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AOBPreview originally published online on August 26, 2005
Annals of Botany 2005 96(6):1019-1026; doi:10.1093/aob/mci254
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© The Author 2005. Published by Oxford University Press on behalf of the Annals of Botany Company. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

A Model for the Circadian Oscillations in Expression and Activity of Nitrate Reductase in Higher Plants

ZONGJIAN YANG* and DAVID J. MIDMORE

Plant Sciences Group, School of Biological and Environmental Sciences, Central Queensland University, Rockhampton, Qld 4702, Australia

* For correspondence. E-mail z.yang{at}cqu.edu.au

Received: 24 March 2005    Returned for revision: 14 June 2005    Accepted: 18 July 2005    Published electronically: 26 August 2005


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MODEL DESCRIPTION
 SIMULATION RESULTS
 DISCUSSION
 ACKNOWLEDGEMENTS
 LITERATURE CITED
 

• Background and Aims Nitrate is the major nitrogen source for many plants. The first step of the nitrate assimilation pathway is the reduction of nitrate to nitrite, catalysed by nitrate reductase (NR). Circadian oscillations in expression and activity of NR have been demonstrated in many plant species. The pathway by which this circadian behaviour is regulated remains to be elucidated. In this study, based on recent experimental observations, a mathematical model is proposed to explain the origin of diurnal and circadian oscillations in NR gene expression and enzyme activity.

• Methods The dynamic model is based on the feedback interconnections between NR and its substrate, nitrate. In the model, NR activity is regulated at the transcriptional level, in response to the balance between nitrate influx and reduction, and at the post-translational levels in response to signals from carbon assimilation. Conditions for the model system to generate self-sustained circadian oscillations are investigated by numerical simulations.

• Key Results and Conclusions Under light/dark cycles, the simulation results are in agreement with the observed diurnal pattern of changes in leaf nitrate concentration, NR transcript level and NR activity. Within a range of kinetic parameter values, circadian oscillation behaviour persists even under constant light, with periods of approx. 24 h. These simulation results suggest that sustained circadian oscillations can originate from the feedback interactions between NR and its substrate, nitrate, without the need to postulate the existence of an endogenous ‘circadian clock’.

Key words: Nitrate reductase, model, nitrate reduction, circadian rhythms, diurnal oscillations, nitrogen metabolism


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MODEL DESCRIPTION
 SIMULATION RESULTS
 DISCUSSION
 ACKNOWLEDGEMENTS
 LITERATURE CITED
 
In higher plants, the expression of genes implicated in several metabolic pathways and developmental responses are circadian-regulated (Harmer et al., 2000Go; Salter et al., 2003Go; Schultz and Kay, 2003Go). Understanding the biochemical mechanism underling these circadian behaviours will lead to new insight into the processes that control plant metabolism and development. Nitrate reductase is one of the enzymes that have been shown to exhibit circadian oscillations in gene expression and enzyme activity.

Nitrate is the major nitrogen source for many plants. The first step of the nitrate assimilation pathway is the reduction of nitrate to nitrite, catalysed by nitrate reductase (NR). The nitrite is further reduced to ammonium by nitrite reductase and subsequently incorporated into the amino acids through the action of glutamine synthetase and glutamate synthase. To avoid the accumulation of nitrite and other side-reaction products, higher plants have developed a complex and redundant control of NR activity at multiple levels. Nitrate assimilation is closely co-ordinated with carbon metabolism. In response to the diurnal changes in photosynthesis, NR expression and activity vary between day and night (Lillo et al., 2001Go; Stitt et al., 2002Go). During a diurnal cycle, NR mRNA level usually peaks at the end of the night or in the early part of the day, then declines and starts to increase towards the end of the night (Scheible et al., 1997Go; Geiger et al., 1998Go). NR activity generally rises to a maximum during the first part of the day and declines during the latter part of the day and night (Matt et al., 2001Go).

