From microbial activities to root uptake kinetics: the role of rhizospheric biology in plant nitrogen uptake
1Hormoz BassiriRad, 2Vincent Gutschick and 1Harbans L. Sehtiya
1Department of Biological Sciences,
I. SUMMARY
In this chapter we will address factors that control nitrogen (N) availability and root system characteristics that control its acquisition by plants. The emphasis is on native ecosystems though the concepts and approaches presented here have considerable utility for agricultural ecosystems. We will begin by highlighting factors that control bioavailabilty of N through internal cycling of this element. In that regard, we first cover soil mineralization as a rate limiting step that determines the labile N pool in the rhizosphere. While traditionally N input from external sources e.g., anthropogenic, have been considered negligible, we present data indicating that since 1960s chronic atmospheric N deposition from either industrial or agricultural activities have become formidable sources of N input in many native ecosystems. Therefore, models of ecosystem N availability must incorporate N input via atmospheric deposition. Another paradigm that has recently been brought to question is that the mineral N forms, NH4+ and NO3-, dominate N supply to plants. We will present recent developments indicating that in some ecosystems, components of soil organic N (SON) such as amino acids can be readily absorbed by the dominant species hence, they can constitute a substantial proportion of plant N budget. Finally, we present a modeling exercise that will highlight the relative importance of soil transport properties as well root system attributes in controlling plant N uptake. We will finish this chapter by suggesting how models of N uptake can be further improved by incorporating other root system characteristics such as mycorrhizal colonization, longevity, and architecture.
II. NITROGE AVAILABILITY
1- Mineralization
Nitrogen availability in crop systems is largely determined by the fertilizer application rates. In relatively undisturbed native ecosystems, however, N becomes available largely as a result of internal cycling of this element. Therefore, conceptual or quantitative models of plant N uptake must effectively incorporate processes of N cycle such as decomposition and mineralization. Mineralization of organic N is particularly important because it is often positively associated with increased net primary productivity (Vitousek and Howarth, 1991; Retch et al., 1997; Joshi et al., 2005). This correlation is not surprising because even in plant communities where a significant plant N budget may be provided via amino acids and amino sugars (uptake of which by plants will be discussed later), mineral N is still the preferred form of N for plants.
The amount of N mineralization varies from one system to the next. In temperate forest ecosystems microbial activities and subsequent N mineralization can release 20-120 kg ha-1 of inorganic N annually (Zak et al., 1993; Fan et al., 1998; Rastetter et al., 2005). Estimates of grassland ecosystem N mineralization range from 30-70 kg ha-1 y-1 in xeric to as much as 270 kg ha-1 y-1 in mesic systems. Even in crop system, N mineralization can account for as much as 50 kg ha-1 of inorganic N mineralization into the soil during a single growing season (Schomberg and Cabrera, 2001).
Despite the clear role of mineralization in determining soil N availability, models of plant N uptake in native systems seldom integrate it with mechanistic parameters such as root uptake kinetics and morphology. This is partly because microbial release of inorganic N is under complex control by soil substrate/litter quality, moisture, temperature and pH (Groffman and Tiedje, 1989; Holmes and Zak, 1994) which can vary substantially from one site to another. Additionally, accurate estimation of N mineralization is further complicated by the dominant microbial types as bacteria and fungi differ markedly in how rapidly they mineralize organic N (Vinten et al., 2002). Nonetheless, we suggest that robust models of plant N uptake require incorporation of soil mineralization characteristics.
Incorporation of N mineralization into physiological uptake models offers serious challenges. Current models of soil N mineralization can be contrasted as following either a: a) functional approach or b) mechanistic approach (Benbi and Richter, 2002). Current analysis of literature does not provide evidence that one approach is consistently more reliable than the other (Wang et al., 2004). The simple functional approach is based on lab incubation results and, in cases where only one soil organic fraction is considered to contribute to mineralization, and the results are described by a first-order kinetics. The functional model approach have also been extended to describe cases where two or more soil organic fractions are assumed to control the over all mineralization. To date, the first order-kinetic models, including the single and double exponential models, remain widely used (Wang et al., 2004).
While it is more realistic to assume that there are multiple soil organic fractions that mineralize at distinctly different rates, double or multiple compartments functional models remain non-mechanistic. Consequently, and, perhaps more importantly, they are highly site-specific. Furthermore, these models do not assess the relative proportion of mineral N that is further nitrified. Therefore, the relative availability of the two inorganic N forms will not be known. Benbi and Richter (2002) suggested, however, that for a given site, functional approach is a reliable tool to predict soil inorganic N release when it is used with at least two compartments of soil organic N; rapidly mineralizing fraction and a more recalcitrant (residual) one.
