Journal of Plankton Research Vol.19 no.12 pp.1881-1897, 1997
A short version of the ammonium-nitrate interaction model
Kevin J.Flynn and Michael J.R.Fasham 1
Swansea Algal and Plankton Research Unit, School of Biological Sciences,
University of Wales Swansea, Singleton Park, Swansea SA2 8PP and
Southampton Oceanography Centre, Empress Dock, Southampton SO14 3ZH,
UK
Abstract. The performance of the complex ammonium-nitrate interaction model (ANIM) of Flynn
et aL (Philos. Trans. R. Soc, 352,1997) is compared with that of a simplified version (SHANIM) in
which the internal pools of inorganic nitrogen (N) and the enzymes of nitrate-nitrite reduction and
glutamine synthetase are absent. Although SHANIM is incapable of simulating cell size-linked processes such as the accumulation of inorganic N and the uncoupling of inorganic N transport from
assimilation, it offers a good compromise for those needing a simplified modelling solution. The
genera] close agreement between ANIM and SHANIM simulations (usually differing in the details
of nutrient transport by phasing of a few hours even in a light-dark cycle) is due to the retention of
two major features of ANIM, namely nutrient history-linked transport rates for nitrate and
ammonium and regulation of transport by an organic product of N assimilation (glutamine).
Introduction
A complex model for the simulation of algal nitrogen (N) physiology, the
ammonium-nitrate interaction model (ANIM), has been developed by Flynn et
aL (1997). This model (Figure 1) contains mechanistic components simulating the
more important biochemical components of algal physiology. Thus, it contains a
link between nutrient status and maximum uptake rates (to simulate enhanced
transport in N-deprived cells, e.g. Syrett et aL, 1986), internal nutrient pools (e.g.
Dortch et aL, 1984), a simulation of the synthesis and control of the enzymes and
activities of nitrate reduction (e.g. Solomonson and Barber, 1990), and modulation of the ammonium-nitrate interaction by an early product of N assimilation
(Flynn, 1991). ANIM offers a modelling strategy capable of simulating all the
major components of the ammonium-nitrate interaction, including light-dark
(L/D) interactions by reference to a PI curve, with concurrent algal growth.
While providing considerable scope for development, simulation and hypothesis setting, ANIM may be considered to be overly complicated for some applications. A short version of ANIM (SHANIM; Figure 1), without internal pools
of ammonium (NH4P), nitrate (NO3P), or representation of the enzymes of
nitrate-nitrite reduction (NNiR), has been developed directly by deletion of
those components from ANIM. While this may be considered a retrograde step,
it is a basic tenet of mathematical modelling to make models as simple as possible without loss of functionality. It is only through the development and operation of ANIM that one may test whether a more simple model may be adequate,
and when it may not be adequate.
Model development
A comparison between the structure of the models is presented in Figure 1. In
ANIM (described in detail by Flynn et aL, 1997), nitrate and ammonium enter
© Oxford University Press
1881
KJ.Frynn and M J.R.Fasham
ANIM
SHANIM
Promotion
• •••
Rtgulttloii
Etltctor
SHANIM-Tq
•SHANIM-GLNP
Promotion
RtgattOco
fltguttUoo
EtlKtor
EllKtor
Fig. L Schematics for ammonium-nitrate interaction models. ANIM is the full model as described in
detail by Flynn et aL (1997). Nutrients cross the plasma membrane via transport proteins NT and AT
for nitrate and ammonium, respectively, entering internal nutrient pools NO3P and NH4P. Conversion of nitrate to ammonium uses the enzymes of nitrate and nitrite reductase (NNiR), the synthesis of which is induced by NO3P and suppressed by the glutamine pool (GLNP). Ammonium is
incorporated by glutamine synthetase (GS) into GLNP, and by amino acid synthesis (AA), into algal
N (Q, the N:C ratio). The value of Q controls C growth via a derivation of the quota model (Caperon,
1968; Droop, 1968). Q affects the number of transport proteins (NT and AT). SHANIM lacks NO3P,
NH4P and the enzymes NNiR, while SHANIM-Tq also lacks the control of NT and AT. SHANIMGLNP lacks any internal nutrient pool except Q, but retains control over NT and AT.
