Computational Model of Water Movement in Plant Root Growth
Zone
Brandy WiegersUniversity of California, Davis
Angela Cheer
Wendy Silk
2005 World Conference on Natural Resource Modeling
June 17, 2005
http://www.uic.edu/classes/bios/bios100/labs/plantanatomy.htm
Research MotivationResearch Motivation
http://www.wral.com/News/1522544/detail.html http://www.mobot.org/jwcross/phytoremediation/graphics/Citizens_Guide4.gif
Presentation OutlinePresentation Outline
Plant BiologyPlant Biology Existing (Osmotic) Root Growth ModelExisting (Osmotic) Root Growth Model New (Internal Source) ModelNew (Internal Source) Model Future WorkFuture Work
Presentation OutlinePresentation Outline
Plant BiologyPlant Biology Existing (Osmotic) Root Growth ModelExisting (Osmotic) Root Growth Model New (Internal Source) ModelNew (Internal Source) Model Future WorkFuture Work
Root BiologyRoot Biology
http://www.emc.maricopa.edu/faculty/farabee/BIOBK/waterflow.gifhttp://www.resnet.wm.edu/~mcmath/bio205/
http://home.earthlink.net/~dayvdanls/root.gif
Photos from Silk’s lab
How do plant cells grow?How do plant cells grow?
Expansive growth of Expansive growth of plant cells is plant cells is
controlled controlled principally by principally by
processes that processes that loosen the wall loosen the wall and enable it to and enable it to
expand expand irreversibly irreversibly
(Cosgrove, 1993).(Cosgrove, 1993).
http://www.troy.k12.ny.us/faculty/smithda/Media/Gen.%20Plant%20Cell%20Quiz.jpg
What are the rules of plant What are the rules of plant root growth?root growth?
Water must be brought into the cell to facilitate Water must be brought into the cell to facilitate the growth (an external water source).the growth (an external water source).
The tough polymeric wall maintains the shape.The tough polymeric wall maintains the shape. Cells must shear to create the needed Cells must shear to create the needed
additional surface area.additional surface area. The growth process is irreversibleThe growth process is irreversible
http://sd67.bc.ca/teachers/northcote/biology12/G/G1TOG8.html
Growth VariablesGrowth Variables
g : growth velocity, mm/hr K : hydraulic conductivity,
cm2/(s bar) L : relative elemental
growth rate (REG) , 1/hr : water potential, bar
Silk and Wagner, 1980
Hydraulic Conductivity, KHydraulic Conductivity, K
Measure of ability of water to move Measure of ability of water to move through the plantthrough the plant
Inversely proportional to the resistance of Inversely proportional to the resistance of an individual cell to water influxan individual cell to water influx
Typical values: Typical values: KKxx ,K ,Kzz = 8 x 10 = 8 x 10-8-8 cm cm22ss-1-1barbar-1-1
Value for a plant depends on growth Value for a plant depends on growth conditions and intensity of water flowconditions and intensity of water flow
Relative Elemental Relative Elemental Growth Rate, L(z)Growth Rate, L(z)
• A measure of the spatial distribution of growth within the root organ.
• L(z) = · g
Erickson and Silk, 1980
Water Potential, Water Potential, ww
w gradient is the driving force in water movement.
http://www.soils.umn.edu/academics/classes/soil2125/doc/s7chp3.htm
Presentation OutlinePresentation Outline
Plant BiologyPlant Biology Existing (Osmotic) Root Growth ModelExisting (Osmotic) Root Growth Model New (Internal Source) ModelNew (Internal Source) Model Future WorkFuture Work
Existing (Osmotic) Model Existing (Osmotic) Model AssumptionsAssumptions
The tissue is cylindrical, with radius x, growing only in the direction of the long axis z.
The distribution of is axially symmetric. The growth pattern does not change in time. Conductivities in the radial (Kx) and longitudinal
(Kz) directions are independent so radial flow is not modified by longitudinal flow.
