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International Journal on Algae, 2012, 14(2): 185-200

185

Modelling Nitrate Uptake and Nitrite Release by Seaweed

V.A. SILKIN1, 2, V.D. DZIZUROV3, V.K. CHASOVNIKOV1 & N.I. ESIN1

1Southern Branch of the P.P. Shirshov Inst. of Oceanology, RAS,

353467 Gelendzhik, Krasnodar Region, Russia

2Institute of Cosmic Research, RAS,

84/32, Profsoyuznaya St., 17997 Moscow, Russia

3Pacific Research Fish Industry Centre,

4, Shevchenko Alley, Vladivostok, Russia

e-mail: vsilkin@mail.ru

e-mail: dzizurov@tinro.ru

ABSTRACT

The kinetics of nitrate uptake, their assimilation in cell and the kinetics of nitrite release under

different initial concentration of nitrates is described with the help of mathematical model The

hypothesis of immutability of ferments which take part in transformation of different forms of

nitrogen is assumed as a basis of the model. The content of these ferments can be changed only; the

induction of their synthesis depends on the initial concentration of nitrates. It is shown that the

maximum velocity of nitrate uptake (equal to the activity of nitratereductase) depends on the initial

concentration of nitrates and may be presented by hyperbolic function with saturation. It is shown on

the example of seaweed Gelidium latifolium (Grev.) Born. et Thur. (Rhodophyta) that the maximum

velocity of nitrate absorption can be 5 times more that the initial one.

KEYWORDS: algae, kinetic, uptake, nitrogen, nitrate, model.

INTRODUCTION

Steady-state kinetics of nutrient uptake and seaweed growth is successfully used in the

course of algae cultivation (Silkin & Khailov, 1988; Silkin et al., 1992). The basis of the

Originally published in Algologia, 2012, 22(1), pp. 44-58 ISSN 1521-9429

©Begell House Inc., 2012

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regulation of uptake process is the dependence of the uptake rate on the nutrient

concentration in the medium that can be expressed by the equation of Michaelis-Menten:

CK

C

max

(1)

С – is the nutrient concentration in the medium, µmol; υ and υmax– specific and maximum

specific uptake rate, µmol/(g·h); K is the half saturation constant, equal to the nutrient

concentration, when υ = υmax/2, µmol.

An adequacy of this equation to experimental data is confirmed by a many

investigations (Hanisak & Harlin, 1978; Haines & Wheeler, 1978; Topinka, 1978; Silkin &

Khailov, 1988; Silkin et al., 1992). It was considered that equation parameters did not

change in time, but they depended on physical factors, such as the light intensity and

temperature. In fact it was revealed that the dependence of specific nutrient uptake rate on

its concentration in the medium can be of multiphase nature, one enzyme system works

under low concentration, another – under high concentration (Conolly & Drew, 1985;

Lavery & McComb, 1991; Cordillo et al., 2002; Martinez & Rico, 2004).

There are two methods of determination of coefficients of Michaelis-Menten equation.

In the first one the specific nutrient uptake rate is measured under its different concentration

in the medium. Rather large initial concentration of nutrient is assigned in the second

method; In the course of nutrient exhausting its concentration is measured and specific

nutrient uptake rate is calculated, and on the basis of data sequence of Ciand Vi values

V(C) dependence is plotted. The second method of parameter estimation of dependence

turned out to be incorrect one by reason of change of parameters themselves; and that has

been demonstrated when research a nonstationary kinetics of nitrate uptake by red alga

Gelidium latifolium (Silkin & Chubсhikova, 2007).

In was shown that after two hours of algae incubation under relatively high nitrogen

concentration in sea water (as compared with the natural ones) maximum specific nitrogen

uptake rate increased, changes of the half-saturation constant are not so evident. Thus, the

method of assessment of model parameters can define a value of these parameters. An

assumption was made that there may be an induction of synthesis of nitratereductase, which

is responsible for nitrate uptake. The increase of the same concentration results in increase

of maximum specific nitrogen uptake rate without changing of the half-saturation constant.