1882
Short version of ammonium-nitrate interaction model
internal nutrient pools after transport into the cell. Following reduction of
internal nitrate to ammonium, the contents of the ammonium pool are used in
the synthesis of the amino acid glutamine (GLN) and then to make other
nitrogenous cellular materials (collectively termed Q, the nitrogen quota of the
cell). The value of Q is then used to regulate the growth of the cell C using a cellquota approach (Caperon, 1968; Droop, 1968). The various levels of feedback
between the internal pools (which are accomplished using rectangular hyperbolic
or sigmoidal response curves) have been normalized to maximum pool sizes and
to the maximum growth rate (Umax). External nutrient concentrations and phytoplankton biomass have units of the mass of N or carbon (C) per unit volume,
while internal nutrient pools, and the flows between them, are all described as
mass ratios of N per unit of C. Growth in the light may be made a function of
light using either a normalized PI curve or, if required, using a more complex
photoadaptive component (Geider et al., 1996; Flynn and Flynn, 1998). In ANIM,
N assimilation (and hence transport) continues in darkness as long as there
remains sufficient surplus C (i.e. Q remains low) to support it (e.g. Cullen and
Horrigan, 1981). Assimilation of N in darkness depletes the surplus C (including
a decrease accounting for the respiratory cost in terms of C for the supply of
reductant for nitrate-nitrite reduction) and increases Q.
In ANIM, the transport of ammonium and nitrate are made functions of the
external nutrient concentration, the nutrient history of the cell (giving maximum
transport rates, Tq values, which are functions of Q), the size of the internal pool
of the inorganic nutrient, and also a function of the size of the internal pool of
GLN (chosen to represent an early organic product of N assimilation involved in
the regulation of inorganic N incorporation). In SHANIM, the link to the GLN
pool (GLNP) is retained, and the post-GLNP components are the same, hence
retaining many of the L/D interaction components present in ANIM. However,
the control of dark assimilation of nitrate (with its linkage to the availability of
reductant operating via the amount of C reserve present) is now absent, as is an
ability to simulate the induction and turnover of the enzymes of nitrate and nitrite
reduction. For the comparisons presented here, all components common to
SHANIM and ANIM share similar equations and constant values (see Flynn et
al., 1997). Thus, the comparisons are solely a reflection of the consequences of
model simplification. Equations and values of constants defining SHANIM are
given in Appendix 1; details are explained in Flynn et al. (1997).
As further comparisons, two other versions were tested. Version SHANIM-Tq
(Figure 1) retains the GLN pool component which regulates the transport rate,
but does not have the nutrient history control of the maximum transport rate (7 q ).
Tq for each nutrient is now fixed and defined as:
where Qmax is the maximum N:C ratio and [/„,„ is the maximum theoretical
growth rate. Version SHANIM-GLNP (Figure 1) does not contain any internal
nutrient pools (other than Q, the ratio of N:C). The GLN pool is now omitted
and nutrient now flows directly into Q, although the link between Q and
1883
KJ.Flynn and MJ.R.Fashjun
maximum transport rates is retained (the values of Tq for nitrate and ammonium
being functions of Q, as in SHANIM and ANIM).
Results
Various simulations have been run, of which a few selected ones are presented
here. The /-ratio is denned as:
NO3T
NO3T + NH4T
where NO3T and NH4T are the rates of nitrate and ammonium transport into
the cell, respectively.
Batch culture
In simulations of batch culture, starting with a total of 10 uM of nutrient N, with
cells grown on ammonium nitrate in continuous light there are very few differences, and arguably no differences of significance, between ANIM and
SHANIM (Figure 2). The general pattern of cell growth (cell growth rate and
disappearance of external nutrients) is nearly identical and the timing of the
switchover between N sources correct to within a few hours out of a total of
several hundred hours (depending on one's area of interest). The difference in
the /-ratio between 25 and 120 h is explained by two factors: (i) the additional
restriction of ammonium flow into the cell in ANIM, which contains an
ammonium pool; and (ii) the subsequent slight decrease in the GLN pool at a
critical part of the control curve which allows entry of nitrate into the internal
nitrate pool in ANIM. Because transport in ANIM is controlled both by the size
of the GLN pool and by the internal pool of the inorganic N source (Figure 1),
transport of ammonium into N-starved cells stops more rapidly in ANIM than
in SHANIM. Conversely, because the nitrate pool is larger than the ammonium
pool, and the development of the GLN pool in ANIM is slower, the transport
of nitrate is actually prolonged in the ANIM simulation. The result of this is that
the/-ratio falls more rapidly in SHANIM during the first few hours of the simulation (not visible at the scale given in Figure 2). In 24 h N-deprived cells supplied with nitrate, SHANIM does not produce the same pattern of nitrate
transport because there is no internal pool to fill, nor any induction of an
enzyme (NNiR) to empty it. Thus, the initial use of nitrate is accelerated in
SHANIM.
