Soil microbial loop and nutrient uptake by plants: a test using a coupled C:N model of plant–microbial interactions

Abstract

We have developed a spatially explicit model of plant root and soil bacteria interactions in the rhizosphere in order to formalise and study the microbial loop hypothesis that postulates that plants can stimulate the release of mineral N from the soil organic matter by providing low molecular weight C molecules to C-limited microorganisms able to liberate into the soil enzymes that degrade the organic matter. The model is based on a mechanistic description of diffusion of solutes in the soil, nutrient uptake by plants, bacterial activity and bacterial predation. Modelled soil bacterial populations grow, mediate transformations among several forms of nitrogen (mineral and organic) and compete for nitrogen with plants. Our objectives were to see if we could simulate the stimulation of turnover of the microbial loop by exudates and to study the effects of diffusion of C and N in the rhizosphere on these different processes. The model qualitatively mimics most of the characteristics of the microbial loop hypothesis. In particular, (1) plant exudates increase the growth of bacteria in the soil and (2) increase the degradation of soil organic matter and N mineralisation. (3) The increased bacterial biomass induces an increase in predator biomass and, as a result, (4) plant mineral N uptake is increased threefold compared with scenarios without exudation. However, the temporal dynamics simulated by the model are much slower than observed dynamics (the increase in uptake appears after a few months). Taking into consideration the diffusion of C and N containing molecules in soil has large effects on the spatial structure of the bacterial and predator biomass. However, the average biomass of bacteria and predators, N mineralisation and plant N uptake were not affected by these properties. The model provides a quantitative and mechanistic explanation of how plants could benefit from liberating low molecular organic matter and the subsequent stimulation of the microbial loop and increases N mineralisation.

Appendices

Appendix A: Pool variations equations

Symbols are the same that were given in the text. $\hbox{Upt}_{P}(\hbox{NH}_{4}^{+})$ and $\hbox{Upt}_{P}(\hbox{NO}_{3}^{-})$ represent respectively ammonium and nitrate uptake rate by plant (see Leadley et al. 1997, for details). $\hbox{Ex}(\hbox{N}_{\rm org}^{i})$ and $\hbox{Ex}(\hbox{C}_{\rm org}^{i})$ are the rate of exudation of organic matter from class i by plant. All these plant variables only occur in the first soil cylinder (against the rhizoplane) and are equal to 0 in the other cylinders. For simplicity sake, variations of concentrations of $\hbox{NH}_{4}^{+}, \hbox{NO}_{3}^{-}$ and organic N or C between cylinders due to diffusion and mass fluxes are expressed by the factor F _c(X). Details on calculating F _c factor between cylinders are given in Leadley et al. (1997).

Subscript A represents a parameter for total biomass of ammonifying bacteria, N for total biomass of nitrifying bacteria and B for the total biomass of every bacterial population (i.e. A+N).

Ammonifying bacteria

Organic N in biomass

$$\eqalign{ \frac{d \hbox{N}_{{\rm org}_{{\rm in}\;A_{\rm N}}}}{dt}& = \hbox{Assim}_{A}(\hbox{NH}_{4}^{+})+ \hbox{Upt}_{A}(\hbox{N}_{\rm org}^{1})\cr \quad-\frac{d\hbox{NRS}_{{A}_{\rm N}}}{dt}-q_{A_{\rm N}}-\hbox{Pred}_{A}\cr &\quad -A_{\rm N}\left(\hbox{synth}_{\rm E}+\mu_{\rm A}(\hbox{NH}_{4}^{+})\right.\cr &\qquad\qquad\left.+\mu_{\rm A} (\hbox{NO}_{3}^{-})+\mu_{\rm A}(\hbox{N}_{\rm org}^{1})\right) } $$

$$ \eqalign{ \frac{d\hbox{N}_{{\rm org}_{{\rm in}\; A_ {\rm C}}}}{dt}& =\hbox{Upt}_{A}(\hbox{C}_{\rm org}^{1})- \frac{d\hbox{NRS}_{A_{\rm C}}}{dt}-q_{A_{\rm C}}\cr \quad-\hbox{C:N}_{A}\cdot \hbox{Pred}_{A}-A_{\rm C}\left(\hbox{C:N}_{\rm E}\cdot \hbox{synth}_{\rm E}\right.\cr &\left. \hskip2.5pt\quad+\mu_{A} (\hbox{CO}_{2})+\mu_{A}(\hbox{C}_{\rm org}^{1})\right) } $$

