Model development is a key task in systems biology, and involves different steps, such as model calibration, experimental design and model refinement which usually take place in an iterative way (see reviews in [1–5]). The process of building a model of a biological system typically starts by generating an initial model candidate, or by taking one from the pre-existing knowledge, and then involves an iterative cycle of hypotheses-driven model modifications, new experimentation and subsequent model identification steps, finally leading to a satisfactory refined model [6, 7]. Thus, model selection, experimentation and model refinement can be considered the basic elements of systems biology [8].

A number of researches have proposed different iterative schemes for model development involving the steps of parameter estimation, identifiability analysis, and optimal experimental design [9–12]. The related topic of optimal experimental design for parameter estimation [3, 13] and for model discrimination [14–16] is receiving increased attention in recent years. Lillacci and Khammash [17] introduced a new method for parameter estimation based on Kalman filtering that can also be used to discriminate among alternate models of the same biological process.

Verheijen [18] presented an overview of model selection practices, highlighting the main criteria for choosing out of a large set of models: level of rigor, accuracy with respect to data, adequacy of the model, and its flexibility and computational complexity. He also identifies developments in optimization-based approaches [19, 20] as very promising, but recognizing its limitations due to numerical and algorithmic challenges. Although research along this line has continued [21, 22], it still remains as a challenging numerical problem.

Here, we present a method to simultaneously select a model and calibrate it in a single step. This contribution is based on the following four key ideas: (i) frequently, iterative model development cycles can be considered in a more compact way if sets of hypotheses can be grouped together and formulated as a parameterized set of models, from which the best alternative must be selected; (ii) we consider the problem of model selection formulating it as a simultaneous model selection and parameter identification problem; (iii) further, in order to make the selection decision in a systematic way, we formulate it as an optimization problem [23] acting on the parameterized set of models; (iv) the optimization problem, which belongs to the class of mixed-integer nonlinear programming (MINLP) problems, is solved by recently developed algorithms based on metaheuristics.

The paper is organized as follows: First, we describe the framework used for model selection and identification, based on the nested models paradigm. Then we state the corresponding optimization problem using a formulation based on mixed-integer non-linear programming subject to differential and algebraic constraints. In the following sections, we describe the application of this methodology to a case study considering a dynamic model of the KdpD/KdpE system of *Escherichia coli*. Finally, we provide a discussion of the results and summarize the main conclusions of the study.