisMententype kinetics
with Monod kinetics while explicitly accounting for enzyme
concentration as a function of biomass concentration.
MichaelisMentenkineticsprescribe
complex in equilibrium with the reactants is formed under
the catalytic action of an enzyme, which then releases the
products and the unchanged enzyme.[24,25]Monod kinetics
describe microbial biomass dynamics as a function of
released products and cell mortality rate.[26,27]In GEBIK,
the enzyme concentration is assumed to change proportion
ally to the biomass concentration.
For m competing isotopologue biochemical enzymatic
reactions with nSreactants and nPproducts, the generic ith
isotopologue reaction is:[3]
14N15NO and
15N14NO isotopomers, respectively. The
thatanactivated
X
nS
j¼1
X
aji
bji¼0
X
bji
xbji
bji
ajSbji
j
þ E!
k1i ð Þ
k2i ð Þ
Ci!
k?
i ð ÞX
nP
h¼1
X
chi
dhi¼0
X
ghi
ughiydhi
dhi
chPghi
hþ E
(2)
where
atoms of tracer isotope and bjsubstituted isotopes,
represents the hth product containing chatoms of tracer
isotope and dh substituted isotopes, Ci is the reversible
activated complex in reaction i, E is the enzyme, xbjiand
ydhiare the stoichiometric coefficients of each reactant
Sj and product Ph, whileughi
coefficient for production of isotopomers of the same
product Ph. The right superscripts bjiand ghiexpress the loca
tion of the tracer element in Sjand Phisotopomers, respec
tively. Finally, k1(i), k2(i)and k?
ith reaction. The GEBIK equations describing the transient
concentration of each component in Eqn. (2) are:
bji
ajS
bji
jis the jth reactant in reaction i containing aj
dhi
chPghi
h
represents a partitioning
i ð Þare the rate constants for the
d
bj
ajS
dt
bj
j
hi
¼
X
m
i¼1
xbjik2 i ð ÞCi
½? ? k1 i ð ÞE ½ ??
Si
????
(3a)
d½Ci?
dt
¼ k1 i ð ÞE ½ ??
Si
??? k2 i ð Þþ k?
i ð Þ
??
Ci
½?
(3b)
ddh
chPgh
dt
h
hi
¼
X
i
ughiydhik?
i ð ÞCi
½?
(3c)
d½E?
dt
¼ zd½B?
dt
?
X
h
i
d½Ci?
dt
(3d)
dB
dt¼ Y
X
h
X
dh
X
gh
ddh
chPgh
dt
h
i
? mB(3e)
where B represents the biomass concentration, z is the
enzyme yield per unit biomass,
reactant substrate in the ith reaction, Y is the biomass
yield per unit of released product, and m is the biomass
mortality rate.
In this form, the GEBIK equations describe the full transient
kinetics of all components of a set of isotopologous reactions.
Under the QuasiSteadyState (QSS) assumption, the rate of
change of reversible activated complexes Cican be assumed
to be nil (dCi/dt = 0); thus Cican be obtained from Eqn.
(3b) as:
?
Siis the most limiting
Ci
½? ?
E0
½??
Si
??
?
Si
??þ Ki 1 þP
initialenzyme
=k1 i ð Þis equivalent to the MichaelisMenten
concentration (see details in the literature[3]). The term in
parentheses in the denominator of Eqn. (4) represents
competitive substrate consumption taking place in each ith
reaction. This feature allows for an explicit accounting of
any effects of substrate isotopic composition on bulk reaction
rates and isotopic effects on each component. In addition,
under the BiomassFree and Enzyme Invariant (BFEI)
assumptions, the total enzyme and biomass concentrations
are assumed to be constant (dE/dt = dB/dt = 0), and the
simplified GEBIK equations can be written as:
h
dt
i¼1
h
dt
i¼1
p6¼i
?
Sp
Kp
??
!
(4)
where
Ki¼ k2 i ð Þþ k?
E0
istheconcentration,and
i ð Þ
??
d
bj
ajS
bj
j
i
? ?
X
m
xbjik?
i ð ÞCi
½? ¼ ?
X
m
i¼1
xbji
ki ð Þ
E0
Ci
½?
(5a)
ddh
chPgh
h
i
?
X
m
ughiydhik?
i ð ÞCi
½? ¼
X
m
i¼1
ughiydhi
ki ð Þ
E0
Ci
½?
(5b)
with Cias in Eqn. (4). When the enzyme concentration E0
can be considered constant as under the BFEI assumption,[3]
the substitutionki ð Þ¼ k?
degree of freedom. Using the generalized reaction in
Eqn. (2) for the NIT, DEN1, DEN2 and DNR reactions in
Eqn. (1) leads to:
i ð ÞE0
½?
allows us to remove one
F. H. M. Tang and F. Maggi
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Copyright © 2012 John Wiley & Sons, Ltd.Rapid Commun. Mass Spectrom. 2012, 26, 430–442
432
Page 4
NITS11
0
þ E!
k1 1 ð Þ
ptk2 1 ð Þ
C1!
k?
1 ð Þ
P11
0
þ E(6a)
NITS11
1
þ E!
k1 2 ð Þ
k2 2 ð Þ
C2!
k?
2 ð Þ
P11
1
þ E(6b)
DEN12 S21
0
þ E!
k1 3 ð Þ
k2 3 ð Þ
C3!
k?
3 ð Þ
P22
0
þ E (6c)
DEN1 S21
0
þ S21
1
þ E!
k1 4 ð Þ
k2 4 ð Þ
C4!
k?
4 ð Þ
ubP22
b
1
þ ugP2
g
2
1
þ E(6d)
DNRS21
0
þ E!
k1 5 ð Þ
k2 5 ð Þ
C5!
k?
5 ð Þ
P31
0
þ E(6e)
DNRS21
1
þ E!
k1 6 ð Þ
k2 6 ð Þ
C6!
k?
6 ð Þ
P31
1
þ E(6f)
DEN2S32
0
þ E!
k1 7 ð Þ
k2 7 ð Þ
C7!
k?
7 ð Þ
P42
0
þ E(6g)
DEN2ubS32
b
1
þ ug S3
g
2
1
þ E!
k1 8 ð Þ
k2 8 ð Þ
C8!
k?
8 ð Þ
P42
1
þ E(6h)
where
1
0S2¼1
2
S32
¼ P2
0S1¼1
1
0S3¼2
g
1
0P3¼14NHþ
0P1¼14NO?