In contrast to simple functional models, the mechanistic mineralization models are process based derived from current understanding of how soil moisture, temperature, pH and texture affect the key processes of N cycle that affect net mineralization (for example, gross mineralization, immobilization and nitrification). The mechanistic models range from non-compartment approaches, where soil organic substrate is considered as a continuum of qualities as opposed to distinct compartments (Agren and Bosatta, 1987), to multicompartment approaches. We know of at least one series of mechanistic models that are based on analytically distinct pools of C and N (including labile and stable plant material, microbial biomass and labile and stable organic mater) that have explicit compartments for exchangeable NH4+-N and NO3--N (Gaunt et al., 2001; Salih and Pansu, 1993).
In general, the mechanistic models are often criticized for lack of robust validation under realistic field condition and, when compared with the simple functional model approaches, they do not always show a clear advantage. Because these models can incorporate N compartments including NH4+ and NO3-, we believe that the mechanistic models may be better suited for integration into a physiologically driven uptake model such as the one we present in this chapter. We also suggest those mineralizaton models, be they simple functional or mechanistic, could improve the reliability of the N uptake models if they capture the high temporal and spatial variability.
2- Atmospheric N deposition
It is estimated that at
the present, anthropogenic N fixation exceeds biological fixation of this
growth limiting nutrient. The best current global estimates of sources of
anthropogenic N are; 80 Tg from industrial and fertilizer use, up to 50 Tg from
increased production of N2-fixing crops, 20 Tg from Fossil fuel combustion and
40 Tg from the release of stored geologic reserves (Vitousek et al., 1997). On
average,
Aber et al. (1989) and
Shultze (1989) proposed conceptual models that attributed temperate forest
decline in North America and
The sources of N
pollution are important, as they determine which inorganic N form is deposited.
While N deposition originating from industrial sources is dominated by NO3-,
N deposition associated with farming activities is made of NH4+
(Lovett, 1994; Schulze, 1989; Skeffington, 1990). For example, atmospheric
deposition in
The uptake and assimilation of nitrate and ammonium require distinct physiological mechanisms and have different consequences on plant growth (Fernandes and Rossiello, 1995). Compared to ammonium nutrition, nitrate nutrition tends to result in greater uptake of cations, higher tissue concentrations of carbohydrates, and smaller root to shoot ratios (Fernandes and Rossiello, 1995). Assimilation of nitrate may also have a higher energetic cost than assimilation of ammonium. For example, the yield of six perennial grass species supplied with nitrate as a sole nitrogen source was only 22% to 48% of the yield when supplied with ammonium (Wiltshire, 1973). Although most of the work comparing plant responses to nitrate and ammonium has been done with agricultural species, non-agricultural species also vary in their capacity to take up and assimilate nitrate (Gebauer et al., 1988; Falkengren-Greu, 1995). Therefore, we recommend that models of plant uptake pay close attention to the relative availability of inorganic N form in the deposited N.
It is also important to
know how fast deposited N becomes available for plant uptake. A number of
studies have shown that atmospheric N deposition may quickly become tied up, so
that the availability at the root surface does not match the deposition rate.
McNulty et al. (1991) sampled the forest floor at eleven sites along an N
deposition gradient in
Stable isotope experiments suggest that most N added to
forests accumulates in the forest floor. The forest floor retained 42-58% of 15N
added to Quercus velutina/ rubra or Pinus resinosa stands in the
3- Dissolved or Soluble Organics N
The fact that soils contain a large pool of soluble organic N (SON) which can be absorbed by plants has been known for sometime (Keeny and Bremner, 1964). It is only during the last two decades, however, that there has been growing recognition that in many native ecosystems, at least, a portion of plant N demand may be met through the uptake of soluble or dissolved organic N (Lipson and Nashlom, 2001; Nashlom and Persson, 2001; Schimel and Bennett, 2004). This recognition is partly motivated by the fact that in many ecosystems the best estimates of annual inorganic N pools and fluxes could not fully account for the yearly increase in standing N biomass (Kielland, 1990; Chapin et al., 1988; Fisk and Schmidt, 1995; Chen and Xu, 2006). Additionally, much evidence has emerged showing that plant roots either in association with or without mycorrhizal fungi (Abudzinadah and Read, 1988; Raab et al., 1996; Raab et al., 1999; Wallenda and Read 1999; Chapin et al., 1993; Henry and Jeffries, 2003; Näshlom et al., 1998; Näshlom et al., 2000; Lipson and Monson, 1998) can effectively take up small molecular weight organic N such as amino acids though larger molecules such as polypeptides and proteins (Abudzinadah and Read, 1986a, 1986b) have also been shown to be taken up by the roots system. Therefore, it is critical that models of plant nitrogen acquisition adequately address the role of soil organic N.
