CPlantBox, a whole plant modelling framework for the simulation of water and carbon related processes

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Lacointe, Harry Vereecken, Guillaume Lobet

To cite this version:

Xiao-Ran Zhou, Andrea Schnepf, Jan Vanderborght, Daniel Leitner, André Lacointe, et al.. CPlant-Box, a whole plant modelling framework for the simulation of water and carbon related processes. in silico Plants, Oxford Academic, 2019, 2 (1), 19 p. �10.1101/810507�. �hal-02789121�

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CPlantBox, a whole plant modelling framework for the

simulation of water and carbon related processes

3

Xiao-Ran Zhou1, Andrea Schnepf1, Jan Vanderborght1, 4

Daniel Leitner2, André Lacointe3, Harry Vereecken1, Guillaume Lobet1 * 5

6

1

: Agrosphäre (IBG-3), Forschungszentrum Jülich GmbH, Jülich, Germany 7

2

: Simulationswerkstatt, Humboldtstraße 40, 4020 Linz, Austria 8

3

: INRA, UMR 547 PIAF, F
63100 Clermont
Ferrand, France

9

*: Correspond Author, Email: g.lobet@fz-juelich.de 10

11

Abstract

The interaction between carbon and flows within the plant is at the center of most growth 13

and developmental processes. Understanding how these fluxes influence each other, and 14

how they respond to heterogeneous environmental conditions, is important to answer 15

diverse questions in forest, agriculture and environmental sciences. However, due to the 16

high complexity of the plant-environment system, specific tools are needed to perform such 17

quantitative analyses. 18

19

Here we present CPlantBox, full plant modelling framework based on the root system model 20

CRootBox. CPlantbox is capable of simulating the growth and development of a variety of 21

plant architectures (root and shoot). In addition, the flexibility of CPlantBox enables its 22

coupling with external modeling tools. Here, we connected it to an existing mechanistic 23

model of water and carbon flows in the plant, PiafMunch. 24

25

The usefulness of the CPlantBox modelling framework is exemplified in four case studies. 26

Firstly, we illustrate the range of plant structures that can be simulated using CPlantBox. In 27

the second example, we simulated diurnal carbon and water flows, which corroborates 28

published experimental data. In the third case study, we simulated impacts of 29

heterogeneous environment on carbon and water flows. Finally, we showed that our 30

modelling framework can be used to fit phloem pressure and flow speed to (published) 31

experimental data. 32

33

The CPlantBox modelling framework is open-source, highly accessible and flexible. Its aim 34

is to provide a quantitative framework for the understanding of plant-environment interaction. 35

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Introduction

38

Plants contribute for around 80% of the global biomass [1], and they strongly control land 39

surface fluxes of water and carbon. Plant water uptake constitutes a major part of the 40

evaporative flux at the land surface but its prediction is extremely variable and uncertain [2– 41

4]. The same is true for the estimation of carbon fluxes [5,6]. As such, understanding the 42

interplay between plant carbon and water flow and their environment is of importance to 43

answer diverse questions in forest, agriculture and environmental sciences. 44

45

The flows of water and carbon in the plant are constrained by both local and overall 46

structures [7–10]. Root architecture is known to have an impact on water uptake [11,12], 47

while shoot structure has an impact on carbon assimilation [13–15]. From an entire plant 48

perspective, root and shoot are tightly connected, forming a complex and dynamic 49

continuum between water and carbon flow. For instance, water availability at the root level 50

influences carbon unloading rate [16,17], while the stomata conductance directly affects root 51

water uptake [18,19]. Knowing the connecting structure of both shoot and root is therefore 52

needed to understand plants better. 53

54

At the organ scale, the different parts of the plant (root, stem, leaves, flowers and fruits) are 55

connected by xylem and phloem vessels (fig. 1) [20,21]. Xylem vessels transport water 56

[8,12,22,23], while phloem vessels translocate carbon [7,24–26]. The movement of water 57

within the xylem vessels is typically explained by the tension-cohesion theory [27,28]. This 58

theory states that transpiration at the leaf level creates a tension within the xylem vessels, 59

which is transmitted to the soil-root interface and drives the water uptake from the soil. The 60

carbon flow in the phloem continuum is explained by the Münch theory [29,30]. Briefly, 61

Münch theory states that source organs (typically mature leaves and storage structures) 62

load carbohydrates into the phloem sieve tubes. This strongly decreases the phloem water 63

potential. As xylem and phloem vessels are tightly connected throughout the whole plant, 64

this decreased osmotic potential in phloem will create a water flow from the xylem toward 65

the phloem at source location (fig. 7C light green line). This in turn increases water pressure 66

in the phloem vessels, leading to a flow toward sink organs (typically roots (fig. 7C light 67

yellow line), young leaves, flower and fruits). [31,32]. Recent experiments have provided the 68

first direct support to the Münch theory by direct measurement [33,34]. 69

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Figure 1. Structures and functions affect

carbon and water flow in plants. Leaf and root contacts the environment. Xylem and phloem connect organs and exchange carbon and water.

70 71

In recent years, new phenotyping techniques [35–43] have enabled the precise 72

measurement of plant structure with high temporal and spatial resolution. However, 73

physiological parameters, such as pressure and flows in plants are still challenging to 74

measure. For example, the first pressure measurement in phloem sieve tubes were 75

conducted only recently with a success rate lower than 30% [33,44]. Another common issue 76

with flow and pressure data is the fragmentation of the acquired data. In other words, as 77

these techniques are complex to conduct, data can only be acquired on specific organs and 78

at specific times, which makes it difficult to structurally understand the processes. More 79

comprehensive and quantitative studies are therefore needed to better understand the 80

complex dynamics between the water and carbon flow within the plant, in response to 81

heterogeneous environments [45,46]. 82

83

Recently, modelling tools have been proven very useful to study water and carbon flows in 84

plants and to analyze environmental controls on these fluxes [16,47]. In particular, 85

Functional-Structural Plant Models (FSPMs) have a long history of simulating water or 86

carbon flows [48–56]. Table 1 lists the most recent FSPMs simulating either the full plant 87

structure (both root and shoot), or water and carbon flows. Among these, only a handful of 88

3D full plant structure models (with both 3D topology and 3D geometry) exist [57–59]. 89

Meanwhile, only two existing models were designed to simulate carbon and water flow 90

simultaneously [60,61]. 91

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We distinguish three approaches to model carbon distribution within the plant. The first 93

approach prescribes allocation rules of assimilates between the different plant organs. The 94

total pool of carbon is divided between different organs, which adjust their growth 95

accordingly [62,63]. Usually, models using such approach do not need a fast-computational 96

method to distribute the carbon. A second approach uses detailed mechanistic relationships 97

to simulate carbon (and sometimes water) flow within a simplified structure. These lumped 98

models often only represent the plant as a small set of objects (fig. 2B) [25,64]. Finally, a 99

third approach resolves carbon and water flow within a 3D structure based on mechanistic 100

relations between the different organs [7,60,61,65]. Although these models can be 101

computationally very intensive, they open the way to more complex representation of the 102

plant-environment system. 103

104

Here we introduce a new framework for functional-structural whole plant modelling, which is 105

based on the structural model CPlantBox. The novelty of CPlantBox is twofold. Firstly, 106

