Local Parametric Sensitivity Analysis

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Local Parametric Sensitivity Analysis AMATH
900 Lecture 5, Jan 27, 2009
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Parametric Sensitivity Analysis
Parameters 1. Enzyme activity levels 2. Kinetics
constants 3. Decay rates 4. Boundary
conditions 5. ....
Variables 1. Concentrations 2. Pathway fluxes 3.
Dynamic response 4. Growth rate 5. ....
Parametric sensitivity analysis investigates the
relationship between the variables and parameters
in a biochemical network.
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Parametric Sensitivity AnalysisExample
reaction kinetics
steady state
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steady state
local sensitivity analysis
effect of perturbation/ intervention
relative sensitivity
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sensitivity analysis vector
notation implicit differentiation
steady state
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complete sensitivity analysis
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Sensitivity Analysis General Computation
model
steady state
differentiate
absolute sensitivity
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Application unregulated chain
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sensitivity of flux J to enzyme activities
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Application product feedback
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p
sensitivity of flux J to enzyme activities
p0
Summation Theorem of Metabolic Control Analysis
conservation law for sensitivities
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Metabolic Control Analysis (MCA)
Sensitivity Analysis in the absence of a
quantitative model of the network
Relative response to a change in enzyme activity
Relative response to a direct change in
reaction flux (by linearity)
glutamate
Succinate
Succinate Semialdehyde
GABA
Control Coefficients
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Utility of MCA
1) If a quantitative (i.e. kinetic) model is
available, equates with (local) parametric
sensitivity analysis
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Utility of MCA
2) In absence of quantitation, allows
qualitative analysis of sensitivities, e.g.
comparing different topologies
The Effect of Feedback
E
E
E
1
2
3
?
Without feedback
With feedback
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Utility of MCA
3) Regardless of quantitation, allows
characterization of constraints on sensitivities
(sensitivity invariants)
The Summation Theorem
glutamate
Succinate
Succinate Semialdehyde
GABA
Relative increase in flux Jk
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The Summation Theorem
Similar results for more complex networks
General results described in terms of the kernel
of the stoichiometry matrix
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Time-Varying Sensitivities
Sensitivities can be addressed over transient or
oscillatory behaviour
Computation
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Example
Perturbation in S1(0)
Perturbation in k1
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Application to Phototransduction Pathway
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Global Sensitivity Analysis

• Addresses system behaviour over a wide range of
  parameter values
• Primarily statistical tools efficient sampling
  methods
• Provides a broader view of behaviour, but
• Results often difficult to interpret

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Applications of Sensitivity Analysis

• Predicting the effect of interventions
• Drug development

Trypanosome metabolism. Bakker et al., 1999,J.
Biol. Chem
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Applications of Sensitivity Analysis

• Predicting the effect of interventions
• Drug development
• Medicine

• Tumour growth and thiamine, Comin-Anduix et
  al., 2001, Eur. J. Biochem.

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Applications of Sensitivity Analysis

• Predicting the effect of interventions
• Drug development
• Medicine
• Metabolic engineering

• Diacetyl production in Lactococcus lactis,
  Hoefnagel et al. 2002, Microbiology

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Applications of Sensitivity Analysis

• Predicting the effect of interventions
• Drug development
• Medicine
• Metabolic engineering
• Model construction and analysis
• Identifying key variables

• NF-?B pathway. Ihekwaba et al., 2004, IEE Sys.
  Biol.

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Applications of Sensitivity Analysis

• Predicting the effect of interventions
• Drug development
• Medicine
• Metabolic engineering
• Model construction and analysis
• Identifying key variables
• Model calibration

• Identifiability. Zak et al. 2003, Genome. Res.