Dynamic optimization of distributed biological systems using robust and efficient numerical techniques

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.

AMIGO2, a toolbox for dynamic modeling, optimization and control in systems biology

“…This is the case in, e.g. model-based metabolic engineering (Villaverde et al , 2016), pattern formation (Vilas et al , 2012) or drug dose optimization (Jayachandran et al , 2015). …”

An Evolutionary Firefly Algorithm for the Estimation of Nonlinear Biological Model Parameters

“…Since our method can find identifiable parameters from experimental data, it can be employed when designing optimal experiments for parameter estimation [30], [31], [40], [49]. In addition, owing to its reduced computation time, parameters of more detailed nonlinear models such as spatially resolved reaction-diffusion models [51], [52], [53] could also potentially be estimated with the method.…”

Model-Based Real Time Operation of the Freeze-Drying Process

“…There are several alternatives for the solution of dynamic optimization problems [11]. In this case, we have chosen the control vector parameterization (CVP) approach [49], because of its capacity to handle large-scale dynamic optimization problems without solving very large non-linear programming (NLP) problems and without dealing with extra junction constraints [50].…”

“…In this context, optimization protocols based on mechanistic, first-principles models [11][12][13] can help to achieve the desired time reductions while keeping quality, and also provide a robust tool to deal 1. It shows how the identification problem (i.e., characterization of product and equipment) can be simplified by solving a (decoupled) sequence of parameter identification problems, this is, by considering food matrix and freeze-drying chamber as two separate subsystems, which are described by physics-based operational models developed to satisfy identifiability.…”