Identifying optimal models to represent biochemical systems

Abstract

Biochemical systems involving a high number of components with intricate interactions often lead to complex models containing a large number of parameters. Although a large model could describe in detail the mechanisms that underlie the system, its very large size may hinder us in understanding the key elements of the system. Also in terms of parameter identification, large models are often problematic. Therefore, a reduced model may be preferred to represent the system. Yet, in order to efficaciously replace the large model, the reduced model should have the same ability as the large model to produce reliable predictions for a broad set of testable experimental conditions. We present a novel method to extract an "optimal" reduced model from a large model to represent biochemical systems by combining a reduction method and a model discrimination method. The former assures that the reduced model contains only those components that are important to produce the dynamics observed in given experiments, whereas the latter ensures that the reduced model gives a good prediction for any feasible experimental conditions that are relevant to answer questions at hand. These two techniques are applied iteratively. The method reveals the biological core of a model mathematically, indicating the processes that are likely to be responsible for certain behavior. We demonstrate the algorithm on two realistic model examples. We show that in both cases the core is substantially smaller than the full model.

Figure 1. Approaches to estimate parameter in Systems Biology.

(A) Common approach, (B) Proposed approach to yield optimal model with fewer parameters.

Figure 2. Illustration of an admissible region for a system with two parameters.

Initially, the admissible region of the system is . In this situation, a reduced model can be obtained either by setting or . When a new dataset from a new experiment is incorporated, the admissible region shrinks to . Thus, . Now, a reduced model can only be obtained when .

Figure 3. Graphical representation of the genes interactions of flowering in Arabidopsis.

(A) The full model, (B) The reduced model.

Figure 4. The concentration dynamics of the proteins.

These proteins are part of dimer complexes in each of the four organ initiation sites for the wildtype dataset. The solid and dashed lines show that the dataset can be fitted by the full model with as well as by the reduced model with .

Figure 5. Model discrimination applied to the first full model and reduced model.

Model discrimination finds that knocking out AG will distinguish the reduced model with from the full model with . When an experiment is conducted for this mutant, we obtain the dataset that is denoted by ‘*’.

Figure 6. The EGFR biochemical network.

A solid arrow represents a reaction with two kinetic parameters and a dashed arrow represents a reaction with one kinetic parameter. (A) The full network from , (B) The optimal network to produce the dynamics of the five target components for any experimental condition in (22).

Figure 7. Dynamics of the target components for the start up dataset.

The solid and dashed lines show that the dataset can be fitted by the full model with as well as by the reduced model with .

Figure 8. Validation of the optimal model with .

The data, marked with “*”, “+”, and “x”, are obtained from random experimental conditions , , and respectively. Predictions from the optimal model are indicated by the dashed lines.