A theoretical description of nitrate uptake kinetics in marine phytoplankton based on bisubstrate kinetics

I. theor. Biol. (1977) 64, 375-379

A Theoretical Description of Nitrate Uptake Kinetics in Marine Phytoplankton Basedon Bisubstrate Kinetics PAUL G. FALKOWSKI Graduate School of Oceanography, University of Rhode Island, Kingston, Rhode Island 02881, U.S.A. (Received 13 October 1975, and in revisedform 24 March 1976)

Using well known equations for bisubstrate enzyme kinetics, a model for nitrate uptake in marine phytoplankton is generated. The model attempts to include both extracellular nitrate concentrations and incident light intensities as substrates required by the cells to take up nitrate. An affinity constant, KLN, is defined which relates nitrate uptake kinetics to light intensities and extracellular nitrate concentrations simultaneously.

1. Introduction

Nitrate uptake kinetics rectangular hyperbolae to extracellular nitrate Rogers & McCarthy, equation

in marine phytoplankton are generally described by (e.g., the Michaelis-Menten expression) with respect concentrations (Eppley & Thomas, 1969; Eppley, 1969; MacIsaac & Dugdale, 1972). The general D = AN/(K,+iV)

(1)

where v is the uptake rate, A is the maximum uptake rate, N is the extracellular nitrate concentration, and K, is the extracellular nitrate concentration at which half the maximum rate is obtained, suitably fits experimental data under constant, or saturating light intensities. However, Grant & Turner (1969) and MacIsaac & Dugdale (1972) have indicated that nitrate uptake velocities (u) are a function of light intensities. In particular, the latter two authors have reported that nitrate uptake velocities are related to light intensities by rectangular hyperbolae (specifically Michaelis-Menten kinetics). Consequently two, independent half-saturation constants have been described to affect v, namely K, (for extracellular nitrate concentrations) and Kt, the light intensity supporting half the maximum uptake velocity. While attempts have been made to relate K, values calculated for different species to the autecology of the organisms, the effects of light intensity on the kinetic parameter (K,) has been largely overlooked (Eppley et al., 1969; Parsons & T.B.

375

25

376

P.

G.

FALKOWSKI

Takahashi, 1973). It is possible that as a result of this oversight, confusing, and sometimes contradictory reports have been made concerning halfsaturation constants for nitrate (e.g., Parsons & Takahashi, 1973, 1974; Hecky & Kilham, 1974). The incorporation of light into biological rate equations as a substrate is often of questionable validity. In the specific case of nitrate, however, the empirical basis for incorporating light intensity in a predictive model is acceptable if (1) the effects of light on nitrate uptake are quantifiable and predictable, (2) light is required for nitrate uptake. Both conditions have been shown to be experimentally satisfied (Falkowski, 1975; MacIsaac & Dugdale, 1972); hence, light is treated as a physiological substrate affecting nitrate uptake. Briefly, both extracellular nitrate and light may be considered substrates affecting the velocity of nitrate uptake. Both substrates have been shown to obey Michaelis-Menten kinetics individually (when the other substrate is constant or saturating). When either substrate is physiologically limiting the maximum uptake velocity of nitrate, Michaelis-Menten kinetics do not adequately describe nitrate uptake kinetics by whole cells. Before considering the mathematical functions necessary to describe bisubstrate enzyme kinetics, attention should be drawn to the treatment of light and extracellular nitrate as independent variables affecting nitrate uptake velocities. A hypothetical three dimensional volume described by rectangular hyperbolae for nitrate uptake velocities (u) and both light intensities (L) and extracellular nitrate concentrations (N) is shown in Fig. 1. A cross section through V-N-L space at any plane greater than N = 0, L = 0 is viewed as a rectangular hyperbola in a two dimensional Cartesian co-ordinate system (Fig. 2). The families of curves corresponding to lightlimited uptake velocities would be seen as truncated sections with apparent V,,, values suppressed by light [Fig. 2(b)]. An analagous family of curves could be related to nitrate-limited uptake velocities at light saturation, When both substrates are saturating, however, the V,,, for nitrate uptake would correspond to an integrated value with respect to light (V&J and nitrate (Vi,,) [Fig. 2(a)]. The apparent half-saturation constants for nitrate uptake that would be determined from the truncated sections are less than the halfsaturation constant obtained when V,&, = Vl,,. It should be stressed here that it is impossible to experimentally distinguish between VkaX and Vi,,; these kinetic parameters are identical over the relatively long time scales currently required to measure them. This restraint does not imply, however, that the steady-state condition represented by Fig. 2(a) always results experimentally. The truncated sections shown by Fig. 2(b) could not be identified as sub-optimal profiles unless both light and