Given that root uptake of amino acids have been shown to be mediated by transporters, (Chapin et al., 1993; Wallenda and Read, 1999), it should be possible to integrate kinetic parameters as well as concentration of amino acids into uptake models such as that described in the following section. However, incorporation of such parameters is outside the scope of this chapter. Nonetheless, we suggest that some important consideration must guide any such effort. For example, it is important to consider the potential interaction between amino acid and inorganic N uptake. The availability of amino acids and their uptake by plants have been shown to significantly affect uptake of inorganic N. For example, high availability of amino acids in the root medium leads to reduced uptake as well the subsequent assimilation of nitrate (Padgett et al., 1993; Aslam et al., 2001). Therefore, accurate modeling of N uptake by plants requires a robust understanding of the interactive effects of inorganic N and amino acids uptake.
The majority of the studies that address SON as a source of plant N focus on soil amino acids. Interestingly, most of these studies deal with plant communities from colder climate such as boreal forest, alpine and arctic ecosystems. It is currently not known if SON are proportionally more important to the N economy of plants in the colder as opposed to moderate and warm climate. While amino acids constitute a significant pool of available N in many native systems (1-25% Chen and Xu, 2006; Yu et al., 2002, Snewo and Tabatabai, 1998) where plant species exhibit a well-developed absorption capacity, the role of amino acids to annual N budget of the native plants remains quite uncertain. Our current knowledge is limited to those studies that simply illustrate presence of amino acid in the soil and plant ability to take them up. Little quantitative data is available to evaluate the relative contribution of amino acids to plant annual N budget. In fact, when these N budget studies are conducted in relative details, serious doubts emerge as to whether amino acids are a major source of plant N economy (Owen and Jones 2001; Jones et al., 2004, 2005; Bennett and Prescott, 2004). In a grazed coastal marsh system, Henry and Jefferies (2002) showed that the uptake of amino acids might only be important when soil inorganic N availability is low. Furthermore, the focus on soil amino acid has taken attention away from a large number of other organic compounds that are often much more prevalent in the soil than amino acids. For example, in many ecosystems, amino sugars and peptides are much more prevalent in the soil than amino acids (Chen and Xu, 2006; Amelung et al., 1999). At the present we don’t know the relative importance of these SON to plant N economy. Even when availability and uptake of soil amino acids are characterized, too often, these studies focus on one or two amino acids (e.g., glycine and glutamine). We suggest that in targeting one or two amino acids, adequate justification be given to such a focus i.e., are the target amino acids available in disproportionately larger concentration that other soil amino acids?
III. MODELING ROOT SYSTEM CHARACTERISTICS
IMPORTANT TO n UPTAKE
1- Leverage of plant attributes and soil environmental factors in nutrient acquisition and growth
A number of attributes of the plant affect the rate of nutrient acquisition per unit mass, thus, the plant’s growth rate, both relative and absolute. These include the root:shoot ratio (r) and the fraction allocated to fine roots (fFR), the kinetic parameters of the uptake carrier proteins (Vmax and Km), and the root geometry as mean root radius (a) and mean root spacing (b); one may further consider the roles of mycorrhizae in “expanding” the effective root geometry. In the soil, the bulk concentration of the chosen nutrient (cb) is important, as is the diffusibility (D), amended by the effect of cation adsorption expressed as the buffering factor (c). Soil water potential directly affects these factors and also the degree of root contact with the soil solution. The rate of renewal of soluble nutrients, particularly mineralization of N, is important for setting the width of depletion zones around roots, thus, the length of the diffusive pathway. Root growth rates affect the relative importance of depletion zones, also, though not as strongly as one might intuit (e.g., Yanai, 1994; Fig. 3 therein). Finally, one may consider plant transpiration rate that generates mass flow of nutrients and that is set by a combination of plant and soil factors.
The roles of all these factors have been discussed at length and ably by a number of authors, including Tinker and Nye (2000) and Yanai (1994). We wish to emphasize selected factors that are not as widely appreciated as the others, or that have been often misinterpreted, or that have effects that defy some intuitive understanding: 1) the generally high leverage of Vmax for uptake rates, in common ranges of other factors, especially bulk nutrient concentration, cb; 2) cb itself, in soils usually regarded as low in nutrients; 3) the low leverage of root:shoot ratio in many conditions, and the apparent primacy of water rather than nutrients in setting r; 4) the lack of any substantial affect of mass flow on rates of nutrient uptake. Let us consider these in turn.
