- We are sorry, but NCBI web applications do not support your browser and may not function properly. More information

- Journal List
- BMC Syst Biol
- v.2; 2008
- PMC2435524

# Optimization in computational systems biology

^{1}Instituto de Investigaciones Marinas, CSIC (Spanish Council for Scientific Research), C/Eduardo Cabello 6, 36208 Vigo, Spain

^{}Corresponding author.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## Abstract

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.

## Background

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 [5], 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 [6] 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.

Non linear programming (NLP) deals with continuous problems where some of the constraints or the objective function are nonlinear. In contrast to LP, NLP problems are much more difficult to solve. Further, the presence of nonlinearities in the objective and constraints might imply nonconvexity, which results in the potential existence of multiple local solutions (multimodality). Thus, in nonconvex problems one should seek the globally optimal solution among the set of possible local solutions. For the simple case of only two decision variables, one can visualize the objective function of a multimodal problem as a terrain with multiple peaks. Simple examples of unimodal and multimodal surfaces are presented in Figure Figure11.

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 [6]. 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 [6] 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.

In fact, optimization is already playing a key rôle. Examples of applications of optimization in systems biology, classified by the type of optimization problem, are given in Table Table1.1. Below, I highlight several topics where optimization has already made significant contributions.

## Optimization of biochemical reaction networks

Optimization methods have been applied in both metabolic control analysis [15,16] and biochemical systems theory [17]. 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 [18]. Examples of success stories are the *in silico *predictions of *Escherichia coli *metabolic capabilities [19], or the genome-scale reconstruction of the *Saccharomyces cerevisiae *metabolic network [20].

Metabolic engineering exploits an integrated, systems-level approach for optimizing a desired cellular property or phenotype [21]. 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 [22]. 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 [27]. 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 [35]. 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 [39], an approach which may offer advantages over traditional methodologies.

## Reverse engineering, modeling and experimental design

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 [40], gene regulatory networks [41-46], signaling pathways [47] 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.

## Conclusion

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 [67], 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 [58] or in the optimization of stochastic gene network models [73].

As stated in [74], 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 [75]. A promising example of what can be done is the OptCircuit framework [76], 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 [77].

Moreover, optimization could also be used after the design and construction phases, inside a model predictive control framework [78], 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 [80].

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 [81]. Thus, game-theoretic approaches, such as evolutionary game theory [82], may provide a better framework studying the evolution of biochemical systems.

Sutherland [2] 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.

## Acknowledgements

The author would like to thank Matt Hodgkinson for his valuable comments, and acknowledges financial support from EU project BaSysBio LSHG-CT-2006-037469

