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 pdq7 fox3 Mass Energy

Resistance/Capacitance Models Campbell, G. S Soil physics with BASIC: Transport models for soil-plant systems. Elsevier. ||

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 || ABA Growth/Regulation Development Network Flows Storage Capacity Storage I/O Physical Eq’nsBiological Eq’ns

Some Basic Vocabulary Transcription RNA Polymerase Protein Synthesis General Metabolism Protein Product DNA Double Helix Transcription Factors modulate reading Example: Diurnal clock mRNA

Multiple Gene Interactions Promoter Region Transcription Factor “A” Gene Codons RNAP DNA Promoter Region RNAP “B” Gene Codons Prot. Syn.

Modeling Multiple Genes Time Expression Rate “A” “B” [A] “B” on “B” off

[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 Multiple neural inputs Electrical (pos & neg A,B) Hopfield Neural Networks Multiple transcription factors (pos & neg w) Chemical (A,B>0) Genetic Neural Networks

Temperature Effects

Modeling Temperature Effects

Time-Dependent Expression Data from Suarez-Lopez et al. LD SD RNA Size 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

Tissue-Specific Expression [TK,01] DNA Promoter Region TargetReporter Fusion Gene

Once upon a time at the ASA…

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? Physiology Development Network Flows Storage Capacity Storage I/O Physical Eq’nsBiological Eq’ns 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.” [

Computing Issues

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 / automated Can be micro-miniaturized / automated Gives quantitative responses Gives quantitative responses Very sensitive (PCR amplification) Very sensitive (PCR amplification) “Scatter gun” methodology “Scatter gun” methodology How it works How it works

Epistasis Experiments ABC WT -A -B -A, -B -A, -B, 35S::A GenotypePhenotype C AB WT -A -B -A, -B -A, -B, 35S::A GenotypePhenotype