Models of protein production along the cell cycle: An investigation of possible sources of noise

Autoři: Renaud Dessalles aff001;  Vincent Fromion aff002;  Philippe Robert aff003
Působiště autorů: Dept. of Biomathematics, UCLA, Los Angeles, CA, United States of America aff001;  MaIAGE, INRA, Université Paris-Saclay, Jouy-en-Josas, France aff002;  INRIA de Paris, Paris, France aff003
Vyšlo v časopise: PLoS ONE 15(1)
Kategorie: Research Article


In this article, we quantitatively study, through stochastic models, the effects of several intracellular phenomena, such as cell volume growth, cell division, gene replication as well as fluctuations of available RNA polymerases and ribosomes. These phenomena are indeed rarely considered in classic models of protein production and no relative quantitative comparison among them has been performed. The parameters for a large and representative class of proteins are determined using experimental measures. The main important and surprising conclusion of our study is to show that despite the significant fluctuations of free RNA polymerases and free ribosomes, they bring little variability to protein production contrary to what has been previously proposed in the literature. After verifying the robustness of this quite counter-intuitive result, we discuss its possible origin from a theoretical view, and interpret it as the result of a mean-field effect.

Klíčová slova:

Biochemical simulations – Cell cycle and cell division – DNA replication – DNA transcription – Messenger RNA – Protein expression – Ribosomes – Simulation and modeling


1. Elowitz MB, Levine AJ, Siggia ED, Swain PS. Stochastic gene expression in a single cell. Science. 2002;297(5584):1183–1186. doi: 10.1126/science.1070919 12183631

2. Ozbudak EM, Thattai M, Kurtser I, Grossman AD, van Oudenaarden A. Regulation of noise in the expression of a single gene. Nature Genetics. 2002;31(1):69–73. doi: 10.1038/ng869 11967532

3. Losick R, Desplan C. Stochasticity and cell fate. Science. 2008;320(5872):65–68. doi: 10.1126/science.1147888 18388284

4. Balaban NQ, Merrin J, Chait R, Kowalik L, Leibler S. Bacterial persistence as a phenotypic switch. Science (New York, NY). 2004;305(5690):1622–1625. doi: 10.1126/science.1099390

5. Acar M, Mettetal JT, van Oudenaarden A. Stochastic switching as a survival strategy in fluctuating environments. Nature Genetics. 2008;40(4):471–475. doi: 10.1038/ng.110 18362885

6. Taniguchi Y, Choi PJ, Li GW, Chen H, Babu M, Hearn J, et al. Quantifying E. coli proteome and transcriptome with single-molecule sensitivity in single cells. Science. 2010;329(5991):533–538. doi: 10.1126/science.1188308 20671182

7. Rigney DR, Schieve WC. Stochastic model of linear, continuous protein synthesis in bacterial populations. Journal of Theoretical Biology. 1977;69(4):761–766. doi: 10.1016/0022-5193(77)90381-2 607033

8. Berg OG. A model for the statistical fluctuations of protein numbers in a microbial population. Journal of theoretical biology. 1978;71(4):587–603. doi: 10.1016/0022-5193(78)90326-0 96307

9. Paulsson J. Models of stochastic gene expression. Physics of Life Reviews. 2005;2(2):157–175. doi: 10.1016/j.plrev.2005.03.003

10. Huh D, Paulsson J. Non-genetic heterogeneity from random partitioning at cell division. Nature genetics. 2011;43(2):95–100. doi: 10.1038/ng.729 21186354

11. Huh D, Paulsson J. Random partitioning of molecules at cell division. Proceedings of the National Academy of Sciences. 2011;108(36):15004–15009. doi: 10.1073/pnas.1013171108

12. Swain PS, Elowitz MB, Siggia ED. Intrinsic and extrinsic contributions to stochasticity in gene expression. Proceedings of the National Academy of Sciences. 2002;99(20):12795–12800. doi: 10.1073/pnas.162041399

13. Fromion V, Leoncini E, Robert P. Stochastic gene expression in cells: a point process approach. SIAM Journal on Applied Mathematics. 2013;73(1):195–211. doi: 10.1137/120879592

14. Shahrezaei V, Swain PS. Analytical distributions for stochastic gene expression. Proceedings of the National Academy of Sciences. 2008;105(45):17256–17261. doi: 10.1073/pnas.0803850105

15. Schwabe A, Rybakova KN, Bruggeman FJ. Transcription Stochasticity of Complex Gene Regulation Models. Biophysical Journal. 2012;103(6):1152–1161. doi: 10.1016/j.bpj.2012.07.011 22995487

16. Dessalles R. Stochastic models for protein production: the impact of autoregulation, cell cycle and protein production interactions on gene expression. Université Paris-Saclay, Paris; 2017.

