Deterministic and stochastic population-level simulations of an artificial lac operon genetic network

BMC Bioinformatics

Volumn 12, Issue , 2011, Pages

  Stamatakis, Michail ^a   Zygourakis, Kyriacos ^a  

^a Rice University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FACILITATED TRANSPORT; FEEDBACK ARCHITECTURE; GENETIC REGULATION; LAC OPERON NETWORKS; POSITIVE FEEDBACK LOOP; REACTION DYNAMICS; STOCHASTIC EFFECTS; STOCHASTIC KINETICS;

CELL CULTURE; CELL PROLIFERATION; COMPUTER SIMULATION; DYNAMICS; GENE EXPRESSION; MONTE CARLO METHODS;

STOCHASTIC SYSTEMS;

ARTICLE; COMPUTER SIMULATION; ESCHERICHIA COLI; FEEDBACK SYSTEM; GENE EXPRESSION REGULATION; GENE REGULATORY NETWORK; GENETICS; HUMAN; LACTOSE OPERON; MONTE CARLO METHOD; STATISTICS;

COMPUTER SIMULATION; ESCHERICHIA COLI; FEEDBACK; GENE EXPRESSION REGULATION; GENE REGULATORY NETWORKS; HUMANS; LAC OPERON; MONTE CARLO METHOD; STOCHASTIC PROCESSES;

EID: 79960690479     PISSN: None     EISSN: 14712105     Source Type: Journal    
DOI: 10.1186/1471-2105-12-301     Document Type: Article

References (45)

