Sap Flow in Plants

Osmotically driven flows in plants and microfluidic devices

The carbon needed for growth of plants is produced in the form of sugars by photosynthesis in the leaves. It is then transported in the sieve cells, which in trees run in the innermost layer of the bark, the so-called phloem, from the leaves to the new shoots and fruits and all the way down to the roots. According to the Münch hypothesis from the 30’ies, this transport is driven by osmotic pressure differences due to the differences in sugar concentrations between the sources (leaves) to the sinks, where sugar is consumed. The relevant sugar concentrations and the corresponding pressures are hard to measure on living trees and so-far the Münch hypothesis has only been indirectly tested. It remains an outstanding problem in plant physiology to what extent the Münch mechanism can account for long distance sugar transport in trees.

To learn more about the feasibility of such flows, we have studied osmotically driven flows both experimentally and theoretically in collaboration with groups at Harvard University, Washington State University and University of Copenhagen. The references are given below. 

Osmotically driven pipe flows and their relation to sugar transport in plants
K.H. Jensen, E. Rio, R. Hansen, C. Clanet, and T. Bohr: Journal of Fluid Mechanics 636, 371-396 (2009) (pdf)

Osmotically driven flows in microchannels separated by a semipermeable membrane
K.H. Jensen, J. Lee, T. Bohr, and H. Bruus: Lab On a Chip 9, 2093-2099 (2009) (pdf)

Self-consistent unstirred layers in osmotically driven flows  
K. Hartvig Jensen, T. Bohr, and H. Bruus: Journal of Fluid Mechanics 662, 197-208 (2010) (pdf)

Analytic solutions and universal properties of sugar loading models in Münch phloem flow
K. H. Jensen, K. Berg-Sørensen, S. M. M. Friis, and T. Bohr : Journal of Theoretical Biology 304, 286-296 (2012) (pdf)

Universality of Phloem Transport in Seed Plants  
K. H. Jensen, J. Liesche , T. Bohr, and A. S. Schulz : Plant, Cell & Environment 35, 1065-1075 (2012) (pdf)

Modeling the hydrodynamics of phloem sieve plates
K.H. Jensen, D.L. Mullendore, N.M. Holbrook, T. Bohr, M. Knoblauch, and H. Bruus : Frontiers in Plant Science 3, article 151 (2012) (pdf)

Efficiency of osmotic pipe flows
L. S. Haaning, K. H. Jensen, C. Hélix-Nielsen, K. Berg-Sørensen and T. Bohr: Physical Review E 87, 053019 (2013) (pdf)

Sap flow and sugar transport in plants
K.H. Jensen, K. Berg-Sørensen, H. Bruus, N.M. Holbrook, J. Liesche, A. Schulz, M.A. Zwieniecki and T. Bohr: Reviews of Modern Physics 88, 035007 (2016) (pdf)

Sugar export limits size of conifer needles
H. Rademaker, M. A. Zwieniecki, T Bohr and K. H. Jensen: Physical Review E 95, 042402 (2017) (pdf)

Diffusion and bulk flow in sugar loading

The survival of plants depends on their ability to produce sugars in their leaves and distribute these sugars to regions of growth and storage. The transport mechanism is a mix of diffusion and pressure driven flow. One mechanism to load the sugar into the transport system is called the “polymer trap”. Sucrose coming from the bundle sheath cell enters the intermediary cell and is enzymatically converted into larger sugar oligomers. The oligomers can not diffuse back through the very narrow plasmodesmata, and are transported away in the sieve elements.

Our recent theoretical study shows, that this mechanism can in principle function. The study further suggests, that not only diffusion, but also bulk flow is involved in the loading mechanism itself, making it more efficient.

Diffusion and bulk flow in phloem loading: A theoretical analysis of the polymer trap mechanism for sugar transport in plants
J. Dölger, H Rademaker, J. Liesche, A Schulz and T. Bohr: Physical Review E90, 042704 (2014) (pdf)

Optimality of the Münch mechanism

Plants require effective vascular systems for the transport of water and dissolved molecules between distal regions. Their survival depends on the ability to transport sugars from the leaves where they are produced to sites of active growth; a flow driven, according to the Münch hypothesis, by osmotic gradients generated by differences in sugar concentration.

The length scales over which sugars are produced (Lleaf) and over which they are transported (Lstem), as well as the radius of the cylindrical phloem cells through which the transport takes place, vary among species over several orders of magnitude; a major unsettled question is whether the Munch transport mechanism is effective over this wide range of sizes.

We have shown that optimization of translocation speed predicts that the radius depends on the product of Lleaf and Lstem to the power 1/3.

Optimality of the Münch mechanism for translocation of sugars in plants  
K. Hartvig Jensen, J. Lee, T. Bohr, H. Bruus, N.M. Holbrook, and M.A. Zwieniecki: Journal of the Royal Society Interface 8, 1155-1165 (2011) (pdf)