Table 3.
Timeline of representative algorithms for inverse problems in BST models.
| Authors | Year | Main Methods and Features | Model | Target Networks |
|
|---|---|---|---|---|---|
| Artificial* | Actual** | ||||
| Voit and Savageau [136] | 1982 | • Decoupling | S-system | (a) | |
| Voit [35] | 2000 | • Review of various bottom-up and top- down methods | S-system | ||
| GMA | |||||
| Seatzu [144] | 2000 | • Smoothing (B-splines) | S-system | (b) | |
| Maki et al. [123] | 2002 | • “Step-by-step” strategy | S-system | (c) | |
| Kikuchi et al. [134] | 2003 | • Simple genetic algorithm (SGA) • Penalty term in the objective function |
S-system | (A) | |
| Kimura et al. [124] | 2004 | • Decomposition method • Numerical integration with local linear regression |
S-system | (A) (B) | |
| Voit and Almeida [128] | 2004 | • Decoupling • ANN smoothing and slope approximation |
S-system | (C) | |
| Kimura et al. [82] | 2005 | • Decomposition • Cooperative coevolution algorithm |
S-system | (A) (B) | (d) |
| Lall and Voit [202] | 2005 | • “Peeling” technique | S-system | (e) | |
| Tsai and Wang [140] | 2005 | • Modified collocation method | S-system | (A) (D) | |
| Cho et al. [163] | 2006 | • S-tree based genetic programming (GP) | S-system | (A) | (f) (g) |
| Chou et al. [37] | 2006 | • Alternating regression (AR) | S-system | (A) (E) | |
| Daisuke and Horton [179] | 2006 | • Distributed genetic algorithm (DGA) • Use of scale-free property |
S-system | (A) | (h) |
| Kim et al. [194] | 2006 | • Genetic programming to estimate slopes and avoid numerical integration | S-system | (E) | |
| Marino and Voit [171] | 2006 | • Gradual increase in model complexity | S-system | (C) | |
| Naval et al. [201] | 2006 | • Particle swarm optimization (PSO) | S-system | (C) | |
| GMA | (i) | ||||
| Polisetty et al. [203] | 2006 | • Branch-and-reduce strategy | GMA | (F) | (i) |
| Tucker and Moulton[155] | 2006 | • Interval analysis | S-system | (A) (E) (G) | |
| Gonzalez et al. [197] | 2007 | • Simulated annealing (SA) | S-system | (C) | (j) |
| Kutalik et al. [83] | 2007 | • Newton-flow method | S-system | (B) (E) (H) (I) | |
| Marin-Sanguino et al. [248] | 2007 | • GMA optimizer • Geometric programming |
GMA | (i) (k) | |
| Noman and Iba [189] | 2007 | • Information criteria-based fitness evaluation • Differential evolution (DE) along with local search heuristics |
S-system | (A) (J) | (l) |
| Tucker et al. [156] | 2007 | • Constraint propagation | S-system | (E) | |
| GMA | (K) | ||||
| Goel et al. [21] | 2008 | • Dynamic flux estimation (DFE) | GMA | (m) | |
| Liu and Wang [164] | 2008 | • Multi-objective optimization | S-system | (A) (B) | (n) (o) (p) |
| Vilela et al. [159] | 2008 | • Eigenvector optimization (EO) | S-system | (A) (E) (H) (L) | |
| Zuñiga et al. [199] | 2008 | • Ant colony optimization (ACO) • Enhanced aggregation pheromone system (eAPS) |
S-system | ||
The artificial target networks used in the representative algorithms are: (A) Five-variable gene regulatory network [72]; (B) Thirty-variable system [81]; (C) Five-variable didactic system (four dependent variables and one independent variable) [128]; (D) Three-variable cascaded system [140]; (E) Four-variable didactic system (similar pathway as model (C) but without independent variables) [37]; (F) Four-variable branched pathway with several feedback inhibitions (three dependent variables and one independent variable) [35]; (G) Three-variable cascaded pathway [35]; (H) Two-variable system [83]; (I) Seven-variable system [83]; (J) Twenty-variable system [189]; (K) Three-variable branched pathway with several feedback inhibition signals (similar pathway as model (F) but without independent variables) [35]; (L) Ten-variable system ([159]).
The real networks used in the representative algorithms are: (a) Four-variable model of ethanol production by yeast [136]; (b) Five-variable forest growth model (four dependent variables and one independent variable) [31]; (c) Gene expression profiles during neural differentiation of P19 EC cells measured with mouse cDNA microarrays representing 15,000 genes [123]; (d) cDNA microarray data of Thermus thermophilus HB8 strains [82]; (e) NMR data from the L. lactis glycolysis pathway (model described in [202]; experimental data from [115,249,250]); (f) Anaerobic fermentation pathway in Saccharomyces cerevisiae (five dependent variables and eight independent variables) [251]; (g) SOS DNA repair system in E. coli [252]; (h) Gene expression profiles of mice (data selected from GDS404 in NCBI [253]) [179]; (i) Anaerobic fermentation pathway in Saccharomyces cerevisiae (same pathway as in model (f) but GMA model) [95]; (j) cadBA in E. coli [254]; (k) Tryptophan operon model in E. coli [255]; (l) Yeast cell-cycle microarray data [256]; (m) NMR data from the L. lactis glycolysis pathway [257] (same pathway as pathway (e) but GMA model [21]); (n) Kinetic model of ethanol fermentation [258]; (o) Circadian oscillations of period proteins in drosophila [259]; (p) Embryonic gene regulatory network in zebrafish [260].