- Open Access
Optimization in computational systems biology
© Banga; licensee BioMed Central Ltd. 2008
- Received: 21 February 2008
- Accepted: 28 May 2008
- Published: 28 May 2008
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.
- Synthetic Biology
- Convex Optimization Problem
- Flux Balance Analysis
- Mathematical Optimization
- Optimal Experimental Design
To optimize means to find the best solution, the best compromise among several conflicting demands subject to predefined requirements (called constraints). Mathematical optimization has been extremely successful as an aid to better decision making in science, engineering and economics.
Optimization and optimality are certainly not new concepts in biology. The structures, movements and behaviors 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 computational biology and bioinformatics has been reviewed recently elsewhere [3, 4]. Here, I aim to illustrate the capabilities, 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 performance 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 (requirements that must be met, usually expressed as equalities and inequalities). Decision variables can be continuous (represented by real numbers), resulting in continuous optimization 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 variables.
As an illustrative example, consider the "diet problem", one of the first modern optimization problems , studied in the 1940s: to find the cheapest combination of foods that will satisfy all the daily nutritional requirements 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 purchased (assumed as continuous variables), and the constraints are the nutritional needs be satisfied, like total calories, or amounts of vitamins, minerals, etc., in the diet.
The "diet problem" has certain interesting properties: it is a continuous problem where both the objective function (total cost, i.e. sum of the costs of each food purchased) and the constraints are linear with respect to the decision variables, so this problem belongs to the important class of linear programming, or LP (note that due to historical reasons, programming is used here in the sense of planning). These linear constraints define a feasible space (space of decision variables where constraints are satisfied) which is a convex polyhedron, so it is a convex problem. Convex optimization problems  are particularly interesting, since they have a unique solution (i.e. they are unimodal) and they can be solved very efficiently and reliably, even for very large number of decisions variables.
The solution of multimodal problems is studied by the subfield of global optimization [7–10]. Many continuous problems and the vast majority of combinatorial optimization problems belong to this class. Most problems in global optimization are very hard to solve exactly in a reasonable computation time. Fortunately, recent developments indicate that convex optimization problems are more prevalent in practice than was previously thought . Thus, it is highly desirable to formulate (or re-formulate) the statement of any optimization problem as a convex one. The book by Boyd and Vandenberghe  gives detailed information on how to recognize, formulate, and solve convex optimization problems.
Model-based optimization is a key methodology in engineering, helping in the design, analysis, construction and operation of all kind of devices. Since engineering approaches are playing a significant role in the rapid evolution of systems biology [11–14], it is expected that mathematical optimization methods will contribute in a significant way to advances in systems biology.
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 ; metabolic flux balancing [18, 83]; review of flux balance analysis in ; use of LP with genome scale models reviewed in ; inference of regulatory networks [40, 42]
Nonlinear programming (NLP)
some of the constraints or the objective function are nonlinear
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 
Bilevel optimization (BLO)
objective subject to constraints which arise from solving an inner optimization problem
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 ; framework for finding biological network topologies ; inferring gene regulatory networks 
Mixed integer nonlinear programming (MINLP)
nonlinear problem with both discrete and continuous decision variables
model calibration minimizing differences between predicted and experimental values
Dynamic optimization (DO)
Optimization with differential equations as constraints (and possible time-dependent decision variables)
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 
Optimization methods have been applied in both metabolic control analysis [15, 16] and biochemical systems theory . Further, optimization (and, more in particular, linear programming) has been the engine behind metabolic flux balance analysis, where the optimal flux distributions are calculated using linear optimization, and are used to represent the metabolic phenotype for certain conditions. This flux balance methodology provides a guide to metabolic engineering and a method for bioprocess optimization . Examples of success stories are the in silico predictions of Escherichia coli metabolic capabilities , or the genome-scale reconstruction of the Saccharomyces cerevisiae metabolic network .
Metabolic engineering exploits an integrated, systems-level approach for optimizing a desired cellular property or phenotype . New optimization-based methods are being developed by using genome-scale metabolic models, which enable identification of gene knockout strategies for obtaining improved phenotypes. However, these problems have a combinatorial nature, so the computational time increases exponentially with the size of the problem for exact methods, so there is a clear need of developing approximate yet faster algorithms . Not surprisingly, optimization will also help in the bioengineering of novel in vitro metabolic pathways using synthetic biology, as the key component in rational redesign and directed evolution [23–26].