## References

- Alexander RM. Optima for animals. London: E. Arnold; 1982.
- Sutherland WJ. The best solution. Nature. 2005;435:569–569. doi: 10.1038/435569a. [PubMed] [Cross Ref]
- Greenberg HJ, Hart WE, Lancia G. Opportunities for combinatorial optimization in computational biology. Informs Journal on Computing. 2004;16:211–231. doi: 10.1287/ijoc.1040.0073. [Cross Ref]
- 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;7:86–112. doi: 10.1093/bib/bbk007. [PubMed] [Cross Ref]
- Dantzig GB. The diet problem. Interfaces. 1990;20:43–47.
- Boyd SP, Vandenberghe L. Convex optimization. Cambridge: Cambridge University; 2004.
- Horst R, Pardalos PM, Romeijn HE. Handbook of global optimization. Dordrecht ; Boston: Kluwer Academic Publishers; 1995.
- Horst R, Pardalos PM, Thoai NV. Introduction to global optimization. 2. Dordrecht ; Boston: Kluwer Academic Publishers; 2000.
- Floudas CA. Deterministic global optimization : theory, methods, and applications. Dordrecht ; Boston: Kluwer Academic Publishers; 2000.
- Floudas CA, Pardalos PM. Optimization in computational chemistry and molecular biology : local and global approaches. Dordrecht ; Boston: Kluwer Academic Publishers; 2000.
- Doyle FJ, Stelling J. Systems interface biology. Journal of the Royal Society Interface. 2006;3:603–616. doi: 10.1098/rsif.2006.0143. [PMC free article] [PubMed] [Cross Ref]
- Kremling A, Saez-Rodriguez J. Systems biology – An engineering perspective. Journal of Biotechnology. 2007;129:329–351. doi: 10.1016/j.jbiotec.2007.02.009. [PubMed] [Cross Ref]
- Wolkenhauer O, Ullah M, Wellstead P, Cho KH. The dynamic systems approach to control and regulation of intracellular networks. Febs Letters. 2005;579:1846–1853. doi: 10.1016/j.febslet.2005.02.008. [PubMed] [Cross Ref]
- Sontag ED. Molecular systems biology and control. European Journal of Control. 2005;11:396–435. doi: 10.3166/ejc.11.396-435. [Cross Ref]
- Heinrich R, Schuster S. The modelling of metabolic systems. Structure, control and optimality. Biosystems. 1998;47:61–77. doi: 10.1016/S0303-2647(98)00013-6. [PubMed] [Cross Ref]
- Heinrich R, Schuster S. The regulation of cellular systems. New York: Chapman & Hall; 1996.
- Torres NV, Voit EO. Pathway analysis and optimization in metabolic engineering. New York: Cambridge University Press; 2002.
- Varma A, Palsson BO. Metabolic flux balancing – basic concepts, scientific and practical use. Bio-Technology. 1994;12:994–998.
- Edwards JS, Ibarra RU, Palsson BO. In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data. Nature Biotechnology. 2001;19:125–130. doi: 10.1038/84379. [PubMed] [Cross Ref]
- Forster J, Famili I, Fu P, Palsson BO, Nielsen J. Genome-scale reconstruction of the Saccharomyces cerevisiae metabolic network. Genome Research. 2003;13:244–253. doi: 10.1101/gr.234503. [PMC free article] [PubMed] [Cross Ref]
- Tyo KE, Alper HS, Stephanopoulos GN. Expanding the metabolic engineering toolbox: more options to engineer cells. Trends in Biotechnology. 2007;25:132–137. doi: 10.1016/j.tibtech.2007.01.003. [PubMed] [Cross Ref]
- Patil KR, Rocha I, Forster J, Nielsen J. Evolutionary programming as a platform for in silico metabolic engineering. BMC Bioinformatics. 2005;6:308. doi: 10.1186/1471-2105-6-308. [PMC free article] [PubMed] [Cross Ref]
- Andrianantoandro E, Basu S, Karig DK, Weiss R. Synthetic biology: new engineering rules for an emerging discipline. Mol Syst Biol. 2006;2:2006.0028. doi: 10.1038/msb4100073. [PMC free article] [PubMed] [Cross Ref]
- 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. doi: 10.1186/1471-2105-7-285. [PMC free article] [PubMed] [Cross Ref]
- Meyer A, Pellaux R, Panke S. Bioengineering novel in vitro metabolic pathways using synthetic biology. Current Opinion in Microbiology. 2007;10:246–253. doi: 10.1016/j.mib.2007.05.009. [PubMed] [Cross Ref]
- Styczynski MP, Fischer CR, Stephanopoulos GN. The intelligent design of evolution. Mol Syst Biol. 2006 [PMC free article] [PubMed]
- Price ND, Reed JL, Palsson BO. Genome-scale models of microbial cells: Evaluating the consequences of constraints. Nature Reviews Microbiology. 2004;2:886–897. doi: 10.1038/nrmicro1023. [PubMed] [Cross Ref]