0P2¼14N2O ,
g
2
¼15N14NO,
4,
3,
1
1S2¼1
S32
P42
¼14N2, P4
1S1¼1
1
b
1
1P3¼15NHþ
1P1¼15NO?
¼ P2
4
,
,
,
3
b
2
1
¼14N15NO
2
101
¼14N15N.
Application of the GEBIK Eqn. (5) to each reaction in Eqn.
(6) results in:
d14NHþ
dt
4
??
¼ ?k?
1 ð ÞC1
½? þ k?
5 ð ÞC5
½?
(7a)
d15NHþ
dt
4
??
¼ ?k?
2 ð ÞC2
½? þ k?
6 ð ÞC6
½?
(7b)
d14NO?
dt
3
??
¼ k?
1 ð ÞC1
½? ? 2k?
3 ð ÞC3
½ ? ? k?
4 ð ÞC4
½? ? k?
5 ð ÞC5
½?
(7c)
d15NO?
dt
3
??
¼ k?
2 ð ÞC2
½? ? k?
4 ð ÞC4
½? ? k?
6 ð ÞC6
½?
(7d)
d14N2O
??
aq
ðÞ
dt
¼ k?
3 ð ÞC3
½ ? ? k?
7 ð ÞC7
½? ? U1
(7e)
d14N15NO
??
aq
ðÞ
dt
¼ ubk?
4 ð ÞC4
½? ? ubk?
8 ð ÞC8
½? ? U2
(7f)
d15N14NO
??
aq
ðÞ
dt
¼ ugk?
4 ð ÞC4
½? ? ugk?
8 ð ÞC8
½ ? ? U3
(7g)
Equations (7e)–(7g) also include the sinks U1, U2and U3
corresponding to the net N2O(g) exsolution (described in
the next section). Following the definition in Eqn. (4), the
activated complexes of Eqn. (7) are:
C1
½? ?
E0
?þ K1 1 þ
?
½?14NHþ
?
4
??
14NHþ
4
?
15NHþ
K2
4
½?
?
(8a)
C2
½? ?
E0
?þ K2 1 þ
?
½
K4
½?15NHþ
?
4
?
15NHþ
4
?
14NHþ
K1
4
½?
?
(8b)
C3
½? ?
E0
½?14NO?
15NO?
3
?
14NO?
3
??þ K3 1 þ
3
?
þ
14NO?
K5
3
½?
þ
15NO?
K6
3
½?
??
(8c)
C4
½? ?
E0
½?15NO?
14NO?
½
K3
3
??
15NO?
3
??þ K4 1 þ
3
?
þ
14NO?
K5
3
½?
þ
15NO?
K6
3
½?
??
(8d)
C5
½? ?
E0
½?14NO?
15NO?
½
K6
3
??
14NO?
3
??þ K5 1 þ
3
?
þ
14NO?
K3
3
½?
þ
15NO?
K4
3
½?
??
(8e)
C6
½? ?
E0
½?15NO?
14NO?
½
K5
3
??
15NO?
3
??þ K6 1 þ
3
?
þ
14NO?
K3
3
½?
þ
15NO?
K4
3
½?
??
(8f)
C7
½? ?
E0
?
½?14N2O
½
??
aq
ðÞ
?aq
½14N2O?aq
ðÞþ K7 1 þ
14N15NO
ðÞþ15N14NO
K8
½?aq
ð Þ
?
(8g)
C8
½? ?
E0
½?
14N15NO
??
aq
ðÞþ
15N14NO
??
aq
ð Þ
?
?
½15N2O? aq
?
ðÞ þ K8
1þ½14N2O? aq
K7
ð Þ
?
(8h)
Equilibrium reactions of gas exsolution
N2O(g)exsolution along the EXS pathway can be written for
each N2O isotopic expression as:
14N2OðaqÞ↔
EXS 14N2Og ð Þ
(9a)
14N15NOðaqÞ↔
EXS 14N15NOg ð Þ
(9b)
15N14NOðaqÞ↔
EXS 15N14NOg ð Þ
(9c)
These reactions are not mediated by microorganisms
and can be assumed to be equilibrium reactions. Under
these hypotheses, Henry’s law can be used to describe
Eqn. (9) as:
h
where Hiis the equilibrium constant specific for the ith reac
tion. Isolating the aqueous species from Eqn. (10) and using a
differential form, enable us to define the sinks U1, U2and U3
introduced earlier in Eqns. (7e)–(7g) as:
1
Hi
bji
ajS
bji
j
i
aq
ðÞ¼
bji
ajS
bji
j
hi
g ð Þ
(10)
Effect of substrate enrichment level
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Copyright © 2012 John Wiley & Sons, Ltd.Rapid Commun. Mass Spectrom. 2012, 26, 430–442
433
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U1¼d
dt
14N2O
??
aq
ðÞ¼ H1
d
dt
14N2O
??
?
?
g ð Þ
(11a)
U2¼d
dt
14N15NO
?
?
?
?
aq
ðÞ¼ H2
d
dt
14N15NO
?
?
g ð Þ
(11b)
U3¼d
dt
15N14NO
aq
ðÞ¼ H3
d
dt
15N14NO
g ð Þ
(11c)
N2O(g)exsolutionisassumednottocompetewithN2O(aq)deni
trificationtoN2inEqns.(8g)–(8h).Thisisnotexpectedtointroduce
largeerrorsasN2(g)isanendproductinthisreactionnetworkand
was not included as a state variable for model calibration.
Isotopic ratio, composition and fractionation
The isotopic ratio of substrates and products in Eqn. (6) can
be defined in several ways depending on the given target.[3]
Here, we use the GEBIF equations defined as:
Rst ð Þ ¼
P
P
P
P
j
P
P
P
P
bj6¼0
P
P
P
P
bj
bjq
bjMSj
bj
ajS
h
dh
chPgh
h
bj
jt ð Þ
hi
jbj6¼0
bj
aj?bj
ð
bjMSj
Þp
bj
ajS
bj
jt ð Þ
i
i
(12a)
RPt ð Þ ¼
hdh6¼0
gh
dhq
dhMPh
ht ð Þ
h
hdh6¼ch
gh
ch?dh
dhMPh
ðÞp
dh
chPgh
ht ð Þ
i
(12b)
whereRS(t) istheisotopicratioofthelabelledtraceratominthe
substrate at time t, RP(t) is the isotopic ratio of the same tracer
atom in the product at time t,bjMSjanddhMPhare the molecular
masses of the jth substrate and the hth product accounting for
the substitutionnumbers bjand dh, respectively, and p and q are
the atomic masses of abundant and rare isotopes.a
These isotopic ratios can be used to calculate the isotopic
compositions, d, relative to a standard Rstd. For the substrate
S and product P, the d values are:
RSt ð Þ
Rstd
?