Coupling constraint-based analysis with optimization has been used to generate a consistent framework for the generation of hypotheses and the testing of functions of microbial cells using genome-scale models . Extensions and modifications of flux balance analysis continue to use optimization methods extensively [28–32].
A particularly interesting question in this context concerns the principles behind the optimal metabolic network operation, i.e. "which are the criteria (objective functions) being optimized in these networks?", a question which has been addressed in detail recently [33, 34]. Constrained evolutionary optimization has also been used to understand optimal circuit design . Moreover, optimization principles have also been used to explain the complexity and robustness found in biochemical networks [36–38], and much more work in this topic is to be expected in the near future. Related to this, the hypothesis that metabolic systems have evolved optimal strategies as a result of evolutionary pressures has been used in cybernetic models , an approach which may offer advantages over traditional methodologies.
Reverse engineering in systems biology aims to reconstruct the biochemical interactions from data sets of a particular biological system. Optimization has been used for inferring important biomolecular networks, such as e.g. transcriptional regulatory networks , gene regulatory networks [41–46], signaling pathways  and protein interaction networks [48, 49].
System identification [50, 51] is a methodology widely used in engineering for building mathematical models of dynamical systems based on measured data. Roughly, this involves selected the structure of the model and estimating the parameters of such model from the available experimental data.
The problem of parameter estimation in biochemical pathways, formulated as a nonlinear programming problem subject to the pathway model acting as constraints, has also received great attention [52–59]. Since these problems are frequently multimodal, global optimization methods are needed in order to avoid local solutions. A local solution can be very misleading when calibrating models: it would indicate a bad fit even for a model which could potentially match perfectly a set of experimental data.
Since biological experiments are both expensive and time consuming, it would be ideal if one could plan them in an optimal way, i.e. minimizing their cost while maximizing the amount of information to be extracted from such experiments. This is the purpose of optimal experimental design and optimal identification procedures [60–66], a topic which can make a great impact in the near future, especially in connection with high-throughput techniques.
Although, as already mentioned, it would be desirable to formulate all the optimization problems as convex ones, in many occasions this is not possible, so we face the solution of global optimization problems, most of which belong to the class of NP-hard problems , where obtaining global optima with guarantees will be impossible in many instances. In these situations, approximate techniques like stochastic global optimization can at least locate a near globally optimal solution in a reasonable time, although the cost to pay is that these methods do not offer full guarantees of global optimality. In this context, evolutionary computation methods are a class of stochastic methods which have shown good performance in systems biology applications [55, 67–69]. Hybrid methods, combining global and local techniques, have also shown great potential with difficult problems like parameter estimation [54, 59, 70]. Much more work is needed to further enhance the efficiency and robustness of these approaches in order to make then applicable to large scale models.
Another important issue is the stochasticity that is inherent in biomolecular systems [71, 72]. This stochastic nature requires advances in optimization methods, and a number of researches are already providing useful approaches, such as in parameter estimation in stochastic biochemical reactions  or in the optimization of stochastic gene network models .
As stated in , it would be desirable to have computer-aided design tools for biological engineering, similarly to what already happens in many other areas of engineering. Such software would guide the improvement of the behaviour of a biological system in silico by optimizing design parameters targeting a selected objective function. The optimization of such synthetic biological systems is in fact receiving increasing attention: optimization algorithms could search for the components (promoters, operators, regulatory proteins, inducers, etc.) and find the best configurations optimizing the dynamic behaviour according to predefined design objectives . A promising example of what can be done is the OptCircuit framework , which can be used as an optimization-based design platform to aid in the construction and fine tuning of integrated biological circuits. Other researches are adapting the workflow developed by the electronics industry to the design and assembly of very large scale integrated genetic systems, claiming that the computer assisted design and fabrication of genetic systems will be a reality by 2012 .