For a number of plant species, when placed in constant light conditions and, thus, deprived of external time cues, circadian oscillations in NR expression and activity persist with periods of approx. 24 h (Deng et al., 1991Go; Pilgrim et al., 1993Go; Jones et al., 1998Go; Lillo et al., 2001Go; Tucker et al., 2004Go). This indicates that these rhythms are endogenous. The pathway by which these circadian rhythms are generated remains to be elucidated. It is widely assumed that a central circadian clock provides metabolic readiness in advance to changing conditions of day and night. An alternative interpretation is that the circadian rhythms in nitrate assimilation arise as a result of self-sustained feedback loops (Lillo and Ruoff, 1984Go; Lillo et al., 2001Go; Lüttge, 2003Go). In this study, based on recent experimental observations (Kaiser et al., 2002Go; Stitt et al., 2002Go; Lillo et al., 2004Go), a mathematical model for the circadian oscillations in NR gene expression and enzyme activity is proposed. Conditions for the model system to generate self-sustained circadian oscillations are investigated. The aim of this modelling study is to test the hypothesis that feedback regulation of NR gene expression and nitrate acquisition can generate and maintain sustained circadian oscillations.


   MODEL DESCRIPTION
TOP
 ABSTRACT
 INTRODUCTION
 MODEL DESCRIPTION
SIMULATION RESULTS
 DISCUSSION
 ACKNOWLEDGEMENTS
 LITERATURE CITED
 
The primary regulator of nitrate reductase activity is its substrate, nitrate (Crawford, 1995Go). There is always a close relationship between the diurnal changes of leaf nitrate level and the diurnal changes of the NR transcript level. Recent studies using transgenic plants have shown that the regulation by nitrate is at the transcriptional level (Pouteau et al., 1989Go; Lin et al., 1994Go; Scheible et al., 1997Go). The molecular mechanism underlying the induction of NR gene expression by nitrate is not established. An induction factor of unknown character may mediate this process (Redinbaugh and Campbell, 1991Go). In the model schematized in Figure 1, nitrate, concentration of which is denoted by Cna, activates NR gene transcription with a coefficient of ktc. NR mRNA is assumed to degrade according to Michaelis–Menten kinetics with a limiting rate Vd,m and a Michaelis constant Kd,m. The differential equation for the concentration of NR mRNA (Cm) is:

(1)
Please refer to Table 1 for units of various parameters and state variables. All concentrations are defined with respect to the fresh weight of shoot biomass.



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  		FIG. 1. Simplified scheme for regulation of nitrate reductase activity. Nitrate activates the synthesis of NR mRNA which is translated into NR protein and degraded. NR protein is phosphorylated in a reversible manner into the form of pNR. Binding of 14-3-3 proteins inactivates pNR. Light acts by activating photosynthesis which affects NR activity by enhancing dephosphorylation of pNR. Accumulation of reduced nitrogen represses nitrate uptake. Solid arrows represent input or output flows, and dashed arrows represent control signals. + indicates positive regulation and – indicates negative regulation.

 

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  		TABLE 1. Normal values of parameters and initial values of state variables

 
Downstream metabolites of nitrate assimilation, such as glutamine (Gln), glutamate (Glu) and malate, were suggested as candidates that exert the negative feedback on NR transcript levels (Müller et al., 2001Go; Stitt et al., 2002Go). However, the evidence for the role of these metabolites in controlling nitrate reduction is conflicting (Foyer et al., 2003Go). More data are required before incorporating this level of feedback control into the model. Sugars can have a dramatic influence on NR gene expression, but only when they fall to critical low levels (Klein et al., 2000Go). No evidence was found for a major influence of sugar levels on NR gene transcription in plants growing in a normal light/dark cycle at high or intermediate light intensities (Stitt et al., 2002Go). Normally, starch remobilization allows relatively high leaf sugar levels to be maintained throughout the night. So, this model does not take into account the effect of photosynthesis on NR gene transcription.

NR exists basically in three states: free NR, phosphorylated NR (pNR) and pNR:14-3-3 protein complex (Kaiser and Huber, 2001Go). Catalysed by protein kinases, NR can be phosphorylated on a serine residue within the hinge 1 region, creating a binding site for 14-3-3 proteins. In the presence of mM concentrations of free Mg2+ or other divalent cations, binding of 14-3-3 proteins to pNR inactivates pNR (Bachmann et al., 1996Go). Dephosphorylation is catalysed by type 2A protein phosphatase (PP2A). The balance between the activities of kinases and phosphatases acting on NR and pNR determines the phosphorylation status of the enzyme. Based on these experimental observations, it is assumed that the relative rate of synthesis of NR proteins by translation is directly proportional to the abundance of NR mRNA with a rate constant ktl. The unphosphorylated form of NR, concentration of which is denoted by CNR, is phosphorylated in a reversible manner into the form of pNR according to Michaelis–Menten kinetics. The temporal variation in concentrations of NR (CNR) and pNR (CpNR) is governed by the following two kinetic equations:

(2)

(3)
where parameters Vph (Vde) and Kph (Kde) denote the limiting rate and Michaelis constant of phosphorylation and dephosphorylation, respectively. Vb and Kb represent the limiting rate and Michaelis constant of binding of 14-3-3 proteins to phosphorylated NR proteins.