The isotopic effects on S and P are normally described in
terms of the kinetic fractionation factor:
aS=Pt ð Þ ¼RSt ð Þ
dSt ð Þ ¼ ? 1
??
?
? 1000(13a)
dPt ð Þ ¼
RPt ð Þ
Rstd
? 1
? 1000(13b)
IRPt ð Þ
(14)
with RS(t) defined in Eqn. (12a) and IRP(t) the instantaneous
isotopic ratio of P defined as:
IRst ð Þ ¼
P
P
h
P
P
dh6¼0
P
P
gh
dhq
dhMPh
d
dh
chPgh
dt
?
h
t ð Þ
?
d
?
hdh6¼ch
gh
ch?dh
dhMPh
ðÞp
dh
chPgh
dt
h
t ð Þ
?
(15)
The GEBIF Eqns. (12) to (15) clearly show that the isotopic
ratio, composition and fractionation factor are all functions of
time. Using GEBIF with the system state variables of Fig. 1
leads to:
RNHþ
4t ð Þ ¼
15 ?
15NHþ
?þ 15 ?
15NO?
?þ 15 ?
ðgÞþ29?14N15NO
?
4
?
?
?
?
14 ?
14NHþ
4
?
?
15NHþ
4
?
?
?
?
(14a)
RNO?
3t ð Þ ¼
15 ?
3
14 ?
14NO?
3
15NO?
3
(14b)
RN2OðgÞt ð Þ¼
29?15N14NO
????
ðgÞ
28?14N2O?ðgÞþ29?15N14NO
?
ðgÞþ29?14N15NO
??
ðgÞ
h
(14c)
where S and P are in moles. Their isotopic compositions are:
dNHþ
4t ð Þ ¼
RNHþ
Rstd
4t ð Þ
? 1
!
? 1000(15a)
dNO?
3t ð Þ ¼
RNO?
Rstd
3t ð Þ
? 1
??
? 1000
!
(15b)
dN2OðgÞt ð Þ ¼
RN2OðgÞt ð Þ
Rstd
? 1
? 1000(15c)
Finally, the instantaneous isotopic ratio of N2O(g)product,
IRN2OðgÞt ð Þ, and the instantaneous fractionation factor relative
to NO3
–substrate and N2O(g)product, aS/P, are calculated as:
IRN2OðgÞt ð Þ ¼
29 ? d15N14NO
??
ðgÞþ 29 ? d14N15NO
?
??
ðgÞ
28 ? d14N2O?ðgÞþ 29 ? d15N14NO
?
ðgÞþ 29 ? d14N15NO
??
ðgÞ
h
(16a)
aS=Pt ð Þ ¼
RNO?
IRN2OðgÞt ð Þ
3t ð Þ
(16b)
Note that bothIRN2OðgÞt ð Þand aS/P(t) area function of time t.
Numerical solution and calibration method
A numerical solution of the model introduced in the Experi
mental section was obtained with an implicit finite difference
technique. An integration time step Δt = 0.5 h was used, and
was verified against numerical stability and solution
convergence.
In the aqueous kinetics of Eqn. (7) and gas exsolution of
Eqn. (11), the rate constants k(i), MichaelisMenten (MM)
concentrations Ki, and isotopomer partitioning coefficients
uband ugwere unknown parameters that required calibra
tion against experiments. However, values ub= 0.50225 for
14N15NO and ug= 0.49775 for15N14NO were used, respec
tively, in Eqns. (7f) and (7g) for all isotopic treatments after
the experiments described in Well et al.[15]The isotopologue
Henry’s law constant H1= 2.5 ? 10–2mol Lit–1atm–1relative
to
whereas H2= H3= 2.50188 ? 10–2mol Lit–1atm–1relative to
the
in Eqns. (11b) and (11c)[28]
not involve atomic rearrangements within the molecule’s
14N2O(aq) was used in Eqn. (11a) for all treatments,[23]
14N15NO(aq) and
15N14NO(aq) isotopomers was used
since gas exsolution does
aS and P in Eqn. (12) are expressed with the unit of grams.
When moles are used, the factorsbjMSj¼ 1 anddhMPh¼ 1
are to be used (both dimensionless).
F. H. M. Tang and F. Maggi
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Copyright © 2012 John Wiley & Sons, Ltd.Rapid Commun. Mass Spectrom. 2012, 26, 430–442
434
Page 6
structure by enzymatic reactions linked to microorganisms.
The standard isotopic ratio Rstd= 0.003663[23]was used in
Eqn. (13). Note that 16 unknown parameters and the initial
d15NN2O(g) value could be calibrated in each treatment
against 18 experimental data points distributed as: 8 points
for the bulk concentrations; 7 points for the d values; and 3
points for the isotopic effects (isotopic ratios and fractionation
factor). Under these conditions, the mathematical model
could be solved because the number of experimental points
was at least equal to the number of parameters.
Model calibration was carried out by solving the inverse
problem, i.e., using experimental values of the state variables
to determine the unknown parameters. To this end, the
LevenbergMarquardt algorithm was used to minimize the
difference between observed and modelled state vari
ables.[29,30]Model accuracy versus experiments was reported
for each treatment using the correlation coefficient (R) and
Normalized Root Mean Square Error (NRMSE) defined as
R ¼cov m;o
s
max o
ðÞ
smso
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
i¼1
f g ? min o
(17a)
NRMSE ¼
1
n
P
n
mi? oi
ðÞ2
f g
(17b)
where m and o are the modelled and observed values of the
state variables, respectively, n is the number of values, and
smand soare the standard deviation of m and o, respectively.
R and NRMSE were calculated relative to the bulk concentra
tions (Rcand NRMSEc) and isotopic compositions and effects
(Rdand NRMSEd) in each treatment.
RESULTS
Bulk concentrations
Calibration of the rate constants k(i)and MM concentrations
Ki of GEBIK Eqn. (7) was performed using experimental
concentrations, dvalues, and avalues of the variable NH4+,
NO3–and N2O(g)as described in the Experimental section. A
summary of the calibrated parameters is given in Table 1
along with initial conditions and accuracy estimators for
each treatment.