CPlantBox can simulate the full plant structure at vegetative growth as a single connected 107

network of organs (both root and shoot). Secondly, the model was coupled with a 108

mechanistic model of carbon and water flow in the plant, PiafMunch [61,66]. The coupling 109

enables fast simulations on large or complex plant structures, which was difficult to achieve 110

before (PiafMunch uses manually defined plant architecture). Previously, PiafMunch is 111

already able to simulate all 3D plant topology. Now, by coupling with CPlantBox, an 112

additional 3D geometry layer is added to PiafMunch. Here we demonstrate the capabilities 113

of the coupled model to generate a variety of plant structures and to reproduce realistic 114

water and carbon flow behaviours. 115

116

A B

Figure 2. A: The flow rate in lumped model depends only on the radius of the segment. In 3D models

117

branching structures affect flows as well. B: On 3D structures, the heterogeneous soil water potential 118

affect xylem water flows. Root in wet soil has more water flow compared to root in dry soil. 119 120 s is ls, ial

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Model Name Authors Structure Species Flow(s) Availability Interface

GRAAL1 [57] 3D full plant Maize Water - GUI

PlaNet-Maize1

[59] 3D full plant Maize Water Open

source

GUI, Web interface

Greenlab [50,67,68] 3D shoot and 0D root

Generic Water or carbon Upon request GUI -2 [60] 3D full plant topology Small plants

Water and carbon - -

L-Peach [69] 3D full plant topology

Peach Carbon - -

AmapSim [70] 3D shoot or root Generic Water or carbon (by coupling)

- -

Piaf-Munch2 [61] 3D full plant topology

Small plants

Water and carbon Upon request

GUI, Command Line.

-2 [58] 3D full plant topology

Generic Water Upon

request

-

CN-Wheat [71,72] 3D shoot, 0D root Wheat Nitrogen and carbon - - This work1 3D full plant Generic Water and carbon

(by coupling)

Open source

GUI, iPython notebook, Web interface

1

Models that has both 3D topology and 3D geometry.

2

Model which can simulate interactions between carbon and water.

All rights reserved. No reuse allowed without permission.

The copyright holder for this preprint

.

http://dx.doi.org/10.1101/810507

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Material and methods

Description of CPlantBox

124

CPlantBox is an extension of the model CRootBox [73]. CRootBox is a fast and flexible 125

FSPM focusing on root architecture and root-soil-interaction. We took advantage of the 126

object-oriented structure of CRootBox to add new modules to represent the different shoot 127

organs (fig. 3B). The main extensions in CPlantBox are: 128

129

- CPlantBox can simulate realistic plant shoots and roots as a single connected network. 130

The output can be coupled with water and carbon flow simulations (fig. 3C, D). 131

132

- As we move from root simulation to a full plant simulation (fig. 3B), more complex 133

relationships between the different organs have been included in the model. For 134

instance, roots can now grow from seed, roots or shoot organs (fig. 3B). 135

136

- The input parameter files are now XML-based (fig. 3A). Comparing to plain-text 137

parameters, XML increases the robustness, flexibility (more parameters for the shoot) 138

and readability. Backward compatibility with previous parameter file (from CRootBox) 139

was insured. 140

141

The output of CPlantBox is a 1-dimensional network (with 3D geometry coordinates) (fig. 142

3C), each node of the network has 3D (3-dimensional) coordinates and other properties, 143

such as an organtype (which indicates if it belongs to root, stem or leaf), a radius (or width) 144

and a water potential. The output format of the structure includes RSML [74], VTP [75] and 145

PiafMunch input format. After the plant structure is simulated (fig. 3B, potentially thousands 146

of segments), an input file for the PiafMunch can be generated. Afterwards, the PiafMunch 147

can be called by CPlantBox to read the input file, run simulation and generate the output 148

files. At the end of the simulation, output files can be interpreted and visualized by the 149

framework. 150

151

The current coupling is done by file exchange and command line automation. Simulating the 152

carbon and water flow within a 300-segments plant for 100 hours growth time takes around 153

1 minute (dependent on parameter setting) on a laptop (CPU: Intel Core i5-6300U 2.4GHz, 154

RAM 8GB 2400MHz). We also created looped functions to run simulations in batch 155

processes. Installation, preprocessing, post processing and visualization are exemplified in 156

the following Jupyter notebook: github.com/Plant-Root-Soil-Interactions-157 Modelling/CPlantBox/blob/master/tutorial/jupyter/CPlantBox_PiafMunch_Tutorial_(include_i 158 nstallation).ipynb. 159 160

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161

Figure 3: Flow chart of four major steps in CPlantBox-PiafMunch coupling. A: Input parameter

162

example (organ parameters with “+” sign means it is collapsed). B: Output of CPlantBox is visualized. 163

C: Coupling between CPlantBox and PiafMunch, where output of CPlantBox can be the input file of

164

PiafMunch. D: Water flow output example from the CPlantBox-PiafMunch coupling. 165

166 167

Description of PIAF-Munch

168

Water and carbon flows in PiafMunch

169

In PiafMunch [61,66], cohesion-tension theory is a precondition of the Münch theory. The 170

cohesion-tension theory says that xylem-water-flow is driven by differences in pressure 171

water potential in the xylem. The water potential in general can be defined as the sum of 172

partial water potentials: the gravimetric water potential:
z (MPa), the pressure water

173

potential
p (MPa) and the osmotic water potential:
o (MPa). According to the

cohesion-174

tension theory, the pressure in the water can be smaller than zero such that a tension 175

r .

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instead of a pressure is applied to a water body. It must be noted though that mostly the 176

water pressure is expressed as the difference between the water pressure and the 177

atmospheric air pressure. Following this definition, a positive pressure corresponds with a 178

pressure in the water that is larger than the atmospheric pressure and a negative pressure 179

with pressure that is smaller than the atmospheric air pressure. Following this definition, a 180

water tension would correspond with a water pressure that is smaller than -105 Pa. If 181

dissolved substances can flow freely within the xylem and phloem tissues, a gradient in 182

concentrations or corresponding osmotic water potentials will not drive a flow within these 183

tissues. Thus, the volume flow between two connected xylem’s nth and (n+1)th segments 184

(JWxyl,n,n+1 mL h-1) can be written as:

185

(1)

where rxyl,n,n+1 (MPa h mL-1) is the xylem resistance and ΔPxyl,n,n+1 = (
z,xyl,n+
p,xyl,n

)-186

(
z,xyl,n+1+
p,xyl,n+1), ΔPxyl,n,n+1 is the difference between the sum of pressure and gravimetric

187

potentials at the (n+1)th and nth segments respectively. Similarly, the volume flow between 188

two connected phloem sieve tubes JWst,n,n+1 is:

189

(2)

where rst,n,n+1 (MPa h mL-1) is the total sieve tube (include sieve plate) resistance between nth

190

and (n+1)th segment and _ΔPst,n,n+1 = (
z,st,n+
p,st,n)-(
z,st,n+1+
p,st,n+1), ΔPst,n,n+1 is the total

191

potential difference between the neighbouring sieve tube segments, nth and (n+1)th. At the 192

nth segment, the volume flow between the neighbouring xylem and phloem, which are 193

separated by a semipermeable membrane, JWlat,n can be written as:

194

(3)

where
p,xyl,n is the water pressure potential in xylem and
p,st,n is the water pressure

195

potential in sieve tubes,
o,xyl,n is the osmotic water potential in xylem and
o,st,n is the

196

osmotic water potential in sieve tubes, rlat,n is the resistance of the membrane between

197

xylem and phloem. Here, we should notice that, at the source location, osmotic pressure 198

drives the JWlat,n. But, at the sink location, the driving force is mainly the pressure water

199

potential, because most osmotic water potential is removed by the unloading of carbon. 200

The water mass balance of xylem is: 201

(4) where _ΔJWxyl,n is the xylem water flux divergence over segment n, which can be written as 202

ΔJWxyl,n = JWxyl,n,n+1 - JWxyl,n-1,n. Similarly, the water mass balance of phloem can be written as: 203

(5) Where ΔJWst,n = JWst,n,n+1 - JWst,n-1,n is the flux divergence over phloem sieve-tube . NZSn is

204

the non-zero sugar volume flow accompanying JSlat,n . At the source location, NZSn =

205

, is the non-zero partial molar volume of sucrose, JSloading,n (mmol h-1) is the

206

loading rate from the source tissue (e.g. parenchyma) to the phloem at the nth node. At the 207

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sink location, NZSn = , JSunloading,n (mmol h-1) is the loading rate from the

208

phloem to the sink tissue. 209

The mass balance of sucrose can be written as: 210

(6) where, JS(un)loading is the source (sink) term, Cst,n-1 is the sucrose concentration in the (n-1)th

211

node, Cst,n is the sucrose concentration in the nth node.

