Optimization of a stochastically simulated gene network model via simulated annealing.

By rearranging naturally occurring genetic components, gene networks can be created that display novel functions. When designing these networks, the kinetic parameters describing DNA/protein binding are of great importance, as these parameters strongly influence the behavior of the resulting gene network. This article presents an optimization method based on simulated annealing to locate combinations of kinetic parameters that produce a desired behavior in a genetic network. Since gene expression is an inherently stochastic process, the simulation component of simulated annealing optimization is conducted using an accurate multiscale simulation algorithm to calculate an ensemble of network trajectories at each iteration of the simulated annealing algorithm. Using the three-gene repressilator of Elowitz and Leibler as an example, we show that gene network optimizations can be conducted using a mechanistically realistic model integrated stochastically. The repressilator is optimized to give oscillations of an arbitrary specified period. These optimized designs may then provide a starting-point for the selection of genetic components needed to realize an in vivo system.

[1]  Douglas B. Kell,et al.  Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation , 1998, Bioinform..

[2]  J. Stelling,et al.  Robustness of Cellular Functions , 2004, Cell.

[3]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[4]  J. Lefèvre,et al.  A new experimental approach for studying the association between RNA polymerase and the tet promoter of pBR322. , 1984, Nucleic acids research.

[5]  D. A. Baxter,et al.  A reduced model clarifies the role of feedback loops and time delays in the Drosophila circadian oscillator. , 2002, Biophysical journal.

[6]  V. Hakim,et al.  Design of genetic networks with specified functions by evolution in silico. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Stephan Klaus,et al.  Jonathan R. Beckwith and David Zipser, The Lactose Operon. 437 S., 150 Abb., 55 Tab. Cold Spring Harbor Laboratory 1970: Cold Spring Harbor Laboratory $ 14.– , 1973 .

[8]  Steven Hahn,et al.  Transcriptional regulation Meeting on Regulatory Mechanisms in Eukaryotic Transcription , 2008 .

[9]  S. Melcher,et al.  Cooperative and anticooperative effects in binding of the first and second plasmid Osym operators to a LacI tetramer: evidence for contributions of non-operator DNA binding by wrapping and looping. , 1996, Journal of molecular biology.

[10]  W. Hillen,et al.  Amino acids determining operator binding specificity in the helix‐turn‐helix motif of Tn10 Tet repressor. , 1991, The EMBO journal.

[11]  A. Arkin,et al.  Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. , 1998, Genetics.

[12]  S. Melcher,et al.  Thermodynamics of the interactions of lac repressor with variants of the symmetric lac operator: effects of converting a consensus site to a non-specific site. , 1997, Journal of molecular biology.

[13]  J. Hasty,et al.  Synthetic gene network for entraining and amplifying cellular oscillations. , 2002, Physical review letters.

[14]  Yiannis Kaznessis,et al.  Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions. , 2005, The Journal of chemical physics.

[15]  Jeffrey W. Smith,et al.  Stochastic Gene Expression in a Single Cell , .

[16]  K. Martin,et al.  Equilibrium DNA-binding of AraC protein. Compensation for displaced ions. , 1987, Journal of molecular biology.

[17]  B. Müller-Hill,et al.  How Lac repressor finds lac operator in vitro. , 1992, Journal of molecular biology.

[18]  D. Gillespie.  The chemical Langevin equation , 2000 .

[19]  Vassilios Sotiropoulos,et al.  Multiscale Hy3S: Hybrid stochastic simulation for supercomputers , 2006, BMC Bioinformatics.

[20]  Vijay K. Madisetti,et al.  The Digital Signal Processing Handbook , 1997 .

[21]  W Hendrickson,et al.  Regulation of the Escherichia coli L-arabinose operon studied by gel electrophoresis DNA binding assay. , 1984, Journal of molecular biology.

[22]  M. Elowitz,et al.  A synthetic oscillatory network of transcriptional regulators , 2000, Nature.

[23]  J. Collins,et al.  Construction of a genetic toggle switch in Escherichia coli , 2000, Nature.

[24]  Tim Hesterberg,et al.  Monte Carlo Strategies in Scientific Computing , 2002, Technometrics.

[25]  X Zhang,et al.  Transcription activation parameters at ara pBAD. , 1996, Journal of molecular biology.

[26]  A. Goldbeter.  Computational approaches to cellular rhythms , 2002, Nature.

[27]  Steven G. Johnson,et al.  FFTW: an adaptive software architecture for the FFT , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[28]  A. Riggs,et al.  The lac represser-operator interaction , 1970 .

[29]  Luonan Chen,et al.  Modelling periodic oscillation in gene regulatory networks by cyclic feedback systems , 2005, Bulletin of mathematical biology.

[30]  A. Riggs,et al.  The lac repressor-operator interaction. 3. Kinetic studies. , 1970, Journal of molecular biology.

[31]  A. Ninfa,et al.  Development of Genetic Circuitry Exhibiting Toggle Switch or Oscillatory Behavior in Escherichia coli , 2003, Cell.

[32]  D. Zipser,et al.  The lactose operon , 1970 .

[33]  W. Hillen,et al.  Dynamics of repressor-operator recognition: the Tn10-encoded tetracycline resistance control. , 1988, Biochemistry.

[34]  Mads Kaern,et al.  The engineering of gene regulatory networks. , 2003, Annual review of biomedical engineering.

[35]  S. Leibler,et al.  Mechanisms of noise-resistance in genetic oscillators , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[36]  M. Elowitz,et al.  Combinatorial Synthesis of Genetic Networks , 2002, Science.

[37]  M. A. Shea,et al.  The OR control system of bacteriophage lambda. A physical-chemical model for gene regulation. , 1985, Journal of molecular biology.

[38]  A. Arkin,et al.  Stochastic mechanisms in gene expression. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[39]  M G Fried,et al.  Free DNA concentration in E. coli estimated by an analysis of competition for DNA binding proteins. , 1994, Journal of theoretical biology.

[40]  T. Hughes,et al.  Signals and systems , 2006, Genome Biology.

[41]  Yiannis N Kaznessis,et al.  Model-driven designs of an oscillating gene network. , 2005, Biophysical journal.

[42]  J. Marko,et al.  How do site-specific DNA-binding proteins find their targets? , 2004, Nucleic acids research.