- Henry CS, Broadbelt LJ, Hatzimanikatis V. Thermodynamics-based metabolic flux analysis. Biophysical Journal. 2007;92:1792–1805. doi: 10.1529/biophysj.106.093138. [PMC free article] [PubMed] [Cross Ref]
- Mahadevan R, Edwards JS, Doyle FJ. Dynamic flux balance analysis of diauxic growth in Escherichia coli. Biophys J. 2002;83:1331–1340. [PMC free article] [PubMed]
- Kauffman KJ, Prakash P, Edwards JS. Advances in flux balance analysis. Current Opinion in Biotechnology. 2003;14:491–496. doi: 10.1016/j.copbio.2003.08.001. [PubMed] [Cross Ref]
- Llaneras F, Pico J. An interval approach for dealing with flux distributions and elementary modes activity patterns. Journal of Theoretical Biology. 2007;246:290–308. doi: 10.1016/j.jtbi.2006.12.029. [PubMed] [Cross Ref]
- Segre D, Vitkup D, Church GM. Analysis of optimality in natural and perturbed metabolic networks. Proc Natl Acad Sci U S A. 2002;99:15112–15117. doi: 10.1073/pnas.232349399. [PMC free article] [PubMed] [Cross Ref]
- Schuetz R, Kuepfer L, Sauer U. Systematic evaluation of objective functions for predicting intracellular fluxes in Escherichia coli. Molecular Systems Biology. 2007;3:15. doi: 10.1038/msb4100162. [PMC free article] [PubMed] [Cross Ref]
- Nielsen J. Principles of optimal metabolic network operation. Molecular Systems Biology. 2007;3:2. doi: 10.1038/msb4100169. [PMC free article] [PubMed] [Cross Ref]
- Alon U. An introduction to systems biology. Chapman and Hall; 2006.
- Stelling J, Sauer U, Szallasi Z, Doyle FJ, Doyle J. Robustness of cellular functions. Cell. 2004;118:675–685. doi: 10.1016/j.cell.2004.09.008. [PubMed] [Cross Ref]
- Carlson JM, Doyle J. Complexity and robustness. Proc Natl Acad Sci U S A. 2002;99:2538–2545. doi: 10.1073/pnas.012582499. [PMC free article] [PubMed] [Cross Ref]
- Tanaka R, Csete M, Doyle J. Highly optimised global organisation of metabolic networks. Iee Proceedings Systems Biology. 2005;152:179–184. doi: 10.1049/ip-syb:20050042. [PubMed] [Cross Ref]
- Varner J, Ramkrishna D. Metabolic engineering from a cybernetic perspective. 1. Theoretical preliminaries. Biotechnology Progress. 1999;15:407–425. doi: 10.1021/bp990017p. [PubMed] [Cross Ref]
- Wang RS, Wang Y, Zhang XS, Chen L. Inferring transcriptional regulatory networks from high-throughput data. Bioinformatics. 2007;23:3056–3064. doi: 10.1093/bioinformatics/btm465. [PubMed] [Cross Ref]
- 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. [PubMed]
- Wang Y, Joshi T, Zhang XS, Xu D, Chen LN. Inferring gene regulatory networks from multiple microarray datasets. Bioinformatics. 2006;22:2413–2420. doi: 10.1093/bioinformatics/btl396. [PubMed] [Cross Ref]
- Kim S, Kim J, Cho KH. Inferring gene regulatory networks from temporal expression profiles under time-delay and noise. Computational Biology and Chemistry. 2007;31:239–245. doi: 10.1016/j.compbiolchem.2007.03.013. [PubMed] [Cross Ref]
- Cho KH, Choo SM, Jung SH, Kim JR, Choi HS, Kim J. Reverse engineering of gene regulatory networks. Iet Systems Biology. 2007;1:149–163. doi: 10.1049/iet-syb:20060075. [PubMed] [Cross Ref]
- 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. doi: 10.1186/1471-2105-8-228. [PMC free article] [PubMed] [Cross Ref]
- 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;99:6163–6168. doi: 10.1073/pnas.092576199. [PMC free article] [PubMed] [Cross Ref]
- 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;84:864–886. doi: 10.1002/bit.10844. [PubMed] [Cross Ref]
- Han S, Yoon Y, Cho KH. Inferring biomolecular interaction networks based on convex optimization. Computational Biology and Chemistry. 2007;31:347–354. doi: 10.1016/j.compbiolchem.2007.08.003. [PubMed] [Cross Ref]
- 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. doi: 10.1186/1471-2105-8-391. [PMC free article] [PubMed] [Cross Ref]
- Ljung L. System identification: theory for the user. 2. Upper Saddle River, NJ: Prentice Hall; 1999.
- Walter E, Pronzato L. Identification of parametric models from experimental data. Berlin; New York; Paris: Springer; Masson; 1997.