212

Comparison with experimental results

213

Recently, Knoblauch et al. experimentally tested the Münch theory on morning glory 214

(Ipomoea nil) [33]. To validate the functions of CPlantBox-PiafMuch and estimated carbon 215

loading/unloading speed, we decided to perform a re-analysis of their experimental dataset 216

(measurements are shown in Table 2). In particular, we used one set of morning glory 217

experimental data (left column of 7.5 m morning glory in Table 2) for calibration and another 218

set (right column of 7.5 m morning glory in Table 2) for validation of our modelling system. 219

We choose to use these datasets for different reasons. Firstly, the experimental 220

measurements match almost directly both the input and output of the CPlantBox-PiafMunch 221

model (fig. 4). Secondly, the authors performed a variety of experimental treatments, 222

allowing us to parametrize our model on one experiment and validate on the other. Finally, 223

the relatively simple architecture of the morning glory allowed us to focus our analysis on the 224

resolution of carbon and water flow themselves. 225

226

In a first experiment (that we used for the parameterization of our simulations is shown in 227

Table 2 and illustrated in fig. 10A), the authors measured the permeability of sieve tubes at 228

three locations (1 m, 4 m and 7 m) on a 7.5 m tall morning glory (referred to as 7.5 m plant 229

in following text). The phloem pressure and phloem flow rates were also measured in the 230

same plant. 231

232

In a second experiment (that we used for validation shown in Table 2 and illustrated in figure 233

10B), another morning glory plant was continuously defoliated except for the top four meters 234

(this plant is referred to as defoliated plant). When the defoliated stem was 2.5 m, 3.5 m, 9 235

m, 10 and 14 m long during its growth, the pressure of the bottom leaf was measured. 236

237

Details about the exact data transformations performed between the experimental 238

measurements and the model parameters can be found in the Supplementary material 1. 239 240 r h he re rs

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Figure 4. Measured parameters (in black text) and estimated parameter (in red text) in comparison

246

with experiment. Length is calculated from simulated architecture (left side of fig. 10 A, B), which is 247

based on the schematic drawing (right side of fig. 10A, B). rst is converted from measured kst

248

(Supplement I, Equation 9). Pressure difference (ΔPst) is the phloem source pressure (Psource) minus

249

phloem sink pressure (Psink). R is the universal gas constant and T is the absolute temperature. Pxyl is

250

the pressure of xylem at source or sink location, those pressures are calculated by carbon loading 251

rate (JSloading) and carbon unloading rate (JSunloading). Arrows highlight our modelling workflow. ΔT is

252

the time difference, Volst is the sieve tube volume. Units are in Table 3 and Supplemental material 1.

253

The fitting of loading and unloading rate to source phloem pressure and flow rate are shown at the 254

end of supplemental material 1. 255 256 257 258 s is 1.

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Table 2. List of experimental measurements

259 260 Measurements Measurements on 7.5 m morning glory Measurements on defoliated morning glory

Architecture Idealized schematic drawing (fig. 10A)

Idealized schematic drawing (fig. 10B)

Sieve tube conductivity (kst) At 1 m, 4 m and 7 m location When plant is 18 m long

Pressure (P) Leaf phloem turgor pressure is measured at 1st, 3rd, 5th, 9th and 10th leaf (blue dots in fig. 10C).

Root turgor pressure is measured in the cortex of elongation zone.

Leaf phloem turgor pressure is measured at bottom leaf of the 4 m foliated stem when plant is 2.5 m, 3.5 m, 9 m, 10 and 14 m long (blue dots in fig. 10D)

Phloem Sieve Tube Flow Speed (Ust)

Between 2nd and 3rd leaf (arrows in fig. 10C)

When plant is 18 m long

Viscosity (η) Assume constant at 1.7 mPas Assume constant at 1.7 mPas 261

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Results

In the following section, we presented four examples obtained with the CPlantBox-264

PiafMunch. Structurally, we present how CPlantBox can represent a wide variety of plant 265

architectures. Functionally, we evaluated the quality of the water and carbon simulation of a 266

three-leaf-two-root plant under either homogeneous or heterogeneous environments. In the 267

end, we made a quantitative comparison between simulations and experimental data. 268

Example 1: Simulation of contrasted plant architectures with

269

CPlantBox

270

Plants can display a variety of forms and architectures, both above and below ground. [76]. 271

Stem branching patterns are important factors determining the above-ground architecture of 272

plants. fig. 5A shows an example of three branching patterns generated by CPlantBox using 273

different parameter files. A second important determinant of the above-ground architecture 274

is the arrangement of the leaves on the stems. fig. 5B includes three leaf arrangements also 275

created by only changing single input parameter. By combining different branching patterns 276

and leaf arrangements, we extended existing CRootBox outputs [73] into full plant 277

architectures (fig. 6). It is worth mentioning here that each unique structure is obtained 278

solely by changing the input parameter files. The source code itself is not modified. 279

280

Figure 5: A: Simulated stem branching pattern

simulated by CPlantBox; B: leaf arrangements simulated by CPlantBox

281

of g

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Figure 6: Simulated whole plant structures.

Brassica oleracea, Brassica napus, Anagallis femina, Juncus squarrosus, Heliantus and Crypsis aculeata.

282

Example 2: Simulation of water and carbon flow with the coupled

283

model CPlantBox - PiafMunch

284

We created a smaller plant (it has three leaves and two roots) to simulate carbon and water 285

flow (figs. 3C and 3D). The input and output parameters values were collected from various 286

sources from the literature (summarized in Table 3)[77]. The simulated values of xylem 287

pressure, flow rate and hydraulic conductivities are within the range of literature values. For 288

example, xylem can sustain flow under pressure between -2.0 to -8.0 MPa, before losing 50 289

of its conductivity [78]. The simulated xylem water flow rate is typically around 1 ml h-1. 290

291

The transpiration rate on each leaf was set to mimic diurnal flow patterns. We set the 292

transpiration rate to 0.2 mmol h-1 (0.0036 ml h-1) per leaf during daytime (from 5:00 to 17:30) 293

and to 0 at nighttime (from 17:30 to 5:00 the next day). As shown in fig. 7A pressure is 294

decreasing from root to leaf. Xylem flow during the day is caused by transpiration, and the 295

phloem flow going back to xylem caused the xylem flow at night (which are lower than 296

0.0005 ml h-1, can be visible when zoom in fig. 7B). There are water moving from xylem to 297

phloem at the source. According to Münch theory, the carbon loaded into the phloem will 298

reduce water potential, so the water crosses the membrane, moves from xylem to phloem. 299

Therefore, phloem carbon flow rates are affected by the diurnal xylem water flow (fig. 7D). 300

301

The loading rate into the phloem at source location is set to a constant value during both 302

day and night. This is consistent with experimental data [79–81] as starch is degraded at 303

night and the generated sucrose can be loaded into the phloem to sustain the flow. 304