Dark feeding
A particularly severe test of the responses of the model is to simulate dark feeding
of N-deprived cells with ammonium nitrate. In the simulation presented (Figure
3), a progression of increasing dilution rates was used (ultimately exceeding the
maximum growth rate), thus gradually relieving the N stress and resulting in a
loss of ability to decouple C fixation and N assimilation.
1884
Short version of ammonium-nitrate interaction model
ANIM
SHANIM
SO
100
150
o
z
ZOO
ISO
SO
Tim* (h)
100
ISO
tOO
ISO
200
ISO
Tim* (hi
9.0 -
75 •
o
OM •
1J 0.0
SO
100
150
200
250
SO
100
ISO
Tim* (h)
Tim* (h)
0.OM -i
O
SO
100
ISO
Tim* (h)
200
0.01
100
ISO
Tim* (h)
Fig. 2. Comparison of ANIM and SHANIM for a simulation of batch culture growth on ammonium
nitrate. C\i is the C-specific growth rate. The/-ratio remains at 1 after 170 min because although concentrations of both nutrients are vanishingly low, there is still more nitrate than ammonium and hence
nitrate transport is still dominant.
An examination of these results shows that SHANIM and SHANIM-Tq are
good at matching ANIM. Notable differences are that some of the spikes in transport following changes in the L/D cycle are absent or depressed, and changes in
transport rates and in the/-ratio occur more rapidly than in ANIM. Although the
1885
KJ.FIynn and MJ.R-Fasham
timing of shifts in the/-ratio are different, the 12 h moving average values for the
/-ratio are very similar (Figure 3).
Results for SHANIM-GLNP are also presented for this simulation (Figure 3). It
is apparent from this that the inclusion of the GLN regulation is important if the
O OJXH -
6 0.004 •
a.
I
5
NO
U4
404
4OS
412
4S1
Thru Ui)
Tim* (h)
10
OJ
Z
I
OJ
04
OJ
00
M4
IH
in
4M
410
4S2
K4
Ttm« (hi
Tim* (hi
— **m
b
— 0.004
/I
, i / l/I
\ AAnAt A
(\± r
I
t
I
I
_ on -
1
&
\J U
M4
U
40»
, '
IH
Tim* IK
4S4
4K
osa -
*«,-
h
MO
OM - PS
"1
SHAWM
«HA»»*-Tq
/
-OOl -
904
U4
4O«
in
4M
4W
904
Tkgit (10
Fig. 3. Comparisons of different models for a simulation of a culture which is fed with ammonium
nitrate in a chemostat with the pump operated only in the dark phase. Dilution is increased stepwise
during the simulation (increasing by 0.01 Ir 1 every 100 h), eventually exceeding the maximum growth
rate of the cells. The section presented (where the dilution rate was 0.04 h~' before 400 h and 0.05 h~'
after) is where the ability to decouple N transport and assimilation from C growth (Cu) isfinallylost;
note the changes in Cu during the dark phase. The maximum theoretical growth rate (Um^) is 0.05
h"1 and the cells are being washed out during the latter part of the simulation which is why Cu, which
is close to maximal before 400 h, alters little when the dilution rate is raised. There are no GLNP data
for SHANIM-GLNP as this model lacks such an internal nutrient pool. Dark phases are indicated by
dark bars on the time axis.
1886
Short version of ammonium-nitrate interaction model
performance of the simulation is not to deviate markedly from ANIM (compare
ANIM and SHANIM-GLNP). This is especially so with reference to diel cycles and
the coupling or decoupling of Cfixationand N transport and assimilation. In contrast, removal of the nutrient history link to transport rates (SHANIM-Tq versus
SHANIM), by thefixationof those transport rates as described in model developments, has relatively little additional effect on the deviation of the short-form
version of the model from the full ANIM. However, nutrient transport may be
overestimated (in this instance nitrate transport) because cells with a high N status
retain the elevated nutrient transport rates normally only seen in N-stressed cells.
