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Mathematical Modeling of the Dynamics of Shoot-Root Interactions and Resource Partitioning in Plant Growth.

Feller C, Favre P, Janka A, Zeeman SC, Gabriel JP, Reinhardt D - PLoS ONE (2015)

Bottom Line: Our main goal was to grasp the dynamic adaptation of shoot:root ratio as a result of changes in light and Pi supply.The results of our study are in agreement with balanced growth hypothesis, suggesting that plants maintain a functional equilibrium between shoot and root activity based on differential growth of these two compartments.Furthermore, our results indicate that resource partitioning can be understood as the emergent property of many local physiological processes in the shoot and the root without explicit partitioning functions.

View Article: PubMed Central - PubMed

Affiliation: Dept. of Mathematics, University of Fribourg, Fribourg, Switzerland.

ABSTRACT
Plants are highly plastic in their potential to adapt to changing environmental conditions. For example, they can selectively promote the relative growth of the root and the shoot in response to limiting supply of mineral nutrients and light, respectively, a phenomenon that is referred to as balanced growth or functional equilibrium. To gain insight into the regulatory network that controls this phenomenon, we took a systems biology approach that combines experimental work with mathematical modeling. We developed a mathematical model representing the activities of the root (nutrient and water uptake) and the shoot (photosynthesis), and their interactions through the exchange of the substrates sugar and phosphate (Pi). The model has been calibrated and validated with two independent experimental data sets obtained with Petunia hybrida. It involves a realistic environment with a day-and-night cycle, which necessitated the introduction of a transitory carbohydrate storage pool and an endogenous clock for coordination of metabolism with the environment. Our main goal was to grasp the dynamic adaptation of shoot:root ratio as a result of changes in light and Pi supply. The results of our study are in agreement with balanced growth hypothesis, suggesting that plants maintain a functional equilibrium between shoot and root activity based on differential growth of these two compartments. Furthermore, our results indicate that resource partitioning can be understood as the emergent property of many local physiological processes in the shoot and the root without explicit partitioning functions. Based on its encouraging predictive power, the model will be further developed as a tool to analyze resource partitioning in shoot and root crops.

No MeSH data available.


Related in: MedlinePlus

Model validation and evaluation of the adaptive potential of plants to a range of different Pi concentrations.Simulations (continuous line) and experimental data (experiment 3; dashed line) are shown for (A) shoot and (B) root growth, (C) root fraction, (D) shoot Pi concentration and (E) root Pi concentration and (F) total Pi per plant for plants grown at 6 different Pi concentrations (1, 10, 30, 100, 300, 1000 μM). The grey line in (a)-(c) represents the value at the beginning of the experiment. Error bars represent the standard deviations (N = 10).
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pone.0127905.g007: Model validation and evaluation of the adaptive potential of plants to a range of different Pi concentrations.Simulations (continuous line) and experimental data (experiment 3; dashed line) are shown for (A) shoot and (B) root growth, (C) root fraction, (D) shoot Pi concentration and (E) root Pi concentration and (F) total Pi per plant for plants grown at 6 different Pi concentrations (1, 10, 30, 100, 300, 1000 μM). The grey line in (a)-(c) represents the value at the beginning of the experiment. Error bars represent the standard deviations (N = 10).

Mentions: For an initial comparison of the two models, Thornley's model was used to simulate the experimental results as with ours (Figs A-H in S2 File; compare with Figs 3–7). In order to compare the performance of the two models in a quantitative way, Pareto fronts were calculated for three pairs of variables, namely shoot and root volume (Vsh(t),Vr(t)), shoot and root Pi concentration , and shoot and root sugar concentration . For each parameter pair, the sum of the relative quadratic errors (RE) between simulated and observed values was determined, denoted by REV, REph, and REsu, respectively. For the calculation of REsu in our model, the mean soluble sugar concentration over 24 hours was used, since the sugar oscillations brought about by the day-and-night cycle in our model would make the comparison with Thornley’s model difficult. Calculation of the Pareto front involves the minimization of the components (REV, REph, REsu) by changing the parameter sets of the two models after separate fitting. One way to compare the two models is to calculate the weighed sum of REV, REph, and REsu. This procedure (Nelder-Mead approach) results in a single number that may be sensitive to the initial condition and therefore is of limited use. To circumvent this problem, another optimization method, a so-called genetic algorithm, was chosen and implemented in matlab (function gaoptimset.m of the global optimization toolbox). For a detailed description of the procedure, the reader is referred to [82]. This approach minimizes independently the three relative errors REV, REph, and REsu. Instead of yielding a single optimal set, as it is the case with the Nelder-Mead approach, the genetic algorithm provides several optimal sets. The smaller the values for all the three criteria (REV, REph, REsu) are, the better a given parameter set is. Keeping only the best points leads to a collection of different optimized points (REV, REph, REsu) called the Pareto front.


