Local Parametric Sensitivity Analysis
AMATH 882 Lecture 4, Jan 17, 2013
Parametric Sensitivity Analysis
Parametric sensitivity analysis investigates the relationship between the variables and parameters in a biochemical network.
Variables
1. Concentrations
2. Pathway fluxes
3. Dynamic response
4. Growth rate
5. ....
Parameters1. Enzyme activity levels2. Kinetics constants3. Decay rates4. Boundary conditions5. ....
Parametric Sensitivity Analysis:Example
reaction kinetics:
steady state:
steady state:
local sensitivity analysis:
effect of perturbation/ intervention:
relative sensitivity:
steady state:
sensitivity analysis:
vector notation
implicit differentiation
complete sensitivity analysis:
Sensitivity Analysis: General Computation
model:
steady state:
differentiate:
absolute sensitivity:
Time-Varying SensitivitiesSensitivities can be addressed over transient or oscillatory behaviour
Computation:
Example
Perturbation in S1(0)Perturbation in k1
Application to Phototransduction
Pathway
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
Applications of Sensitivity Analysis
Trypanosome metabolism. Bakker et al., 1999,J. Biol. Chem
• Predicting the effect of interventions
• Drug development
Applications of Sensitivity Analysis
• Predicting the effect of interventions
• Drug development
• Medicine
Tumour growth and thiamine, Comin-Anduix et al., 2001, Eur. J. Biochem.
Applications of Sensitivity Analysis
• Predicting the effect of interventions
• Drug development
• Medicine
• Metabolic engineering
Diacetyl production in Lactococcus lactis, Hoefnagel et al. 2002, Microbiology
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.
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.