In alternative hypothesis a synthesis of nitratereductase takes place with other properties,

and, as result, other parameters of equation. It is difficult to discriminate one or another

hypothesis by experimental method. Besides, nitrite release into environment was observed

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187

in the course of these experiments, it was connected with the process of nitrate uptake. The

process of nitrite release in time has one maximum, and a value of maximum nitrite

concentration depends on the initial nitrates concentration in the medium.

In the present work, this is a sequel of our previous paper (Silkin & Chubchikova,

2007) an attempt is made to describe the processes of nitrate uptake and nitrite release with

the help of mathematical model. It is based on the hypothesis that when nitrate

concentration increases, the induction of synthesis of nitratereductase takes place and this

resulted in growth of maximum specific nitrogen uptake rate the; half-saturation constant

does not change.

The goal of modelling is a quantitative assessment of changes of maximum specific

nitrogen uptake rate and its dependence on initial nitrate concentration sea water.

MATERIAL AND METHODS

Red sea alga Gelidium latifolium serves as an object of research. Algae gathered in

November in Sevastopol bay (the Black Sea) at the depth of 0-0.5 m were a source material

for these experiments. Algae after the cleaning from epiphytes by portion of 25 g of raw

biomass were placed into glass vessel (bulk 4 L) with sea water, which was sampled at the

distance of 10 miles from shore. This secures purity of water and low, close to zero,

concentration of nitrogen and phosphorus. Algae were kept under the light intensity about

30 W/ m2 PAR, mixing was fulfilled by air blowing; water was replaced once a day.

Algae samples for experiments (4 g of wet biomass, what is equal to 1.13 g of dried

biomass) were placed into cultivation system with regulation of light (30 W/m2 PAR) and

temperature (20±1 °С) conditions. Volume of medium in photo bioreactor was 1 L. Mixing

was implemented by compressed air. Water samples were collected every hour. Content of

nitrates and nitrites was measured.

RESULTS

Experimental values of nitrate and nitrite concentration in water were obtained (Figures 1-

5). Decrease of nitrate concentration was observed in all experiments, and the dynamics of

concentration was close to exponential curve. In all experiments nitrite concentration

during the starting period increased and then after 3-4 hours of exposition it decreased.

Maximum accumulation of nitrites in experiment was in directly proportional dependence

of the initial concentration of nitrites.

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Model structure

Generally accepted scheme of nitrogen metabolism of photoautotrophic organisms assumed

as a basis of the model (Syrett, 1981; Takabayashi et al., 2005). Nitrates are carried into the

cells by the use of nitratereductase and are transformed into nitrites. By the use of

nitritereductase nitrites change into ammonium form, the latter one is joined with the

products of carbonic metabolism by key ferment of glutaminsynthetase with the production

of amino acids. It is supposed that the work of all ferments fellow the Michaelis-Menten

equation (1). Every process is characterized by two parameters, i.e. maximum rate and half-

saturation constant (Table). Activity of nitratereductase depends on the nitrate content in

medium CNO3, activity of nitritereductase depends on nitrate content in biomass QNO3, the

process of nitrite transformation into ammonium form is regulated by the nitrite content in

biomass QNO2. Nitrite form of nitrogen can diffuse from the cell. Such a process depends on

the quality of cell membrane, which can be express through the diffusion coefficient KLA.

Reasoning from accepted hypothesis, all ferments participating in the process of

uptake and assimilation can change their content in biomass. The half-saturation constant

for every of them does not change in time, the diffusion coefficient of nitrites keeps to be

steady too (Table). A value of the half-saturation constant for the process of nitrate

absorption KNO3 was found by an experimental studies earlier (Silkin & Chubchikova,

2007). Half-saturation constants KNO2 and KNH4 were assigned from expert evaluation and

considered to be constant one. Determination of the rest parameters υNO3, υNO2, υNH4 was

made by setting of numerical solutions of the system of differential equations.