Steady-state f-ratios
Figure 4 presents steady-state response curves for simulations where nitrate is
non-limiting (100 uM) and the concentration of ammonium varied; the plots with
nitrate concentrations set at a more realistic 5 uM are almost identical. The
concentration of ammonium which effectively has no effect on nitrate transport
is the same for all simulations. However, progressive simplification of the model
by deletion of internal pools results in a shift towards greater sensitivity (i.e. lower
concentrations of ammonium affect nitrate transport more with simpler models).
1.0 i
0.8 -
ANIM
•
SHANIM
D
SHANIM-Tq
O
*-•
0.6 -
SHANIM-GLNP
•
k ± 95X limit
1.64 ±0.072
±0.048
-1.84 ±0.091
2.39 ±0.090
O
i_
I
"-
0.4 H
f=e(k.NH4*l
0.2 -
0
J
i
0.5
1.0
1.5
2.0
NH 4 +
Fig. 4. Steady-state predictions for the suppression of nitrate transport (as indicated by the /-ratio)
with increasing concentrations of ammonium for each of the models. The curves fitted all have r2
values >0.99, but it is apparent that there is increasing deviation at high ammonium values for the fits
of SHANIM-Tq and SHANIM-GLNP.
1887
KJ.Flynn and M J.R.Fasham
Discussion
While a few other models for N assimilation in phytoplankton include biochemical components (e.g. Parker, 1993; Stolte and Riegman, 1996), none attain
the complexity of ANIM (Flynn et al., 1997). Simplification of models is rather
a double-edged sword because of the risk of losing resolution and flexibility in
an attempt to remove degrees of freedom in model structure. In this paper, four
versions of a dynamic model simulating ammonium-nitrate interactions in
phytoplankton have been compared, ranging from a model (SHANIM-GLN)
which is similar to a quota model with two N source inputs controlled by the
nutrient history of the cell, through to a complex model (ANIM) which strives
to reproduce major facets of the underlying biochemistry of the interaction.
None of these models incorporate a direct inhibition term relating external
nutrient concentrations to differential transport rates (as used by Harrison et al.,
1982; Collos, 1989; Fasham, 1993), but rather they all use various control processes linked to indicators of intracellular physiology. The omission of the GLN
pool (as in SHANIM-GLNP) indicates the importance of such a step (see Figure
3). However, although the inclusion of a linkage of transport rates to nutrient
history is desirable, the precise definition appears to be of lesser importance (as
suggested by SHANIM-Tq). This is important because of the potential problems
in parameterizing the response curve between Q and maximum transport rates
for ammonium and nitrate (discussed by Flynn et al., 1997). Accordingly, the
remainder of this discussion will centre on a comparison between SHANIM and
ANIM.
At first sight (Figure 1), SHANIM may be likened to ANIM with very small
internal pools of inorganic N, except that such a model would also result in a very
rapid termination of transport via transinhibition of the porters because posttransport processes removing nutrient from pools are rate limiting. In reality,
then, there are significant differences between the two versions.
As negative aspects, in SHANIM there are:
(i) No inorganic pools to fill rapidly prior to assimilation, and thus a limited
capability to decouple transport from assimilation. ANIM should be used
when considering cell size-related functions which may affect the size of
internal inorganic N pools (Stolte and Riegman, 1996).
(ii) No induction process for nitrate assimilation, and thus no capacity to simulate delays in the incorporation of nitrate, or for the development of a simulation of processes leading to nitrite release. ANIM needs to be the basis for
the development of a model to simulate the release of nitrite by cells transporting nitrate under conditions which adversely affect rates of reduction
through to ammonium (Sciandra and Amara, 1994). Such a model has been
developed (Flynn and Flynn, 1998).
(iii) No direct link between the N status of the cell (Q) and the ability to reduce
nitrate for assimilation, and thus no capability to restrict nitrate assimilation
differentially rather than ammonium assimilation in darkness (Syrett, 1956).