Intra-cellular ammonium

$$ \eqalign{ \frac{d\hbox{NH}_{{4}_{\rm in}}^{+}}{dt}& = \hbox{Upt}_{A}(\hbox{NH}_{4}^{+})+\hbox{Red}_{A} (\hbox{NO}_{3}^{-})\cr &\quad -\hbox{Assim}_{A}(\hbox{NH}_{4}^{+}) } $$

Intra-cellular nitrate

$$ \frac{d\hbox{NO}_{{3}_{\rm in}}^{-}}{dt} = \hbox{Upt}_{A}(\hbox{NO}_{3}^{-})-\hbox{Red}_{A} (\hbox{NO}_{3}^{-}) $$

Nitrate reduction enzymatic system

Relation is given in Eq. (7).

Nitrifying bacteria

Organic N in biomass

$$ \begin{aligned} \frac{d\hbox{N}_{{\rm org}_{{\rm in}\; N_{\rm N}}}}{dt} = & \hbox{Assim}_{N}(\hbox{NH}_{4}^{+})- \frac{d\hbox{NRS}_{N_{\rm N}}}{dt}-q_{N_{\rm N}}-\hbox{Pred}_{N}\\ & -N_{\rm N}\left(\mu_{N}(\hbox{NH}_{4}^{+})+\mu_{\rm N}(\hbox{NO}_{3}^{-})+ \mu_{\rm N}(\hbox{N}_{\rm org}^{1})\right) \end{aligned} $$

$$ \eqalign{ \frac{d\hbox{N}_{{\rm org}_{{\rm in}\;N_{\rm C}}}}{dt} &= \hbox{Assim}_{N}(\hbox{CO}_{2})- \frac{d\hbox{NRS}_{N_{\rm C}}}{dt}-q_{N_{\rm C}}\cr &\quad-\hbox{C:N}_{N} \cdot \hbox{Pred}_{N}\cr & \quad-N_{\rm C}\left(\mu_{\rm N}(\hbox{CO}_{2})+\mu_{\rm N}(\hbox{C}_{\rm org}^{1})\right) }$$

Intra-cellular ammonium

$$\eqalign{ \frac{d\hbox{NH}_{{4}_{\rm in}}^{+}}{dt} = \hbox{Upt}_{N}(\hbox{NH}_{4}^{+})+\hbox{Red}_{N} (\hbox{NO}_{3}^{-})\cr\quad-\hbox{Assim}_{N}(\hbox{NH}_{4}^{+})-\hbox{Redox} }$$

Intra-cellular nitrate

$$ \frac{d\hbox{NO}_{{3}_{\rm in}}^{-}}{dt} = \hbox{Upt}_{N}(\hbox{NO}_{3}^{-})-\hbox{Red}_{N} (\hbox{NO}_{3}^{-}) $$

Nitrate reduction enzymatic system

Relation is given in Eq. (7).

Mineral soil products

Soil solution ammonium

$$ \eqalign{\frac{d\hbox{NH}_{4}^{+}}{dt} = A_{\rm N}\mu_{A}(\hbox{NH}_{4}^{+})+ N_{\rm N}\mu_{N}(\hbox{NH}_{4}^{+})\cr \quad+M_{B}(\hbox{NH}_{4}^{+})+ q_{A_{\rm N}}-\hbox{Upt}_{B}(\hbox{NH}_{4}^{+})\cr \quad-\hbox{Upt}_{P}(\hbox{NH}_{4}^{+})+ F_{\rm c}(\hbox{NH}_{4}^{+})} $$

Soil solution nitrate

$$ \eqalign{ \frac{d\hbox{NO}_{3}^{-}}{dt}& = A_{\rm N}\mu_{A}(\hbox{NO}_{3}^{-})+ N_{\rm N}\mu_{N}(\hbox{NO}_{3}^{-})+\hbox{Redox}\cr \quad+M_{B}(\hbox{NO}_{3}^{-})+ q_{N_{\rm N}}-U_{B}(\hbox{NO}_{3}^{-})\cr &\quad-\hbox{Upt}_{P}(\hbox{NO}_{3}^{-}) +F_{\rm c}(\hbox{NO}_{3}^{-}) } $$

Soil carbon dioxide

$$ \frac{d\hbox{CO}_{2}}{dt}=B_{\rm N}\cdot\mu_{B}(\hbox{CO}_{2})+ q_{B_{\rm C}}-\hbox{Assim}_{N}(\hbox{CO}_{2}) $$

Soil organic matter

Organic matter (n classes)

The equation given here is general. Functions that has not been defined in the text like those concerning organic compounds larger than n, are assumed to be zero.

