Parameter estimation using simulated annealing for S

36 Pages·2006·0.79 MB·English

Parameter estimation using
simulated annealing for S-
system models of biochemical
networks
Orland Gonzalez
Outline
• S-systems quick review
• Definition of the problem
• Simulated annealing
– Perturbation function
– Demonstration
• General techniques
– Decoupling
– Structure identification
• The cadBA network in E. coli
Outline
• S-systems quick review
• Definition of the problem
• Simulated annealing
– Perturbation function
– Demonstration
• General techniques
– Decoupling
– Structure identification
• The cadBA network in E. coli
S-systems review
• Coupled ODEs
– Power-laws
• Special form of GMAs
– Production and degradation fluxes are
aggregated
n: number of dependent variables
m: number of independet variable
S-system example
Very simple symbolic setup!
X production:
1
X&+ =αX g X g where: g > 0 since X is produced from X
10 12 10 1 0
1 1 0 2 g < 0 since X is inhibited by X
12 1 2
X degradation:
1
X&− = βX h11 where: h > 0 since we expect the current
11
1 1 1
state of X affects its own
1
degradation rate.
Therefore:
X& =αX g10 X g12 −βX h11
1 1 0 2 1 1
S-system example
Very simple symbolic setup!
Whole Network:
&
g g h
X =α X X − βX
10 12 11
1 1 0 2 1 1
&
g h
X =α X − β X
21 22
2 2 1 2 2
where α = β and h = g since the amount of X degraded
2 1 11 21 1
is the amount of X that is produced.
2
Outline
• S-systems quick review
• Definition of the problem
• Simulated annealing
– Perturbation function
– Demonstration
• General techniques
– Decoupling
– Structure identification
• The cadBA network in E. coli
Parameter Estimation
• From literature
– From K s and other enzyme data
m
• From perturbation experiments
– From a system in steady state: a single
perturbation is made
• From time series data (biochemical
profiles)
– Inverse problem
– Curve fitting
Inverse problem ex.
Given the network:
And the profile: Problem: Find the parameters
that fit the data.
Challenges
• Mathematical redundancy
– Multiple possible solutions
• Computational complexity
– Abundant local minima
– Extreme computational requirements
• due to numerical integration
An early EXTREME example (Kikuchi et. al. 2003, Bioinformatics) :
•System with 5 variables
•Artificial data
•Cluster of 1040 Pentium-III 933MHz processors
Each algorithmic loop took about 10 hours!!!