This could be of importance in considerations of diel migrations when the
question of accumulation or assimilation of inorganic N during darkness is
1888
Short version of ammonium-nitrate interaction model
an issue (Cullen and Horrigan, 1981; Rainbault and Mingazzini, 1987;
Probyn etal, 1996).
ANIM offers a more complete model for the setting of hypotheses in algal
physiology, while SHANIM can be used as a general model of ammonium-nitrate
interaction when the above-mentioned conditions are of lesser importance.
As positive aspects, in SHANIM:
(i) The model is much simpler, requiring less parameterization or estimation of
parameters which are difficult to measure (see below). In addition, from the
results of SHANIM-Tq, the precise formulation of the response curve relating the nutrient history (as indicated by Q) to transport rates (giving 7^)
appears to be non-critical. However, it should be noted that under certain
conditions, especially for species where there may be differences of an order
of magnitude between transport rates for ammonium or nitrate (Syrett et
aL, 1986), or where transport rates of ammonium increase and nitrate
decrease (Dortch et al., 1982), the absence of such Tq values could have significant consequences on the simulation.
(ii) The high flows of nutrient through small internal nutrient pools (especially
ammonium) which require small integration steps are deleted so the model
may run quicker.
(iii) The model still retains the essential elements of transport being related to Q
(i.e. transport rates being higher in N-stressed cells) and to the presence of
an early product of N assimilation (i.e. GLN).
There are no reasons to suspect that a general ecosystem model using
SHANIM to simulate total phytoplankton ammonium-nitrate interactions
should behave significantly different to one using ANIM. While aspects of the
timing of the interaction are different (usually by a few hours), and some of the
resolution lost, generally SHANIM works well and further simplification seems
unwarranted. SHANIM still offers the advantage of having an internal pool,
which thus operates as a delaying mechanism facilitating the modelling of timelag events (cf. Davidson et al., 1993; Davidson and Cunningham, 1996).
Parameterization of ANIM and SHANIM requires determinations of the size
of internal nutrient pools. Although in theory this is not difficult (Dortch et al,
1984), complications arise because the conventional colorimetric assays for inorganic N may be adversely affected by other compounds present in cell extracts
(thus, pools of nitrate may appear to be present in ammonium-grown cells).
Internal pools of ammonium are often very low and there are large errors in their
estimation because of analytical and scaling problems. Neither of these problems
are encountered in SHANIM as it lacks inorganic N pools. GLN must be determined by HPLC (Flynn and Flynn, 1992) which, although it may be readily automated, is time consuming and the equipment not always readily available.
However, SHANIM could be parameterized using the entire internal pool of
amines and (with a much lower response factor) peptides, making use of the sensitive and rapid determination using fluorescamine (e.g. Dortch, 1982). This
would give a pool size considerably in excess of that for GLN, which would have
a slower response time to filling and emptying (GLN only represents a few per
1889
KJ.FTynn and MJ.R.Fasham
cent of the total internal pool of free amines), but this approach would still retain
a link to the assimilation of inorganic N.
Comparison with the Quota model
AN1M and even SHANIM have various parameters which are not readily estimated from experimental results. In comparison between these models and the
traditional Quota model of Caperon (1968) and Droop (1968), there is a more
complex control of nutrient transport (including, of course, the handling of two
nutrients), and a variant of the Quota control of growth which as a major change
excludes the contribution of the N in the GLNP (and from inorganic N pools in
ANIM) in the determination of growth rates.
Using the terms described for SHANIM, and with reference to Appendix 1,
Table I and the legend to Figure 5, transport of nutrient N for the Quota model
is given by:
'N = NVmax • N
N + NJfc-r'
where NVmax replaces the variable NTq in SHANIM, and cell growth by:
Cu = £/„,„' •
Q'-Qo'
Q' - Go' + V
In a dynamic simulation of a batch culture using a Quota model parameterized
from steady-state SHANIM simulations, there is little difference between the
models (Figure 5; note the similarity between values for constants for the
control of growth rates, kq, Qo and l/max, given in the legend). Similar comparisons have been made with different values of A:q. There is a delay in the growth
response of SHANIM due to the presence of an additional internal pool
(GLNP) and the form of the equation for amino acid synthesis [see equation (7)
in Appendix 1]. However, such a delay in processing time has been found to be
a useful modification to the Quota model for the handling of transient events
(Davidson et ai, 1993; Davidson and Cunningham, 1996). Thus, for a first
approximation, it appears to be quite satisfactory to parameterize the growth
control section of SHANIM using values derived from conventional Quota
methods.