If i>1, variations in the organic pools are expressed as:

$$ \eqalign{ \frac{d\hbox{N}_{\rm org}^{i}}{dt}& = \hbox{Ex}(\hbox{N}_{\rm org}^{i})+A_{\rm N}\mu_{A} (\hbox{N}_{\rm org}^{i})+N_{\rm N}\mu_{N}(\hbox{N}_{\rm org}^{i})\cr \quad+\mu_{\rm E}\hbox{E}_{\rm N}+ M_{B}(\hbox{N}_{\rm org}^{i})+F_{\rm c}(\hbox{N}_{\rm org}^{i})-D_{i}(\hbox{N}_{\rm org}^{i})\cr &\quad +D_{i+1}(\hbox{N}_{\rm org}^{i+1})-S_{i+1} (\hbox{N}_{\rm org}^{i+1}) } $$

$$ \eqalign{ \frac{d\hbox{C}_{\rm org}^{i}}{dt}& = \hbox{Ex}(\hbox{C}_{\rm org}^{i})+A_{\rm N}\mu_{A} (\hbox{C}_{\rm org}^{i})+N_{\rm N}\mu_{N}(\hbox{C}_{\rm org}^{i})\cr \quad+\hbox{C:N}_{\rm E} \mu_{\rm E}\hbox{E}_{\rm N}+M_{B}(\hbox{C}_{\rm org}^{i})+F_{\rm c}(\hbox{C}_{\rm org}^{i})\cr &\quad -D_{i}(\hbox{C}_{\rm org}^{i})+D_{i+1}(\hbox{C}_{\rm org}^{i+1})-S_{i+1} (\hbox{C}_{\rm org}^{i+1}) } $$

If i=1, the equation is :

$$ \eqalign{ \frac{d\hbox{N}_{\rm org}^{1}}{dt} & =\hbox{Ex}(\hbox{N}_{\rm org}^{1})-\hbox{Upt}_{A}(\hbox{N}_{\rm org}^{1})+ A_{\rm N}\mu_{A}(\hbox{N}_{\rm org}^{1})\cr \quad+N_{\rm N}\mu_{N}(\hbox{N}_{\rm org}^{1})+ \mu_{\rm E}\hbox{E}_{\rm N}+M_{B}(\hbox{N}_{\rm org}^{1})\cr \quad +F_{\rm c}(\hbox{N}_{\rm org}^{1})-S_{1}(\hbox{NH}_{4}^{+})+\sum_{j=1}^{n}S_{j} (\hbox{N}_{\rm org}^{j}) } $$

$$ \eqalign{ \frac{d\hbox{C}_{\rm org}^{1}}{dt} &= {\rm Ex}(\hbox{C}_{\rm org}^{1})-\hbox{Upt}_{A}(\hbox{C}_{\rm org}^{1})+ A_{\rm N}\mu_{A}(\hbox{C}_{\rm org}^{1})\cr \quad+N_{\rm N}\mu_{N}(\hbox{C}_{\rm org}^{1})+ \hbox{C:N}_{\rm E}\mu_{\rm E}E_{\rm N}+M_{B}(\hbox{C}_{\rm org}^{1})\cr \quad+F_{\rm c}(\hbox{C}_{\rm org}^{1})+\sum_{j=1}^{n}S_{j}(\hbox{C}_{\rm org}^{j}) } $$

External enzymes

Variations for this pool are given in Eq. (15).

Appendix B: Plant and soil parameters

Plant parameters are given in Table 5, soil parameters are given in Table 6.

Table 5 Symbols, units and common values of plant parameters

Table 6 Symbols, units and common values of soil parameters