305

50%

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Range

Xylem Resistance rxyl Input 0.011 to 3.3 by

Stem [82] MPa h mL -1 2.08 by Stem 6.9×10-2 by Segment (0.25cm) 0.081 by Stem 0.0005 by Segment (5cm) 0.071 to 0.191 by Stem 0.0005 by Segment (5cm)

Phloem Resistance rphl Input 40 to 90 [33] MPa h mL

-1 70 by segment

(0.25 cm)

Supplement Material I fig. 13

Supplement Material I fig. 13

Transpiration - Input 0 to 1 × 106 m-2 [83,84] mmol h-1 0.2 or diurnal 0.2 0.2 Soil Water Potential - Input -0.2 to -0.8 [8,12] MPa -0.6 -0.6 -0.6

Loading Rate JSloading Input -- mmol h-1 0.0007 on each

source segment

6.4×10-6 on each source segment

6.4×10-6 on each source segment

Unloading Rate JSunloading Input -- mmol h

-1 0.00028 × Cst 1 0.012 × Cst 3 0.012 × Cst 3

Xylem Pressure Pxyl Output -0.2 to -8 [78] MPa 0 to -0.7 0 to -0.7 0 to -0.7

Phloem Pressure Pphl Output 0 to 1.44 [85] MPa 0 to 1.8 0 to 1.4 0 to 1.8

Xylem Water Flow Rate

JWxyl Output 0 to 3.6

[77]

mL h-1 0.20 to 0.62 0 to 1.2 0 to 1.2

Phloem Solut Flow Rate JWst Output -0.02 to 0.02 [31,86] mL h-1 -0.001 to 0.0006 -0.002 to 0.0006 -0.002 to 0.0006 Phloem Carbon Flow Rate JSst Output -- mmol h -1 0 to 0.00022 0 to 0.00022 0 to 0.00022 3

Cst: Carbon contraction in sieve tubes (details in Supplemental material 1, Equation 11).

All rights reserved. No reuse allowed without permission.

The copyright holder for this preprint

.

http://dx.doi.org/10.1101/810507

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307

308 309

Figure 7 A: Transpiration creates xylem pressure gradients during the day, whereas the pressure

310

remains comparatively stable during the night. B: The pressure gradient caused xylem water flow 311

during daytime, the water flow at night is low, it is the water flow from phloem to xylem. C: The water 312

flows from xylem to phloem at source location, whereas it flows from phloem to xylem at sink location. 313

D: Phloem (sieve-tube) carbon flow fluctuations are caused by diurnal xylem water flow, the trend of

314

changing is qualitatively consistent with previous studies [81]; E: Plant structure where the colors 315

correspond to the flow figures from A to D, the dashed line shows the segments between the first and 316

second bottom leaves. The flows going to circled segments are also shown as dashed lines in B and 317

D. The pressure or flow exchanges of the circled segments are shown in A and C. The loading rate

318

inside the phloem at source location is set to constant during both day and night, because starch is 319

degraded to sucrose and then loaded into the phloem at night [79–81]. 320 321 322 323 324 325 r n. f nd d

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Example 3: Simulations of water and carbon flow in response to

326

heterogeneous environments.

327

Heterogeneous environments can have a large impact on plant growth and development. 4D 328

FSPM can be used to simulate and visualize such environmental impact. To observe the effect 329

of heterogeneous soil water availability on the carbon flow within the root system, we manually 330

assigned two different soil water potentials at two root tips (bottom root in blue color with -0.2 331

MPa, upper root in red color with -0.4 MPa in fig. 8A). In fig. 8B, we observe a pressure 332

difference between two roots, which causes hydraulic redistribution at night from the wet to the 333

dry parts of the root system (fig. 8C). During the day, the water flow to the wet part is larger than 334

the flow to the root in the dry soil. We also observed that the carbon concentration in the high 335

water potential root is lower (red line in fig. 8D). In fig. 8F, we can see that total carbon flow in 336

wet root is lower than the flow in the dry root. 337

338

Different temperature or developmental stages can also cause heterogeneous leaf transpiration 339

rate. We assigned the 0.3 mmol h-1 (0.0054 ml h-1) transpiration on the top left leaf (higher 340

transpiration leaf in fig. 9A with red color), 0.2 mmol h-1 (0.0036 ml h-1)transpiration on the right 341

leaf (middle transpiration leaf in fig. 9A with green color), 0.1 mmol h-1 (0.0018 ml h-1) 342

transpiration on the bottom left leaf (lower transpiration leaf in fig. 9A with blue color). In fig. 9B 343

and C we can observe the pressure and flow gradient of three leaves at different transpiration 344

rate. In fig. 9D and 9E, we can observe that carbon concentrations are different, but flows are 345

slightly different between the different leaves as loading rate is kept constant. In fig. 9F, we can 346

see that, when transpiration changes between day and night, the carbon flow in high 347

transpiration leaf is more sensitive to the changes. However, the total carbon flow did not 348

change significantly. In this example we keep the loading and unloading speed homogeneous 349

and constant. It is because physiologically the starch degradation will compensate a temporal 350

loss on the leaf level, just the same as the night carbon loading. Of course, the carbon loading 351

will decrease in the long term, but it might not take effect in a few days. 352

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354 355 356

Figure 8. A: Soil water potential around the lower root (blue color) is higher than the upper root (red

357

color). B: Pressure values at the boundary location are different according to the higher or lower soil 358

water potential C: The bottom root (blue color, in wet soil) xylem, has higher water flow. The flow rate in 359

upper root (red color) is negative at night. it means that, at night the water is coming out from the upper 360

root to the soil, which is also called the hydraulic redistribution (in other words, the plant root system 361

behaves as a pathway for water flow from wet to dry (or salty) soil areas). D: Carbon concentration in the 362

dry (upper) root is higher than the wet root. E: Water flows from xylem to phloem at sink location only in 363

the wet root (blue line) shortly at the beginning, then water flows from phloem to xylem in both roots at a 364

similar rate. F: Carbon flow decreased in the high water potential (lower) root phloem. 365

366

e a

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367 368

Figure 9. A: The lower left leaf (in blue) has lower transpiration rate and the top left leaf (in red) has

369

higher transpiration rate. B: The pressure in each leaf is changed according to their transpiration rate. C: 370

The water flow in each leaf is changed according to the transpiration rate. D: Carbon concentration on the 371

higher transpiration leaf (red line) is higher. B: Water going from xylem to phloem at source location is 372

lower at the higher transpiration leaf (red line). F: Carbon flow rates are the same at steady status, leave 373

with higher water transpiration (red line) are more sensitive to the changes. 374

:

he e

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Example 4: Comparison between experimental and simulated

375

water and carbon flow in morning glory

376

To assess whether CPlantBox-PiafMunch was able to simulate realistic carbon and water 377

flow values, we simulated experiments conducted with morning glory [33]. Three simulations 378

were performed: 379

1. Fitting parameters to measurements in literature (fig. 10 A, B, C, Table 2) : firstly we 380

reproduced the plant structure based on schematic drawing. Then, we assigned the 381

physiological parameters (phloem resistance) and used the estimated loading and 382

unloading rate to fit the pressure and flow rate measured in phloem (fig. 4 and fig. 10C 383

by method in Supplemental material 1, Table 4). In this case, we assumed that all leaves 384

have homogeneous loading (which is also implicitly assumed in the experiment). 385

Testing fitted parameters (fig. 10 D): we validated the loading and unloading rate on 386

the 5 structures of the defoliated plant. The pressure matched the measurements. 387

2. Conceptual experiment with individual loading/unloading on leaves (fig. 11 A, B, C, 388

D): The individual measured pressures are not consistent with the simulated pressure on 389

each leaf, this could be a result of plant growth during the measurement or 390

heterogeneous loading/unloading speed. Here we gave one possible example of the 391

impact of heterogeneous loading/unloading speed on individual leaves. 392

393

4.1 Predicting carbon loading and unloading for contrasted morning glory

394

shoot architectures.

