Abstract
BackgroundSystems 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.ResultsHere, 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.ConclusionsIn 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.
Highlights
Systems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation
Experiments show that simple chemical reactions and some elementary interactions can lead to the formation of complex spatio-temporal patterns that are sensitive to changes in the experimental conditions and may undergo complete rearrangement in response to particular stimuli [52]
The first example is related to the bacterial chemotaxis process while the second, the FitzHughNagumo model, provides a qualitative description of some physiological processes, such as the neuron firing in the brain or the heart beat
Summary
Systems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation. 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 challenging when the system is described by partial differential equations. Despite the success of modeling efforts in systems biology, the truth is that only in few occasions those models have been used to design or to optimize desired biological behaviors This may be explained by the difficulty on formulating and solving those problems and in the limited number of software tools that may be used for that purpose [8]. The recently developed toolbox DOTcvpSB [9] can handle the dynamic optimization of lumped systems (described in terms of ordinary differential equations), such as those related to biochemical processes (see the reviews by Banga et al [7,8,10] and the works cited therein), or to biomedical systems [11,12,13,14,15,16]
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