There are more important differences in the control of nutrient transport; the
Quota model assumes that V ^ is a constant, while in SHANIM it (termed NTq)
varies with the CN status (i.e. Q) of the cell. Values of N/cT for Quota models
derived for steady-state systems really indicate the half-saturation constants for
growth, not for transport per se. However, a comparison of values of transport
rates V with Q (Figure 6) shows that transport rates in SHANIM are likely to be
higher than for Quota at a given substrate value, exceeding the reaUstic need for
transport at that nutrient status. Excess transport capacity is regulated in
SHANIM (and ANIM) by the size of GLNP. However, from the results from
SHANIM-Tq (see above), the absolute shape of the curves relating V to Q (giving
1890
Short version of ammonium-nitrate interaction model
SHANIM —
Quota
0.25 -i
r '0
20
_
°"
T_
E
6 0.15 0.10 0.05 -
• 02
J
- 0.0
0.00
20
40
SO
so
100
Tim* (h)
0.20
0.03 •
• 0.18
- 0.16
i
• 0.14 O
0.02 -
0.12 O
O
• 0.10
0.01 -
0.08
0.00
J
0.06
20
40
60
80
100
Time (h)
Fig. 5. Comparison between SHANIM and the Quota model (Caperon, 1968; Droop, 1968) for a batch
culture using ammonium at an initial concentration of 1 uM. Quota model constants were derived
from results gained from running SHANIM to steady-state conditions at different dilution rates with
the inclusion of both GLNP and Q in the calculation of the N quota (Q1) for the Quota model. Values
of constants for both models were (Quota constants being marked with '):fcq= 0.05, Jfeq' = 0.0487; Qo
= 0.05, Qo' = 0.0502; UnMi = 0.05, U^' = 0.0494; Nkr = 0.014, NkT' = 0.002799; ^ = NTq, V^' =
0.007401 (units as given in Table I for SHANIM).
Nr q ) is not critical. In total, we can conclude that the parameterization of
SHANIM is no more problematic than for the Quota model, especially bearing
in mind that SHANIM operates a nutrient preference ability as well.
Acknowledgements
This work was supported by the Natural Environment Research Council of the
UK.
1891
KJ.Ftynn and MJ.RJasham
0.04 -
'max
Quota
SHANIM
0.03 -
0.02 -
r
1.0jiM
0.01 'max
I.OpM
v
0.00
J
O.1fjM
Need
0.05
0.10
0.15
0.20
Q (N:C)
Fig. 6. Comparison of initial transport rates of ammonium by SHANIM and Quota models (as used
in Figure 5) against Q (for SHANIM excluding the contribution of GLNP) and Q' for the Quota
model. Vm,s are maximum rates at infinite substrate, V)pM and VO.IHM aic rates at substrate concentrations of 1 and 0.1 uM, respectively. 'Need' indicates the transport rate required to support growth
matching that defined by Q; a transport rate above this line will result in a higher Q and growth rate.
For the Quota model, V is constant, while for SHANIM (as for ANIM), V varies with Q, but is also
subject to feedback regulation from GLNP.
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1892
Short version of ammonium-nitrate interaction model
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Probyn.T.A., Waldron,H.N., Searson.S. and Owens.NJ.P. (1996) Diel variability in nitrogenous
nutrient uptake at photic and sub-photic depths. / Plankton Res., 18, 2063—2080.
RainbaulM1. and Mingazzini,M. (1987) Diurnal variations of intracellular nitrate storage by marine
diatoms: effects of nutritional state. /. Exp. Mar. BioL EcoL, 112, 217-232.
Sciandra,A. and Amara.R. (1994) Effects of nitrogen limitation on growth and nitrite excretion rates
of the dinoflagellate Prorocentrum minimum. Mar. EcoL Prog. Ser., 105, 301—309.
Solomonson,L.P. and BarberJVIJ. (1990) Assimilatory nitrate reductase: functional properties and
regulation. Annu. Rev. Plant PhysioL Plant Mol. BioL, 41, 225-253.
Stolte.W. and Riegman.R. (1996) A model approach for size selective competition of marine phytoplankton for fluctuating nitrate and ammonium. / PhycoL, 32,732-740.