395

In order to simulate Knoblauch et al.’s experimental results on the morning glory, we created 396

six virtual plants with contrasted architectures, based on the idealized schematics of the 397

original paper. As described in Table 2, the reference plant was 7.5 meters long, with 12 398

homogeneously distributed leaves and one shoot tip(fig. 10A). The defoliated plants each 399

had four leaves and one shoot tip near the apex of the stem, with different length for the 400

defoliated section (fig.10B). 401

402

Regarding the physiological parameterization for the carbon and water flow simulation, in 403

both the experiments and the modelling exercise, the morning glory was simplified to 1-404

source-1-sink system. Therefore, we assumed that the 12 leaves and the shoot tip are all 405

homogeneous sources with the same carbon loading rate. The carbon unloading rates in the 406

sinks were also considered homogeneous. Thus, we could create a 1-source-1-sink 407

scenario as shown in fig. 10C, where the higher red dashed line box is the source and lower 408

black dashed line box is the sink. 409

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411

Figure 10: Steps of comparison between simulations and experiments. A: one in silico plant structure

412

is created based on schematic drawing of the 7.5 m plant (resistance fitting can be found on 413

Supplemental material 1, fig. 13). B: five in silico plant structures are created based on schematic 414

drawing of defoliated plant. C: In phloem, physiological parameters such as source average pressure 415

and sieve tube flow rate are fitted by applying homogeneous loading rate on each leaf, and 416

homogeneous unloading rate at each root tip. Detailed parameters can be found in Table 2. D: By 417

applying the fitted unloading rate and loading rate on 5 in silico plants, simulated pressure values 418

match the measured values in experiment. 419

420 421

As shown in fig. 10C, we used the measured pressure and measured flow rate to find our 422

initial input parameters, in particular the carbon loading and unloading rate. We estimated 423

the corresponding loading and unloading rate using a looped least square fitting (lower part 424

of fig. 10C, details are in Supplemental material 1, Table 4). 425

426

The carbon loading and unloading rate estimated on the 7.5-meter plant were then applied 427

on the defoliated plants directly (Table 2 and fig. 10D). None of the parameters used in 7.5 428

m plant simulation were modified except the plant structure (fig. 10B). As shown in fig. 10D, 429

we could see that the simulated pressure values in the sieve tubes were in good agreement 430

with the experimental values. 431

432

re

re

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4.2 Studying source-sink relations at the organ level.

433 434

In the previous section, the plant architecture was simplified to a 1-source-1-sink structure 435

(fig. 10C), as in the experimental data analysis. In addition, we wondered if the model would 436

be able to simulate the detailed relationship between different leaves inside the single 437

source. It should be noticed that, as the large variance between the leaves might be caused 438

by experimental variations, such detailed fitting might not be biologically relevant. However, 439

it remains an interesting conceptual exercise, to test the flexibility and capabilities of our 440 models. 441 442 443

A

B

Figure. 11 Comparison of simulations with (A) equal loading rate on all leaves to fit average pressure and

444

(B) individual loading / unloading fitted pressure on each single leaf; A: Result for using homogeneous 445

loading rate on each leaf; B: Fitted individual loading and unloading rate on each leaf; C: Flows are all 446

heading to root when all leaves are sources with same loading rate (the scenario we used for parameter 447

fitting); D: Flows directions changed (in red color) when the individual leave pressure are fitted (it is only 448

one of the possible solutions, to show that we could change loading/unloading value on each source). 449

450

First, we reused the calibration obtained on the 7.5 m plant (figs. 10 A and C). As shown in 451

fig. 11A, it is obvious that the simulated pressure in each single leave does not fit the 452 ld d nd r ly

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measured pressure. Therefore, we fitted each single leaf pressure by assigning independent 453

carbon loading and unloading rate. We can observe that, when we reached a good fit on fig. 454

11B, the flow direction changed significantly compared to the flow when fitting the 455

parameters globally (lower line plot of fig. 10C). Indeed, with the individual fitting, some 456

leaves become carbon sinks instead of carbon sources. In fig. 11D the red arrows indicate a 457

change on the carbon flow directions compared to the 1-source-1-sink scenario, as well 458

changes in the total carbon loading (fig. 11C). 459

460

Discussions

CPlantBox generates full plant architectures

462

Historically, root and shoot models have been developed independently. Most models 463

indeed focus on either part of the plant, representing the other one as a boundary condition. 464

Some existing models are able to simulate both root and shoot, but for specific plant species 465

[54,57,58,61,69]. Here, we presented CPlantBox, the first model, to our knowledge, able to 466

represent both root and shoot, as a single network, for a variety of plant species (see 467

example 1 in the Results section, and figs. 5 and 6). 468

469

CPlantBox was designed to be flexible and amenable for multiple plant studies. For the root 470

part, CPlantBox inherited the flexibility of the model it was built upon, CRootBox. As 471

CRootBox is able to generate any type of root architecture, so is CPlantBox. For the shoot 472

part, we implemented several branching and leaf arrangement patterns. By combining these 473

patterns, many types of shoot architectures can be simulated. Both root and shoot 474

architectural parameters are defined into the model parameter file, making it easy to setup 475

and reproduce. 476

CPlantBox-PiafMunch simulates water and carbon flow in the full

477

plant

478 479

We combined CPlantBox with a mechanistic phloem and xylem model, PiafMunch [61]. The 480

coupled model allowed us to simulate water and carbon flow within complex full plant 481

architectures, which was not possible before. In the results section, we demonstrated four 482

examples. Example 1 is focusing on structures, while example 2 focuses on diurnal 483

carbon/water flow compared to literature measurements. Example 3 shows that the 484

combinations of structures and functions could reproduce literature experiments qualitatively. 485

Example 4 firstly reproduce the experimental results then use conceptual experiments to 486

prove that the heterogeneous environments (in Example 3) is helpful to explain experimental 487

results. 488

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In our simulation, we could observe a strong interplay between xylem and phloem flows. 490

The diurnal transpiration patterns (the high peak in fluxes in the morning and the sharp 491

decline when the light was stopped followed by an increase in flux during night) (fig. 7), 492

consistent with previous experiment and modelling [81]. The low water potential in the xylem 493

vessels during the day (as a result of the high transpiration rate) limits the water movement 494

toward the phloem. During the night, as the stomata closes, the xylem water potential 495

increases, leading to a higher water flow toward the phloem sieve tubes and a higher flow of 496

carbon throughout the whole plant (fig. 7D). However, the higher night carbon flow might be 497

caused by constant loading rate, whereas in some cases, the loading rate at night is 498

reduced to 60% of the day value [87], so that the overall carbon flow may not be increased. 499

In turn, the water flow from the xylem to the phloem induced a small upward water flow 500

during the night, even in the absence of transpiration flux (fig. 7B). These results from our 501

coupled models are comparable to previous published modelling results [61,66,88] and are 502

consistent with experimental data (see Table 2 for details) [89]. 503

CPlantBox-PiafMunch considers the impact of heterogeneous

504

environments

505 506

One of the main advantages of functional-structural plant models is their ability to explicitly 507

consider the influence of heterogeneous environments (in space and time). In our third 508

example, we used our coupled CPlantBox-PiafMunch modelling framework to simulate the 509

influence of heterogeneous soil and atmospheric conditions on the carbon and water flows 510

in the plant. 511

512

First, we imposed different soil water potentials to the different roots of our plant (fig. 8A). In 513

response to this heterogeneity, we could make two main observations. Firstly, root water 514

potential and water flow (fig. 8B, 8C) was directly influenced by the soil water potential. As 515

the soil water potential decreases, the water flow in the xylem decreases. This is a well-516

known effect, observed both in vivo [90,91] and in silico [23,92]. Secondly, we observed that 517

the carbon flow (fig. 8F) in the phloem was inversely correlated with the soil water potential. 518