1. Control exerted by
root kinetics (Vmax) and by soil properties
Uptake of nutrients ultimately occurs at the root surface, but how much do the carrier proteins control uptake rates, when low nutrient concentration in soil (cb) or low diffusivity of a nutrient in soil can enforce a low concentration at the root surface? The question is of long standing, and models parameterized with experimental data offer the best route toward a quantitative understanding. In contrast, one cannot adjust Vmax and Km in replicate plants at will in an experimental apparatus, nor the root geometry. Consequently, simulations have been pursued for decades, with an early synthesis presented by Nye and Tinker (1977). Another important effort is modeling the effect of varied root geometries (root diameter, spacing, and vertical distribution) on uptake and growth (Gardner, 1960; Lynch and Brown, 2001).
The most basic effort toward this goal is then modeling uptake, and also resultant plant growth rate, as a function of important root and soil properties. We will not attempt to reproduce the wide range of simulations done to date, but will provide a visualization of the sensitivity of growth rate that may be compelling. The focus will be the relative growth rate, RGR, of a young plant, for which plant RGR is a critical trait and one that is most sensitive to nutritional status, uncomplicated by reproductive allocation, stand density, and other effects.
We use as a growth model the functional balance model presented earlier (BassiriRad et al., 2001). This model assumes a tight coupling of uptake to use of the nutrient in photosynthesis. Thus, one must specify the root uptake capacity and the photosynthetic nutrient-use efficacy (p*, as grams of photosynthate per gram N in leaves per day), as well as an efficiency of converting raw photosynthate into dry matter (β, gDM g-1). Root uptake capacity can be specified directly as the rate, v, or, for later discussion, derived from the combination of the root’s Michaelis-Menten kinetics (Vmax, Km) with a soil nutrient transport model that requires specification of bulk concentration (cb), diffusivity (D), root radius (a), and mean root spacing (2b). The allocations to roots and to leaves are specified as root:shoot ratio (r) and fraction of shoot mass as leaf mass (αL). Our model also uses two factors representing product suppression of photosynthesis (significant in some simulations at elevated CO2) and enforcement of a maximum RGR (from limitation on meristem activity and number). We choose a base case representing a fast-growing ruderal or crop: p*=40 gPSate gN d-1, β=0.5 gDM gPSate-1, v=0.017 gN gDM,root-1 d-1, r=0.4, and αL=0.5. The molar concentrations of photosynthate that half-repress photosynthesis and RGR are, respectively, 1.0 and 0.5.
Subsequently, we explore the effect of varying soil and root properties. In order to generate a single useful plot, we consider variations in the two soil parameters, cb and D, over ranges covering high stress to high nutrient availability (0.1 to 2.0 mol m-3 and 10-11 to 2x10-10 m2 s-1, respectively). We set a single value of Vmax, 8x10-8 mol m-2 s-1. With a=20 μm and dry matter constituting 25% of fresh mass, this is equivalent to Vmax=115 μmol gDM,root-1 h-1 or 0.032 gN gDM,root-1 d-1 at an effective 20 h per day uptake, similar to that found experimentally on the ruderal, Helianthus annus (Gutschick, 1993; Gutschick and Kay, 1995). To test the effect of changes in Vmax, we rerun the simulations with 50% larger Vmax. We then compute the sensitivity,
In the functional balance model, the maximal value of S is 0.5, resulting from RGR varying as the square root of uptake
rate (e.g., an increase in RGR by a
factor 
= 20.5requires another factor of in tissue nutrient
content, or a factor of =2 in nutrient uptake rate).
The results are shown in Fig. 1. It is clear that RGR is sensitive to cb and D only at rather low magnitudes of each. At the same time that RGR stabilizes in response to variations in cb and D, RGR becomes very sensitive to Vmax (S approaches 0.4, or 80% of its theoretical maximum). That is, Vmax is the controlling factor over the major range of soil conditions. The simulations can be repeated for other choices of plant parameters. For a slower-growing plant, with or without lower Vmax, the range of cb and D where these exert strong control shrinks roughly in proportion to either factor (RGR or Vmax; results not shown).
The conclusion is that Vmax is a strong contributor to plant performance. This is supported by many experimental studies showing tight regulation of Vmax under varying growth conditions (reviewed in Glass, 2005). One might expect that the optimal value of Vmax might be predictable, based on balancing the cumulative cost of acquiring and metabolizing nutrients against their declining utility when they are accumulated in excess. However, a number of simulations fail to generate optimal uptake rates of N and optimal tissue N contents in realistic ranges (Gutschick, 1993; Gutschick and Kay, 1995). Constraints on development, hence, on nutrient uptake, may well be important, and so might tradeoffs of increased risk of herbivory as N content rises.