Syrett,PJ. (1956) The assimilation of ammonia and nitrate by nitrogen starved cells of ChloreUa vulgaris.
Ill Differences of metabolism dependent on the nature of the nitrogen source. PhysioL Plant, 9,28-37.
Syrett^J., Flynn.KJ., MoUoy.CJ., Dixon.G.K., Peplinska.A.M. and Cresswell.R.C. (1986) Effects of
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Received on March 19, 1997; accepted on August 7, 1997
Appendix 1: Equations of the SH ANIM model
Parameters, state variables and their units are defined in Tables I and II. The
equations are written for a chemostat or mixed layer with an external supply of
nutrient with a dilution rate D (h"1). For a batch experiment, D - 0.
1893
KJ.FTynn and MJ.R.Fasham
Table L Constants and their definitions for SHANIM
Constant
Value
Unit
1
AAsk
0.001
NO
Crest
CresQ
0.01
None
0.2
NO'
D
As required
0.02
0.05
h-'
NO1
NH4A
NH4B
NH4hG
NH4kT
NH4mG
NH4r
NO3A
NO3B
NO3C
NO3hG
NO3kT
NO3mG
NO3qmin
NO3r
Co
Redco
0.2
0.1
N O 1 h-'
h"1
None
1.4
ugNl-'
0.01
As required
-0.075
NO'
0.2
-0.4
0.005
ug N 1-'
None
None
None
None
1.4
MgNl-'
0.003
NO'
5.6
CN-'
As required
ug N I-'
0.2
NO'
NO1
0.05
1.71
0.05
CN-'
C O 1 h-'
Definition
Km for amino add (AA) synthesis; substrate is GLN
(i.e. G)
Constant for computing C reserve
Value of Q when there is no reserve C for dark N
assimilation
Dilution rate
Constant for control of growth rate from Q
Constant for curve fit for NH4Tq
Constant for curve fit for NH47q
ALh for GLN (G) suppression of NH,+ transport; relative to
NH4mGLN
K, for NK,+ (i.e. NH4) transport rate
Size of the GLN pool (G) which stops NH«+ transport
Reservoir concentration of ammonium (for chemostat)
Constant for curve fit for NO37"q
Constant for curve fit for NO37"q
Constant for curve fit for NO3r q
Kh for GLN (G) suppression of NO3" transport; relative to
NO3mGLN
K, for NO," (i.e. NO3) transport rate
Size of the GLN pool (G) which stops NO3" transport
Maximum Q~x at which NO3" transport stops; constant for
curve fit forNO3Tq
Reservoir concentration of nitrate (for chemostat)
Maximum N O ' ; maximum structural N quota
Minimum N O ' ; minimum structural N quota
Mass of C respired for dark reduction of nitrate to
ammonium
Maximum theoretical C-specific growth rate
Table IL Definition of state variables for SHANIM
Level
c
Unit
Definition and comment
ugCl"'
Algal carbon
Internal glutamine pool as a mass ratio relative to C (GLNP in Figure 1)
Ammonium in growth medium
Nitrate in growth medium
Cell N:C mass ratio; structural N quota
G
NH4
NO3
NO'
Q
NO'
MgNH
ugNH
Equations for external nitrate and ammonium concentration and transport
The concentration of nitrate and ammonium in the medium is controlled by the
supply from the external pool and the transport into cells. Thus
1894
dNO3 = D(NO3r - NO3) - C.tNO3
df
(1)
dNH4 = D(NH4r - NH4) - C.tNH4
dt
(2)
Short version of ammonium-nitrate interaction model
where D is the dilution rate, NO3r and NH4r are the external reservoir concentrations, and tNO3 and tNH4 are the transport rates of nitrate and ammonium.
The transport of nitrate or ammonium is determined by the following general
equation, where the symbol N stands for either NO3 or NH4:
)
NmG
where NTq is the maximum transport rate, Nkf is the half-saturation constant for
transport, and NmG and NhG are constants of the fourth-order Hill equation
parameterizing the suppression of nutrient transport by the accumulation of glutamine in the cell. Note that when G > NmG, transport is assumed to cease.