As a whole equations set, which describes the process of nitrate uptake, their

transformation into nitrites, release of the latter into the water and transformation into

ammonium form looks like:

WC

dt

1)

33

333

NO NO

NONONO

CK

dC

2)

32

32

33

33

3

NO NO

NO

Q

NO

NONO

NO

C

NONO

K

Q

K

C

dt

dQ

3)

)(

22

24

24

32

32

2

NONO LA

NONH

NO

Q

NH

NONO

NO

Q

NONO

C WQK

K

Q

K

Q

dt

dQ

4)

24

24

4

NONH

NO

Q

NHNH

K

Q

dt

dQ

5)

)(

22

2

NONOLA

NO

C WQK

dt

dC

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Model setting

Model construction and setting were performed in the MS Exсel medium. Two evident

variables, i.e. nitrate concentration CNO3 and nitrite CNO2 in the medium, are present in the

model (Table). The rest variables, namely content in biomass of nitrate QNO3,, nitrite QNO2

and ammonium forms of nitrogen QNН4, were implicit ones, and their determination was

possible with the help of the present mathematical model. A precise determination of

parameters – coefficients of Michaelis-Menten equation for the processes of nitrogen

uptake and assimilation, were done by the model setting. It was in minimization of function

F = (Cexp – Сcal)2 for experimental and calculated nitrate and nitrite concentration in the

medium. Parameters υNO3, υNO2, υNH4 were determined for each of them, and calculated

values of nitrate and nitrite concentration agreed with experimental data or were close to

them (Figures 1-5).

TABLE. Basic parameters of mathematical model of nitrate uptake and

nitrite release by seaweed

Name Indication

Value and

dimension

Nitrate concentration in the medium CNO3 µmol

Nitrite concentration in the medium CNO2 µmol

Algae biomass W g/L

Maximum nitrate uptake rate υNO3 µmol/(g·h)

Half-saturation constant for the process of nitrate uptake KNO3 19 µmol

Nitrate content in biomass QNO3 µmol/g

Maximum rate of nitrate transformation to nitrite υNO2 µmol/(g·h)

Half-saturation constant for the process of nitrate transformation to

nitrite

KNO2 0.05 µmol/g

Nitrite content in biomass QNO2 µmol/g

Maximum rate of nitrite transformation to ammonium form υNH4 µmol/(g·h)

Half-saturation constant for the process of nitrite transformation into

ammonium form

KNH4 0.05 µmol/g

Nitrite diffusion coefficient to the medium KLA 1.38 g/h

Content of ammonium form in biomass QNH4 µmol/g

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Results of modelling

The model setting resulted in obtaining of calculated values both evident and implicit

variables (Figures 1-6). Calculated values of evident variables – nitrate concentrations

agree with experimental values, and those of nitrite are close to them (Figures 1-5). Nitrate

and nitrite contents in biomass are implicit variables, and these parameters were calculated

with the help of the model (Figures 6, 7).

Nitrate and nitrite content in biomass. Dynamics of the nitrate content in biomass is of

an accumulative nature (Figure 6). But its nature can change considerably depending on the

initial nitrates concentration in water. So, when nitrate concentration is of 6.84 µmol,

nitrate pool from the first hour of exposition fills to maximum value being 0.8 µmol/g and

keeps to be constant during 4 hours; and then it sharply decreases almost to zero. When the

initial concentration is 17.4 µmol, nitrate content in biomass was constant one (2 µmol/g)

during 3 hours, and then its growth occurred up to 10 µmol/g, then its decrease was

observed. Under the other initial concentrations of nitrates (34.26; 52.42; 69.84) more

intensive accumulation was fixed after the third hour of exposition. Nitrite content also was

accumulative one with maximum, and then it decreased almost down zero in the end of

exposition (Figure 7). A maximum level of nitrite accumulation in biomass depended on

the initial concentration of nitrates (Figure 8), and such dependence was similar to the

dependence of maximal concentration of nitrites in the medium on the nitrate concentration

in the beginning of the exposition (Silkin & Chubchikova, 2007).

