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.