In order to avoid the accumulation of the downstream products of the NR reaction, the regulation of NR activity is closely coupled to photosynthesis. Post-translational activation of NR is triggered by photosynthesis (Kaiser et al., 1999Go). Most probably, assimilates exported out of the chloroplast function as signals (Kaiser and Huber, 2001Go). In the dark, or in the light with CO2 free air, a larger part of NR is in the inhibited form. NR can be activated in the dark by feeding sugars to the leaves. The activation of NR by light and sugar feeding may be mediated through the balance of kinases and phosphatases acting on NR and pNR proteins (Bachmann et al., 1995; Kaiser and Huber, 2001Go). To take into account the effect of photosynthesis on the post-translational activation of NR, the limiting rate of pNR dephosphorylation (Eqn 3) is multiplied by an activation factor ka,c:

(4)
where Cc is the concentration of substrate carbon.

NR has a rather short half-life of several hours. Thus, the existing amount of NR protein depends not only on the rate of synthesis, but also on the rate of degradation. The signals triggering NR protein degradation have not been identified. Some studies suggested that NR degradation is triggered by phosphorylation and binding of 14-3-3 proteins (Kaiser and Huber, 1997Go; Weiner and Kaiser, 1999Go). So, in the model presented here, the degradation of free and phosphorylated NR unbound by 14-3-3 proteins is not considered.

Although the physiological mechanisms are unclear, many reports have shown a negative relationship between nitrate uptake and the internal concentration of substrate nitrogen (Johnson, 1985Go; Imsande and Touraine, 1994Go; Soussana et al., 2002Go). Some studies suggested that nitrogen metabolites resulting from nitrate reduction may act as regulatory signals to control the rate of nitrate uptake by roots (Geßler et al., 1998Go; Gojon et al., 1998Go; Lejay et al., 1999Go; Loqué et al., 2003Go). Since reactions downstream of nitrite are not considered in the model, the specific rate of nitrate uptake with an hourly time step is assumed to be down-regulated by internal concentration of nitrogen in nitrite form (Cni). The variation in concentration of nitrate is determined by the relative rates of nitrate uptake and reduction:

(5)
where Vna is the maximum specific rate of nitrate uptake and Ki,ni is the inhibition constant. The reaction rate of nitrate reduction is determined by the concentration of active nitrate reductase (CNR+CpNR) and the concentration of nitrate. Parameter kr represents the reducing power per unit of active NR proteins, and Kr is the Michaelis constant for nitrate reduction. Nitrate is partitioned between an active metabolic pool in the cytosol and a storage pool in the vacuole. For simplicity, this compartmentation is not considered in the model.

The variation in concentration of nitrogen in nitrite form (Cni) is determined by the rate of nitrate reduction and the rate of nitrite usage:

(6)
where vg is relative rate of plant growth in biomass and fni is the nitrogen cost to produce a unit of fresh plant biomass. To avoid the introduction of additional variables, reactions downstream of nitrite are combined. Cni can be interpreted as a combined variable representing concentration of nitrite and all other forms of downstream substrate nitrogen. Hence the value of this variable is set significantly higher than the realistic value of nitrite concentration.

Plant growth is dependent on the supply of carbon from the shoot and the supply of mineral nutrients and water from the roots. In the present model, it is assumed that nitrogen is the most limiting factor among the mineral nutrients supplied by the roots when all other mineral nutrients and water supply are maintained near optimal levels. So the relative rate of plant growth is mainly determined by the internal concentrations of substrate carbon and assimilated nitrogen. An additive model (O'Neill et al., 1989Go) is used as a function to calculate carbon- and nitrogen-determined plant growth in fresh biomass:

(7)
where K1 and K2 are Michaelis constants and Vg is the potential relative rate of plant growth.

