Cellular Metabolism Simulation in the Post Genomic Era

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Cellular Metabolism Simulation in the Post
Genomic Era

• Xin-Guang Zhu1, Eric deSturler2, Stephen P. Long1
• 1. Department of Plant Biology, UIUC
• 2. Department of Computer Science, UIUC

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Road-Map

• Why Metabolism Modeling
• Modeling Techniques
• Constraint based modeling
• Data based approach (top down approach)
• Kinetic modeling
• Photosynthesis Modeling and Challenges ahead

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Why Metabolism Modeling

• Extract system properties or rules responsible
  for system regulation, robustness and efficiency
• Predict the alternation of metabolism under
  stress conditions or altered genetic conditions,
  provide ways for identify targets for genetic
  manipulation
• Discover new interactions between pathway in
  metabolism
• Extract new physiological parameters carrying
  information of system properties
• Choice of steady state
• Changes in metabolism path under different
  conditions

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More Reasons

• Metabolite levels are system properties,
  determined by activities of all enzymes and
  effectors
• Metabolism regulation of gene expression
• Silent Mutation.
• Functional redundancy in metabolite system
• Ability of system to stay in similar flux by
  varying substrate concentrations

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Techniques

• Constraint Based Modeling
• Data based Modeling
• Kinetic Modeling

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Constraint Based Modeling

• Assumption system property can be effectively
  detected using the stochiometry constraints.
• Data source
• Procedure for build a model
• Application
• Detection of elementary (or extreme) pathway
• Flux distribution under different conditions
• Phase plane analysis
• Relationship of extreme pathway microarry data
• Weakness

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Genome-scale Metabolic Network Reconstruction
Pallson et al Presentation
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Edwards et al 2002 Environ. Microbio.
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Reed and Palsson 2003, J Bacter.
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Determining Regulation from Metabolic Network
Structure

• Efficiency of an elementary mode modes output
  (growth or ATP) relative to its investment
• Control effective fluxes for a reaction average
  flux through this reaction for all elementary
  modes, weighed by each modes efficiency.

Stelling et al 2002
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Determining Regulation from Metabolic Network
Structure
As cellular control is achieved by genetic
regulation, control effective flux (CEF) should
correlate with messenger RNA levels. Theoretical
transcript ratios for growth on two alternative
substrates T(S1,S2)CEF(S1)/ CEF(S2)in
comparison with gene expression data(r20.6)
Stelling et al 2002
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Weakness

• No dynamics
• No interface for combining the gene regulatory
  mechanism
• No interface for implementing discrete and
  stochastic events
• Can not include the inhibition effects of
  metabolites on enzymes

Zhu, 2005
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Data Based Modeling

• The major assumption guilt by association.
• Data metabolomics, microarray
• Algorithm
• Cluster Analysis  e.g. Fiehn et al, 2000
  Roessner et al, 2001
• Principal Component Analysis  e.g. Fiehn et al,
  2000 Roessner et al, 2001
• Simple Correlations  e.g. Roessner et al, 2001
• Parallel Analysis of Transcript and Metabolic
  Profiles. E.g. Urbanczyk-Wochniak et al., 2003
• Methods to infer reaction mechanisms e.g.
  Crampin et al, 2004

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Principle Component Analysis

• Application
• Capture the major variance of the dataset
• potentially identify pioneer signaling molecules
• PCA should be done before cluster analysis to
  improve the accuracy of CA.
• Algorithm
• Singular Value Decomposition (SVD) on the
  covariance matrix of the data.
• The first PC is the eigenvector with the greatest
  eigenvalue for the covariance matrix of the
  dateset.

http//www.ucl.ac.uk/oncology/MicroCore/HTML_resou
rce/PCA_1.htm
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Methods to Deduce Biochemical Network Mechanisms
(1)

• Perturbation Methods
• Assumption linear behavior near steady state
• Data periodic random perturbation, or using
  different initial conditions.
• Application study the interaction between
  different substrates (entries of J) and the
  stability of the system (eigenvalue of J)

Crampin et al (2004) Prog. Biophy Mol. Biol.
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Methods to Deduce Biochemical Network Mechanisms
(2)

• Network Connectivity
• Assumption guilt by association
• Data time series data after perturbation
• Application study connectivity between different
  metabolites.

Crampin et al (2004) Prog. Biophy Mol. Biol.
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Methods to Deduce Biochemical Network Mechanisms
(3)

• Nonlinear Reaction Model
• Assumption explicitly representation of mass
  action in model increase ability to identify
  reaction mechanism
• Data source biochemical time series data
• Application study reaction mechanisms
• Algorithm See equation. Genetic Programming
  needed for parameterization

-
Crampin et al (2004) Prog. Biophy Mol. Biol.
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Weakness

• Difficult to infer reaction mechanism
• Generally good in fitting the training data, not
  well for new data set
• Large number of degree of freedom for parameters,
  make it intractable.
• Difficult to define the complexity of the model,
  e.g. number of the basis functions

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Kinetic Modeling

• Philosophy The more complete, the better.
• Parameter data
• Data for validating model
• Algorithm for Model development
• Applications
• Weakness

