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

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

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, Daviswiegers@math.ucdavis.eduhttp://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