Moreover, optimization could also be used after the design and construction phases, inside a model predictive control framework , to optimally manipulate the resulting biological systems. This is the dream of metabolic engineering [26, 79] and synthetic biology [21, 25, 74]. We are still not there, but the purpose of this paper has been to show that we are getting close. Several issues must be addressed before we reach that goal. First, we need robust and efficient methods for optimization under uncertainty, and for the optimization of stochastic models, that are also able to scale-up, hopefully even at the level of genome-scale models. Second, since neither we nor nature rarely have a single objective, we need multicriteria optimization methods that are better able to cope with the scale and complexity of models from systems biology .
Finally, it should be recognized that standard optimization can be sometimes insufficient for gaining deeper insights regarding certain aspects of systems biology, such as in the evolution of biological systems. While evolving towards optimal properties, the environment may change or organisms may even change their own environment, which in turn alters the optimum. In an evolutionary system, continuing development is needed so as to maintain its fitness relative to the systems it is co-evolving with. In other words, everyone has to keep improving in order to survive, which is known as the "Red Queen" effect . Thus, game-theoretic approaches, such as evolutionary game theory , may provide a better framework studying the evolution of biochemical systems.
Sutherland  claims that, in a context of increasing calls for biology to be predictive, optimization is the only approach biology has for making predictions from first principles. This claim is substantiated by an increasing body of research. We should expect, therefore, even wider use of optimization theory and practice in systems biology.
The author would like to thank Matt Hodgkinson for his valuable comments, and acknowledges financial support from EU project BaSysBio LSHG-CT-2006-037469
- Alexander RM: Optima for animals. 1982, London: E. ArnoldGoogle Scholar
- Sutherland WJ: The best solution. Nature. 2005, 435 (7042): 569-569. 10.1038/435569aView ArticlePubMedGoogle Scholar
- Greenberg HJ, Hart WE, Lancia G: Opportunities for combinatorial optimization in computational biology. Informs Journal on Computing. 2004, 16 (3): 211-231. 10.1287/ijoc.1040.0073.View ArticleGoogle Scholar
- Larranaga P, Calvo B, Santana R, Bielza C, Galdiano J, Inza I, Lozano JA, Armananzas R, Santafe G, Perez A, Robles A: Machine learning in bioinformatics. Briefings in Bioinformatics. 2006, 7 (1): 86-112. 10.1093/bib/bbk007View ArticlePubMedGoogle Scholar
- Dantzig GB: The diet problem. Interfaces. 1990, 20 (4): 43-47.View ArticleGoogle Scholar
- Boyd SP, Vandenberghe L: Convex optimization. 2004, Cambridge: Cambridge UniversityView ArticleGoogle Scholar
- Horst R, Pardalos PM, Romeijn HE: Handbook of global optimization. 1995, Dordrecht ; Boston: Kluwer Academic PublishersView ArticleGoogle Scholar
- Horst R, Pardalos PM, Thoai NV: Introduction to global optimization. 2000, Dordrecht ; Boston: Kluwer Academic Publishers, 2View ArticleGoogle Scholar
- Floudas CA: Deterministic global optimization : theory, methods, and applications. 2000, Dordrecht ; Boston: Kluwer Academic PublishersView ArticleGoogle Scholar
- Floudas CA, Pardalos PM: Optimization in computational chemistry and molecular biology : local and global approaches. 2000, Dordrecht ; Boston: Kluwer Academic PublishersView ArticleGoogle Scholar