The panels in Fig. 2 show that the net concentration
of source NO3
and DNR pathways had a combined net effect larger than
NO3–production along the NIT pathway. Conversely, the
NH4+bulk concentration increased, meaning that NH4+
production along the DNR pathway had a larger effect than
consumption along the NIT pathway. The N2O(g) concen
tration increased as the effect of N2O(aq) production from
NO3–and N2O(aq)exsolution EXS to N2O(g)was greater than
the effect of N2O(aq)consumption to N2along DEN2. These
features appeared persistent over an 80 h timescale in the
five treatments as these tests were conducted with similar
initial bulk concentrations and in controlled temperature
and soil moisture conditions. The model described with
greataccuracyexperimental
an aggregated correlation coefficient Rc≥99.96% and error
NRMSEc≤1.11% (Table 1).
–decreased as consumption along the DEN1
bulk concentrationswith
Isotopic compositions
Although the overall effect of increasing the d15NNO3–
values on the bulk concentrations was nearly undetectable
from Fig. 2, its effect on the isotopic composition of the
species under analysis here was relatively important. The
d15NNH4+values in Fig. 3 show that the observed and mod
eled bulk NH4+gradually evolved from15N depletion over
80 h (the d15NNH4+value decreased in treatment 1, Fig. 3(a))
to15N enrichment (the d15NNH4+value increased in treatment
5, Fig. 3(e)) for increasing d15NNO3–values. We explain this
smooth change toward
amended
during NO3–dissimilatory reduction along the DNR pathway.
Conversely to the d15NNH4+values, the d15NNO3–values
persistently increased over time in all treatments – behavior
that was captured relatively well by the model. The increas
ing d15NNO3–values during NO3–consumption complied
with the expected isotopic effects in NO3–. In fact, NO3–was
the supplied substrate undergoing consumption along the
DEN1 and DNR reaction pathways (Fig. 3), thereby being
subjected to a net15N enrichment.
The observed and modeled d15NN2O(g)values showed a
progressive change from
decreased over time in treatments 1 and 2: Figs. 3(a) and 3
(b), respectively) to enrichment (d15NN2O values increased
over time in treatments 3, 4 and 5: Figs. , 3(c), 3(d) and 3(e),
respectively). One possible explanation for these results is
that the fraction of15NO3–reduced to N2O(aq)and emitted
as N2O(g) could have been directly proportional to the
amended
to 5. Another possible explanation is that the fraction of
15NO3–reduced to N2O(aq)and emitted as N2O(g)could have
increased proportionally faster than the fraction of consumed
14NO3–. These explanations are both plausible but there is no
fully exhaustive proof at this stage of our interpretation
because N2O(aq) isotopic composition was not measured
by Mathieu et al.[1]Regardless of these explanations, we
cannot exclude the possibility that14NO3–and15NO3–adsorp
tion to the mineral phase could preferentially have buffered
and fractionated14N over15N species in contraposition to bio
logical processes. The analysis presented in the following sec
tions brings further evidence of the mechanisms responsible
for the observed and modeled isotopic compositions and
effects.
15NNH4+enrichment as due to
15NO3–, which was next converted into
15NH4+
15N depletion (d15NN2O values
15N, which increased greatly from treatment 1
Isotopic effects
For the purpose of model comparison with experiments, the
instantaneous ratio IR(t) of Eqn. (16a) was calculated with
the discrete difference corresponding to Δt = 20 h to comply
with the calculations originally presented in Mathieu et al.[1]
Figure 4(a) shows that increasing initial d15NNO3–values
caused an increase inRNO?
t = 68 h, which was a direct effect of amended15N on the
DEN1 and DEN2 reactions, respectively. As already noted
in Mathieu et al.,[1]the fractionation factor decreased as
the d15NNO3–values of amended NO3–increased through
the treatments (Fig. 4(b)). A decreasing a(t) implied that the
NO3–substrate became relatively less enriched in15N than
the N2O(g)product during the course of the DEN2 and DNR
reactions. We support this interpretation of a, noting that
3t ð Þ
andIRN2O g ð Þt ð Þ
at time
Effect of substrate enrichment level
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435
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Table 1. ParametersandinitialconditionsusedintheGEBIKequationsdescribingnitrification(NIT),denitrification(DEN1andDEN2)anddissimilatoryNO3–reduction(DNR)
Treatment
1
2
3
4
5
15N
Atom%
0.37
0.40
0.50
0.75
1.0
cd15N?NO3
?
%
0
100
350
1000
1700
Parameter
Reaction
Substrate
Product
k(1)? 10–6
[mmol/kgsoils]
NIT
14NH4+
14NO3–
3.0245
2.9836
2.9845
2.8564
2.2790
k(2)? 10–6
[mmol/kgsoils]
NIT
15NH4+
15NO3–
3.0010
2.9842
2.9140
2.8056
2.2457
k(3)? 10–6
[mmol/kgsoils]
DEN1
2 ?14NO3–
14N2O
16.489
17.348
16.937
17.511
14.879
k(4)? 10–6
[mmol/kgsoils]
DEN1
14NO3–,15NO3–
14N15NO,14N15NO
16.202
16.889
16.262
1.822
14.715
k(5)? 10–6
[mmol/kgsoils]
DNR
14NO3–
14NH4+
70.253
139.44
207.10
323.98
768.97
k(6)? 10–6
[mmol/kgsoils]
DNR
15NO3–
15NH4+
69.299
110.13
186.73
278.81
754.14
k(7)? 10–6
[mmol/kgsoils]
DEN2
14N2O
14N2
47.217
80.537
86.129
108.67
109.25
k(8)? 10–6
[mmol/kgsoils]
DEN2
14N15NO,14N15NO
14N15N
47.134
74.519
76.530
103.83
106.33
K1
[mmol/kgsoil]
NIT
14NH4+
14NO3–
2.05
2.34
2.58
2.66
3.49
K2
[mmol/kgsoil]
NIT
15NH4+
15NO3–
2.38
4.53
4.17
3.64
3.89
K3
[mmol /kgsoil]
DEN1
14NO3–
14N2O
2.29
0.87
0.62
0.25
0.041
K4
[mmol /kgsoil]
DEN1
14NO3–,15NO3–
14N15NO,14N15NO
2.30
0.85
0.59
0.30
0.039
K5
[mmol/kgsoil]
DNR
14NO3–
14NH4+
39.97
28.82
38.61
22.29
10.26
K6
[mmol/kgsoil]
DNR
15NO3–
15NH4+
41.40
27.34
48.13
34.57
21.59
K7
[mmol/kgsoil]
DEN2
14N2O
14N2
0.00981
0.0053
0.0061
0.0054
0.0085
K8
[mmol/kgsoil]
DEN2
14N15NO,14N15NO
14N15N
0.0101
0.0048
0.0052
0.0049
0.0075
aH1
[mol/Lit atm]
EXS
14N2O
14N2O
2.5
2.5
2.5
2.5
2.5
bH2= H3
[mol/Lit atm]
EXS
14N15NO,14N15NO
14N15NO,14N15NO
2.5019
2.5019
2.5019
2.5019
2.5019
NH4+(aq)
[mg N/kgsoil]
9.90
9.80
9.30
8.80
8.70
NO3–(aq)
[mg N/kgsoil]
143.70
165.00
159.00
171.50
161.80
N2O(g)
[mg N/kgsoil]
2.11
2.11
2.11
2.11
2.54
Rc
%
99.99
99.98
99.96
99.98
99.99
NRMSEc
%
0.46
0.86
1.11
0.80
0.68
Rd
%
99.34
99.98
99.99
99.98
99.99
NRMSEd
%
4.46
0.83
0.85
1.53
1.12
aFrom [23];bfrom [28];camended values; effective experimental values are represented in Fig. 3.
