Genomic Science and its Relation to Soil-Plant-Atmosphere Continuum

Studies

S.M. Welch, J.L. Roe, M.B. Kirkham

Kansas State University

Third in a Series of Talks• Next Generation Crop Growth Models: Physics,

Genomics, Soil Characterization, and Computation

– ASA Annual Meeting, Salt Lake City, 1999

• Modeling the Genetic Control of Flowering in Arabidopsis thaliana

– ASA Annual Meeting, Minneapolis, 2000

• Genomic Science and its Relation to Soil-Plant-Atmosphere Continuum Studies

– ASA Annual Meeting, Charlotte, 2001

A Network Conception of Plants ...

• Plants can be viewed as networks of parts in space that develop and grow with time…

• These parts induce, constrain, and modulate a network of matter and energy flows…

• Networks of genes manage the system either by direct action or through the establishment of physiological mechanisms

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Mass Energy

Resistance/Capacitance Models

Campbell, G. S. 1985. Soil physics with BASIC: Transport models for soil-plant systems. Elsevier.

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But, one should be careful ...

• “However, in the case of a living plant, and all the more so in the case of a growing plant, we are in danger of gross oversimplifications.” (Hillel, 1998)

• “On the other hand, every biological organism, whatever its complexity, exists and operates within a physical setting requiring it to interact with its environ-ment in obedience to physical principles.” (Ibid.)

Network Mathematics

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ABA

p

sq

i

e

0

( , , , )d

dtB s p e i 0

Growth/Regulation

, # #N N N NDevelopment

( , ) R

C C

iN s p

iNetwork Flows

( , , )C C q s pStorage Capacity

d

dt Cq i

Storage I/O

Physical Eq’ns Biological Eq’ns

Some Basic Vocabulary

Transcription

RNA Polymerase

Protein Synthesis

General Metabolism

Protein Product

DNA Double Helix

Transcription Factors modulate reading

Example: Diurnal clockmRNA

Multiple Gene Interactions

Promoter Region

Transcription Factor

“A” Gene CodonsRNAP DNA

DNA

PromoterRegion

RNAP“B” Gene Codons

Prot. Syn.

Modeling Multiple Genes

Time

Exp

ress

ion

Rat

e

“A”

“B”

[A]

“B” on

“B” off

(A)

( )d B

B a Adt k

[CR,00]

ABA Gene Network

Some genes influence ABA biosysnthesis in response to exo- or endogenous stimuli while many others modulate plant response to ABA levels;

Individual stimuli such as low water potential can alter both;

Effects range from short-term physiology (closing stomates) to affecting growth patterns (through cell cycle control?) to developmental effects (e.g. interaction between ABI3 and the CO flowering-time gene).

Antagonistic

Stimulatory

Relationship to Neural Networks

i ii

d BB a w A

dt k

• Multiple neural inputs • Electrical (pos & neg A,B)

Hopfield Neural Networks

i i

i

d BB a w A

dt k

• Multiple transcription factors (pos & neg w)

• Chemical (A,B>0)

Genetic Neural Networks

Temperature Effects

0%

20%

40%

60%

80%

100%

20 30 40 50 60

Days after planting (d)

Tra

nsi

tio

n p

erce

nt

CO

FVE

Modeling Temperature Effects

1 0( )TQ

0 /Tt e

i i

i

d BB a w A

dt k

0

1

/10

/1

( )

( )

TT

TT

k e Q

a e Q

Time-Dependent Expression

0

6

12

18

24

0 8 16 24Time (h)

CO

act

ivit

y

LD SD

Data from Suarez-Lopez et al.

LD SD

RNASize sorted RNA

Autoradiograph

One sample track

Radio-labeled complementary DNA

From approximated models… (Dong, et al., 2001)

We have demonstrated the utility of genomic information in the prediction of flowering time;

Complex interactions between temperature and photoperiod can be explained in terms of a network of nodes with various functions (oscillators, threshold devices, products, etc.)

Elaborate, difficult to parameterize, nonlinear models can, on occasion, be simply approximated;

For the first time, specific genes are implicated as underpinning mathematical formalisms (photothermal days, degree-days, etc.) commonly used to model floral transition times.

Transport in Growing Tissues

Elongation Region

Fescue tiller (Martre, et al., 2001)

RC

Water storage is often ignored in transport models• RC time constants for trees and

tomatoes are ca 75 min & 1 min, respectively (Nobel, 1991);

Yet storage is key to plant growth.

RC

Tissue-Specific Expression

[TK,01]

AtPLD

DNA

PromoterRegion

Target Reporter

Fusion Gene

Once upon a time at the ASA…

p

df

dt M M MV k V F

( )p

dC T Q

dt

dq s

dt

0pp

MV

0p

0p RT

GCM Primitive Equations

Although exceptionally complex, all global climate models are, at their cores, formulated around six mathematical field equations. The remainder of each model adapts the equations to the specifics of Earth’s air and ocean circulation.

Conservation of Momentum

First Law of Thermodynamics

Mass Continuity

Conservation of Mass

The Hydrostatic Equation

The Ideal Gas Law

Plant Primitive Equations?

, , ,d

dt

pB s e i 0

gPhysiology

, # #N N N NDevelopment

( , ) R

C C

iN s p

iNetwork Flows

( , , )C C q s pStorage Capacity

d

dt Cq i

Storage I/O

Physical Eq’ns Biological Eq’ns

1T T

d

dt g K g A Wg

Genetic Control

Needed Eq’ns

Energy Balance

Solute Transport

?

NSF Project 2010

• “To exploit the revolution in plant genomics by understanding the function of all genes of a reference species within their cellular, organismal and evolutionary context.”

• “The ultimate expression of our goal is nothing short of a virtual plant which one could observe growing on a computer screen, stopping this process at any point in that development, and with the click of a computer mouse, accessing all the genetic information expressed in any organ or cell under a variety of environmental conditions.”

[www.arabidopsis.org/workshop1.html]

Computing Issues

0.01

0.1

1

10

100

1000

10000

1970 1980 1990 2000 2010

MIP

S

Software Organization Issues

• Sets of equations that change with time

• Tissue-specific features

• Spatial structure

• Efficient numerical methods needed

• Visualization of large amounts of output

• Etc.

Integration Testbed (Ruiqing He)

Plant parts are modeled as Java objects with internal variables for size, location, rules for developmental, and physiological state. Object methods:

– Manage associated ODE systems;

– Solve them to compute growth and transpiration;

– Instantiate new plant parts in response to development triggers;

– Generate 3D rendering commands for vegetation/circuit images.

A single plant part

Summary• Genomics is bringing to light the ultimate control

mechanisms of plants;• Networks of interacting genes can be modeled

by sets of ordinary differential equations;• As many physical/physiological processes can

be similarly represented, a unified theory of the soil-plant-atmosphere continuum is conceivable and appears computationally tractable;

• Whatever the theory’s final form, Dr. Campbell’s many contributions will have a visible role.

Microarray Technology

• Can be micro-miniaturized / automatedCan be micro-miniaturized / automated

• Gives quantitative responsesGives quantitative responses

• Very sensitive (PCR amplification)Very sensitive (PCR amplification)

• “ “Scatter gun” methodologyScatter gun” methodology

• How it worksHow it works

Epistasis Experiments

A B C

WT

-A

-B

-A, -B

-A, -B, 35S::A

Genotype Phenotype

C

A B

WT

-A

-B

-A, -B

-A, -B, 35S::A

Genotype Phenotype