- Doyle FJ, Stelling J: Systems interface biology. Journal of the Royal Society Interface. 2006, 3 (10): 603-616. 10.1098/rsif.2006.0143.PubMed CentralView ArticleGoogle Scholar
- Kremling A, Saez-Rodriguez J: Systems biology – An engineering perspective. Journal of Biotechnology. 2007, 129 (2): 329-351. 10.1016/j.jbiotec.2007.02.009View ArticlePubMedGoogle Scholar
- Wolkenhauer O, Ullah M, Wellstead P, Cho KH: The dynamic systems approach to control and regulation of intracellular networks. Febs Letters. 2005, 579 (8): 1846-1853. 10.1016/j.febslet.2005.02.008View ArticlePubMedGoogle Scholar
- Sontag ED: Molecular systems biology and control. European Journal of Control. 2005, 11 (4–5): 396-435. 10.3166/ejc.11.396-435.View ArticleGoogle Scholar
- Heinrich R, Schuster S: The modelling of metabolic systems. Structure, control and optimality. Biosystems. 1998, 47 (1–2): 61-77. 10.1016/S0303-2647(98)00013-6View ArticlePubMedGoogle Scholar
- Heinrich R, Schuster S: The regulation of cellular systems. 1996, New York: Chapman & HallView ArticleGoogle Scholar
- Torres NV, Voit EO: Pathway analysis and optimization in metabolic engineering. 2002, New York: Cambridge University PressView ArticleGoogle Scholar
- Varma A, Palsson BO: Metabolic flux balancing – basic concepts, scientific and practical use. Bio-Technology. 1994, 12 (10): 994-998.View ArticleGoogle Scholar
- Edwards JS, Ibarra RU, Palsson BO: In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data. Nature Biotechnology. 2001, 19 (2): 125-130. 10.1038/84379View ArticlePubMedGoogle Scholar
- Forster J, Famili I, Fu P, Palsson BO, Nielsen J: Genome-scale reconstruction of the Saccharomyces cerevisiae metabolic network. Genome Research. 2003, 13 (2): 244-253. 10.1101/gr.234503PubMed CentralView ArticlePubMedGoogle Scholar
- Tyo KE, Alper HS, Stephanopoulos GN: Expanding the metabolic engineering toolbox: more options to engineer cells. Trends in Biotechnology. 2007, 25 (3): 132-137. 10.1016/j.tibtech.2007.01.003View ArticlePubMedGoogle Scholar
- Patil KR, Rocha I, Forster J, Nielsen J: Evolutionary programming as a platform for in silico metabolic engineering. BMC Bioinformatics. 2005, 6: 308- 10.1186/1471-2105-6-308PubMed CentralView ArticlePubMedGoogle Scholar
- Andrianantoandro E, Basu S, Karig DK, Weiss R: Synthetic biology: new engineering rules for an emerging discipline. Mol Syst Biol. 2006, 2: 2006.0028- 10.1038/msb4100073PubMed CentralView ArticlePubMedGoogle Scholar
- Villalobos A, Ness JE, Gustafsson C, Minshull J, Govindarajan S: Gene Designer: a synthetic biology tool for constructing artificial DNA segments. BMC Bioinformatics. 2006, 7: 285- 10.1186/1471-2105-7-285PubMed CentralView ArticlePubMedGoogle Scholar
- Meyer A, Pellaux R, Panke S: Bioengineering novel in vitro metabolic pathways using synthetic biology. Current Opinion in Microbiology. 2007, 10 (3): 246-253. 10.1016/j.mib.2007.05.009View ArticlePubMedGoogle Scholar
- Styczynski MP, Fischer CR, Stephanopoulos GN: The intelligent design of evolution. Mol Syst Biol. 2006Google Scholar
- Price ND, Reed JL, Palsson BO: Genome-scale models of microbial cells: Evaluating the consequences of constraints. Nature Reviews Microbiology. 2004, 2 (11): 886-897. 10.1038/nrmicro1023View ArticlePubMedGoogle Scholar
- Henry CS, Broadbelt LJ, Hatzimanikatis V: Thermodynamics-based metabolic flux analysis. Biophysical Journal. 2007, 92 (5): 1792-1805. 10.1529/biophysj.106.093138PubMed CentralView ArticlePubMedGoogle Scholar
- Mahadevan R, Edwards JS, Doyle FJ: Dynamic flux balance analysis of diauxic growth in Escherichia coli. Biophys J. 2002, 83 (3): 1331-1340.PubMed CentralView ArticlePubMedGoogle Scholar