1. Jacob F, Perrin D, Sanchez C, Monod J. L'operon: groupe de gènes à expression coordonnée par un opérateur. Comptes Rendus Hebdomadaires des Séances de L'Académie des Sciences Serie D: Sciences naturelles 1960, 250:1727-1729.
2. Santillán M, Mackey MC. Quantitative approaches to the study of bistability in the lac operon of Escherichia coli. J R Soc Interface 2008, 5(Suppl 1):S29-S39. 2504340, 18426771.
3. Stamatakis M. Stochasticity and Cell Population Heterogeneity in an Artificial lac Operon Genetic Network. PhD thesis. Houston: Rice University 2009,
4. Vilar JMG, Guet CC, Leibler S. Modeling network dynamics: the lac operon, a case study. J Cell Biol 2003, 161(3):471-476. 10.1083/jcb.200301125, 2172934, 12743100.
5. van Kampen NG. Stochastic processes in physics and chemistry. 1992, New York, Amsterdam: North-Holland-Personal-Library.
6. Gillespie DT. The chemical Langevin equation. J Chem Phys 2000, 113(1):297-306.
7. Gillespie DT. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys 1976, 22(4):403-434.
8. Gillespie DT. Exact stochastic simulation of coupled chemical reactions. J Phys Chem 1977, 81(25):2340-2361.
9. Fredrickson AG. Formulation of Structured Growth Models. Reprinted from Biotechnology and Bioengineering, Vol. XVIII, No. 10, Pages 1481-1486 (1976). Biotechnol Bioeng 2000, 67(6):720-725. 10.1002/(SICI)1097-0290(20000320)67:6<720::AID-BIT10>;3.0.CO;2-I, 10699853.
10. Stamatakis M, Zygourakis K. A Mathematical and Computational Approach for Integrating the Major Sources of Cell Population Heterogeneity. J Theor Biol 2010, 266(1):41-61. 10.1016/j.jtbi.2010.06.002, 20685607.
11. Elowitz MB, Levine AJ, Siggia ED, Swain PS. Stochastic Gene Expression in a Single Cell. Science 2002, 297(5584):1183-1186. 10.1126/science.1070919, 12183631.
12. Mantzaris NV. From Single-Cell Genetic Architecture to Cell Population Dynamics: Quantitatively Decomposing the Effects of Different Population Heterogeneity Sources for a Genetic Network with Positive Feedback Architecture. Biophys J 2007, 92:4271-4288. 10.1529/biophysj.106.100271, 1877777, 17384073.
13. van Hoek M, Hogeweg P. The effect of stochasticity on the lac operon: An evolutionary perspective. PLoS Comput Biol 2007, 3(6):e111. 10.1371/journal.pcbi.0030111, 1894820, 17590077.
14. van Hoek MJA, Hogeweg P. In silico evolved lac operons exhibit bistability for artificial inducers, but not for lactose. Biophys J 2006, 91(8):2833-2843. 10.1529/biophysj.105.077420, 1578483, 16877514.
15. Mantzaris NV. Single-cell gene-switching networks and heterogeneous cell population phenotypes. Comput Chem Eng 2005, 29(3):631-643.
16. Mantzaris NV. Stochastic and deterministic simulations of heterogeneous cell population dynamics. J Theor Biol 2006, 241(3):690-706. 10.1016/j.jtbi.2006.01.005, 16487980.
17. Stamatakis M, Mantzaris NV. Comparison of Deterministic and Stochastic Models of the lac Operon Genetic Network. Biophys J 2009, 96(3):887-906. 10.1016/j.bpj.2008.10.028, 2996131, 19186128.
18. McAdams HH, Arkin A. Stochastic mechanisms in gene expression. Proc Nat Acad Sci USA 1997, 94(3):814-819. 10.1073/pnas.94.3.814, 19596, 9023339.
19. McAdams HH, Arkin A. Simulation of prokaryotic genetic circuits. Annu Rev Biophys Biomol Struct 1998, 27:199-224. 10.1146/annurev.biophys.27.1.199, 9646867.
20. McAdams HH, Arkin A. It's a noisy business! Genetic regulation at the nanomolar scale. Trends Genet 1999, 15(2):65-69. 10.1016/S0168-9525(98)01659-X, 10098409.
21. Gibson MA, Bruck J. Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels. J Phys Chem A 2000, 104(9):1876-1889.
22. Lu T, Volfson D, Tsimring L, Hasty J. Cellular growth and division in the Gillespie algorithm. Syst Biol 2004, 1(1):121-128.
23. Swain PS, Elowitz MB, Siggia ED. Intrinsic and extrinsic contributions to stochasticity in gene expression. Proc Nat Acad Sci USA 2002, 99(20):12795-12800. 10.1073/pnas.162041399, 130539, 12237400.
24. McQuarrie DA. Stochastic Approach to Chemical Kinetics. J Appl Probab 1967, 4(3):413-478.
25. Ramkrishna D. Population Balances: Theory and Applications to Particulate Systems in Engineering. 2000, San Diego, CA: Academic Press.
26. Crudu A, Debussche A, Radulescu O. Hybrid stochastic simplifications for multiscale gene networks. Bmc Syst Biol 2009, 3:89. 10.1186/1752-0509-3-89, 2761401, 19735554.
27. Saiz L, Vilar JMG. Protein-protein/DNA interaction networks: versatile macromolecular structures for the control of gene expression. IET Syst Biol 2008, 2(5):247-255. 10.1049/iet-syb:20080091, 19045820.
28. Vilar JM, Leibler S. DNA looping and physical constraints on transcription regulation. J Mol Biol 2003, 331(5):981-989. 10.1016/S0022-2836(03)00764-2, 12927535.
29. Saiz L, Vilar JMG. Ab initio thermodynamic modeling of distal multisite transcription regulation. Nucleic Acids Res 2008, 36(3):726-731. 2241893, 18056082.
30. Vilar JMG. Accurate Prediction of Gene Expression by Integration of DNA Sequence Statistics with Detailed Modeling of Transcription Regulation. Biophys J 2010, 99(8):2408-2413. 10.1016/j.bpj.2010.08.006, 20959080.
31. Goeddel DV, Yansura DG, Caruthers MH. Binding of Synthetic Lactose Operator DNAs to Lactose Repressors. Proc Nat Acad Sci USA 1977, 74(8):3292-3296. 10.1073/pnas.74.8.3292, 431535, 333432.
32. Riggs AD, Newby RF, Bourgeois S. lac Repressor-Operator interaction II. Effect of galactosides and other ligands. J Mol Biol 1970, 51(2):303-314. 10.1016/0022-2836(70)90144-0, 4320936.
33. Riggs AD, Newby RF, Bourgeois S. lac Repressor-Operator interaction I. Equilibrium studies. J Mol Biol 1970, 48(1):67-83. 10.1016/0022-2836(70)90219-6, 4915295.
34. Lin S-Y, Itakura K, Rosenberg JM, Wilcox G, Bahl C, Wu T, Narang SA, Dickerson RE, Riggs AD. Molecular Mechanisms in the Control of Gene Expression. 1976, 143-158. New York: Academic Press, Nielich DP, Rutter WJ, Fox CF.
35. Elf J, Li GW, Xie XS. Probing transcription factor dynamics at the single-molecule level in a living cell. Science 2007, 316(5828):1191-1194. 10.1126/science.1141967, 2853898, 17525339.
36. Trueba FJ, Woldringh CL. Changes in cell diameter during the division cycle of Escherichia coli. J Bacteriol 1980, 142(3):869-878. 294112, 6769914.
37. Dreisigmeyer DW, Stajic J, Nemenman I, Hlavacek WS, Wall ME. Determinants of bistability in induction of the Escherichia coli lac operon. IET Syst Biol 2008, 2(5):293-303. 10.1049/iet-syb:20080095, 19045824.
38. Oehler S, Alberti S, Müller-Hill B. Induction of the lac promoter in the absence of DNA loops and the stoichiometry of induction. Nucleic Acids Res 2006, 34(2):606-612. 10.1093/nar/gkj453, 1345695, 16432263.
39. Narang A. Effect of DNA looping on the induction kinetics of the lac operon. J Theor Biol 2007, 247(4):695-712. 10.1016/j.jtbi.2007.03.030, 17490688.
40. Krishna S, Banerjee B, Ramakrishnan TV, Shivashankar GV. Stochastic simulations of the origins and implications of long-tailed distributions in gene expression. Proc Nat Acad Sci USA 2005, 102(13):4771-4776. 10.1073/pnas.0406415102, 555697, 15772163.
41. Stamatakis M. Cell population balance, ensemble and continuum modeling frameworks: Conditional equivalence and hybrid approaches. Chem Eng Sci 2010, 65(2):1008-1015.
42. Mantzaris NV. Effects of Population Heterogeneity on the Dynamics of Cell Populations. 7th IFAC Symposium on Dynamics and Control of Process Systems 2004, Cambridge, MA.
43. Mantzaris NV. A cell population balance model describing positive feedback loop expression dynamics. Comput Chem Eng 2005, 29(4):897-909.
44. Harvey RJ, Marr AG, Painter PR. Kinetics of Growth of Individual Cells of Escherichia coli and Azotobacter agilis. J Bacteriol 1967, 93(2):605-617. 276485, 5335966.
45. Marr AG, Harvey RJ, Trentini WC. Growth and division of Escherichia coli. J Bacteriol 1966, 91(6):2388-2389. 316226, 5329289.