The maximum transport rates are assumed to be a function of the cell nutrient
status as indicated by Q. However, this relationship is parameterized differently for
ammonium and nitrate. For ammonium, it is assumed that 7q increases with declining Q (i-e. the more starved the cell, the higher the potential transport) and so:
NH4rq = (NH4A - NH4B.0 • - ^ g -
(4)
where NH4A and NH4B are empirically derived constants using cells with a Umax
of 0.05 (Flynn et al. 1997); the ratio f/mM/0.05 thus scales NH47q for cells with
other values of f/mai.
Observations on nitrate transport have shown that as Q declines Tq initially
increases as for ammonium, but then, at lower Q, Tq decreases. The following
equation was used to represent this behaviour:
NO3T
= N O 3 A ( 1 - e N O 3 B <1/!2 - NO3qmin))>eNO3C (VQ - NO3qmin)
^
0.005
v
'
where NO3A, NO3B, NO3C and NO3qmin are empirically derived constants.
When NO3qmin > Q~l, nitrate transport ceases.
Equations for internal glutamine concentration
The equation for glutamine is:
^ = tNH4 + tNO3 - AAs - Cu.G
at
(6)
where AAs is the rate of amino acid synthesis and C\i is the algal growth rate in
C units [see equation (11)]. Thus, the glutamine pool is increased by the transport of nitrate and ammonium, and decreased by amino acid synthesis. The last
term represents the decrease of G (which is expressed as N per cell-C content)
with cell carbon growth (see Flynn et al., 1997).
1895
and M J.R.Fashflm
Control of the 'preferential' transport of ammonium over nitrate thus depends
in the short term on the interaction between the size of the glutamine pool and
transport [N/iG and NmG in equation (3)], and in the longer term on the interaction between the N status, as defined by Q, on the maximum possible transport
rate of the N sources [Tq in equations (4) and (5)].
The maximum rate of amino acid synthesis is given by Umax • Qmax, i.e. the
maximum C-specific growth rate multiplied by the maximum cell quota. The
equation for the realized rate is:
AAs=Umai-Qmax-
°
• nQ~Q°
G + AAsk Q-Q0
-(2-
+ kq
g
~ Q ° )-CAAs (7)
Q^ - Qo
The maximum rate is limited by the concentration of the glutamine pool using a
Michaelis-Menten expression with half-saturation constant AAsk. The next factor
makes amino acid synthesis a function of the nutrient status of the cell, on the basis
that an N-starved cell will not have the biochemical machinery to perform all processes at maximum rates. A consequence of this is that the lag phase for the
recovery of N-starved cells on refeeding becomes longer with lower values of Q.
However, an additional term, [2 - (Q - Qo)KQmia - C?o)]> n a s a ' s o been included
which ensures that amino acid synthesis is raised when Q is close to Qo; without
this term, the lag phase can become unreasonably long. Finally, the quantity CAAs
allows for amino acid synthesis using the carbon reserve. It is defined as:
Q
(1
Cresg
CAAs -PS +
(1
Q
CresQ
Y
(8)
Y +Cresk
PS takes the value 1 if the light is on and 0 if it is off. If Q <, CresQ, then the C
reserve will not be used for amino acid synthesis. However, when Q > CresQ,
then some amino acid synthesis will take place in the dark or when PS < 1.
Equations for cell quota and cell carbon
The equations for these variables are:
^ =AAs-Qi-G
at
^-=Cii-C-DC
(9)
(10)
The equation for cell quota is simply the increase due to amino acid synthesis less
the decrease caused by the increased carbon content of the cell. The algal cell
carbon within the medium will increase due to cell growth and decrease due to
washout from the chemostat.
1896
Short version of ammonium-nttrate interaction model
It only remains to define the C-specific growth rate Cu as:
C\i = PS-Umax-
_ Q" Q°
- Redco. tNO3
Q - Go + kq
(11)
The first term is the standard growth term for a cell quota model (Caperon, 1968;
Droop, 1968) multiplied by the light function PS. In the model described above,
PS takes the values 0 or 1, depending on whether the light is off or on. However,
it is a simple modification to replace this representation with one of the standard
expressions that describe the limiting effect of light (Platt et ai, 1977). The second
term in equation (11) represents the respiration required to support the reduction of nitrate to ammonium. Further respiration is not accounted for on the basis
that no further differentiation is made between nitrate N and ammonium N.
1897