The variation in concentration of substrate carbon is given as:

(8)
where Vc is the potential rate for carbon assimilation by photosynthesis which is down-regulated by the internal concentration of substrate carbon with a inhibition constant Ki,c. Parameter fc denotes the carbon cost for producing a unit of plant fresh biomass.


   SIMULATION RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MODEL DESCRIPTION
 SIMULATION RESULTS
DISCUSSION
 ACKNOWLEDGEMENTS
 LITERATURE CITED
 
Numerical simulations were performed using fourth-order Runge–Kutta algorithm, with a 0·1-h fixed step. For simplicity, many metabolic steps (such as carbon storage, nitrate compartmentation and further downstream steps of nitrogen metabolism) are neglected, so some parameter values may not exactly reflect the biologically realistic values.

Diurnal pattern of oscillations in response to light/dark cycling
In the light phase of the light/dark cycle, the potential rate of carbon assimilation (Vc) is maintained at the normal value given in Table 1, but reduced to zero in the dark phase. In responses to the light/dark (12 h/12 h) cycling, the system is entrained precisely to the external period of 24 h. With appropriate combinations of parameter values, the simulation results are in qualitative agreement with the reported diurnal pattern of changes in levels of leaf nitrate, NR mRNA abundance and NR activity regarding period and phase relationships. Figure 2 shows the oscillations obtained under light/dark cycle entrainment with a set of parameter values given in Table 1. During a day/night cycle, following the replenishment and depletion of the leaf nitrate pool, the NR transcript level increases gradually during the dark period, reaches a maximum in the early part of the light period and decreases thereafter. NR activity rises to a maximum after 6 h in the light, and then declines during the late light period and dark period (Fig. 2).



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  		FIG. 2. Diurnal pattern of oscillations generated by the model in response to light/dark cycling (12 h/12 h, indicated by the white and black bars, respectively) with the parameter values given in Table 1.

 
In the model, light is taken into account mainly through the feedback loops describing the effect of substrate carbon on pNR dephosphorylation (eqn 4) and the inhibition of nitrate acquisition by the accumulation of reduced nitrogen (eqn 5). Entrainment of the circadian oscillations by light/dark cycling occurs within a limited range. Outside this range, no entrainment is found. A 10 % decrease or increase in value of a single parameter does not affect the period of the diurnal oscillations entrained by the light/dark cycles, and only slightly affect the phase and amplitude. But a 20 % change in values of kr or ktl can affect the ability of entrainment by light/dark cycles. The range within which entrainment still occurs is determined by the deviation of the free-running period from the period of light/dark cycling. The entrainment ability is most affected by parameters that exert the largest effect on the period of the free-running oscillations under continuous light.

Circadian oscillations under continuous light
Circadian oscillations persist when the model system is released into continuous light. Continuous light conditions are achieved by holding the potential rate of carbon assimilation (Vc) at a constant normal value (Table 1). Although the environmental conditions remain constant, the system generates sustained oscillations within a range of kinetic parameter values. With appropriate combination of parameter values, free-running periods close to 24 h are easy to achieve. Figure 3 shows the self-sustained oscillation generated by the model with a period of 23·9 h for a given set of parameter values (Table 1). In contrast to the results obtained in constant light, sustained oscillations are damped very quickly in constant dark (Fig. 4).



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  		FIG. 3. Sustained oscillations generated by the model under continuous light for the parameter values given in Table 1. (A) Oscillations in levels of leaf nitrate, NR mRNA abundance and NR activity. (B) Evolution toward a limit cycle after the system is released into continuous light.

 


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  		FIG. 4. Damped oscillations in continuous dark.

 
Sustained oscillations under continuous light occur over a wide range of parameter values. For example, while keeping all the other parameters at their normal values given in Table 1, the domain of sustained oscillations is bounded by two critical values of Vd,m. Below the lower critical value (0·1), the concentration of nitrate reductase is so high that it prevents circadian cycling. Above the higher critical value of Vd,m (10), the NR mRNA is degraded so rapidly that nitrate reductase cannot reach the level required for effective reduction of nitrate. The range for parameter ktl within which self-sustained oscillations persist is 0·1–25. The dependence of the self-sustained oscillations on the degradation rate of NR mRNA (Vd,m) is shown in Fig. 5. Loss of sustained oscillations caused by a change in value of one parameter can be rescued by simultaneously changing the values of other parameters.



