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

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.