2. Bulk concentration
of nutrient and attendant concentration in soil solution
Studies of root uptake kinetics consistently show that the high-affinity uptake system (HATS) for a given nutrient has Km values in the tens of micromolar (<0.1 mol m-3). One might infer that nutrient concentrations at the root surface are similarly low; Klipp and Heinrich (1994) argue that natural selection tends to drive Km to magnitudes at or below substrate concentrations, for enzymes in general. We note briefly that cb is commonly much higher, even in soils considered nutrient-poor. The example of nitrogen in desert soils is offered. The data of Schaeffer et al. (2003) and Titus et al. (2002) indicate that, in our hottest and most N-poor desert, bulk concentrations average more (often much more) than 2 ppm as mass of N per mass of soil. At a bulk soil density of 1.3 tones m-3, this is equivalent to 2.6 gN m-3, or approximately 0.18 mol m-3. The nutrient is actually carried in soil water that represents, on average, about 10% of the soil volume; consequently, concentration in this soil solution is on the order of 1.8 mol m-3 or greater. There are undoubtedly episodes when this concentration is depleted, including by rapid growth of plant (or microbial) communities; otherwise, we should not observe responses of plant growth to added N that would only raise cb even higher above saturation of the HATS. It is a challenge to resolve the large temporal excursions of cb. Current experimental techniques, such as the use of bags of ion-exchange resin, are not up to the task. The relative importance of the low-affinity uptake system in natural conditions is also a challenge.
3. Control exerted by
allocation to roots
Generally, root:shoot ratios (r) are larger in ecosystems low in nutrients - which includes most “natural” ecosystems, in contrast to agricultural systems. It is also common that r increases with nutrient stress, within a single genotype. Therefore, it is reasonable to assume that increased r has a significant net benefit, and, moreover, that r is relatively close to its optimal value in both unstressed and stressed conditions. However, this assumption has not been rigorously tested on the basis of the fundamental physiology of growth? Such assessments can be addressed by using functional growth models. One simple model, the functional balance model, gives a negative answer, under the presumption that nutrient status is the dominant signal for root allocation. This model has been tested experimentally (Gutschick, 1993; Gutschick and Kay, 1995; Zerihun et al., 2000) and shown to have acceptable accuracy in explaining RGR and nutrient content under varying nutrient availability. However, the model indicates that the optimal root:shoot ratio is unity, for any growth conditions. We may inspect the final expression for RGR, which is derived in the cited references:
The variables have the same meaning as presented
earlier. One can use simple calculus to
show that the factor involving r is
maximal at r=1 (that is, (d/dr)[
/(1+r) ] =0 at r=1). Note that changes of r by factors of 50% (to 0.5
and 1.5) change the whole factor by a much smaller amount (-6% and -2%,
respectively). The cited references note
this quandary in some detail.
This conclusion has some vulnerabilities. One assumption is that root properties (root fineness, spacing, Vmax, Km) do not vary as r varies. However, any variations in the other properties do not change the conclusion that RGR would improve under any choice of these properties, if r attains the value of 1. One might also consider that the fraction of root mass as fine roots (fFR) can vary, both with age and with nutrient stress. However, this only introduces the factor fFR under the radical in the above equation, separately from the factor r, and RGR should still increase until r=1.
One possible resolution is that r may be set primarily by the need to balance water uptake to plant transpiration, E. The smaller the root system (smaller r), the smaller the magnitude of E that can be supported. For a given shoot size, lower E requires lower stomatal conductance, gs, which decreases the photosynthetic rate per leaf area, A. An increased root fraction can allow larger gs and A. However, these reach plateau values at large r, while the diversion of mass from photosynthetic tissue (the factor 1/(1+r) above) eventually curtails RGR. A more detailed argument in given in the Appendix here. Values of r well below unity are supported at typical magnitudes of physiological traits. The problem remains that r varies in response to nutrient stress at high water status, such as in hydroponics. One might invoke the common correlation between low nutrient status and low water status in the field, to argue that natural selection has linked the two responses. There is no basis as yet to make this assertion.
4. Lack of substantial
effect of mass flow
The argument that we develop here may be succinctly stated so: Mass flow sweeps nutrients toward the root surface, but it flattens (or even reverses) the diffusional gradient. The cancellation of the interference term (mass flow X diffusion) is almost exact. Consequently, nutrient uptake is expected to be identical with and without mass flow, under a very wide range of conditions.
