Bio Med Central BMC Systems Biology

Open Access Commentary

Optimization in computational systems biology

Julio R Banga

Address: Instituto de Investigaciones Marinas, CSIC (Spanish Council for Scientific Research), C/Eduardo Cabello 6, 36208 Vigo, Spain

Email: Julio R Banga-julio@iim.csic.es

Abstract

Optimization aims to make a system or design as effective or functional as possible. Mathematical

optimization methods are widely used in engineering, economics and science. This commentary is

focused on applications of mathematical optimization in computational systems biology. Examples

are given where optimization methods are used for topics ranging from model building and optimal

experimental design to metabolic engineering and synthetic biology. Finally, several perspectives for

future research are outlined.

Background

To optimize means to find the best solution, the best com-promise among several conflicting demands subject to predefined requirements (called constraints). Mathemati-cal optimization has been extremely successful as an aid to better decision making in science, engineering and eco-nomics.

Optimization and optimality are certainly not new con-cepts in biology. The structures, movements and behav-iors of animals, and their life histories, have been shaped by the optimizing processes of evolution or of learning by trial and error [1,2]. Moreover, optimization theory not only explains current adaptations of biological systems, but also helps to predict new designs that may yet evolve [1,2]. The use of optimization in the close fields of com-putational biology and bioinformatics has been reviewed recently elsewhere [3,4]. Here, I aim to illustrate the capa-bilities, opportunities and benefits that mathematical optimization can bring to research in systems biology. First, I will introduce several basic concepts that can help readers unfamiliar with mathematical optimization. The key elements of mathematical optimization problems are the decision variables (those which can be varied during the search of the best solution), the objective function (the per-formance index which quantifies the quality of a solution defined by a set of decision variables, and which can be maximized or minimized), and the constraints (require-ments that must be met, usually expressed as equalities and inequalities). Decision variables can be continuous (represented by real numbers), resulting in continuous opti-mization problems, or discrete (represented by integer numbers), resulting in integer optimization (also called combinatorial optimization) problems. In many instances, there is a mix of continuous and integer decision varia-bles.

As an illustrative example, consider the \"diet problem\", one of the first modern optimization problems [5], stud-ied in the 1940s: to find the cheapest combination of foods that will satisfy all the daily nutritional require-ments of a person. In this classical problem, the objective function to minimize is the cost of the food, the decision variables are the amounts of each type of food to be pur-chased (assumed as continuous variables), and the con-straints are the nutritional needs be satisfied, like total calories, or amounts of vitamins, minerals, etc., in the diet.

Published: 28 May 2008

BMC Systems Biology 2008, 2:47doi:10.1186/1752-0509-2-47Received: 21 February 2008 Accepted: 28 May 2008

This article is available from: http://www.doczj.com/doc/9cacd32fb4daa58da0114a8a.html/1752-0509/2/47

? 2008 Banga; licensee BioMed Central Ltd.

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