# 3.3 Modeling Without Parameter Tuning: A Case Study of Metabolic Networks

In the previous section, we introduced a simple model for reproducing several structural properties observed in real-world biological networks. Furthermore, this model network shows good qualitative and quantitative agreement with real data.

For model fitting, we need to tune model parameters. The parameters may be estimated by minimizing the difference between the model and real data using statistical methods. However, the optimal solutions may require substantial calculation, after which multiple optimal solutions may be obtained. Furthermore, the possibility of trivial agreements (e.g., over-fittings) may remain if the model has several tunable parameters.

In order to avoid this problem, we need to eliminate parameter tunings and construct models in which parameters are determined from observable statistics obtained from real-network data, such as the number of nodes.

In this chapter, we focus on metabolic networks and introduce a network model without parameter tuning.

## 3.3.1 Network Model

Here, we consider metabolic networks in which nodes and edges represent metabolites and metabolic reactions (substrate–product relationships based on atomic tracing [26]) and propose a simple model that reproduces the structural properties of metabolic networks with two parameters, p and q. These parameters are determined from the statistics of real data (see Section 3.3.3 for details).

In general, it is believed that ...