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Table 1 Examples of applications of optimization in systems biology, classified by type of optimization problem (note that several types overlap)

From: Optimization in computational systems biology

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 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]