The simplest case to treat, and the case with the most likely contribution of mass flow, is that of a non-adsorbed nutrient such as nitrate. We treat the quasi-steady state, when diffusive gradients have become established; corrections for dynamics are discussed at the end.
Consider a soil with water moving with (vector) velocity 
at a given location, at or away from the root surface. The soil offers a diffusivity D to the nutrient (taken as isotropic,
with no real loss of generality). The
nutrient has a concentration c at the given location.
Roots are typically nearly cylindrical and long relative to
their diameter. In cylindrical
coordinates, nutrient flow in the external solution is typically almost fully
in the radial direction only. So, too,
is the velocity of water, . We may then write a
scalar equation for this radial component of the nutrient flux density. Using J
as the magnitude of the total flux, we have
(2)
On the right side, we have changed to a more intuitive convention, that positive flux (j) and positive water flow (v) are into the root . Let us assume that flow is essentially in steady state - that is, new root growth is not fast, nor are nutrient reserves readily depleted. In this case, there is no time-dependence and c depends only upon r; we may then replace ∂c/∂r with dc/dr, a total derivative. This formulation is an approximation of more complete equations (e.g., Darrah et al., 2006; Tinker and Nye, 2000; Yanai, 1994) that account for spatial variation in water content and solid-liquid equilibria of solutes.
In steady state, the flux across any radius (a shell at distance r) is equal to the flux at any other radius. The area that the flux crosses is proportional to r, so that the flux density multiplied by r is a constant. In particular, we can refer all flux densities (of water and of nutrients) to their value at the root surface, which we take as r = a, the root radius:
(3)
With these substitutions, we may reorder Eq. (2) into a differential equation for c(r):
(4)
This explicit (analytical) solution of this equation is a bit complicated but is readily derived, such as with the adjoint differential equation:
, with 
(5)
An equivalent form was derived by Nye and Spiers (1964). There are interesting limiting cases of behavior. If there is no mass flow (va=0; the case of zero transpiration), then k à 0, and the limit of (1/k) times the quantity in the square brackets reaches a limiting logarithmic form. Consider (r/a)-k as exp(-k*ln(r/a)); for small k, this becomes 1-k*ln(r/a), and we get simply
(6)
That is, there is a logarithmic profile away from the root surface. We shall use this formula to evaluate the contribution of mass flow, by difference from the solution (for flux, not c) from that in Eq. (5). In no case is ca, the concentration at the root surface, separable into diffusive and mass-flow components.
Uptake rates at the root surface are responsive to the concentration at the root surface, ca. We need to incorporate an accurate model of uptake to get a complete, consistent solution for both ca and uptake rate ja. An essentially universal form for nutrient uptake (review: Tinker and Nye, 2000) is the Michaelis-Menten form,
(7)
Here, Vmax is the saturated rate and Km is the Michaelis-Menten constant, the concentration at which uptake is at half-maximal rate. One can include a back-leakage term, but this is often very small. We may substitute Eq. (7) into Eq. (5) to obtain an equation solely in terms of the concentration ca. We may solve the combined equation, a quadratic in ca, for the value of ca. We can then substitute this value of ca into Eq. (7) to obtain the estimate of the nutrient uptake rate.
We have simulated uptake and the role of mass flow for a variety of test cases, ranging over: 1) relatively low bulk concentrations (Mojave Desert; data from Schaeffer et al., 2003; Titus et al., 2002) to high concentrations (taken as 10 times higher), 2) soil diffusivities from high (2x10-10 m2 s-1; cf. Tinker and Nye, 2000) to low (1/5 of former; at much lower diffusivities, uptake is less important), and 3) zero to high transpiration rates, equivalent to water velocities at the root surface from 0 through 5x10-10 m s-1 to 1.1x10-7 m s-1). The results are shown in Table 1. Note that the increment in nutrient uptake when mass flow is present is only 0.01% to 1.23%. Mass flow appears large only as the crude measure of concentration multiplied by water velocity. This is the measure commonly cited (e;g., Marshner et al., 1991; Kage, 1997). However, this measures omits the interference term (suppression of diffusion) that essentially cancels the crude increment exactly. We offer that mass flow need not be considered in estimating nutrient uptake in general. We have omitted consideration of a few phenomena that contribute modestly to uptake. One is mass flow into young root tips, apical to the maturation zone. In our most favorable case, it represents 7% of diffusive uptake, but this is to be weighted by the low fraction of root in this condition,and we may still neglect it (Brady et al., 1993). Uptake by root tips also occurs before the diffusive gradient develops, such that mass flow is again important. Yanai (1994) shows that this generates a modest correction (always less than 20% in her conditions). These and several other factors will be discussed in a later publication.
