Better Education with Experiential Resources: Mathematical Model of Leaf Growth

or

Students Working Intently on Models

An Exercise in Leaf Growth Modeling for Introductory Students

adapted from “Modeling Plant Growth”

Yaffa Grossman

Goal

Model Fluency

Factors that Influence Plant Growth

Building Understanding• Biological context• Transferring biological observations to an idea of a

model• Simple model• “Realistic” model & manipulation– Hypotheses, predictions & testing

• Testing the model– experimental design & implementation

• Applications– Basic biological questions– Practical applications

Simple Model Construction

Simple Model Construction

Initial leaf area + CHO = new leaf area

Links

• Worksheet• Models– Simple– More complex model with manipulations

• Applications-example PEACH

Variablesinitial leaf area (cm2; this variable refers to the area of leaves at the beginning of the experiment)

0.5

Net photosynthesis rate (µmol m-2 -1; this variable refers to the total amount of carbon dioxide fixed by the plant in photosynthesis minus the amount lost during cellular respiration)(function of CO2. Light & temperature)

5

conversion efficiency (g CHO/g DW; this variable converts the amount of carbohydrates produced during photosynthesis to a dry weight of the plant. This takes into account the amount of carbohydrates that are used for respiration and the fact that approx 42% of the of the plant biomass is carbon and that carbohydrates is 40% of the carbon)

1.261

mass specific leaf area (g/cm2; this variable converts leaf weight into area)

0.002

% plant mass as leaf (this variable takes into account what percent of the plant is leaf vs. roots and stems)

60

Carbohydrate mass (g mol-1; this refers to the amount of carbohydrate produced related to the amount of carbon dioxide that is fixed during photosynthesis)

30

Environmental Variables

0

2

4

6

8

10

12

14

16

0 10 20 30 40 50 60

Temperature (C)

Net C

O2

Assi

mila

tion

A, u

mol

m-

2 se

c-1

-5

0

5

10

15

20

0 100 200 300 400 500

PPFD, umol m-2 sec-1

Net C

O2

Assi

mila

tion

Rate

, A,

umol

m-2

sec

-1

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12

Nitrogen (units)

Phot

osyn

thes

is (f

ract

ion

of

max

imum

)

Model Verification• Leaf Area (Image J)• Leaf Wt• Mass specific leaf

area• Net photosynthesis

– Temperature– Light– Nutrients

Using Fast Plants for Model Verification

Young, enthusiastic student!!

ReferencesFarazdaghi, Hadi, 2005. Theory and Model for the Reaction of RuBP

Carboxylase/Oxygenase and Photosynthesis in C3-Plants. Presented at GRC, CO2 Assimilation in Plants:Genome to Biome, Aussois, France, Sept. 11-16, 2005.

Grossman, Yaffa. 2009. Growth Modeling. Science or Nature or PNAS

Gustavo, Habermann ; Machado Eduardo Caruso ; Rodrigues João Domingos ; Medina Camilo Lázaro, 2003. CO2 assimilation, photosynthetic light response curves, and water relations of 'Pêra' sweet orange plants infected with Xylella fastidiosa. Brazilian Journal of Plant Physiology 15(2):79-87

Peterson, Andrew G. ; J. Timothy Ball ; Yiqi Luo ; Christopher B. Field ; Peter B. Reich ;

Peter S. Curtis ; Kevin L. Griffin ; Carla S Gunderson ; Richard J. Norby ; David T. Tissue ; Manfred Forstreuter ; Ana Rey ; Christoph S. Vogel ; CMEAL collaboration. 1998. Technical Report. Desert Research Inst., Biological Sciences Center. 39p.