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


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 13C 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 time-course 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 time-dependent decision variables)

discovery of biological network design strategies [94]; dynamic flux balance analysis [29]; optimal control for modification of self-organized dynamics [95]; optimal experimental design [66]

Mixed-integer dynamic optimization (MIDO)

Optimization with differential equations as constraints and both discrete and continuous decision variables (possibly time-dependent)

computational design of genetic circuits [76]

Banga BMC Systems Biology 2008 2:47   doi:10.1186/1752-0509-2-47

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