Indeed, our simulation results show that carbon flow is slightly higher in the portion of the 519

root system in contact with a dry soil (red line in fig. 8F). This is due to the lower carbon 520

concentration of root phloem in wet soil (blue line in fig. 8D). The lower carbon concentration 521

in wet root phloem (blue line in fig. 8D) is a result of dilution by water from wet root xylem to 522

wet root phloem along the root until the root tip (like tap root in light yellow color). At the root 523

tip, the unloading rate is proportional to the carbon concentration. Thus, the flow rates of two 524

split root are similar. Because the flow rates are similar, but concentration is lower in the wet 525

root, the total carbon flow is lower in the wet root (fig. 8F). Again, this dynamic was observed 526

experimentally for several plant species in split root experiment [93–95]. 527

528

To simulate heterogeneous atmospheric environment, we imposed different transpiration 529

rates to the different leaves of our plant (fig. 9A). Like water potential change at the sink 530

location, the transpiration rate at the source location directly induced changes of xylem 531

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pressure (fig. 9B) and xylem water flow rate (fig. 9C). Heterogeneous transpiration rates on 532

leaves are also observed in vivo and simulated in silico [96,97]. In fig. 9D, we could observe 533

that the carbon concentration in phloem is increased, because in fig. 9E we could observe 534

that in the high transpiration leaf (red line), less water is moving from xylem to phloem. This 535

is because the water potential increases (red line in fig. 9B) and pressure drops (red line in 536

fig 9A) in the high water potential leave. Thus, the final phloem carbon flow rate did not 537

change at steady state (lines are aggregating in fig. 9F) 538

Limitations of the model and future perspectives

539

In this paper we highlighted some of the capabilities of our new coupled model CPlantBox-540

PiafMunch. We have shown that we can simulate realistic water and carbon flow within a full 541

plant structure. However, it is important to stress the current limitations and future 542

developments of our model. 543

544

Firstly, all the simulations were done with static plants. At this stage, we did not explore the 545

impact of the carbon distribution on the growth and development of the plant. In the future, 546

we will explicitly connect the growth function in CPlantBox to the local carbon availability as 547

prescribed by PiafMunch. 548

549

Secondly, in the presented simulations, the environment was static as well. In order to 550

explore only the resolution of carbon and water within the plant, we did not connect our 551

models to dynamic representations of the environment. Again, this will be done in the future, 552

as we plan to integrate CPlantBox into the modeling framework DuMuX [98]. By doing so, 553

we will be able to explore the feedbacks between the plant, the soil and the environment. 554

555

Finally, in the version of the models, carbon production is prescribed at the article level. 556

Again, this what not an issue so far, as we wanted to explore the flow distribution only. 557

However, in the near future, we plan to include leaf-level photosynthesis module [99,100], to 558

be able to better represent the dynamic response of the plant to its changing environment. 559

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Conclusions

Models can be used as analysis tools for complex experimental setups. Experimental 562

measurements of carbon and water flow can be challenging. Most available measuring 563

methods are time consuming and destructive [33,44], preventing the continuous observation 564

of these flow as the plant develops. 565

566

Here we have used our coupled models to reverse estimate hidden experimental 567

parameters. For instance, by using measured carbon flow, phloem resistance and phloem 568

pressure, we were able to give consistent estimates of carbon loading and unloading rate in 569

the phloem, in the different plant organs. 570

571

More generally, this is a good example of using models as complex analysis tools. As 572

experimental setup and biological questions become more and more complex, it becomes 573

harder to interpret the results. Models such as CPlantBox-PiafMunch can help integrate 574

such results and replace them into a whole plant perspective. Carefully using the model can 575

then give access to additional parameters that were not available experimentally. 576

577

Exploring the interplay between the environment, the plant architecture, and the plant water 578

and carbon flow is experimentally challenging. Measurements take time and are often 579

destructive. However, functional structural plant models have been shown to be able to 580

efficiently represent plant-environment interplay in silico. 581

582

Here we have presented a new whole plant framework, CPlantBox. We have shown that 583

CPlantBox is able to represent a variety of plant architectures, both root and shoot. We also 584

connected CPlantBox to a mechanistic model carbon and water flow, PiafMunch. The 585

coupled model was able to reproduce realistic flow behavior in complex plant structures. We 586

were also able to use the models to reproduce experimental data and estimate hidden 587

experimental variables. 588

589

In the future, the model will be extended to more realistic growth behaviours, environmental 590

changes and photosynthesis dynamics. 591

592

Model and data availability

593

- CPlantBox is open source under GPL 3.0 license, available at https://github.com/Plant-594

Root-Soil-Interactions-Modelling/CPlantBox/tree/master/ and 595

http://doi.org/10.5281/zenodo.3518068 596

- Model parameter files are available at: http://doi.org/10.6084/m9.figshare.9785396 597

- PiafMunch output of simulation example 2, 3, 4 can be found here: 598

https://figshare.com/articles/Output_of_CPlantBox-PiafMunch_coupling/9971225 599

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Acknowledgements

600

We would also like to show our gratitude to Xavier Draye, Mathieu Javaus, Michael 601

Knoblauch, Clément Saint Cast for sharing their pearls of wisdom with us during this 602 research. 603 604

Authors contributions

Writing – original draft: XRZ, GL; Writing – review & editing: JV, AL, HV, GL, XRZ; 606

Conceptualization: GL, AS, HV, JV, XRZ; Software: XRZ, DL, AL, AS, GL; Visualization: 607 XRZ, GL, JV 608 609 610 611

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References

613

1. Bar-On YM, Phillips R, Milo R. The biomass distribution on Earth. Proc Natl Acad Sci U S 614

A. 2018;115: 6506–6511. 615

2. Trenberth KE, Smith L, Qian T, Dai A, Fasullo J. Estimates of the Global Water Budget and 616

Its Annual Cycle Using Observational and Model Data. J Hydrometeorol. 2007;8: 758–769. 617

3. Jasechko S, Sharp ZD, Gibson JJ, Birks SJ, Yi Y, Fawcett PJ. Terrestrial water fluxes 618

dominated by transpiration. Nature. 2013;496: 347–350. 619

4. Vereecken H, Huisman J-A, Franssen HJH, Brüggemann N, Bogena HR, Kollet S, et al. 620

Soil hydrology: Recent methodological advances, challenges, and perspectives. Water 621

Resour Res. 2015;51: 2616–2633. 622

5. Metz B, Davidson O, De Coninck H, Loos M, Meyer L. IPCC special report on carbon 623

dioxide capture and storage. Intergovernmental Panel on Climate Change, Geneva 624

(Switzerland). Working …; 2005. Available: https://www.osti.gov/biblio/20740954 625

6. Ayllón D, Grimm V, Attinger S, Hauhs M, Simmer C, Vereecken H, et al. Cross-disciplinary 626

links in environmental systems science: Current state and claimed needs identified in a 627

meta-review of process models. Sci Total Environ. 2018;622-623: 954–973. 628

7. Bidel L, Pages L, Riviere LM, Pelloux G, Lorendeau JY. MassFlowDyn I: a carbon transport 629

and partitioning model for root system architecture. Ann Bot. 2000;85: 869–886. 630