MODEL

FOR

NITRATE

377

UPTAKE

V

FIG. 1. Hypothetical three dimensional volume describedby independent hyperbolic functions of light intensities(L) and extracellularnitrate concentrations(N) on the velocity of nitrate uptake (v). When either light or nitrate is limiting uptake, the kinetic profiles that describethe uptake velocitieswill correspond to sectionsthrough V-N-L space in any V-N or V-L plane greater than N = 0, L = 0. Two such sectionsare indicated at N = a and L = a’. The apparent V,., for nitrate uptake (V, and V.,) is less than V&.. and Ea. (V&.. = Vi&

nitrate were saturating simultaneously. Complete descriptions of the truncated profiles might be obtained by including half-saturation constants that are calculated when both light and nitrate are saturating. Half-saturation constants cannot be derived solely from V,,, values, however, and must be calculated from experimental data; determinants could be constructed to include both V,,,, and half-saturation constants. Thus :

378

P. G. FALKOWSKI L = L/N Vmm mm

K’

K N at constant L ot constant

L>O AC-0

FIG. 2. Two dimensionalrepresentationof the sectionsshown in Fig. 1. The maximum uptake rate observedin Fig. 1 when both light and nitrate are saturating is describedby curve a (I&, = Vz*,). Both of the truncated sections (at N = a and L = a’) are representedby curve b. The apparent half-saturation constant obtained from curve b (K’) is lessthan the half-saturation constant describingcurve a (K).

where KL is the incident light intensity

supporting

half-maximum

nitrate

uptake velocities at saturating nitrate concentrations. KS is the nitrate concentration supporting half-maximum nitrate uptake velocities at saturating light intensities. To fit this determinant to a linear transformation of the Michaelis-Menten expression, for example, the Lineweaver-Burk double reciprocal relationship, the determinant can be easily rearranged: v;..

-&

-Iv”,,, 4 1

(lb)

1

When either substrate is limiting, however, the affinity of the phytoplankton cells may not be adequately described by either KL or KS (i.e., Michaelis-Menten kinetics). If the cells are considered to be uptake sites

379

MODEL FOR NITRATE UPTAKE

requiring two substrates (light and nitrate), a hypothetical mediate complex is formed.

L+Ne+C+LNeC*

ternary inter-

+ CNi

(2)

where L is a unit of ambient light energy supporting the uptake of one mole of nitrate, N, and N1 are the mole fractions extracellular and intracellular nitrate, respectively, C is the phytoplankton cell, *(hypothetical ternary intermediary complex). The affinity constant (KLN) is defined as:

CLWI KLN= CLlCNelCCl

GO

In the steady-state condition [e.g., Fig. 2(a)], KLN is a product of the substrate concentrations (L and NJ supporting half-maximum uptake velocities (determined when both substrates are saturating). Relating the families of determinants given in equation (la) to bisubstrate enzyme kinetics (e.g., Alberty, 1956) and solving for KLN, the following equation is generated :

KLN= -LN I+%+$-+

>

KLN represents a physiological parameter inversely proportional to the affinity of the phytoplankton for nitrate but also dependent on light intensity. It is suggested that values of KLNmay be useful in predicting the integrated effects of the two substrates on nitrate uptake kinetics. In conclusion, the simple model described by equation (3) attempts to treat nitrate uptake as a two substrate system. The application of this model to field conditions will hopefully yield data on the effective half-saturation constants in situ for mixed phytoplankton communities. The units of KLN might be designated as PM-langley/min. The mathematical values of KLNdo not indicate the relative importance of light or extracellular nitrate in controlling nitrate uptake, but do appear to relate the combined effects of these two parameters on nitrate uptake simultaneously. REFERENCES ALBERTY, R. A. (1956). Adv. Enzymol. 17, 1. EPPLEY, R. W. & THOMAS, W. H. (1969). J. Phycd. 5,375. EPPLEY, R. W., ROGERS, J. N. & MCCARTHY, J. J. (1969). Limnol. Oceanogr. FALKOWSKI, P. G. (1975). Limnol. Oceanogr. 20,412. GRANT, B. R. & TURNER, I. M. (1969). Comp. Biochem. Physiol. 29,995. HECKY, R. E. & KILHAM, P. (1974). Limnof. Oceanogr. 19,361. MACISAAC, J. J. & DUGDALE, R. C. (1972). Deep-Sea Res. 19,209. hRSCINS,

T. R. 8c T -HI,

PARSONS,

T. R. & TAKAI-LGHI,

M. (1973). Limnol. Oceanogr. 18,511. M. (1974). Limnol. Oceanogr. 19,366.

14,912.