Our results appear superficially at variance with some experimental indications that the nighttime transpiration is negatively correlated with nutrient status, enhanced by N amendments (Bucci et al., 2006). The relation that they found may be correlational rather than causal, via some mechanism that acts adaptively for a physiological or ecological activity not directly related to nutrition. Bucci et al. (2006) noted that N and P fertilization changed the full hydraulic architecture of the plants.
IV Integrating other
root system characteristics
Improving our knowledge of plant N uptake and subsequent development of predictive models will ultimately depend on a keen understanding of root system characteristics that collectively control N uptake. A number of important characteristics distinguishes nitrogen availability in native vs. managed ecosystems. Unlike crops where fertilizer application minimizes N limitation, native ecosystems are often nitrogen limited. Nitrogen availability in natural ecosystems also differ from those of agroecosystems in terms of temporal and spatial heterogeneity. For example, early season flushes of N mineralization and pulses of increased N availability after a rain event add an element of uncertainty to N availability that is absent in a typical crop system.
These differences have undoubtedly resulted in the evolution of a number of root system characteristics that would not necessarily be favored in crop production practices of today. For example, the degree of mycorrhizal infection in native plants is far more perfuse than that observed in agronomic species. Integrating the relative contribution of mycorrhizal colonization in N uptake models is a challenging task. While a large number of studies indicate a positive effect on N uptake due to mycorrhizal associations, the enhancement is highly species specific (BassiriRad et al., 2001; BassiriRad, 2006) and varies with the stages of plant development. Previously we attempted to integrate the role of mycorrhizal colonization in a similar but simpler version of the functional balance model presented here (BassiriRad et al., 2001). There, we concluded that effects of mycorrhizal fungi on plant N uptake must be viewed in the context of both enhancing plant N status as well as the potential effects on carbon balance. Clearly, more mechanistic understanding of biology of mycorrhizal fungi needs to emerge before we can quantitatively assess their leverage on plant N uptake via modeling exercises recommended here.
Another root system characteristic that may have a large leverage on determining plant N uptake is root longevity or lifespan. Most crop plants are annuals where root turnover may not confer a significant advantage for N uptake. On the other hand, roots of may native species such as sugar maple may live as long as a year or longer (Hendrick and Pregitzer, 1993). While, there is some recognition of the importance of root longevity to N uptake (See Bloomfield et al., 1996; Eissenstat and Yanai, 1997), there is little effort in integrating root lifespan into models of plant N uptake. We suggests that such integration will improve models of N uptake. Finally, much has been described about root architecture and topological differences among native species and how such differences may have evolved in response to soil N status (Fitter, 1991). We suggest that root architecture plays a role in N uptake of plants. However, we are far from being able to determine the extent of that role. It is argued that root systems branching patterns fall into two categories: (1) herringbone and (2) dichotomous (Fitter, 1987, 1991). Fitter (1991) argued that herringbone topology gives rise to a larger specific root length thus is more effective than the dichotomous rooting branching pattern in N uptake from infertile sites. However, a number of studies show that such a relationship is not universal (Pregitzer et al., 2002; Einsman et al., 1999).
V Concluding Remarks
Development of robust models of N uptake requires greater efforts to integrate factors that control availability of N at the root surface together with the root system characteristics that regulate its absorption into the plant. In this chapter we offer road maps by which mechanistic models of soil N availability can be linked to physiological plant growth models to accomplish that effort. Soil properties that control N transport to the root surface have long been recognized and well-characterized. We offer selected insights as to how such information can be integrated into uptake models. In particular, we suggested that the relative importance of mass flow to overall N concentration at the root surface in previous studies may have been overestimated. We argued that internal cycling of N via mineralization is a major contributor to N availability in native systems. Efforts of linking physiological growth models (e.g., functional balance models) with mechanistic models of N mineralization should significantly improve predictability of N uptake by native plants. We highlighted the need to characterize and incorporate atmospheric deposition as well as soil organic N sources into models of uptake for improved predictability. We also suggested that adjustments in kinetics of root N uptake have a relatively large effect on plant performance under varying N supply but, efforts to assign optimal values for Vmax remain incomplete. It is also concluded that while increased biomass allocation to roots have beneficial outcomes for N uptake, plant growth is adversely affected so that optimal r value appears to be around 1; concurrent improvement of water uptake may drive the allocation patterns. Finally, we encourage studies that further examine the role of root system characteristics that have rarely been incorporatedinto uptake models such as mycorrhizal colonization, longevity and architecture. To avoid making modeling efforts too cumbersome to parameterize for so many inputs, empirical studies must prove that changes in a given root system characteristic infers a significant change in plant performance in response to varying N availability. AcknowledgementThis work was partly supported by funding from National Science Foundation.
