3-d computational model of water movement in plant root growth zone brandy wiegers university of...
DESCRIPTION
How do plant cells grow? Expansive growth of plant cells is controlled principally by processes that loosen the wall and enable it to expand irreversibly (Cosgrove, 1993).TRANSCRIPT
3-d Computational Model of Water Movement in Plant Root
Growth Zone
Brandy WiegersUniversity of California, Davis
Dr. Angela CheerDr. Wendy Silk
2007 Joint Mathematics MeetingJanuary 8, 2007New Orleans, LA
http://faculty.abe.ufl.edu/~chyn/age2062/lect/lect_15/MON.JPG
Photos from Silk’s lab
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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
Water Potential, Water Potential, ww
w gradient is the driving force in water movement.
w = s + p + m
Gradients in plants cause an inflow of water from the soil into the roots and to the transpiring surfaces in the leaves (Steudle, 2001).
http://www.soils.umn.edu/academics/classes/soil2125/doc/s7chp3.htm
Osmotic Root Growth Osmotic Root Growth Model AssumptionsModel Assumptions
The tissue is cylindrical, with radius r, growing only in the direction of the long axis z.
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.
The water needed for primary root-growth is obtained only from the surrounding growth medium.
Solving for Solving for
L(z) =·(K· )(1)
L(z) = Kxxx+ Kyyy + Kzzz+ Kxxx +
Kyyy + Kz
zz (2)
Given Experimental DataGiven Experimental Data
• Kx, Kz : 4 x10-8cm2s-1bar-1 - 8x10-8 8cm2s-1bar-1
• L(z) = · g
Erickson and Silk, 1980
Boundary Conditions (Boundary Conditions (Ω)Ω)
= 0 on Ω Corresponds to
growth of root in pure water
rmax = 0.4 mm Zmax = 10 mm
rmax
zmax
Solving for Solving for L(z) =·(K· ) (1)
L(z) = Kxxx+ Kyyy + Kzzz+ Kxxx +
Kyyy + Kz
zz (2)
Known: L(z), Kx, Ky, Kz, on ΩUnknown:
3D Osmotic Model 3D Osmotic Model ResultsResults
*Remember each individual element will travel through this pattern*
Analysis of 3D ResultsAnalysis of 3D Results
Empirical Results Longitudinal
gradient does exist No radial gradient
Model Results Boyer and Silk, 2004
Phloem SourcePhloem Source
Gould, et al 2004
New Model AssumptionsNew Model Assumptions• The tissue is cylindrical, with radius x,
growing only in the direction of the long axis z.
• 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.
• The water needed for primary root-growth is obtained from the surrounding growth medium AND the phloem sources.
http://home.earthlink.net/~dayvdanls/root.gif
3D Phloem Source Model3D Phloem Source Model
Comparison of ResultsComparison of Results
Osmotic 3-D Model Results
Internal Source 3-D Model Results
My Future Work…My Future Work…
• Sensitivity Analysis: Looking at different plant root anatomies, source values, geometry, and initial value
• Plant Root Micro-Environment
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.
Thank you! Do you have Thank you! Do you have any further questions?any further questions?
Brandy WiegersUniversity of California, [email protected]://math.ucdavis.edu/~wiegers
My Thanks to Dr. Angela Cheer, Dr. Wendy Silk, the JMM organizers and everyone who came to my talk today.
This material is based upon work supported by the National Science Foundation under Grant #DMS-0135345