Maximum nitrate uptake rate and transformation of nitrates to nitrites. After two hours

of exposition maximum nitrate uptake rate increased (Figures 1-5) almost in all

experiments and 3-5 hours later it reached maximum values, which depended on the initial

nitrate concentration in the medium. Such dependence can be expressed by hyperbolic

curve that is shifted left relatively to zero on the axis of abscissas (Figure 9). Ultimate value

of maximum nitrate uptake rate was about 20 µmol/(g h), half saturation took place when

the initial concentration of nitrates was about 10 µmol.

After 6 hours of exposition maximum nitrate uptake rate decrease with the subsequent

stabilization from 7 to 12 µmol/(g h) was observed subject to the initial nitrates

concentration. When initial nitrate concentration was 6.84 and 17.97 µmol, maximum rate

of nitrate transformation into nitrites increased to the maximum level being 2 µmol/(g h)

after two hours of exposition, then after 3 hours it returned to the staring level. When initial

concentrations of nitrates were 34.26; 52.42 and 69.84 µmol, maximum level of

transformation rate of nitrates into nitrites was higher and it was 3 µmol/(g h). Then 3-4

hours later and by 7th hour it became the former.

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.

Figure 1. Dynamics of the experimental and calculated values of nitrate and nitrite concentration,

calculated values of maximum nitrate uptake rate, maximum rate nitrate transformation to nitrite

and maximum rate nitrite transformation to amminium when the initial concentration of nitrates

was 6.84 µmol

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Figure 2. Dynamics of the experimental and calculated values of nitrate and nitrite concentration, and

calculated values of maximum nitrate uptake rate, maximum rate nitrate transformation to nitrite

and maximum rate nitrite transformation to amminium when the initial concentration of nitrates

was 17.97 µmol

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Figure 3. Dynamics of the experimental and calculated values of nitrate and nitrite concentration, and

calculated values of maximum nitrate uptake rate, maximum rate nitrate transformation to nitrite

and maximum rate nitrite transformation to amminium when the initial concentration of nitrates

was 34.26 µmol

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Figure 4. Dynamics of the experimental and calculated values of nitrate and nitrite concentration, and

calculated values of maximum nitrate uptake rate, maximum rate nitrate transformation to nitrite

and maximum rate nitrite transformation to amminium when the initial concentration of nitrates

was 52.42 µmol

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Figure 5. Dynamics of the experimental and calculated values of nitrate and nitrite concentration, and

calculated values of maximum nitrate uptake rate, maximum rate nitrate transformation to nitrite

and maximum rate nitrite transformation to amminium when the initial concentration of nitrates

was 69.48 µmol

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Figure 6. Dynamics of nitrate content in biomass under different initial concentrations in the medium

Figure 7. Dynamics of nitrite content in biomass under different initial nitrate concentrations

in the medium

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Figure 8. Dependence of maximum content of nitrites in biomass on the initial nitrate

concentration in the medium

Figure 9. Dependence of maximum nitrate uptake rate on the initial nitrate concentration

in the medium

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DISCUSSIONS

Model structure. An idea of monophase mechanism of uptake is put into the model. It is

formed by enzymatic transportation of nitrates from the medium into the cell, and can be

described by the equation of Michaelis-Menten. Assumption of single-ferment process of

nitrate absorption means that the change of maximum nitrate uptake rate depends on the

number of enzymatic unit, indicate to the dependence of the enzymatic unit number on the

initial concentration of nitrates in the medium. If algae are transported from depleted

nitrogen medium to sea water with high nitrates concentration, gene expression takes place,

which are responsible for nitratereductase synthesis, and two hours later the content of this

ferment increases. Decrease in time of nitrate concentration in the medium results in

lowering of nitratereductase synthesis. Thus, nitrate concentration is a factor, which

controls the nitratereductase content in the cell.

