Table 1.

Organization of the Reviewed Material

Section 2: Modeling approaches

2.1 Model requirements

2.2 Stoichiometric pathway models

2.3 Kinetic models of pathway steps

2.3.1 Mechanistically based functions

2.3.2 Ad hoc modeling approaches

2.3.3 Canonical models

2.3.4 Dynamic models of gene regulatory networks

Section 3: Kinetic model construction

3.1 Forward or bottom-up modeling

3.2 Model retrieval from steady-state data

3.3 Inverse or top-down modeling

3.4 Challenges of the top-down modeling approach and current solution strategies

3.4.1 Data related issues

3.4.2 Model related issues

3.4.3 Computational issues

3.4.4 Mathematical issues

Section 4: Parameter estimation techniques for top-down modeling approaches

4.1 Methods based on integrating differential equations

4.2 Slope estimation

4.3 Constraining the parameter search space

4.4 Reducing the complexity of the inference task

4.5 Algorithms for determining optimal parameter estimates

4.5.1 Gradient-based algorithms

4.5.2 Stochastic search algorithms

4.5.3 Other algorithms

Section 5: Inference of network structure

5.1 Model-free structure identification approaches

5.1.1 Methods based on the Jacobian matrix

5.1.2 Direct observation

5.1.3 Correlation-based approach

5.1.4 Bayesian network approach

5.2 Model-based structure identification methods

5.2.1 ‘Simple-to-general’ and ‘general-to-specific’ modeling

5.2.2 Use of time series data

Section 6: Toward a streamlined “work-flow” for inverse modeling

6.1 Benchmarking framework

6.2 Work-flow strategy

6.2.1 Goals

6.2.2 Flow diagram of inverse modeling strategy

Section 7: Open issues