- Kauffman KJ, Prakash P, Edwards JS: Advances in flux balance analysis. Current Opinion in Biotechnology. 2003, 14 (5): 491-496. 10.1016/j.copbio.2003.08.001View ArticlePubMedGoogle Scholar
- Llaneras F, Pico J: An interval approach for dealing with flux distributions and elementary modes activity patterns. Journal of Theoretical Biology. 2007, 246 (2): 290-308. 10.1016/j.jtbi.2006.12.029View ArticlePubMedGoogle Scholar
- Segre D, Vitkup D, Church GM: Analysis of optimality in natural and perturbed metabolic networks. Proc Natl Acad Sci U S A. 2002, 99 (23): 15112-15117. 10.1073/pnas.232349399PubMed CentralView ArticlePubMedGoogle Scholar
- Schuetz R, Kuepfer L, Sauer U: Systematic evaluation of objective functions for predicting intracellular fluxes in Escherichia coli. Molecular Systems Biology. 2007, 3: 15-10.1038/msb4100162.View ArticleGoogle Scholar
- Nielsen J: Principles of optimal metabolic network operation. Molecular Systems Biology. 2007, 3: 2-10.1038/msb4100169.View ArticleGoogle Scholar
- Alon U: An introduction to systems biology. 2006, Chapman and HallGoogle Scholar
- Stelling J, Sauer U, Szallasi Z, Doyle FJ, Doyle J: Robustness of cellular functions. Cell. 2004, 118 (6): 675-685. 10.1016/j.cell.2004.09.008View ArticlePubMedGoogle Scholar
- Carlson JM, Doyle J: Complexity and robustness. Proc Natl Acad Sci U S A. 2002, 99: 2538-2545. 10.1073/pnas.012582499PubMed CentralView ArticlePubMedGoogle Scholar
- Tanaka R, Csete M, Doyle J: Highly optimised global organisation of metabolic networks. Iee Proceedings Systems Biology. 2005, 152 (4): 179-184. 10.1049/ip-syb:20050042View ArticlePubMedGoogle Scholar
- Varner J, Ramkrishna D: Metabolic engineering from a cybernetic perspective. 1. Theoretical preliminaries. Biotechnology Progress. 1999, 15 (3): 407-425. 10.1021/bp990017pView ArticlePubMedGoogle Scholar
- Wang RS, Wang Y, Zhang XS, Chen L: Inferring transcriptional regulatory networks from high-throughput data. Bioinformatics. 2007, 23 (22): 3056-3064. 10.1093/bioinformatics/btm465View ArticlePubMedGoogle Scholar
- Dasika M, Gupta A, Maranas C: A mixed integer linear programming (MILP) framework for inferring time delay in gene regulatory networks. Pac Symp Biocomput. 2004, 474-486.Google Scholar
- Wang Y, Joshi T, Zhang XS, Xu D, Chen LN: Inferring gene regulatory networks from multiple microarray datasets. Bioinformatics. 2006, 22 (19): 2413-2420. 10.1093/bioinformatics/btl396View ArticlePubMedGoogle Scholar
- Kim S, Kim J, Cho KH: Inferring gene regulatory networks from temporal expression profiles under time-delay and noise. Computational Biology and Chemistry. 2007, 31 (4): 239-245. 10.1016/j.compbiolchem.2007.03.013.View ArticlePubMedGoogle Scholar
- Cho KH, Choo SM, Jung SH, Kim JR, Choi HS, Kim J: Reverse engineering of gene regulatory networks. Iet Systems Biology. 2007, 1 (3): 149-163. 10.1049/iet-syb:20060075View ArticlePubMedGoogle Scholar
- Thomas R, Paredes CJ, Mehrotra S, Hatzimanikatis V, Papoutsakis ET: A model-based optimization framework for the inference of regulatory interactions using time-course DNA microarray expression data. BMC Bioinformatics. 2007, 8: 228- 10.1186/1471-2105-8-228PubMed CentralView ArticlePubMedGoogle Scholar
- Yeung MKS, Tegner J, Collins JJ: Reverse engineering gene networks using singular value decomposition and robust regression. Proceedings of the National Academy of Sciences of the United States of America. 2002, 99 (9): 6163-6168. 10.1073/pnas.092576199PubMed CentralView ArticlePubMedGoogle Scholar
- Lin XX, Floudas CA, Wang Y, Broach JR: Theoretical and computational studies of the glucose signaling pathways in yeast using global gene expression data. Biotechnology and Bioengineering. 2003, 84 (7): 864-886. 10.1002/bit.10844.View ArticlePubMedGoogle Scholar