Boundary Conditions (Boundary Conditions (Ω)Ω)
= 0 on Ω Corresponds to
growth of root in pure water
Δx = Δz = 0.1 mm Xmax = 0.5 mm Zmax = 10 mmxmax
zmax
Solving for Solving for
Known: L(z), Kx, Kz, on Ω
Unknown:
L(z) =·(K·) (1)
L(z) = Kxxx+Kzzz+ Kxxx + Kz
zz (2)
ResultsResults
*Remember each individual element will travel through this pattern*
Distribution of Water Fluxes
Growth Sustaining Distribution
Analysis of ResultsAnalysis of Results
Empirical Results No radial gradient Longitudinal
gradient does exist
Model Results
Presentation OutlinePresentation Outline
Plant BiologyPlant Biology Existing (Osmotic) Root Growth ModelExisting (Osmotic) Root Growth Model New (Internal Source) ModelNew (Internal Source) Model Future WorkFuture Work
Phloem SourcePhloem Source
Adds internal known sources
Doesn’t change previous matrix:
L = [Coeff]
Gould, et al 2004
Model ResultsModel Results
Preliminary ResultsNew (Internal Source)
Existing (Osmotic)
New Model AssumptionsNew Model Assumptions
• The tissue is cylindrical, with radius x, growing only in the direction of the long axis z.
• The distribution of is axially symmetric.
• The growth pattern does not change in time.
• Conductivities in the radial (Kx) and longitudinal (Kz) directions are independent so radial flow is not modified by longitudinal flow.
http://home.earthlink.net/~dayvdanls/root.gif
Presentation OutlinePresentation Outline
Plant BiologyPlant Biology Existing (Osmotic) Root Growth ModelExisting (Osmotic) Root Growth Model New (Internal Source) ModelNew (Internal Source) Model Future WorkFuture Work
End Goal…End Goal…
Computational 3-d box of soil through Computational 3-d box of soil through which we can grow plant roots in which we can grow plant roots in real time while monitoring the real time while monitoring the change of growth variables.change of growth variables.
Do you have any further Do you have any further questions?questions?
Brandy Wiegers
Graduate Group of Applied Mathematics (GGAM)University of California, Davis
Email:[email protected]
This material is based upon work supported by the National Science Foundation under Grant #DMS-0135345
ReferencesReferences
John S. Boyer and Wendy K. Silk, Hydraulics of plant growth, Functional Plant Biology 31 (2004), 761:773.
C.A.J.Fletcher, Computational techniques for fluid dynamics: Specific techniques for different flow categories, 2nd ed., Springer Series in Computational Physics, vol. 2, Springer-Verlag, Berlin, 1991.
Cosgrove DJ and Li Z-C, Role of expansin in developmental and light control of growth and wall extension in oat coleoptiles., Plant Physiology 103 (1993), 1321:1328.
Ralph O. Erickson and Wendy Kuhn Silk, The kinematics of plant growth, Scientific America 242 (1980), 134:151.
Nick Gould, Michael R. Thorpe, Peter E. Minchin, Jeremy Pritchard, and Philip J. White, Solute is imported to elongation root cells of barley as a pressure driven-flow of solution, Functional Plant Biology 31 (2004), 391:397.
Jeremy Pritchard, Sam Winch, and Nick Gould, Phloem water relations and root growth, Austrian Journal of Plant Physiology 27 (2000), 539:548.
J. Rygol, J. Pritchard, J. J. Zhu, A. D. Tomos, and U. Zimmermann, Transpiration induces radial turgor pressure gradients in wheat and maize roots, Plant Physiology 103 (1993), 493:500.
W.K. Silk and K.K. Wagner, Growth-sustaining water potential distributions in the primary corn root, Plant Physiology 66 (1980), 859:863.
T.K.Kim and W. K. Silk, A mathematical model for ph patterns in the rhizospheres of growth zones., Plant, Cell and Environment 22 (1999), 1527:1538.
Hilde Monika Zimmermann and Ernst Steudle, Apoplastic transport across young maize roots: effect of the exodermis, Planta 206 (1998), 7:19.
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