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Appendix:
Optimization of root:shoot ratio for water
relations
At any given root:shoot ratio, r, there is a potential rate of water uptake, U, equal to the root mass, mr, multiplied by the uptake rate per mass of root, vw. This must match the whole-plant rate of transpiration, E, which equals the leaf area of the plant, ap, multiplied by the transpiration rate per unit leaf area, ELa. This can only occur if ELa is adjusted to the sustainable rate by an appropriate magnitude of leaf conductance for water vapor, gbs. (The subscript ‘bs’ refers to the combination of boundary-layer and stomatal conductances.) The relation of ELa to the conductance gbs, the vapor-pressure deficit D (leaf to air difference in partial pressure of water vapor), and total air pressure P is simple:
(A1)
The plant’s leaf area is simply the dry mass of leaves, mL, divided by the mass per leaf area, mLa (inverse of specific leaf area). In turn, the mass of leaves can be expressed as the total shoot mass, ms, multiplied by the fraction of shoot mass as leaves, αL. Thus, we have
(A2)
Assuming that these parameters are essentially stable at a stage in growth (particularly, in early growth, where all leaves experience similar environments), we can solve for the required value of conductance that balances water uptake and water use:
(A3)
This value of the conductance constrains the rate of
photosynthetic CO2 uptake by the whole plant, Ap, and thus the growth rate, GR, which is Ap
multiplied by a biosynthetic efficiency, β (as grams dry matter pre gram
of photosynthate produced, or, if Ap
is in molCO2 per area per time, as grams dry matter per mol CO2). The whole-plant rate, Ap, is, like water use, a product of whole-plant leaf
area with photosynthetic rate per unit leaf area,
(A4)
Here, the conductance for CO2, gbs with a prime, is closely related to that for water vapor (about 2/3 the latter, depending upon the relative importance of boundary-layer and stomatal conductances); Ca and Ci are, respectively, the CO2 partial pressures in ambient air and inside the leaf (more precisely, at the site of carboxylation, such that there is an extra resistance in liquid-phase transport inside the leaf, ignored here; see Gutschick, 2006); Vc,max is the maximum rate of carboxylation or CO2 fixation; Γ is the CO2 compensation partial pressure; and KCO is the effective Michaelis constant for CO2 binding to Rubisco enzyme in the presence of O2. The latter two parameters are functions only of leaf temperature and the mixing ratio of O2 to CO2.
The relation above can be rearranged to a quadratic equation
for Ci, given the
magnitudes of all the parameters gbs’,
Ca, P, Vc,max, Γ, and KCO. These values
are readily obtained for plants growing in normal air and at known
temperatures, and with known rates of photosynthesis in unstressed
conditions. Once Ci is known, Eq. (A4) can be used to compute the leaf
rate of photosynthesis,
Here we have used the relation that ms/mp = ms/(ms+mr), which becomes 1/(1+r) upon dividing numerator and denominator by ms.
The key tradeoff in optimizing r is that increasing r will increase water uptake U and allow a higher leaf conductance,
One may ask if this argument shows the optimum value of r to be near observed values. Let us consider a young herbaceous plant,
with r = 0.5, a leaf fraction αL = 0.5, an unstressed
leaf conductance gbs’ =
0.25 molCO2 m-2 s-1, and leaf photosynthetic
capacity Vc,max = 100 μmol m-2 s-1 (achieved rate
near 20 in same units). We take the
environmental descriptors as P = 105
Pa (about sea level pressure), Ca
= 38 Pa (thus, the current CO2 mixing ratio), and a leaf temperature
near 25ºC, which puts Γ near 4
Pa and KCO near 90
Figure legends
Fig. 1. Modelled response of relative growth rate (RGR) of a ruderal or crop plant, in early growth, to various combinations of nutrient concentration in bulk soil (cb) and diffusivity in soil (D). Solid lines are RGR (at fixed Vmax); gray lines are logarithmic sensitivity to changes in root maximal uptake rate, Vmax, as d ln(RGR)/d ln(Vmax).
Fig. 2. Occurrence of a root:shoot ratio, r, that optimizes relative growth rate (RGR), in the model of water balance between uptake and transpiration as presented in the text. Note the continued rise, at higher r, of leaf-internal CO2 partial pressure (Ci, as ratio to ambient value Ca) and leaf photosynthetic rate (A, as ratio to limiting value of about 25 μmol m-2 s-1 ).
Figures
Fig. 1
Fig. 2