- Zwolak JW, Tyson JJ, Watson LT. Globally optimised parameters for a model of mitotic control in frog egg extracts. Iee Proceedings Systems Biology. 2005;152:81–92. doi: 10.1049/ip-syb:20045032. [PubMed] [Cross Ref]
- Jaqaman K, Danuser G. Linking data to models: data regression. Nature Reviews Molecular Cell Biology. 2006;7:813–819. doi: 10.1038/nrm2030. [PubMed] [Cross Ref]
- Rodriguez-Fernandez M, Egea JA, Banga JR. Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems. BMC Bioinformatics. 2006;7:483. doi: 10.1186/1471-2105-7-483. [PMC free article] [PubMed] [Cross Ref]
- Moles CG, Mendes P, Banga JR. Parameter estimation in biochemical pathways: A comparison of global optimization methods. Genome Research. 2003;13:2467–2474. doi: 10.1101/gr.1262503. [PMC free article] [PubMed] [Cross Ref]
- Famili I, Mahadevan R, Palsson BO. k-cone analysis: Determining all candidate values for kinetic parameters on a network scale. Biophysical Journal. 2005;88:1616–1625. doi: 10.1529/biophysj.104.050385. [PMC free article] [PubMed] [Cross Ref]
- Segrè D. From Annotated Genomes to Metabolic Flux Models and Kinetic Parameter Fitting. OMICS. 2003;7:301–316. doi: 10.1089/153623103322452413. [PubMed] [Cross Ref]
- Reinker S, Altman RM, Timmer J. Parameter estimation in stochastic biochemical reactions. Iee Proceedings Systems Biology. 2006;153:168–178. doi: 10.1049/ip-syb:20050105. [PubMed] [Cross Ref]
- 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. doi: 10.1186/1752-0509-2-26. [PMC free article] [PubMed] [Cross Ref]
- 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;41:2425–2430. doi: 10.1021/ie010183d. [Cross Ref]
- 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;79:726–739. doi: 10.1177/0037549703040943. [Cross Ref]
- 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;79:717–725. doi: 10.1177/0037549703040937. [Cross Ref]
- Gadkar KG, Gunawan R, Doyle FJ. Iterative approach to model identification of biological networks. BMC Bioinformatics. 2005;6:155. doi: 10.1186/1471-2105-6-155. [PMC free article] [PubMed] [Cross Ref]
- 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;1:190–202. doi: 10.1049/iet-syb:20060065. [PubMed] [Cross Ref]
- Feng XJ, Rabitz H, Turinici G, Le Bris C. A closed-loop identification protocol for nonlinear dynamical systems. Journal of Physical Chemistry A. 2006;110:7755–7762. doi: 10.1021/jp056189o. [PubMed] [Cross Ref]
- Balsa-Canto E, Alonso AA, Banga JR. FOSBE (FOUNDATIONS OF SISTEMS BIOLOGY AND ENGINEERING): 2007. Stuttgart (Germany); 2007. An optimal identification procedure for model development in systems biology.
- Goodacre R. Making sense of the metabolome using evolutionary computation: seeing the wood with the trees. Journal of Experimental Botany. 2005;56:245–254. doi: 10.1093/jxb/eri043. [PubMed] [Cross Ref]
- Kell DB. Metabolomics, modelling and machine learning in systems biology – towards an understanding of the languages of cells. Febs Journal. 2006;273:873–894. doi: 10.1111/j.1742-4658.2006.05136.x. [PubMed] [Cross Ref]
- Mendes P, Kell DB. Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation. Bioinformatics. 1998;14:869–883. doi: 10.1093/bioinformatics/14.10.869. [PubMed] [Cross Ref]
- Rodriguez-Fernandez M, Mendes P, Banga JR. A hybrid approach for efficient and robust parameter estimation in biochemical pathways. Biosystems. 2006;83:248–265. doi: 10.1016/j.biosystems.2005.06.016. [PubMed] [Cross Ref]
- Kaznessis YN. Models for synthetic biology. BMC Syst Biol. 2007;1:47. doi: 10.1186/1752-0509-1-47. [PMC free article] [PubMed] [Cross Ref]
- Ma'ayan A, Blitzer RD, Iyengar R. Toward predictive models of mammalian cells. Annual Review of Biophysics and Biomolecular Structure. 2005;34:319–349. doi: 10.1146/annurev.biophys.34.040204.144415. [PMC free article] [PubMed] [Cross Ref]
- Tomshine J, Kaznessis YN. Optimization of a stochastically simulated gene network model via simulated annealing. Biophysical Journal. 2006;91:3196–3205. doi: 10.1529/biophysj.106.083485. [PMC free article] [PubMed] [Cross Ref]
- Heinemann M, Panke S. Synthetic biology – putting engineering into biology. Bioinformatics. 2006;22:2790–2799. doi: 10.1093/bioinformatics/btl469. [PubMed] [Cross Ref]