- Han S, Yoon Y, Cho KH: Inferring biomolecular interaction networks based on convex optimization. Computational Biology and Chemistry. 2007, 31 (5–6): 347-354. 10.1016/j.compbiolchem.2007.08.003.View ArticlePubMedGoogle Scholar
- Wang RS, Wang Y, Wu LY, Zhang XS, Chen L: Analysis on multi-domain cooperation for predicting protein-protein interactions. BMC Bioinformatics. 2007, 8: 391- 10.1186/1471-2105-8-391PubMed CentralView ArticlePubMedGoogle Scholar
- Ljung L: System identification: theory for the user. 1999, Upper Saddle River, NJ: Prentice Hall, 2Google Scholar
- Walter E, Pronzato L: Identification of parametric models from experimental data. 1997, Berlin; New York; Paris: Springer; MassonGoogle Scholar
- Zwolak JW, Tyson JJ, Watson LT: Globally optimised parameters for a model of mitotic control in frog egg extracts. Iee Proceedings Systems Biology. 2005, 152 (2): 81-92. 10.1049/ip-syb:20045032View ArticlePubMedGoogle Scholar
- Jaqaman K, Danuser G: Linking data to models: data regression. Nature Reviews Molecular Cell Biology. 2006, 7 (11): 813-819. 10.1038/nrm2030View ArticlePubMedGoogle Scholar
- Rodriguez-Fernandez M, Egea JA, Banga JR: Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems. BMC Bioinformatics. 2006, 7: 483- 10.1186/1471-2105-7-483PubMed CentralView ArticlePubMedGoogle Scholar
- Moles CG, Mendes P, Banga JR: Parameter estimation in biochemical pathways: A comparison of global optimization methods. Genome Research. 2003, 13 (11): 2467-2474. 10.1101/gr.1262503PubMed CentralView ArticlePubMedGoogle Scholar
- Famili I, Mahadevan R, Palsson BO: k-cone analysis: Determining all candidate values for kinetic parameters on a network scale. Biophysical Journal. 2005, 88 (3): 1616-1625. 10.1529/biophysj.104.050385PubMed CentralView ArticlePubMedGoogle Scholar
- Segrè D: From Annotated Genomes to Metabolic Flux Models and Kinetic Parameter Fitting. OMICS. 2003, 7 (3): 301-316. 10.1089/153623103322452413View ArticlePubMedGoogle Scholar
- Reinker S, Altman RM, Timmer J: Parameter estimation in stochastic biochemical reactions. Iee Proceedings Systems Biology. 2006, 153 (4): 168-178. 10.1049/ip-syb:20050105View ArticlePubMedGoogle Scholar
- Balsa-Canto E, Peifer M, Banga JR, Timmer J, Fleck C: Hybrid optimization method with general switching strategy for parameter estimation. BMC Syst Biol. 2008, 2: 26- 10.1186/1752-0509-2-26PubMed CentralView ArticlePubMedGoogle Scholar
- Banga JR, Versyck KJ, Van Impe JF: Computation of optimal identification experiments for nonlinear dynamic process models: a stochastic global optimization approach. Industrial & Engineering Chemistry Research. 2002, 41 (10): 2425-2430. 10.1021/ie010183d.View ArticleGoogle Scholar
- Cho KH, Shin SY, Kolch W, Wolkenhauer O: Experimental design in systems biology, based on parameter sensitivity analysis using a Monte Carlo method: A case study for the TNF alpha-mediated NF-kappa B signal transduction pathway. Simulation-Transactions of the Society for Modeling and Simulation International. 2003, 79 (12): 726-739. 10.1177/0037549703040943.View ArticleGoogle Scholar
- Faller D, Klingmuller U, Timmer J: Simulation methods for optimal experimental design in systems biology. Simulation-Transactions of the Society for Modeling and Simulation International. 2003, 79 (12): 717-725. 10.1177/0037549703040937.View ArticleGoogle Scholar
- Gadkar KG, Gunawan R, Doyle FJ: Iterative approach to model identification of biological networks. BMC Bioinformatics. 2005, 6: 155- 10.1186/1471-2105-6-155PubMed CentralView ArticlePubMedGoogle Scholar