Bold font used for the parameter values obtained by calibration.
F. H. M. Tang and F. Maggi
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436
Page 8
the DEN2 reaction involving15N substrate increased in rele
vance compared with the reaction involving14N, as demon
strated by d15NN2O values increasing over time and across
the treatments (Fig. 3). The model could describe relatively
well the observed isotopic compositions, ratios and effects
over time (Rd≥99.34% and error NRMSEd≤4.46%, Table 1).
Analysis of the parameters
The calibrated parameters are summarized in Table 1 and are gra
phically represented in Fig. 5 against the initial d15NNO3–values.
Pairs of rate constants in isotopologuous reactions (e.g., k(1)
and k(2) for NIT, k(3) and k(4) for DEN1, etc.) showed a
spectrum of responses to increasing d15NNO3–values in the
five treatments. Their response ranged from relatively low
sensitivity (within the measurement accuracy for k(1)and k(2)
in NIT, and k(3)and k(4)in DEN1), to a moderate increase
(about 100% for k(7)and k(8)of DEN2), up to an important
increase (about 10 times for k(5)and k(6)of DNR). The higher
sensitivity of the DEN2 and DNR rate constants to d15N
NO3–values can be ascribed to the fact that these reactions
used NO3–as a substrate, while NIT and DEN1 used NO3–
products as substrates and were only secondarily affected
by d15N values. We also note that k(i)values relative to14N
were slightly higher than k(i+1)values relative to15N in all
reactions (Fig. 5(a)). This finding complies with the vast
majority of theoretical and observed isotope kinetics studies,
where isotopically light substrates are expected to react
slightly more rapidly than heavy substrates.[4]
With regard to MM concentrations, we observed a rela
tively less regular response to the initial d15NNO3–values
(Fig. 5(b)). Here, the pairs K1and K2of NIT, and K7and K8
of DEN2 oscillated around nearly the same value, whereas
K3and K4for DEN1, and K5and K6for DNR decreased with
increasing d15NNO3–values. Conversely to the rate constants
in Fig. 5(a), the MM concentrations relative to the15N isoto
pologues were on average slightly higher than those relative
to the14N isotopologues. The combined effect of k(i)and Ki
on bulk reaction rates could not precisely be quantified a
priori as these parameters affected the kinetics of each compo
nent in a nonlinear way within the GEBIK equations. To high
light these aspects, a detailed analysis is presented in the
following sections.
Effect of15N content on bulk NH4+, NO3–, and N2O(aq)
consumption rates
Figures 2 and 3 indicate that the bulk concentrations and isoto
pic compositions can be affected by the d15NNO3–values. To
quantify the cumulative effect of increasing the d15NNO3–
values on the net rate of change of individual substrates, a
different approach was exploited and is described as follows.
020406080
0
30
60
90
120
150
180
Time [h]
Bulk concentration [mg N/kgsoil]
Bulk concentration [mg N/kgsoil]
Bulk concentration [mg N/kgsoil]
Bulk concentration [mg N/kgsoil]
Bulk concentration [mg N/kgsoil]
NH4
NO3
N2O(g), exp.
NH4, model
NO3, model
N2O(g), model
+, exp.
−, exp.
020406080
0
30
60
90
120
150
180
Time [h]
0 204060 80
0
30
60
90
120
150
180
Time [h]
020 406080
0
30
60
90
120
150
180
Time [h]
020406080
0
30
60
90
120
150
180
Time [h]
(a)(b)(c)(d)(e)
Figure 2. Experimental and modeled NH4+and NO3–aqueous concentrations, and N2O gaseous concentration for five
treatments at (a) 0.37, (b) 0.40, (c) 0.50, (d) 0.75, and (e) 1.0015N atom%, corresponding to an initial d15NNO3–equal to 0,
100, 350, 1000, and 1700%, respectively. Experiments are redrawn from Mathieu et al.[1]
020406080
−20
−10
0
10
20
Time [h]
NH4
NO3
N2O(g), exp
NH4
NO3
N2O(g), model
+, exp.
−, exp.
+, model
−, model
020406080
0
10
40
50
60
70
80
Time [h]
02040 6080
0
10
20
240
250
260
270
Time [h]
0 20406080
0
20
40
60
80
720
740
760
Time [h]
020406080
0
10
20
30
40
1200
1210
1220
1230
1240
1250
Time [h]
δ 15N o/oo
δ 15N o/oo
δ 15N o/oo
δ 15N o/oo
δ 15N o/oo
(a)(b)(c)(d)(e)
Figure 3. Experimental and modeled Nisotopic composition of NH4+, NO3–and N2O(g)for five treatments at (a) 0.37, (b) 0.40,
(c) 0.50, (d) 0.75, and (e) 1.0015N atom% corresponding to an initial d15NNO3–equal to 0, 100, 350, 1000, and 1700%, respectively.
Experiments are redrawn from Mathieu et al.[1]
Effect of substrate enrichment level
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437
Page 9
The parameters k(i)and Kiof Table 1 were used in our
GEBIK and GEBIF equations under uniform initial conditions
across all treatments to allow for model comparison. Next,
the cumulative rates of change r of bulk NH4
N2O(aq)were calculated relative to their bulk concentration
and15N to14N isotopic ratio as:
?
