Table 1 

Examples of applications of optimization in systems biology, classified by type of optimization problem (note that several types overlap) 

Problem type or application 
Description 
Examples with references 


Linear programming (LP) 
linear objective and constraints 
maximal possible yield of a fermentation [83]; metabolic flux balancing [18,83]; review of flux balance analysis in [30]; use of LP with genome scale models reviewed in [27]; inference of regulatory networks [40,42] 
Nonlinear programming (NLP) 
some of the constraints or the objective function are nonlinear 
applications to metabolic engineering and parameter estimation in pathways [69]; substrate metabolism in cardiomyocytes using ^{13}C data [84]; analysis of energy metabolism [85] 
Semidefinite programming (SDP) 
problems over symmetric positive semidefinite matrix variables with linear cost function and linear constraints 
partitioning the parameter space of a model into feasible and infeasible regions [86] 
Bilevel optimization (BLO) 
objective subject to constraints which arise from solving an inner optimization problem 
framework for identifying gene knockout strategies [87]; optimization of metabolic pathways under stability considerations [88]; optimal profiles of genetic alterations in metabolic engineering [89] 
Mixed integer linear programming (MILP) 
linear problem with both discrete and continuous decision variables 
finding all alternate optima in metabolic networks [90,91]; optimal intervention strategies for designing strains with enhanced capabilities [91]; framework for finding biological network topologies [47]; inferring gene regulatory networks [41] 
Mixed integer nonlinear programming (MINLP) 
nonlinear problem with both discrete and continuous decision variables 
analysis and design of metabolic reaction networks and their regulatory architecture [92,93]; inference of regulatory interactions using timecourse DNA microarray expression data [45] 
Parameter estimation 
model calibration minimizing differences between predicted and experimental values 
tutorial focused in systems biology [53]; parameter estimation using global and hybrid methods [52,54,55,59,70]; parameter estimation in stochastic models [58] 
Dynamic optimization (DO) 
Optimization with differential equations as constraints (and possible timedependent decision variables) 
discovery of biological network design strategies [94]; dynamic flux balance analysis [29]; optimal control for modification of selforganized dynamics [95]; optimal experimental design [66] 
Mixedinteger dynamic optimization (MIDO) 
Optimization with differential equations as constraints and both discrete and continuous decision variables (possibly timedependent) 
computational design of genetic circuits [76] 


Banga BMC Systems Biology 2008 2:47 doi:10.1186/17520509247 