- Casey FP, Baird D, Feng Q, Gutenkunst RN, Waterfall JJ, Myers CR, Brown KS, Cerione RA, Sethna JP: Optimal experimental design in an epidermal growth factor receptor signalling and down-regulation model. Iet Systems Biology. 2007, 1 (3): 190-202. 10.1049/iet-syb:20060065View ArticlePubMedGoogle Scholar
- Feng XJ, Rabitz H, Turinici G, Le Bris C: A closed-loop identification protocol for nonlinear dynamical systems. Journal of Physical Chemistry A. 2006, 110 (25): 7755-7762. 10.1021/jp056189o.View ArticleGoogle Scholar
- Balsa-Canto E, Alonso AA, Banga JR: An optimal identification procedure for model development in systems biology. FOSBE (FOUNDATIONS OF SISTEMS BIOLOGY AND ENGINEERING): 2007. 2007, Stuttgart (Germany)Google Scholar
- Goodacre R: Making sense of the metabolome using evolutionary computation: seeing the wood with the trees. Journal of Experimental Botany. 2005, 56 (410): 245-254. 10.1093/jxb/eri043View ArticlePubMedGoogle Scholar
- Kell DB: Metabolomics, modelling and machine learning in systems biology – towards an understanding of the languages of cells. Febs Journal. 2006, 273 (5): 873-894. 10.1111/j.1742-4658.2006.05136.xView ArticlePubMedGoogle Scholar
- Mendes P, Kell DB: Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation. Bioinformatics. 1998, 14 (10): 869-883. 10.1093/bioinformatics/14.10.869View ArticlePubMedGoogle Scholar
- Rodriguez-Fernandez M, Mendes P, Banga JR: A hybrid approach for efficient and robust parameter estimation in biochemical pathways. Biosystems. 2006, 83 (2–3): 248-265. 10.1016/j.biosystems.2005.06.016View ArticlePubMedGoogle Scholar
- Kaznessis YN: Models for synthetic biology. BMC Syst Biol. 2007, 1: 47- 10.1186/1752-0509-1-47PubMed CentralView ArticlePubMedGoogle Scholar
- Ma'ayan A, Blitzer RD, Iyengar R: Toward predictive models of mammalian cells. Annual Review of Biophysics and Biomolecular Structure. 2005, 34: 319-349. 10.1146/annurev.biophys.34.040204.144415.PubMed CentralView ArticlePubMedGoogle Scholar
- Tomshine J, Kaznessis YN: Optimization of a stochastically simulated gene network model via simulated annealing. Biophysical Journal. 2006, 91 (9): 3196-3205. 10.1529/biophysj.106.083485PubMed CentralView ArticlePubMedGoogle Scholar
- Heinemann M, Panke S: Synthetic biology – putting engineering into biology. Bioinformatics. 2006, 22 (22): 2790-2799. 10.1093/bioinformatics/btl469View ArticlePubMedGoogle Scholar
- Sotiropoulos V, Kaznessis YN: Synthetic tetracycline-inducible regulatory networks: computer-aided design of dynamic phenotypes. BMC Syst Biol. 2007, 1: 7- 10.1186/1752-0509-1-7PubMed CentralView ArticlePubMedGoogle Scholar
- Dasika MS, Maranas CD: OptCircuit: An optimization based method for computational design of genetic circuits. BMC Syst Biol. 2008, 2:24PubMed CentralView ArticlePubMedGoogle Scholar
- Cai Y, Hartnett B, Gustafsson C, Peccoud J: A syntactic model to design and verify synthetic genetic constructs derived from standard biological parts. Bioinformatics. 2007, 23 (20): 2760-2767. 10.1093/bioinformatics/btm446View ArticlePubMedGoogle Scholar
- Bagheri N, Stelling J, Doyle FJ: Circadian phase entrainment via nonlinear model predictive control. International Journal of Robust and Nonlinear Control. 2007, 17 (17): 1555-1571. 10.1002/rnc.1209.View ArticleGoogle Scholar
- Jung GY, Stephanopoulos G: A functional protein chip for pathway optimization and in vitro metabolic engineering. Science. 2004, 304 (5669): 428-431. 10.1126/science.1096920View ArticlePubMedGoogle Scholar
- Handl J, Kell DB, Knowles J: Multiobjective optimization in bioinformatics and computational biology. Ieee-Acm Transactions on Computational Biology and Bioinformatics. 2007, 4 (2): 279-292. 10.1109/TCBB.2007.070203.View ArticlePubMedGoogle Scholar