1414NHþ
4
d 1414NHþ
4
?
¼14 ?k1 ð ÞC1
1515NHþ
+, NO3
–, and
rNHþ
4t ð Þ ¼
1
RNHþ
?
4t ð Þ
?
d 1414NHþ
?
4
?þ 1515NHþ
?
4
??
4
? ?.
dt
?þ 1515NHþ
4
?
?þ 15 ?k2 ð ÞC2
4
??
¼
?þ 1515NHþ
1515NHþ
? ?.
dt
4
½ ? þ k5 ð ÞC5
½?
?
? ? k5 ð ÞC5
1515NO?
?
½ ? ? k6 ð ÞC6
½?
??
?
?þ 15 k2 ð ÞC2
3
(18a)
rNO?
3t ð Þ ¼14 k1 ð ÞC1
½? ? 2k3 ð ÞC3
½ ? ? k4 ð ÞC4
½½?
?
½? ? k4 ð ÞC4
½? ? k6 ð ÞC6
½?
??
??
(18b)
rN2OðgÞt ð Þ ¼28 k3 ð ÞC3
½? ? k7 ð ÞC7
2915N14NO
½
?
? ? U1
??þ 29 k4 ð ÞC4
½ ? ? k8 ð ÞC8
½ ? ? U2? U3
??
?
g ð Þþ 2914N15NO
??
g ð Þ
(18c)
The equations above take into account all the production
and consumption contributions to a substrate and describe,
therefore, the net rate of change of NH4+, NO3–, and N2O(aq).
Equation (18), represented in Fig. 6 as a function of time,
shows that rNHþ
in d15N values (compare thin and thick lines), while the rates
rNO?
more sensitive thanrNHþ
increasing d15N values. Because rNHþ
were expressed relative to the instantaneous15Ν content, we
explain these decreases in rNO?
to an increasing weight of heavy15N isotopologue reactions. In
fact, reactions involving15N occur more slowly than those invol
ving14N and can lead to an overall decrease in the bulk reaction
rate if the15N content is high enough. This effect was evident for
rNO?
as15NO3–, and forrN2OðgÞt ð Þ, which rapidly received15N along the
DEN1pathway.TheraterNHþ
15N were recycled through the NITand DNR pathways.
4t ð Þ was only slightly sensitive to an increase
3t ð Þ (negative in these experiments) and rN2OðgÞt ð Þ were
4t ð Þand showed a strong decrease with
4t ð Þ, rNO?
3t ð Þ and rN2OðgÞt ð Þ
3t ð Þ and rN2OðgÞt ð Þ as being due
3t ð Þ,whichwasdirectlyaffectedby15Namendedinthesystem
4t ð Þwaslesssensitiveasboth14Nand
Effect of15N content on NIT, DEN and DNR reaction rates
Along with the effects of d15NNO3–values on individual sub
strate consumption rates, it is meaningful to assess also the
effects on individual reactions, i.e., on bulk nitrification (NIT),
denitrification (DEN1 and DEN2) and dissimilatory reduction
(DNR).Tothis end,themodelparameters andinitialconditions
were used as in the previous section, while the reaction rates
rNIT, rDEN1, rDEN2and rDNRrelative to the corresponding bulk
substrate concentration and isotopic ratio were calculated as:
rNITt ð Þ ¼
1
RNHþ
4t ð Þ
14k1 ð ÞC1
1414NHþ
½ ? þ 15k2 ð ÞC2
?þ 1515NHþ
?
½?
4
?
4
?? ¼
¼14k1 ð ÞC1
½? þ 15k2 ð ÞC2
1515NHþ
½
4
??
(19a)
0100 350 10001700
10−4
10−5
10−6
10−1
10−2
10−3
102
101
100
k(1)
k(2)
NIT
k(3)
k(4)
DEN1
k(5)
k(6)
DNR
k(7)
k(8)
DEN2
14N
15N
010035010001700
K1
K2
NIT
K3
K4
DEN1
K5
K6
DNR
K7
K8
DEN2
MM concentration [mmol/kgsoil]
14N
15N
δ15N−NO3
− [o/oo]
Rate constant [mmol kgsoil
−1 s−1]
δ15N−NO3
− [o/oo]
(a)
(b)
10−3
Figure 5. (a) Rate constants and (b) MichaelisMenten con
centrations relative to nitrification (NIT), denitrification
(DEN1 and DEN2) and dissimilatory nitrate reduction
(DNR). Gray and black lines refer to14N and15Nrelated
parameters, respectively.
010035010001700
3
4
5
6
7
8
δ15N o/oo
R [−]
RNO3
RNO3
Ri
N2O(g)
Ri
N2O(g)
−, exp.
−, model
, exp.
, model
010035010001700
1.01
1.015
1.02
1.025
1.03
αS/P [−]
Exp.
Model
(a)
(b)
x 10−3
δ15N o/oo
Figure 4. (a) Experimental and modeled Nisotopic ratio of
NO3–and N2O(g)as defined in Eqn. (14). (b) Kinetic isotopic
fractionation factor a(t) for treatments at 0.37, 0.40, 0.50,
0.75, and 1.0015N atom% corresponding to an initial d15N
NO3–equal to 0, 100, 350, 1000, and 1700%, respectively.
Experiments are redrawn from Mathieu et al.[1]
(19a)
F. H. M. Tang and F. Maggi
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Copyright © 2012 John Wiley & Sons, Ltd.Rapid Commun. Mass Spectrom. 2012, 26, 430–442
438
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rDEN1t ð Þ ¼14k3 ð ÞC3
½? þ 15k4 ð ÞC4
1515NO?
½?
3
?
?
?
?
?
?
(19b)
rDNR t ð Þ ¼14k5 ð ÞC5
½? þ 15k6 ð ÞC6
1515NO?
½?
3
(19d)
rDEN2t ð Þ ¼14k7 ð ÞC7
½? þ 15k8 ð ÞC8
1515NO?
½?
3
(19c)
These rates are represented in Fig. 7 as a function of time.
Generally, we observed a clear pattern in the NIT reaction,
which was characterized by a strong decrease in rNIT for
increasing initial d15NNO3–values (Fig. 7(a)). The DEN1
and DNR reaction rates rDEN1and rDNRshowed an initial
increase, which was followed by a continuing decrease for
d15NNO3–values >100% (Figs. 7(b) and 7(c)). Conversely,
we have not observed a clear pattern in the DEN2 reaction
rate (Fig. 7(d)), but our results suggest that an average
increase in the reaction rate rDEN2occurred for d15NNO3–
values >100%.