8. Draye X, Kim Y, Lobet G, Javaux M. Model-assisted integration of physiological and 631

environmental constraints affecting the dynamic and spatial patterns of root water uptake 632

from soils. J Exp Bot. 2010;61: 2145–2155. 633

9. Fiorani F, Schurr U. Future scenarios for plant phenotyping. Annu Rev Plant Biol. 2013;64: 634

267–291. 635

10. Lobet G, Hachez C, Chaumont F, Javaux M, Draye X. Root water uptake and water flow in 636

the soil-root domain. 2013. Available: 637 https://dial.uclouvain.be/downloader/downloader.php?pid=boreal:120731&datastream=PDF 638 _02&disclaimer=39a424961eea8028479841d8a268bfdad08f7f69c4b7c5dcfc29b9fdbef41d 639 43 640

11. Lynch JP. Steep, cheap and deep: an ideotype to optimize water and N acquisition by 641

maize root systems. Ann Bot. 2013;112: 347–357. 642

12. Lobet G, Couvreur V, Meunier F, Javaux M, Draye X. Plant water uptake in drying soils. 643

Plant Physiol. 2014;164: 1619–1627. 644

13. Lichtenthaler HK, Buschmann C, Döll M, Fietz HJ, Bach T, Kozel U, et al. Photosynthetic 645

activity, chloroplast ultrastructure, and leaf characteristics of high-light and low-light plants 646

and of sun and shade leaves. Photosynth Res. 1981;2: 115–141. 647

14. Boardman NK. Comparative Photosynthesis of Sun and Shade Plants. Annu Rev Plant 648

Version preprint

Physiol. 1977;28: 355–377. 649

15. Zhu X-G, Long SP, Ort DR. Improving photosynthetic efficiency for greater yield. Annu Rev 650

Plant Biol. 2010;61: 235–261. 651

16. Fatichi S, Pappas C, Zscheischler J, Leuzinger S. Modelling carbon sources and sinks in 652

terrestrial vegetation. New Phytol. 2019;221: 652–668. 653

17. Hummel I, Pantin F, Sulpice R, Piques M, Rolland G, Dauzat M, et al. Arabidopsis plants 654

acclimate to water deficit at low cost through changes of carbon usage: an integrated 655

perspective using growth, metabolite, enzyme, and gene expression analysis. Plant 656

Physiol. 2010;154: 357–372. 657

18. Tuzet A, Perrier A, Leuning R. A coupled model of stomatal conductance, photosynthesis 658

and transpiration. Plant Cell Environ. 2003;26: 1097–1116. 659

19. De Schepper V, Steppe K. Development and verification of a water and sugar transport 660

model using measured stem diameter variations. J Exp Bot. 2010;61: 2083–2099. 661

20. Jyske T, Hölttä T. Comparison of phloem and xylem hydraulic architecture in Picea abies 662

stems. New Phytol. 2015;205: 102–115. 663

21. Savage JA, Clearwater MJ, Haines DF, Klein T, Mencuccini M, Sevanto S, et al. Allocation, 664

stress tolerance and carbon transport in plants: how does phloem physiology affect plant 665

ecology? Plant Cell Environ. 2016;39: 709–725. 666

22. Schröder T, Javaux M, Vanderborght J, Körfgen B, Vereecken H. Effect of Local Soil 667

Hydraulic Conductivity Drop Using a Three-Dimensional Root Water Uptake Model. Vadose 668

Zone J. 2008;7: 1089–1098. 669

23. Javaux M, Schroeder T, Vanderborght J, Vereecken H. Use of a three-dimensional detailed 670

modeling approach for predicting root water uptake. Vadose Zone J. 2008;7: 1079–1088. 671

24. Van Bel AJE. The phloem, a miracle of ingenuity. Plant Cell Environ. 2003;26: 125–149. 672

25. De Swaef T, De Schepper V, Vandegehuchte MW, Steppe K. Stem diameter variations as 673

a versatile research tool in ecophysiology. Tree Physiol. 2015;35: 1047–1061. 674

26. Savage JA, Zwieniecki MA, Holbrook NM. Phloem transport velocity varies over time and 675

among vascular bundles during early cucumber seedling development. Plant Physiol. 676

2013;163: 1409–1418. 677

27. Steudle E. THE COHESION-TENSION MECHANISM AND THE ACQUISITION OF 678

WATER BY PLANT ROOTS. Annu Rev Plant Physiol Plant Mol Biol. 2001;52: 847–875. 679

28. Tyree MT. The Cohesion-Tension theory of sap ascent: current controversies. J Exp Bot. 680

1997;48: 1753–1765. 681

29. Münch E, b. Stoffbewegungen in der Pflanze. 1930. Available: http://agris.fao.org/agris-682

search/search.do?recordID=US201300422975 683

30. Knoblauch M, Peters WS. What actually is the Münch hypothesis? A short history of 684

assimilate transport by mass flow. J Integr Plant Biol. 2017;59: 292–310. 685

Version preprint

31. Comtet J, Jensen KH, Turgeon R, Stroock AD, Hosoi AE. Passive phloem loading and 686

long-distance transport in a synthetic tree-on-a-chip. Nat Plants. 2017;3: 17032. 687

32. Jensen KH, Mullendore DL, Holbrook NM, Bohr T, Knoblauch M, Bruus H. Modeling the 688

hydrodynamics of Phloem sieve plates. Front Plant Sci. 2012;3: 151. 689

33. Knoblauch M, Knoblauch J, Mullendore DL, Savage JA, Babst BA, Beecher SD, et al. 690

Testing the Münch hypothesis of long distance phloem transport in plants. Elife. 2016;5. 691

doi:10.7554/eLife.15341 692

34. Savage JA, Beecher SD, Clerx L, Gersony JT, Knoblauch J, Losada JM, et al. Maintenance 693

of carbohydrate transport in tall trees. Nat Plants. 2017;3: 965–972. 694

35. Yong ZHANG NZ. Imaging technologies for plant high-throughput phenotyping: a review. 695

Front Agr Sci Eng. 2018;5: 406–419. 696

36. Lobet G, Paez-Garcia A, Schneider H, Junker A, Atkinson JA, Tracy S. Demystifying roots: 697

A need for clarification and extended concepts in root phenotyping. Plant Sci. 2019;282: 698

11–13. 699

37. Hui F, Zhu J, Hu P, Meng L, Zhu B, Guo Y, et al. Image-based dynamic quantification and 700

high-accuracy 3D evaluation of canopy structure of plant populations. Ann Bot. 2018;121: 701

1079–1088. 702

38. van Dusschoten D, Metzner R, Kochs J, Postma JA, Pflugfelder D, Bühler J, et al. 703

Quantitative 3D Analysis of Plant Roots Growing in Soil Using Magnetic Resonance 704

Imaging. Plant Physiol. 2016;170: 1176–1188. 705

39. Fiorani F, Rascher U, Jahnke S, Schurr U. Imaging plants dynamics in heterogenic 706

environments. Curr Opin Biotechnol. 2012;23: 227–235. 707

40. Rellán-Álvarez R, Lobet G, Lindner H, Pradier P-L, Sebastian J, Yee M-C, et al. GLO-708

Roots: an imaging platform enabling multidimensional characterization of soil-grown root 709

systems. Elife. 2015;4. doi:10.7554/eLife.07597 710

41. Lobet G, Draye X. Novel scanning procedure enabling the vectorization of entire rhizotron-711

grown root systems. Plant Methods. 2013;9: 1. 712

42. Rellán-Álvarez R, Lobet G, Dinneny JR. Environmental Control of Root System Biology. 713

Annu Rev Plant Biol. 2016;67: 619–642. 714

43. Marshall-Colon A, Long SP, Allen DK, Allen G, Beard DA, Benes B, et al. Crops In Silico: 715

Generating Virtual Crops Using an Integrative and Multi-scale Modeling Platform. Front 716

