Modeling core-box

Model reduction involves the identification and elimination of such parts of a model that are unrelated to some specific features of a model. The nature of such features might vary from situation to situation. In the core-box modeling framework, the feature in focus is identifiability (and agreement) with respect to the available data. We first review the state-of-the-art methods for identifiability, and then those for model reduction. 

Example 1. Let us consider an example that exemplifies step 3 in the core-box modeling framework. The system to be studied consists of one substance, A, with concentration x = [A]. There are two types of interaction that affect the concentration negatively degradation and diffusion. Both processes are assumed to be irreversible and to follow simple mass action kinetics with rate constants p and P2, respectively. Further, there is a synthesis of A, which increases its concentration. This synthesis is assumed to be independent of x, and its rate is described by the constant parameter p3. Finally, it is possible to measure x, and the measurement noise is denoted d. The system is thus given in state space form by the following equations ... 

The system identification step in the core-box modeling framework has two major sub-steps parameter estimation and model quality analysis. The parameter estimation step is usually solved as an optimization problem that minimizes a cost function that depends on the model s parameters. One choice of cost function is the sum of squares of the residuals, Si(t p) = yi(t) — yl(t p). However, one usually needs to put different weights, up (t), on the different samples, and additional information that is not part of the time-series is often added as extra terms k(p). These extra terms are large if the extra information is violated by the model, and small otherwise. A general least-squares cost function, Vp(p), is thus of the form... 

Core-Box Modeling in the Biosimulation of Drug Action 5.2.4.2 Model Quality Analysis... 

The determination of has many advantages. First, it is a way to compare in-vivo and in-vitro parameters for the same system [11]. Second, it gives an interpretation of the results obtained in the system identification step of the core model. Nevertheless, the final step in the core-box modeling framework is not achieved until the gray-box model has obtained all the estimated features of the estimated core model,... 

A Core-Box Model for Insulin Receptor Phosphorylation and Internalization in Adipocytes... 

A more detailed description of the complete core-box model, including the insulin signaling, is available in Refs. [6, 8, 10]. 

The central questions in the core-box modeling framework are of the following form What type of information can one extract from the available in-vivo data How does this information relate to the details of the existing gray-box models for the system What kind of predictions are most supported by the in-vivo data, and which parts of the gray-box models are merely based on in-vitro characterizations, or on even more vague experimental evidence ... 

The obtaining of different models for the same system that may easily be exchanged for each other is important not only in the biosimulations of a single system, for instance in the core-box modeling framework, but also when developing models for systems of systems. Such models are often referred to as hierarchical models, because they are formulated at different levels of complexity. For an hier-... 

It is clear, therefore, that core-box models with the additional characteristics of Eq. (11) (such as the insulin model in Section 5.3) have major potential in the future developments of hierarchical models describing larger systems. In this way, the potential drug targets predicted by the core-box model may be judged, not only by their quality tag, but also through their translated importance on the whole-body behavior. Both of these possibilities are very important to achieve the full potential of biosimulation of potential dmg targets. 

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