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Zhu, 2004 , PHD Thesis
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Photosynthesis

• Set the maximum potential crop yield
• Sink for atmospheric CO2, help alleviate the
  greenhouse gases
• Easy to probe with biophysical methods, e.g. CO2
  uptake, O2 release, fluorescence, spectroscopy.
• Easily to separate into independent units

Zhu, 2004 , PHD Thesis
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Photosynthesis is a series of molecular steps
that depends on proteins located in chloroplasts
photosynthesis uses light energy, utilizes CO2
and H2O to generate carbohydrate.
http//www.bio.umass.edu/biology/conn.river/photos
yn.html
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Divide and Conquer Strategy

• CRITERIA
• Relatively independent from other metabolism,
  i.e. the input and output molecules are
  minimized.
• Having measurable signal to detect the
  performance of modules.

Light ? Electron ? PQH2
PQH2 ? Electron transfer ? NADPH ATP
The Calvin cycle, PCOP, Starch synthesis, TP
export
Zhu, 2004 , PHD Thesis
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Carbon Metabolism
Zhu, 2004 , PHD Thesis
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Maximum Enzyme Rates
Max. Vel. Enzyme Reaction Vm mmol l-1 s-1 Reference
V1 Rubisco RuBPCO2?2PGA 3.738 (Harris Koniger 1997)
V2 PGA Kinase PGAATP ? ADP DPGA 11.76 (Harris Koniger 1997)
V3 GAP dehydragenase DPGANADPH ?GAP OPNADP 5.04 (Harris Koniger 1997)
V4 Triose phosphate isomerase DHAP ?GAP 40.53 (Harris Koniger 1997)
V5 Aldolase GAPDHAP ?FBP 5.52 (Harris Koniger 1997)
Zhu, 2004 , PHD Thesis
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Michaelis Menton Constant
RN1 Reaction Parameter Value (mM) 2Description Reference
111 RuBP CO2 ? 2 PGA KO 330 O2 (Long 1991)
111 RuBP CO2 ? 2 PGA KC 0.46 CO2 (Long 1991)
112 2-PGCA H2O ? GCA Pi KM112 0.026 PGCA (Christeller Tolbert 1978)
112 2-PGCA H2O ? GCA Pi KI1121 94 GCA (Christeller Tolbert 1978)
Zhu, 2004 , PHD Thesis
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Initial Metabolite Concentrations
Metabolite Concentration (mmol l-1) Reference
DHAP 0.480 (Harris Koniger 1997)
FBP 0.670 (Harris Koniger 1997)
E4P 0.050 (Harris Koniger 1997)
S7P 2.000 (Harris Koniger 1997)
SBP 0.300 (Harris Koniger 1997)
ATP 0.680 (Igamberdiev et al. 2001)
NADPH 0.210 (Giersch et al. 1980)
Zhu, 2004 , PHD Thesis
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AB ? CD
Rate Equation
AB ? CD
If inhibitor (E) exist,
(Cleland, 1963, Segal, 1975)
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Reactions not Following Michaelis-Menten Equation
ADP-glucose pyrophosphorylase, Phosphate
translocator ATP synthase Rubisco
Pettersson and Ryde-pettersson 1988 Von
Caemmerer, 2000
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RuBP
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The System of ODE
dx/dt f(x, y, t) x is metabolites used in the
model y is some constants f is a nonlinear
systems

• No analytical solution
• Stiff system.
• ode15s of MATLAB

Zhu, 2004 , PHD Thesis
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The system reach a steady state solution.
O2
1
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The system keep its right kinetics under
perturbation.
Zhu, 2004 , PHD Thesis
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O2
O2
1
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O2
O2
Zhu, 2004 , PHD Thesis
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Zhu, 2004 , PHD Thesis
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Carbon Metabolism
Zhu, 2004 , PHD Thesis
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PCOP Metabolism

• Simulations revealed that
• enzymes in PCOP are in excess of what is needed
  to maintain the flux of PCOP under current
  atmospheric conditions.
• This excess of enzyme activities may be an
  insurance against environmental conditions that
  promote photorespiration that could otherwise
  result in carbon accumulating within PCOP and
  slowing regeneration of RuBP.

Zhu, 2004 , PHD Thesis
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Zhu, 2004 , PHD Thesis
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Applications of Kinetic Models

• Control Analysis
• System function dynamics
• System Property analysis
• Stability of the steady states
• Phase plane and vector field
• Elementary bifurcations
• One central question what determines what states
  system need to be in or which metabolism status?
• Reverse engineering to infer post-translational
  regulatory properties
• Gene function identification
• Identification of targets for genetic engineering
  better metabolism for desired property.

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Acknowledgement

• Prof. Stephen P. Long (Plant Biology/UIUC)
• Prof. Eric deSturler (Computer Science/UIUC)
• Prof. Keith Mott (Biology/USU)
• Dr. Xin-Guang Zhu (Plant Biology/UIUC)
• Dr. Nahil Sobh (NCSA/UIUC)
• Dr. Lei Liu
• Contact Xinguang Zhu (zhu3_at_uiuc.edu)

NSF, NCSA