Methods and models



A mechanistic model of phloem sap transfer to predict distribution of carbon among multiple sinks


The model PiafMunch was designed to simulate the dynamics of photoassimilate transport and partitioning among different sink organs within complex plant architectures. It is based on a discretized representation of the vascular system, including both xylem and phloem pathways which are interconnected. At network nodes, sieve-tube cross-membrane solute and water fluxes are driven by biophysical membrane properties and local solute availability in relation to local metabolism (Fig. 1). According to the Münch model (Fig. 2), this generates solute gradients within the phloem system, which in turn generate pressure gradients driving long distance transfers. More details are given in Lacointe and Minchin (2019).


Figure 1 : Discretization of architecture



Figure 2 : The Münch model (1928)


Originally designed as a Spice™ application (Daudet et al., 2002), PiafMunch (v.2) is presently (Lacointe and Minchin, 2019) a semi-compiled C++ application that provides the modeler with great flexibility to design both the architectural patterns and physiological details of pathways, sinks/sources and boundary conditions, including user-defined dynamic changes in those parameters or conditions. The differential, generally non-linear, equations describing the model are then solved using state-of-the-art algorithms, involving both sparse linear and non-linear solvers. The model has been validated on an experimental system using 11C labelling (Thorpe et al., 2011).


Figure 3 : The PiafMunch user interface. This simulation example shows the dynamics of phloem solute concentration in a theoretical sieve tube with constant loading at one end end and concentration-dependent unloading at the other end, with a temporary, local sharp change in phloem resistance at t = 50 hrs.


The PiafMunch model has been applied to different theoretical systems, e.g. to investigate the effect of water status, as affected by transpiration, on carbon allocation among sinks (Fig. 4), or the impact of local unloading/reloading along the pathway on long distance transport (Minchin and Lacointe, 2017). It has been included as the partitioning module in the functional-structural plant model CPlantBox (Zhou et al. 2018).


Figure 4 : Effect of transpiration rate on assimilate partitioning among 2 michaelian sinks of equal maximum import rate (Vmax) but differing in affinity (kM) (Lacointe and Minchin, 2008)

Contact :


Key references :

Giraud M. et al. (2023) CPlantBox: a fully coupled modelling platform for the water and carbon fluxes in the soil–plant–atmosphere continuum, in silico Plants, vol. 5, Issue 2. DOI:

Zhou X.-R., Schnepf A., Vanderborght J., Leitner D., Lacointe A., Vereecken H., Lobet G. (2020) CPlantBox, a whole-plant modelling framework for the simulation of water- and carbon-related processes. in silico Plants, vol. 2. DOI:

Lacointe, A, Minchin, P.E.H. (2019). A mechanistic model to predict distribution of carbon among multiple sinks. In : Liesche, J. (ed), Phloem : Methods and Protocols (chapter 28), Methods in Molecular Biology, vol. 2014, Berlin, DEU, Springer, DOI :

References cited :

Münch, E. (1928). Versuche über den Saftkreislauf. Deutsche botanische Gesellschaft 45, 340-356

Minchin, P., Lacointe, A. (2017). Consequences of phloem pathway unloading/reloading on equilibrium flows between source and sink: a modelling approach. Functional Plant Biology, 44 (5), 507-514. , DOI : 10.1071/fp16354.

Thorpe, M., Lacointe, A., Minchin, P. (2011). Modelling phloem transport within a pruned dwarf bean: a 2-source-3-sink system. Functional Plant Biology, 38 (2), 127-138. , DOI : 10.1071/FP10156.

Lacointe, A., Minchin, P. (2008). Modelling phloem and xylem transport within a complex architecture. Functional Plant Biology, 35 (10), 772-780. , DOI : 10.1071/FP08085.

Daudet, F.A., Lacointe, A., Gaudillère, J.P., Cruiziat, P. (2002). Generalized Münch coupling between sugar and water fluxes for modelling carbon allocation as affected by water status. Journal of Theoretical Biology, 214, 481-498.

Zhou X., Lacointe A., Leitner D., Lobet G., Schnepf A., Vanderborght J., Vereecken H. (2018). Presentation of CPlantBox: a whole functional-structural plant model (root and shoot) coupled with a mechanistic resolution of carbon and water flows. Presented at 6th International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications - PMA2018, Hefei (Chine), CHN. CHN : PMA2018. A0.

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Modification date : 01 December 2023 | Publication date : 13 May 2019 | Redactor : D.Marcon