Over all, Fig. 7 indicates that increasing d15NNO3–values
generally resulted in an average decrease of the rate of change
of all the biochemical reactions immediately consuming NO3–
as a substrate. Secondary effects appeared also in reactions
that consumed the first successor to NO3–, such as NH4+and
N2O(aq), along the DNR and DEN1 pathways.
Effect of15Ncontentontimedependent isotopefractionation
According to Eqn. (16b), the fractionation factor a is a
dependent variable, which changes with the isotopic ratios
of NO3–and N2O(g) during denitrification reactions. Time
varying isotopic effects may become more visible under
highly increasing initial d15NNO3–values. We have analysed
how the isotopic effects in the five treatments were affected.
As expected from the theoretical considerations considered
above, Fig. 8 shows that the fractionation factor a was not
constant and that da/dt was not negligible in these experi
ments. Rather, we observed that increasing15N content led
to a persistent increase in the average slope da/dt across the
treatments. This persistent increase in da/dt suggests that
the NO3–substrate became relatively more15N enriched over
time as denitrification DEN1 occurred. We can explain these
experimental and modeling results as being due to a specific
selectivity of microorganisms to15NO3–and14NO3–. In parti
cular, under the assumption that the NO3–metabolic require
ment by DEN is constant across the treatments and that
the DEN pathway has a higher affinity to
15NO3–, it is likely that
time
14NO3–than to
14NO3–would be consumed at an
0 255075100
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0.3
Time [h]
δ15N = 0 o/oo
δ15N = 100 o/oo
δ15N = 350 o/oo
δ15N = 1000 o/oo
δ15N = 1700 o/oo
0 255075100
−0.22
−0.2
−0.18
−0.16
−0.14
−0.12
−0.1
−0.08
−0.06
Time [h]
02550 75100
0
0.05
0.1
0.15
0.2
0.25
0.3
Time [h]
rN2O(g) [mg−N h−1 mg−15N−1]
rNO−
rNH4
+ [mg−N h−1 mg−15N−1]
3 [mg−N h−1 mg−15N−1]
(a) (b)(c)
Figure 6. Net d15N effect on the rate of change of bulk NH4+(a), NO3–(b), and N2O gaseous (c)
after initial d15NNO3–values ranging from 0% to 1700%.
0 255075100
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Time [h]
0255075100
0.5
1
1.5
2
Time [h]
rDEN1 [h−1]
2550 75100
Time [h]
rDNR [h−1]
0 25 5075100
0.5
1
1.5
2
2.5
3
3.5
Time [h]
rDEN2 [h−1]
2.5
0.01
0.015
0.02
0.025
0.03
0.035
0.04
4
rNIT [h−1]
δ15N = 0 o/oo
δ15N = 100 o/oo
δ15N = 350 o/oo
δ15N = 1000 o/oo
δ15N = 1700 o/oo
Figure 7. Net d15N effect on the rate of change of NIT (a), DEN1 (b), DRN (c), and DEN2 (d) after initial d15N
NO3–values ranging from 0% to 1700%.
Effect of substrate enrichment level
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increasing rate as the15NO3–concentration increased through
the treatments. This relative increase in the14NO3–to15NO3–
consumption rate may ultimately have resulted in NO3– 15N
enrichments.
DISCUSSION
Weanalysedtheeffectsof15Nisotopicenrichmentonthekinetic
fractionation of
denitrification and dissimilatory reduction reactions. In these
analyses,wetookintoaccountvariousaspectsincludingthecom
binatorialstructureofthechemicalreactionsinrelationtovarious
isotopologues and isotopomers speciation, substrate competi
tions, and transient kinetics effects. We also made simplifications
while modelling these reactions, which are discussed as follows.
The biochemical reactions analysed here were aggregated
for simplicity, whereas intermediate compounds are known
to be formed. For example, ammonium NH4+is first
converted into nitrite NO2–and next into nitrate NO3–.[31]
Similarly, NO3–denitrification to N2involves four reactions
along the chain NO3–! NO2–! NO ! N2O ! N2, where
each component is the electron acceptor of a reduction
reaction.[32,33]In our approach, the first three reactions were
accounted for in DEN1, while DEN2 described N2O con
sumption only. As a final example, dissimilatory NO3–reduc
tion, which occurs along the reactions NO3–! NO2–! NH4+
in typical anaerobic conditions,[19]was simplified into one
reaction with NO3–and NH4+as the substrate and final
electron acceptor, respectively. In these instances, the inter
mediate reactions were not modelled explicitly as they are
normally assumed to occur rapidly enough to allow for only
low concentrations of free NO2–and NO. These simpli
fications meet both laboratory and field observations.[22,34]
However, we note that the complexity of soil characteristics,
microbial species, and chemical compounds present in real
environments may lead to conditions that allow for the accu
mulation of NO2–such as by adsorption to the mineral phase.
We did not analyse this type of interaction here and we
cannot exclude the possibility that NO2–and NO could
also have been marginally produced and accumulated in
14N and
15N isotopes during nitrification,
Mathieu’s experiments. On the one hand, these processes
may partly explain the difference between the modelled
and observed d15N values at high initial d15NNO3–values
(treatments 4 and 5). On the other hand, we are confident that
our modeling approach captured the relevant dynamical
features with an adequate degree of mechanism as substan
tiated by the overall accuracy against experimental bulk
concentrations and isotopic compositions.
Nitrification,denitrification
reduction, as well as other reactions of the nitrogen cycle,
are performed in natural soils by various microorganism
strains. These can be described by functional groups under
the assumption that, within the same functional group, they
catalyze reactions through similar enzymes.[33]For example,
nitrification is performed by Ammonium Oxidizing Bacteria
(AOB) and Nitrite Oxidizing Bacteria (NOB) groups, while
denitrification is performed by the Denitrifying Bacteria
(DEN) group.[35–39]The original GEBIK and GEBIF equations
allowed us to take into account an arbitrary number of func
tional groups and enzymes, as well as their dynamics. How
ever, this capability was not exploited in this work as the
assumptions of quasisteady state, and biomass and enzyme
invariance, were invoked to allow for mathematical simplifi
cations. We believe that the possibility of simultaneously
measuring the concentration of microbial functional groups
in addition to the chemical species could be exploited in this
modelling framework to improve our understanding of isoto
pic effects linked to biochemical reactions.
