An iterative identification procedure for dynamic modeling of biochemical networks

<p>Abstract</p> <p>Background</p> <p>Mathematical models provide abstract representations of the information gained from experimental observations on the structure and function of a particular biological system. Conferring a predictive character on a given mathematical formulation often relies on determining a number of non-measurable parameters that largely condition the model's response. These parameters can be identified by fitting the model to experimental data. However, this fit can only be accomplished when identifiability can be guaranteed.</p> <p>Results</p> <p>We propose a novel iterative identification procedure for detecting and dealing with the lack of identifiability. The procedure involves the following steps: 1) performing a structural identifiability analysis to detect identifiable parameters; 2) globally ranking the parameters to assist in the selection of the most relevant parameters; 3) calibrating the model using global optimization methods; 4) conducting a practical identifiability analysis consisting of two (<it>a priori </it>and <it>a posteriori</it>) phases aimed at evaluating the quality of given experimental designs and of the parameter estimates, respectively and 5) optimal experimental design so as to compute the scheme of experiments that maximizes the quality and quantity of information for fitting the model.</p> <p>Conclusions</p> <p>The presented procedure was used to iteratively identify a mathematical model that describes the NF-<it>κ</it>B regulatory module involving several unknown parameters. We demonstrated the lack of identifiability of the model under typical experimental conditions and computed optimal dynamic experiments that largely improved identifiability properties.</p

Compartmental models: theory and practice using the SAAM II software system.

Understanding in vivo the functioning of metabolic systems at the whole-body or regional level requires one to make some assumptions on how the system works and to describe them mathematically, that is, to postulate a model of the system. Models of systems can have different characteristics depending on the properties of the system and the database available for their study; they can be deterministic or stochastic, dynamic or static, with lumped or distributed parameters. Metabolic systems are dynamic systems and we focus here on the most widely used class of dynamic (differential equation) models: compartmental models. This is a class of models for which the governing law is conservation of mass. It is a very attractive class to users because it formalizes physical intuition in a simple and reasonable way. Compartmental models are lumped parameter models, in that the events in the system are described by a finite number of changing variables, and are thus described by ordinary differential equations. While stochastic compartment models can also be defined, we discuss here the deterministic versions--those that can work with exact relationships between model variables. These are the models most widely used in discussions of endocrinology and metabolism. In this chapter, we will discuss the theory of compartmental models, and then discuss how the SAAM II software system, a system designed specifically to aid in the development and testing of multicompartmental models, can be used