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Background: Systems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation. The possibility of perturbing biological systems in different manners calls for the design of perturbations to achieve particular goals. Examples would include, the design of a chemical stimulation to maximize the amplitude of a given cellular signal or to achieve a desired pattern in pattern formation systems, etc. Such design problems can be mathematically formulated as dynamic optimization problems which are particularly challenging when the system is described by partial differential equations. This work addresses the numerical solution of such dynamic optimization problems for spatially distributed biological systems. The usual nonlinear and large scale nature of the mathematical models related to this class of systems and the presence of constraints on the optimization problems, impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques. Results: Here, the use of a control vector parameterization approach combined with efficient and robust hybrid global optimization methods and a reduced order model methodology is proposed. The capabilities of this strategy are illustrated considering the solution of a two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model. Conclusions: In the process of chemotaxis the objective was to efficiently compute the time-varying optimal concentration of chemotractant in one of the spatial boundaries in order to achieve predefined cell distribution profiles. Results are in agreement with those previously published in the literature. The FitzHugh-Nagumo problem is also efficiently solved and it illustrates very well how dynamic optimization may be used to force a system to evolve from an undesired to a desired pattern with a reduced number of actuators. The presented methodology can be used for the efficient dynamic optimization of generic distributed biological systems. [ABSTRACT FROM AUTHOR]

Background: 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. Results: 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 (a priori and a posteriori) 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. Conclusions: The presented procedure was used to iteratively identify a mathematical model that describes the NF-_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. [ABSTRACT FROM AUTHOR]

Background: Modeling and simulation of cellular signaling and metabolic pathways as networks of biochemical reactions yields sets of non-linear ordinary differential equations. These models usually depend on several parameters and initial conditions. If these parameters are unknown, results from simulation studies can be misleading. Such a scenario can be avoided by fitting the model to experimental data before analyzing the system. This involves parameter estimation which is usually performed by minimizing a cost function which quantifies the difference between model predictions and measurements. Mathematically, this is formulated as a non-linear optimization problem which often results to be multi-modal (non-convex), rendering local optimization methods detrimental. Results: In this work we propose a new hybrid global method, based on the combination of an evolutionary search strategy with a local multiple-shooting approach, which offers a reliable and efficient alternative for the solution of large scale parameter estimation problems. Conclusion: The presented new hybrid strategy offers two main advantages over previous approaches: First, it is equipped with a switching strategy which allows the systematic determination of the transition from the local to global search. This avoids computationally expensive tests in advance. Second, using multiple-shooting as the local search procedure reduces the multi-modality of the non-linear optimization problem significantly. Because multiple-shooting avoids possible spurious solutions in the vicinity of the global optimum it often outperforms the frequently used initial value approach (single-shooting). Thereby, the use of multiple-shooting yields an enhanced robustness of the hybrid approach. [ABSTRACT FROM AUTHOR]

This article is part of a collection entitled “Models for Safety, Quality and Competitiveness of the Food Processing Sector,” published in Comprehensive Reviews in Food Science and Food Safety. It has been peer-reviewed and was written as a follow-up of a pre-IFT workshop, partially funded by the USDA NRI grant 2005-35503-16208. Mathematical models are the basis of modern process engineering methods. Mathematical optimization is at the kernel of systematic and efficient tools for (1) experimental design, model development, and identification, (2) development of optimal operating procedures, and (3) implementation of those procedures by means of model-predictive controllers. Here, we review and discuss how these model-based optimization techniques can be used at the core of computer-integrated manufacturing systems for the food industry. These systems will be able to bring the operation of food processing plants closer to the best possible product quality and safety, at a reduced cost and with minimal environmental impact. [ABSTRACT FROM AUTHOR]

Abstract: Thermal processing is widely used for ensuring food safety and extended shelf life. However, standard methods of thermal processing have a significant impact on food quality due to thermal degradation of nutrients and other quality factors. Model-based methods can be successfully used for thermal process design, optimization and control. However, building sound models requires suitable estimation of the unknown kinetic parameters. Further, the accuracy of these estimates will largely depend on the quality and quantity of the available experimental data. Optimal experimental design (OED) of dynamic experiments allows for the calculation of the scheme of controls and measurements which improve the estimation of model parameters. In this contribution, the OED problem is formulated as a general dynamic optimization problem where the objective is to find those experimental conditions which result in maximum information content, as measured by the Fisher information matrix. The numerical solution of this problem is then approached using a combination of the control vector parameterization approach with a non-linear global optimization solver. As an illustrative application, we consider the optimal experimental design for the parameter estimation of the thiamine degradation kinetic parameters during the thermal processing of canned tuna. Results confirm that the use of optimal dynamic experiments not only improves identifiability but also results in reduced confidence regions for the parameters (a maximum error of the 2% in the parameter estimates), substantially decreasing the experimental effort (up to a 50%). Particularly the use of six optimally designed experiments results in a 30% reduction of the confidence regions with respect to previously published results using 10 typical experiments. [Copyright &y& Elsevier]