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  		FIG. 5. The dependence of the oscillations on the value of parameter Vd,m representing the maximum rate of NR mRNA degradation.

 
To test the robustness of the oscillation to parameter variations, simulations were done in which each individual parameter was increased and decreased by 20 % of its normal value. Figure 6 shows the effect of parameter variation on amplitude and period of the circadian rhythms under continuous light. It turns out that parameters related to NR translation (ktl), mRNA degradation (Vd,m) and NR catalytic activity (kr) influence predominantly the period and amplitude of the free-running oscillations under continuous light.



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  		FIG. 6. Sensitivity of the period and amplitude of the free-running oscillations to parameter variations, a 20% increase (+) and decrease (–) in value of each individual parameter. Each parameter is varied at a time while keeping all the other parameters at their normal value. The control point is indicated by the filled circle.

 


   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MODEL DESCRIPTION
 SIMULATION RESULTS
 DISCUSSION
ACKNOWLEDGEMENTS
 LITERATURE CITED
 
A mathematical model for circadian oscillations in gene expression and enzyme activity of nitrate reductase is presented. This model is based on self-sustained feedback loops in which nitrate activates NR gene expression and the NR catalytic activity represses nitrate accumulation. Although the model is constructed on the basis of minimal requirement, it displays the necessary characteristics of the experimentally observed circadian oscillation behaviour with respect to free-running period and light/dark entrainment.

NR mRNA level starts to increase towards the end of the night and this pattern of oscillation persists even under constant light in many plant species. It is widely assumed that the endogenous ‘circadian clock’ provides metabolic readiness in advance for efficient nitrogen metabolism the next day. This modelling study suggests that sustained circadian oscillations under continuous light conditions can be explained by feedback control of nitrate acquisition and NR gene transcription, without the need to postulate the existence of an endogenous ‘clock’. To test this hypothesis experimentally, further study is being undertaken to investigate the nitrogen-induced resetting of the circadian rhythms. In higher plants, the expression of genes implicated in several metabolic pathways is circadian-regulated (Harmer et al., 2000Go; Schaffer et al., 2001Go; Lüttge, 2003Go). Oscillations in metabolism are probably not just the outputs of the ‘circadian clock’; metabolic elements could also contribute to the oscillation generation. This has been demonstrated by previous modelling studies for the circadian rhythms of crassulacean acid metabolism (Blasius et al., 1997Go).

Current evidence suggests that nitrate and metabolites generated further downstream in nitrogen metabolism are involved in the control of many aspects of plant metabolism, growth and development (Crawford, 1995Go; Stitt, 1999Go; Coruzzi and Zhou, 2001Go). Nitrogen factors could regulate plant development either per se as limiting raw materials needed for growth, or as signals that act, directly or indirectly, to regulate gene expression and trigger metabolic and developmental responses. Clarifying the origin and functions of diurnal and circadian oscillations in nitrogen metabolism is of fundamental importance for understanding the circadian-regulated developmental responses.

For simplicity, many metabolic steps (such as carbon storage, nitrate compartmentation and downstream steps in nitrite assimilation) are not considered in the model, so some parameter values and model outputs may not be quantitatively accurate. Since further downstream events in nitrogen metabolism are not considered, the repression of NR gene transcription by accumulation of downstream metabolites (such as glutamate and malate) is not taken into account. Such ignorance could affect the sensitivity and robustness of the model. Another important level of control that co-ordinates the carbon and nitrogen metabolism is the shoot/root functional balance (Cannell and Dewar, 1994Go). But inclusion of this level of control will largely complicate the model. There are two ways to improve the model: (1) adding more details to improve the accuracy of the model predictions; and (2) simplifying the model to its minimum requirement so that an in-depth analysis of the dynamic characteristics of the system can be done.


   ACKNOWLEDGEMENTS
TOP
 ABSTRACT
 INTRODUCTION
 MODEL DESCRIPTION
 SIMULATION RESULTS
 DISCUSSION
 ACKNOWLEDGEMENTS
LITERATURE CITED
 
We would like to acknowledge the financial support by Central Queensland University under the Research Advancement Award Scheme.


   LITERATURE CITED
TOP
 ABSTRACT
 INTRODUCTION
 MODEL DESCRIPTION
 SIMULATION RESULTS
 DISCUSSION
 ACKNOWLEDGEMENTS
 LITERATURE CITED
 

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