AMIGO2: Advanced model identification using global optimization

AMIGO2 is a multi-platform MATLAB based toolbox designed to solve mathematical optimization problems which are at the core of systems biology:

• in the context of model parametric identification
• as the underlying hypothesis for model development
• in the optimal control of biological systems to synthetically achieve the desired behaviour

Parameter identification

As part of model building, deals with the computation of model unknowns (initial or boundary conditions and parameters) from experimental data.

Parameter identification is usually formulated as a non-linear optimization problem aimed to find the model unknowns which minimize some measure of the distance among model predictions and experimental data.

For the case of (large scale) non-linear models solving such a problem is usually a very challenging task due mainly to the presence of several suboptimal solutions or of several equivalent solutions, in other words, to poor or lack of practical identifiability.

AMIGO2 covers all the steps of the iterative identification procedure: local and global sensitivity analysis, local and global ranking of parameters, parameter estimation, identifiability analysis, regularization and optimal experimental design.

The ultimate goal is to enable the computation of model unknowns with the maximum accuracy and at a minimum experimental cost.

Optimization based modeling

Optimality principles have been successfully used to describe the design, organization and behavior of biological systems at different levels. In the context of cell biology, mathematical optimization is the underlying hypothesis in applications such as (dynamic) flux balance analysis and the analysis of activation of metabolic pathways.

These problems can be formulated as general dynamic optimization problems; the objective is to compute time varying control profiles, usually fluxes or enzyme concentrations and the corresponding expression rates, to maximize or minimize a given cost function, such as the amount of a specific metabolite or the time needed to reach a given amount of product, subject to the system dynamics (the model) and algebraic constraints, for example in the maximum amount of enzyme available. In addition, multi-objective formulations can be posed aimed at finding those control profiles which offer the best trade-offs among different objectives.

AMIGO2 enables the possibility of using optimality principles for modeling through multi-objective dynamic optimization.

Optimal control

Models can be used to confirm hypotheses, to draw predictions but also to design or optimize a certain aspect of the biological system. In this concern, once a suitable model system is available, it is possible to define new multi-objective dynamic optimization problems

to find those optimal stimulation conditions that result in a particular desired behavior. This is the case in, for example, model based metabolic engineering, optimal control or drug dose optimization, to name a few.

AMIGO2 enables the possibility of computing optimal designs and stimulation conditions using multi-objective dynamic optimization.