- Sotiropoulos V, Kaznessis YN. Synthetic tetracycline-inducible regulatory networks: computer-aided design of dynamic phenotypes. BMC Syst Biol. 2007;1:7. doi: 10.1186/1752-0509-1-7. [PMC free article] [PubMed] [Cross Ref]
- Dasika MS, Maranas CD. OptCircuit: An optimization based method for computational design of genetic circuits. BMC Syst Biol. 2008;2 [PMC free article] [PubMed]
- 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;23:2760–2767. doi: 10.1093/bioinformatics/btm446. [PubMed] [Cross Ref]
- Bagheri N, Stelling J, Doyle FJ. Circadian phase entrainment via nonlinear model predictive control. International Journal of Robust and Nonlinear Control. 2007;17:1555–1571. doi: 10.1002/rnc.1209. [Cross Ref]
- Jung GY, Stephanopoulos G. A functional protein chip for pathway optimization and in vitro metabolic engineering. Science. 2004;304:428–431. doi: 10.1126/science.1096920. [PubMed] [Cross Ref]
- Handl J, Kell DB, Knowles J. Multiobjective optimization in bioinformatics and computational biology. Ieee-Acm Transactions on Computational Biology and Bioinformatics. 2007;4:279–292. doi: 10.1109/TCBB.2007.070203. [PubMed] [Cross Ref]
- Nowak MA, Sigmund K. Evolutionary dynamics of biological games. Science. 2004;303:793–799. doi: 10.1126/science.1093411. [PubMed] [Cross Ref]
- Pfeiffer T, Schuster S. Game-theoretical approaches to studying the evolution of biochemical systems. Trends in Biochemical Sciences. 2005;30:20–25. doi: 10.1016/j.tibs.2004.11.006. [PubMed] [Cross Ref]
- Papoutsakis ET. EQUATIONS AND CALCULATIONS FOR FERMENTATIONS OF BUTYRIC-ACID BACTERIA. Biotechnology and Bioengineering. 1984;26:174–187. doi: 10.1002/bit.260260210. [PubMed] [Cross Ref]
- Vo TD, Pallsson BO. Isotopomer analysis of myocardial substrate metabolism: A systems biology approach. Biotechnology and Bioengineering. 2006;95:972–983. doi: 10.1002/bit.21063. [PubMed] [Cross Ref]
- 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;91:15–22. doi: 10.1016/j.ymgme.2007.01.012. [PubMed] [Cross Ref]
- Kuepfer L, Sauer U, Parrilo PA. Efficient classification of complete parameter regions based on semidefinite programming. BMC Bioinformatics. 2007;8:12. doi: 10.1186/1471-2105-8-12. [PMC free article] [PubMed] [Cross Ref]
- Burgard AP, Pharkya P, Maranas CD. OptKnock: A bilevel programming framework for identifying gene knockout strategies for microbial strain optimization. Biotechnology and Bioengineering. 2003;84:647–657. doi: 10.1002/bit.10803. [PubMed] [Cross Ref]
- Chang YJ, Sahinidis NV. Optimization of metabolic pathways under stability considerations. Computers & Chemical Engineering. 2005;29:467–479. doi: 10.1016/j.compchemeng.2004.08.013. [Cross Ref]
- Gadkar KG, Doyle FJ, Edwards JS, Mahadevan R. Estimating optimal profiles of genetic alterations using constraint-based models. Biotechnology and Bioengineering. 2005;89:243–251. doi: 10.1002/bit.20349. [PubMed] [Cross Ref]
- 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;24:711–716. doi: 10.1016/S0098-1354(00)00323-9. [Cross Ref]
- Vital-Lopez FG, Armaou A, Nikolaev EV, Maranas CD. A computational procedure for optimal engineering interventions using kinetic models of metabolism. Biotechnology Progress. 2006;22:1507–1517. doi: 10.1021/bp060156o. [PubMed] [Cross Ref]
- Hatzimanikatis V, Floudas CA, Bailey JE. Analysis and design of metabolic reaction networks via mixed-integer linear optimization. Aiche Journal. 1996;42:1277–1292. doi: 10.1002/aic.690420509. [Cross Ref]
- Hatzimanikatis V, Floudas CA, Bailey JE. Optimization of regulatory architectures in metabolic reaction networks. Biotechnology and Bioengineering. 1996;52:485–500. doi: 10.1002/(SICI)1097-0290(19961120)52:4<485::AID-BIT4>3.0.CO;2-L. [PubMed] [Cross Ref]
- Adiwijaya BS, Barton PI, Tidor B. Biological network design strategies: discovery through dynamic optimization. Molecular Biosystems. 2006;2:650–659. doi: 10.1039/b610090b. [PubMed] [Cross Ref]
- 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;19:3763–3798. doi: 10.1142/S0217979205032498. [Cross Ref]

