Systems Simulation and Optimization

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Systems Simulation and Optimization
Zhijun Wu Department of Mathematics Program on
Bio-informatics and Computational Biology Iowa
State University July 28, 2004 Systems Biology
Seminar Baker Center on Bioinformatics and
Biological Statistics
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Systems Biology
System level understanding of biological
systems --
Kitano 2002
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The elephant is like a rope
http//www.jainworld.com/literature/story25.htm
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Central Themes

• System Structure
• Gene, Metabolic Network Construction
• Parameter Identification
• Dynamic Behaviors
• Gene Regulation
• Metabolic Reaction
• Design and Control
• Robustness, Stability, Feedback Control
• Design of Novel Systems

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Data Tools

• Data
• Gene Expression Data
• Enzyme and Metabolite Concentrations
• Tools
• Collection of Data Microarray
• Data Analysis

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Computational Tools

• Simulation
• Steady-State Flux Distribution
• Time-Dependent Metabolic Simulation
• Optimization
• Parameter Identification
• Design of Certain Metabolic Functions

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Biological Systems
Macromolecular Modeling, Metabolic Networks
Engineering Systems
Simulation Optimization
Crash Analysis, Airplane Design, Pipeline Network
Economic Systems
Stock Market Prediction, Portfolio Optimization
Information Systems
Communication Network, Computer Systems
Social Systems?
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Simulation
Studies the changes of certain system properties
in space or time Solves systems of differential
equations to obtain the trajectories
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Optimization
Determines system variables or parameters to
maximize certain outcomes of the
system Maximizes a linear or nonlinear function
with a set of linear or nonlinear constraints
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Protein Electron Density Distribution
structure factor
density function
http//www.ai.mit.edu/people/wang/phd-thesis
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Classical Mechanical Model of Protein Motion
Initial Value Problem
Boundary Value Problem
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Direct Problems
Given parameters p1, , pm, determine x1, , xn.
Inverse Problems
Given x1, , xn, determine parameters p1, , pm.
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Steady States of Metabolic Networks
E2
E1
E4
X0
S1
S2
X1
E3
D. Fell 1997 Proceedings of International
Conference on Complex Systems
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E2
v2
E1
E4
X0
S1
S2
X1
v1
v4
v3
E3
Mass Balance Equation
stoichiometry matrix
metabolic fluxes
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min v3 Subject to Sv b Sol v1 v2 v4
x, v3 0
Flux Optimization
E2
v2
E1
E4
X0
S1
S2
X1
v1
v4
v3
E3
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Jason Papin et al. 2002 Genome Research
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vi f (X, S, K, Ei) Flux Control
Coefficients Ci,j ?vi/?Ej Ej/vi ? i Ci,j
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Flux Control
Kacser and Burns 1973
E2
v2
E1
E4
X0
S1
S2
X1
v1
v4
v3
E3
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Time Resolved Simulation
Irreversible HIV Proteinase Inhibition
M
S
P
E
ES
EP
EI
EJ
I
Petr Kuzmic 1996 Analytical Biochemistry
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Reaction Mechanism
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Reaction Equations
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Parameter Estimation
Inverse Problems
Given S1, , Sn, determine k1, , km.
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Nonlinear Least-Squares
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Questions

• How sufficient and accurate is the data?
• How reliable are the models?
• What are the computational challenges?
• Big impacts in biology and medicine?

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Think Big, Act Small!
http//www.bradenprint.com/articles/weights/MouseE
lephant.gif
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More References
Hiroaki Kitano, 2002, Systems biology Towards
system-level understanding of biological systems,
http//www.bioinformatics.iastate.edu/systemsbiolo
gy/papers.html Pedro Mendes and Douglas Kell,
1998, Nonlinear optimization of biochemical
pathways applications to metabolic engineering
and parameter estimation, Bioinformatics 14,
869-883 David Fell, 1997, Systems properties of
metabolic networks, Proceedings of International
Conference on Complex Systems (1997) Petr
Kuzmic, 1996, Program DYNAFIT for the analysis of
enzyme kinetic data Application to HIV
proteinase, Analytical Biochemistry 237, 260-273