It is worth noting that while AOB and NOB require O2dur
ing NH4+and NO2–nitrification, the DEN functional group
requires organic carbon (OC) compounds as an electron
donor to perform denitrification reactions. In partly saturated
conditions, O2is readily accessible by AOB and NOB, and
NO3–production from NH4+is favoured. On the other hand,
denitrification of NO3–to N2 and dissimilatory reduction
of NO3–to NH4+are expected to be high in soils with high
OC availability.[19,32]Hence, the isotopologue reactions in
Mathieu’s experiments competed not only for Nbased sub
strates, but also for O2and OC. In the modelling proposed
here, we have assumed that O2and OC substrates were not
limiting the reactions, whereas it is possible that their concen
tration became low enough to decrease the reaction rates in
Mathieu’s experiments. In this case, the reaction rates would
be somehow slower, but we do not expect that decreasing
O2and OC concentrations could interfere to the extent that
the rate constants k(i)and MM concentrations Kiare substan
tially affected.
We remark that isotopic effects may also be affected by
the proportion of14N and15N incorporated in microorga
nismal cells. For example, it is not known to what extent
immobilization within bacterial cells could contribute to
isotopic fractionation, and if cells may be responsible for
variable and inverse isotopic effects in biochemical reac
tions.[2]In an earlier work, variable and inverse kinetic
isotopic effects were demonstrated to be possible also
when the fraction of nutrient uptake by microorganisms
was neglected.[3]We expect that bacterial cell may act as
a buffer to14N and15N species, but this aspect is not yet
fully understood.
The significance of our results stems from two specific
aspects of the interpretation of isotopic effects in bio
chemical reactions. When labelled compounds are used
and dissimilatorynitrate
20 40 6080
0.96
0.98
1
1.02
1.04
Time [h]
α [−]
δ15N = 0 o/oo
δ15N = 100 o/oo
δ15N = 350 o/oo
δ15N = 1000 o/oo
δ15N = 1700 o/oo
Figure 8. Kinetics isotope fractionation factor a(t) relative to
NO3–substrate and N2O(g) product for d15NNO3–values
ranging from 0% to 1700%. Experiments are redrawn from
Mathieu et al.[1]
F. H. M. Tang and F. Maggi
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Copyright © 2012 John Wiley & Sons, Ltd.Rapid Commun. Mass Spectrom. 2012, 26, 430–442
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to track the pathways of atomic movement through one
or more reactions, high enrichment levels in the substrate
can be employed appropriately. However, high enrich
ment levels in the substrate should not be used to deter
mine turnover time and reaction rates, because they affect
the bulk reaction rate, as shown in our results. For exam
ple, if the reaction rate and isotope fractionation factor
are to be estimated for a reaction where the substrate
and product are not recycled, enriching the product in
labelled atoms is expected not to affect the bulk reaction
rate and kinetic isotopic effects. Conversely, if the reac
tion recycles the product as in the coupled NIT and
DNR pathways analyzed here, the interpretation of the
isotopic effects should take into account the enrichment
level. Along this line, and as a practical example, a
DNR rate of about 0.6 mg NO3–/g soil was estimated by
Silver et al.[19]using an amended solution of KNO3 at
14% atom in
content of 0.4% atom in NH4+. According to our results,
recycled
NIT, and a variable effect on DEN1 and DNR ranging
between about ?10% and about +10% over a period of
time of a few days (<100 h). The effects on shorter time
scales could be much higher and could lead to decreases
in DEN1 and DNR rates as great as those proposed in
Fig. 7, or greater (say up to 60%). We therefore recommend
that the absolute content in labelled stable isotope tracers
should be taken into account when assessing reaction rates
from isotopic signature analysis.
15N, which resulted in an average
15N
15N would lead to a decrease of about 10% in
CONCLUSIONS
The analyses presented here were instrumental in highlight
ing various effects of15Nenrichment levels on the parameters
and rates of nitrification, denitrification and dissimilatory
nitrate reduction reactions in soils. To carry out these ana
lyses, we took into account various aspects including the
combinatorial structure of the chemical reactions of isotopolo
gue and isotopomer speciation, substrate competitions, and
transient kinetics effects. Our results showed nearly linear
increases in the reaction rate constants (by about 270%) and
decreases in the MichaelisMenten concentrations (by about
30%) over the tested d15N values (ranging from 0% to
1700%). We also showed that these effects were not minor,
but could lead to substantial decreases in bulk nitrification
rate (up to 50%), denitrification rate (up to 60%) and dissimi
latory nitrate reduction rate (up to 60%). These results sug
gested, therefore, that chemical kinetic parameters should
not be considered constant but, rather, a function of the
enrichment level itself in all applications in which highly
enriched isotopic substrates are used.
Acknowledgements
The authors thank Olivier Mathieu for the help provided in
interpreting the experimental results. The authors acknowl
edge the Summer Scholarship Research Program of the
School of Civil Engineering, The University of Sydney, for
the support provided to Fiona Tang for this project.
LIST OF SYMBOLS
aS/P
b, g
m
d
B
C
E
E0
H
K
k
Μ
m
n
nS
nP
o
p, q
R
IR
Rstd
S,P
U
u
x, y
Y
z
NRMSE
R
[?] kinetic isotope fractionation factor
[?] isotopomer expression
[1/s] biomass mortality rate
[?] isotopic composition in %
[mg/kgsoil] biomass concentration
[mmol/kgsoil] reversibleactivatedcomplexconcentration
[mmol/kgsoil] enzyme concentration
[mmol/kgsoil] initial enzyme concentration
[M/atm] Henry’s law constant
[mmol/kgsoil] MichaelisMenten concentration
[s–1] rate constant
[g/mol] molecular weight
[?] modelled state variable
[?] number of values m and o
[?] number of reactants
[?] number of products
[?] observed state variable
[g/mol] atomic weight
[?] isotopic ratio
[?] instantaneous isotopic ratio
[?] standard isotopic ratio
[mmol/kgsoil] reactant and product concentration
[mmol/kgsoil] gas exsolution rate
[?] partitioning coefficient
[?] stoichiometric coefficients
[g/mol] biomass yield coefficient
[mol/mol] enzyme yield coefficient
[?] normalized root mean square error
[?] correlation coefficient
subscript for bulk concentrations
subscript for isotopic composition
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