Plant Sci. 2017;8: 786. 717

44. Knoblauch J, Mullendore DL, Jensen KH, Knoblauch M. Pico gauges for minimally invasive 718

intracellular hydrostatic pressure measurements. Plant Physiol. 2014;166: 1271–1279. 719

45. Thompson MV, Wolniak SM. A plasma membrane-anchored fluorescent protein fusion 720

illuminates sieve element plasma membranes in Arabidopsis and tobacco. Plant Physiol. 721

2008;146: 1599–1610. 722

46. Mullendore DL, Windt CW, Van As H, Knoblauch M. Sieve tube geometry in relation to 723

Version preprint

phloem flow. Plant Cell. 2010;22: 579–593. 724

47. Mencuccini M, Manzoni S, Christoffersen B. Modelling water fluxes in plants: from tissues 725

to biosphere. New Phytol. 2019;222: 1207–1222. 726

48. De Reffye P, Hu B-G. Relevant qualitative and quantitative choices for building an efficient 727

dynamic plant growth model: GreenLab case. International Symposium on Plant Growth 728

Modeling, Simulation, Visualization and their Applications-PMA’03. Springer and Tsinghua 729

University Press; 2003. pp. 87–107. 730

49. Pradal C, Dufour-Kowalski S, Boudon F, Fournier C, Godin C. OpenAlea: a visual 731

programming and component-based software platform for plant modelling. Funct Plant Biol. 732

2008;35: 751–760. 733

50. Kang MZ, Cournède PH, de Reffye P, Auclair D, Hu BG. Analytical study of a stochastic 734

plant growth model: Application to the GreenLab model. Math Comput Simul. 2008;78: 57– 735

75. 736

51. Leitner D, Klepsch S, Bodner G, Schnepf A. A dynamic root system growth model based on 737

L-Systems. Plant Soil. 2010;332: 177–192. 738

52. Vos J, Evers JB, Buck-Sorlin GH, Andrieu B, Chelle M, de Visser PHB. Functional-739

structural plant modelling: a new versatile tool in crop science. J Exp Bot. 2010;61: 2101– 740

2115. 741

53. Xu L, Henke M, Zhu J, Kurth W, Buck-Sorlin G. A functional–structural model of rice linking 742

quantitative genetic information with morphological development and physiological 743

processes. Ann Bot. 2011;107: 817–828. 744

54. Lobet G, Pagès L, Draye X. A modeling approach to determine the importance of dynamic 745

regulation of plant hydraulic conductivities on the water uptake dynamics in the soil-plant-746

atmosphere system. Ecol Modell. 2014;290: 65–75. 747

55. Sievänen R, Godin C, DeJong TM, Nikinmaa E. Functional-structural plant models: a 748

growing paradigm for plant studies. Ann Bot. 2014;114: 599–603. 749

56. Zhu X-G, Lynch JP, LeBauer DS, Millar AJ, Stitt M, Long SP. Plants in silico: why, why now 750

and what?—an integrative platform for plant systems biology research. Plant Cell Environ. 751

2016;39: 1049–1057. 752

57. Drouet J-L, Pagès L. GRAAL: a model of GRowth, Architecture and carbon ALlocation 753

during the vegetative phase of the whole maize plant: model description and 754

parameterisation. Ecol Modell. 2003;165: 147–173. 755

58. Janott M, Gayler S, Gessler A, Javaux M, Klier C, Priesack E. A one-dimensional model of 756

water flow in soil-plant systems based on plant architecture. Plant and Soil. 2011. pp. 233– 757

256. doi:10.1007/s11104-010-0639-0 758

59. Lobet G, Pagès L, Draye X. A modeling approach to determine the contribution of plant 759

hydraulic conductivities on the water uptake dynamics in the soil-plant-atmosphere system. 760

2012 IEEE 4th International Symposium on Plant Growth Modeling, Simulation, 761

Visualization and Applications. 2012. pp. 235–241. 762

Version preprint

60. Seleznyova AN, Hanan J. Mechanistic modelling of coupled phloem/xylem transport for L-763

systems: combining analytical and computational methods. Ann Bot. 2018 [cited 5 Feb 764

2018]. doi:10.1093/aob/mcx204 765

61. Lacointe A, Minchin PEH. Modelling phloem and xylem transport within a complex 766

architecture. Funct Plant Biol. 2008;35: 772–780. 767

62. Heuvelink E. Dry Matter Partitioning in Tomato: Validation of a Dynamic Simulation Model. 768

Ann Bot. 1996;77: 71–80. 769

63. Marcelis LFM. Sink strength as a determinant of dry matter partitioning in the whole plant. J 770

Exp Bot. 1996;47: 1281–1291. 771

64. Steppe K, Sterck F, Deslauriers A. Diel growth dynamics in tree stems: linking anatomy and 772

ecophysiology. Trends Plant Sci. 2015;20: 335–343. 773

65. Lopez G, Favreau RR, Smith C, Costes E, Prusinkiewicz P, DeJong TM. Integrating 774

simulation of architectural development and source--sink behaviour of peach trees by 775

incorporating Markov chains and physiological organ function submodels into L-PEACH. 776

Funct Plant Biol. 2008;35: 761–771. 777

66. Minchin PEH, Lacointe A. Consequences of phloem pathway unloading/reloading on 778

equilibrium flows between source and sink: a modelling approach. Funct Plant Biol. 779

2017;44: 507–514. 780

67. Hu B-G, De Reffye P, Zhao X, Yan H-P, Kang MZ. Greenlab: A new methodology towards 781

plant functional-structural model--structural part. Plant growth modelling and applications. 782

TsingHua University Press and Springer; 2003. pp. 21–35. 783

68. Kang M, Hua J, de Reffye P, Jaeger M. Parameter identification of plant growth models 784

with stochastic development. 2016 IEEE International Conference on Functional-Structural 785

Plant Growth Modeling, Simulation, Visualization and Applications (FSPMA). 2016. pp. 98– 786

105. 787

69. Da Silva D, Qin L, DeBuse C, DeJong TM. Measuring and modelling seasonal patterns of 788

carbohydrate storage and mobilization in the trunks and root crowns of peach trees. Ann 789

Bot. 2014;114: 643–652. 790

70. Barczi J-F, Rey H, Caraglio Y, de Reffye P, Barthélémy D, Dong QX, et al. AmapSim: a 791

structural whole-plant simulator based on botanical knowledge and designed to host 792

external functional models. Ann Bot. 2008;101: 1125–1138. 793

71. Barillot R, Chambon C, Andrieu B. CN-Wheat, a functional–structural model of carbon and 794

nitrogen metabolism in wheat culms after anthesis. I. Model description. Annals of Botany. 795

2016. pp. 997–1013. doi:10.1093/aob/mcw143 796

72. Barillot R, Chambon C, Andrieu B. CN-Wheat, a functional–structural model of carbon and 797

nitrogen metabolism in wheat culms after anthesis. II. Model evaluation. Annals of Botany. 798

2016. pp. 1015–1031. doi:10.1093/aob/mcw144 799

73. Schnepf A, Leitner D, Landl M, Lobet G, Mai TH, Morandage S, et al. CRootBox: a 800

structural–functional modelling framework for root systems. Ann Bot. 2018;121: 1033–1053. 801