- Nowak MA, Sigmund K: Evolutionary dynamics of biological games. Science. 2004, 303 (5659): 793-799. 10.1126/science.1093411View ArticlePubMedGoogle Scholar
- Pfeiffer T, Schuster S: Game-theoretical approaches to studying the evolution of biochemical systems. Trends in Biochemical Sciences. 2005, 30 (1): 20-25. 10.1016/j.tibs.2004.11.006View ArticlePubMedGoogle Scholar
- Papoutsakis ET: EQUATIONS AND CALCULATIONS FOR FERMENTATIONS OF BUTYRIC-ACID BACTERIA. Biotechnology and Bioengineering. 1984, 26 (2): 174-187. 10.1002/bit.260260210.View ArticlePubMedGoogle Scholar
- Vo TD, Pallsson BO: Isotopomer analysis of myocardial substrate metabolism: A systems biology approach. Biotechnology and Bioengineering. 2006, 95 (5): 972-983. 10.1002/bit.21063.View ArticlePubMedGoogle Scholar
- Vo TD, Lee WNP, Palsson PO: Systems analysis of energy metabolism elucidates the affected respiratory chain complex in Leigh's syndrome. Molecular Genetics and Metabolism. 2007, 91 (1): 15-22. 10.1016/j.ymgme.2007.01.012.View ArticlePubMedGoogle Scholar
- Kuepfer L, Sauer U, Parrilo PA: Efficient classification of complete parameter regions based on semidefinite programming. BMC Bioinformatics. 2007, 8: 12- 10.1186/1471-2105-8-12PubMed CentralView ArticlePubMedGoogle Scholar
- Burgard AP, Pharkya P, Maranas CD: OptKnock: A bilevel programming framework for identifying gene knockout strategies for microbial strain optimization. Biotechnology and Bioengineering. 2003, 84 (6): 647-657. 10.1002/bit.10803.View ArticlePubMedGoogle Scholar
- Chang YJ, Sahinidis NV: Optimization of metabolic pathways under stability considerations. Computers & Chemical Engineering. 2005, 29 (3): 467-479. 10.1016/j.compchemeng.2004.08.013.View ArticleGoogle Scholar
- Gadkar KG, Doyle FJ, Edwards JS, Mahadevan R: Estimating optimal profiles of genetic alterations using constraint-based models. Biotechnology and Bioengineering. 2005, 89 (2): 243-251. 10.1002/bit.20349.View ArticlePubMedGoogle Scholar
- Lee S, Phalakornkule C, Domach MM, Grossmann IE: Recursive MILP model for finding all the alternate optima in LP models for metabolic networks. Computers & Chemical Engineering. 2000, 24 (2–7): 711-716. 10.1016/S0098-1354(00)00323-9.View ArticleGoogle Scholar
- Vital-Lopez FG, Armaou A, Nikolaev EV, Maranas CD: A computational procedure for optimal engineering interventions using kinetic models of metabolism. Biotechnology Progress. 2006, 22 (6): 1507-1517. 10.1021/bp060156oView ArticlePubMedGoogle Scholar
- Hatzimanikatis V, Floudas CA, Bailey JE: Analysis and design of metabolic reaction networks via mixed-integer linear optimization. Aiche Journal. 1996, 42 (5): 1277-1292. 10.1002/aic.690420509.View ArticleGoogle Scholar
- Hatzimanikatis V, Floudas CA, Bailey JE: Optimization of regulatory architectures in metabolic reaction networks. Biotechnology and Bioengineering. 1996, 52 (4): 485-500. 10.1002/(SICI)1097-0290(19961120)52:4<485::AID-BIT4>3.0.CO;2-L.View ArticlePubMedGoogle Scholar
- Adiwijaya BS, Barton PI, Tidor B: Biological network design strategies: discovery through dynamic optimization. Molecular Biosystems. 2006, 2 (12): 650-659. 10.1039/b610090bView ArticlePubMedGoogle Scholar
- Lebiedz D: Exploiting optimal control for target-oriented manipulation of (bio)chemical systems: A model-based approach to specific modification of self-organized dynamics. International Journal of Modern Physics B. 2005, 19 (25): 3763-3798. 10.1142/S0217979205032498.View ArticleGoogle Scholar
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