**BioMed Central**

## Formats:

- Article |
- PubReader |
- ePub (beta) |
- PDF (327K)

- Computational procedures for optimal experimental design in biological systems.[IET Syst Biol. 2008]
*Balsa-Canto E, Alonso AA, Banga JR.**IET Syst Biol. 2008 Jul; 2(4):163-72.* - The Beta Workbench: a computational tool to study the dynamics of biological systems.[Brief Bioinform. 2008]
*Dematté L, Priami C, Romanel A.**Brief Bioinform. 2008 Sep; 9(5):437-49. Epub 2008 May 7.* - P systems applications to systems biology.[Biosystems. 2008]
*Gheorghe M, Krasnogor N, Camara M.**Biosystems. 2008 Mar; 91(3):435-7. Epub 2007 Jul 17.* - Synthetic biology in the analysis and engineering of signaling processes.[Integr Biol (Camb). 2010]
*Kämpf MM, Weber W.**Integr Biol (Camb). 2010 Jan; 2(1):12-24. Epub 2009 Nov 16.* - Models for synthetic biology.[BMC Syst Biol. 2007]
*Kaznessis YN.**BMC Syst Biol. 2007 Nov 6; 1:47. Epub 2007 Nov 6.*

- ODE Constrained Mixture Modelling: A Method for Unraveling Subpopulation Structures and Dynamics[PLoS Computational Biology. ]
*Hasenauer J, Hasenauer C, Hucho T, Theis FJ.**PLoS Computational Biology. 10(7)e1003686* - MEIGO: an open-source software suite based on metaheuristics for global optimization in systems biology and bioinformatics[BMC Bioinformatics. ]
*Egea JA, Henriques D, Cokelaer T, Villaverde AF, MacNamara A, Danciu DP, Banga JR, Saez-Rodriguez J.**BMC Bioinformatics. 15136* - mRNA translation and protein synthesis: an analysis of different modelling methodologies and a new PBN based approach[BMC Systems Biology. ]
*Zhao YB, Krishnan J.**BMC Systems Biology. 825* - Solving the Differential Biochemical Jacobian from Metabolomics Covariance Data[PLoS ONE. ]
*Nägele T, Mair A, Sun X, Fragner L, Teige M, Weckwerth W.**PLoS ONE. 9(4)e92299* - Composing Problem Solvers for Simulation Experimentation: A Case Study on Steady State Estimation[PLoS ONE. ]
*Leye S, Ewald R, Uhrmacher AM.**PLoS ONE. 9(4)e91948*

- PubMedPubMedPubMed citations for these articles
- TaxonomyTaxonomyRelated taxonomy entry
- Taxonomy TreeTaxonomy Tree

- Optimization in computational systems biologyOptimization in computational systems biologyBMC Systems Biology. 2008; 2()47PMC

Your browsing activity is empty.

Activity recording is turned off.

See more...