Mathematical Modeling of the Dynamics of Shoot-Root Interactions and Resource Partitioning in Plant Growth.

Feller C, Favre P, Janka A, Zeeman SC, Gabriel JP, Reinhardt D - PLoS ONE (2015)

Model validation and evaluation of the adaptive potential of plants to a range of different Pi concentrations.Simulations (continuous line) and experimental data (experiment 3; dashed line) are shown for (A) shoot and (B) root growth, (C) root fraction, (D) shoot Pi concentration and (E) root Pi concentration and (F) total Pi per plant for plants grown at 6 different Pi concentrations (1, 10, 30, 100, 300, 1000 μM). The grey line in (a)-(c) represents the value at the beginning of the experiment. Error bars represent the standard deviations (N = 10).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4495989&req=5

pone.0127905.g007: Model validation and evaluation of the adaptive potential of plants to a range of different Pi concentrations.Simulations (continuous line) and experimental data (experiment 3; dashed line) are shown for (A) shoot and (B) root growth, (C) root fraction, (D) shoot Pi concentration and (E) root Pi concentration and (F) total Pi per plant for plants grown at 6 different Pi concentrations (1, 10, 30, 100, 300, 1000 μM). The grey line in (a)-(c) represents the value at the beginning of the experiment. Error bars represent the standard deviations (N = 10).
Mentions: For an initial comparison of the two models, Thornley's model was used to simulate the experimental results as with ours (Figs A-H in S2 File; compare with Figs 3–7). In order to compare the performance of the two models in a quantitative way, Pareto fronts were calculated for three pairs of variables, namely shoot and root volume (Vsh(t),Vr(t)), shoot and root Pi concentration , and shoot and root sugar concentration . For each parameter pair, the sum of the relative quadratic errors (RE) between simulated and observed values was determined, denoted by REV, REph, and REsu, respectively. For the calculation of REsu in our model, the mean soluble sugar concentration over 24 hours was used, since the sugar oscillations brought about by the day-and-night cycle in our model would make the comparison with Thornley’s model difficult. Calculation of the Pareto front involves the minimization of the components (REV, REph, REsu) by changing the parameter sets of the two models after separate fitting. One way to compare the two models is to calculate the weighed sum of REV, REph, and REsu. This procedure (Nelder-Mead approach) results in a single number that may be sensitive to the initial condition and therefore is of limited use. To circumvent this problem, another optimization method, a so-called genetic algorithm, was chosen and implemented in matlab (function gaoptimset.m of the global optimization toolbox). For a detailed description of the procedure, the reader is referred to [82]. This approach minimizes independently the three relative errors REV, REph, and REsu. Instead of yielding a single optimal set, as it is the case with the Nelder-Mead approach, the genetic algorithm provides several optimal sets. The smaller the values for all the three criteria (REV, REph, REsu) are, the better a given parameter set is. Keeping only the best points leads to a collection of different optimized points (REV, REph, REsu) called the Pareto front.

Bottom Line: Our main goal was to grasp the dynamic adaptation of shoot:root ratio as a result of changes in light and Pi supply.The results of our study are in agreement with balanced growth hypothesis, suggesting that plants maintain a functional equilibrium between shoot and root activity based on differential growth of these two compartments.Furthermore, our results indicate that resource partitioning can be understood as the emergent property of many local physiological processes in the shoot and the root without explicit partitioning functions.

View Article: PubMed Central - PubMed

Affiliation: Dept. of Mathematics, University of Fribourg, Fribourg, Switzerland.

ABSTRACT
Plants are highly plastic in their potential to adapt to changing environmental conditions. For example, they can selectively promote the relative growth of the root and the shoot in response to limiting supply of mineral nutrients and light, respectively, a phenomenon that is referred to as balanced growth or functional equilibrium. To gain insight into the regulatory network that controls this phenomenon, we took a systems biology approach that combines experimental work with mathematical modeling. We developed a mathematical model representing the activities of the root (nutrient and water uptake) and the shoot (photosynthesis), and their interactions through the exchange of the substrates sugar and phosphate (Pi). The model has been calibrated and validated with two independent experimental data sets obtained with Petunia hybrida. It involves a realistic environment with a day-and-night cycle, which necessitated the introduction of a transitory carbohydrate storage pool and an endogenous clock for coordination of metabolism with the environment. Our main goal was to grasp the dynamic adaptation of shoot:root ratio as a result of changes in light and Pi supply. The results of our study are in agreement with balanced growth hypothesis, suggesting that plants maintain a functional equilibrium between shoot and root activity based on differential growth of these two compartments. Furthermore, our results indicate that resource partitioning can be understood as the emergent property of many local physiological processes in the shoot and the root without explicit partitioning functions. Based on its encouraging predictive power, the model will be further developed as a tool to analyze resource partitioning in shoot and root crops.

No MeSH data available.


Related in: MedlinePlus