local parametric sensitivity analysis amath 882 lecture 4, jan 17, 2013
TRANSCRIPT
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.