Nitrites. In the present model the process of nitrate transformation into nitrite and into

ammonium form are assumed to be single-ferment ones. Regulation of rate of this process

is performed by the change of nitrate content in the cell. Probably, it is a reductive scheme

of nitrogen metabolism of photoautotrophic organisms. But there are no experimental data,

which can prejudice such an approach. A complication of the scheme will result in

appearing of new parameters, and it will make awkward to use proposed method of

searching of the basic parameters of the model.

Nitrite release in the medium realized by means of their diffusion through the cell

membrane. Residual F function for the experimental and calculated values of nitrite

concentration in the medium was different from zero almost for every hour of the

exposition. Probably, this is connected with the fact that the processes of the nitrite release

and their back uptake has a enzymatic nature. Inclusion of such processes into the model

will considerably complicate the model, and new parameters will appear. The use of

diffusion equation seems to be very convenient, since only one implicit parameter is

inserted, namely a coefficient of molecular diffusion KLA.

υNO3, υNO2, υNH4 parameters. Maximum nitrate uptake rate depends on the initial

concentration of nitrates and the curve of such dependence tends to saturation (Figure 9).

Ultimate values of maximum nitrate uptake rate were close to 20 µmol/(g h), the half-

saturation constant was 10 µmol. It is obvious, that these parameters depend on the initial

conditions, in which cells were placed. Ultimate values of maximum nitrate uptake rate

20.6 µmol/(g h) was observed, when nitrate concentration was 69.84 µM. It is not ruled out,

that another mechanism of uptake works under this concentration (diffusion, or another

enzymatic system), as it has been pointed earlier (Silkin & Chubchikova, 2007). In was

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ascertained for diatoms and flagellates, which the area of the change of nitrate uptake from

one to another mechanism is near 40-60 µmol (Lomas & Glibert, 2000). Taking this into

consideration, we can conclude that the ultimate values of maximum nitrate uptake rate is

about 17 µmol/(g h). Maximum nitrate uptake rate increases after 2 hours of exposition and

reaches its maximum values by 3-5 hours, and after that it decreases and stabilizes at the

level, higher than an initial one. When algae thallus were contained before the beginning of

the exposition in the medium with nitrate concentration were close to zero, nitrogen became

a limiting factor, and sell metabolism was shifted to the accumulation of carbohydrates.

Transportation of biomass into the medium with heightened concentration of nitrates

resulted in expression of genes responsible for the nitratereductase synthesis. Two hours

later the beginnings of the exposition new enzymatic units are formed, their number

depended on the starting concentration of nitrates. Then the decrease of nitratereductase

activity down 7-12 µmol/(g h) happened, depending on the starting concentration of

nitrates, and a new (as compared with the initial conditions) protein synthesis happens in

cell. There may be several mechanisms of decrease, but the most probable is the decrease

of number of enzymatic complexes for a unit of the cell’s area (Alwyn & Ress, 2007).

Rate of nitrate transformation into nitrites and the latter into ammonium form

increases after two hours of exposition under heightened concentration of nitrates, then it

becomes somewhat low again. Since ammonium is connected with the key ferment of

nitrogen and carbon metabolism – glutaminsynthetase, a fine regulation of nitrate uptake

and assimilation happens on the level of this ferment. It is shown that intensity of

glutaminsynthetase synthesis is proportionate to ammonium form content, which is formed

from the processing of extracellular nitrates (Takabayashi et al., 2005). The reduction of the

whole complex of ferments of nitrogen metabolism from nitratereductase to

glutaminsynthetase after 5 hours of exposition can be connected with the decrease of nitrate

concentration in the medium (Figures 1-5).

Thus transportation of alga biomass from the sea water to the medium with high

nitrate concentration results in increasing of maximum rate of their uptake after two hours

of exposition. Increase in 2.5-5 times depends on the initial concentration of nitrates

according to hyperbolic curve, and ultimate values of maximum uptake rate do not exceed

20 µmol/(g h). After 3-5 hours of exposition maximum uptake rate becomes somewhat less,

and is fixed at the level, which also depends on the initial concentration of nitrates. The

growth of initial concentration of nitrates results in short-term increase of maximum rate of

nitrate transformation into nitrites and nitrites into ammonium form.