17. Koch AL, Levy HR. Protein turnover in growing cultures of Escherichia coli. Journal of Biological Chemistry. 1955;217(2):947–958. 13271454

18. Soltani M, Vargas-Garcia CA, Antunes D, Singh A. Intercellular variability in protein levels from stochastic expression and noisy cell cycle processes. PLOS Comput Biol. 2016;12(8):e1004972. doi: 10.1371/journal.pcbi.1004972 27536771

19. Bertaux F, Marguerat S, Shahrezaei V. Division Rate, Cell Size and Proteome Allocation: Impact on Gene Expression Noise and Implications for the Dynamics of Genetic Circuits. Royal Society Open Science. 2018;5(3):172234. doi: 10.1098/rsos.172234 29657814

20. Bar-Ziv R, Voichek Y, Barkai N. Dealing with Gene-Dosage Imbalance during S Phase. Trends in Genetics. 2016;32(11):717–723. doi: 10.1016/j.tig.2016.08.006 27575299

21. Narula J, Kuchina A, Lee DYD, Fujita M, Süel GM, Igoshin OA. Chromosomal Arrangement of Phosphorelay Genes Couples Sporulation and DNA Replication. Cell. 2015;162(2):328–337. doi: 10.1016/j.cell.2015.06.012 26165942

22. Walker N, Nghe P, Tans SJ. Generation and filtering of gene expression noise by the bacterial cell cycle. BMC Biology. 2016;14:11. doi: 10.1186/s12915-016-0231-z 26867568

23. Kempe H, Schwabe A, Crémazy F, Verschure PJ, Bruggeman FJ, Matera AG. The Volumes and Transcript Counts of Single Cells Reveal Concentration Homeostasis and Capture Biological Noise. Molecular Biology of the Cell. 2014;26(4):797–804. doi: 10.1091/mbc.E14-08-1296 25518937

24. Padovan-Merhar O, Nair GP, Biaesch AG, Mayer A, Scarfone S, Foley SW, et al. Single Mammalian Cells Compensate for Differences in Cellular Volume and DNA Copy Number through Independent Global Transcriptional Mechanisms. Molecular Cell. 2015;58(2):339–352. doi: 10.1016/j.molcel.2015.03.005 25866248

25. Thomas P. Intrinsic and Extrinsic Noise of Gene Expression in Lineage Trees. Scientific Reports. 2019;9(1):474. doi: 10.1038/s41598-018-35927-x 30679440

26. Fromion V, Leoncini E, Robert P. A stochastic model of the production of multiple proteins in cells. SIAM Journal on Applied Mathematics. 2015;75(6):2562–2580. doi: 10.1137/140994782

27. Thomas P, Terradot G, Danos V, Weiße AY. Sources, Propagation and Consequences of Stochasticity in Cellular Growth. Nature Communications. 2018;9(1):4528. doi: 10.1038/s41467-018-06912-9 30375377

28. Lin J, Amir A. Homeostasis of Protein and mRNA Concentrations in Growing Cells. Nature Communications. 2018;9(1):4496. doi: 10.1038/s41467-018-06714-z 30374016

29. Wang P, Robert L, Pelletier J, Dang WL, Taddei F, Wright A, et al. Robust growth of Escherichia coli. Current biology: CB. 2010;20(12):1099–1103. doi: 10.1016/j.cub.2010.04.045 20537537

30. Tyson JJ, Diekmann O. Sloppy size control of the cell division cycle. Journal of Theoretical Biology. 1986;118(4):405–426. doi: 10.1016/s0022-5193(86)80162-x 3520151

31. Soifer I, Robert L, Barkai N, Amir A. Single-cell analysis of growth in budding yeast and bacteria reveals a common size regulation strategy. arXiv:14104771 [cond-mat, q-bio]. 2014.

32. Osella M, Nugent E, Lagomarsino MC. Concerted control of Escherichia coli cell division. Proceedings of the National Academy of Sciences. 2014;111(9):3431–3435. doi: 10.1073/pnas.1313715111

33. Robert L, Hoffmann M, Krell N, Aymerich S, Robert J, Doumic M. Division in Escherichia coli is triggered by a size-sensing rather than a timing mechanism. BMC Biology. 2014;12(1):17. doi: 10.1186/1741-7007-12-17 24580833

34. Hilfinger A, Paulsson J. Separating intrinsic from extrinsic fluctuations in dynamic biological systems. Proceedings of the National Academy of Sciences of the United States of America. 2011;108(29):12167–12172. doi: 10.1073/pnas.1018832108 21730172

35. Blake WJ, Kærn M, Cantor CR, Collins JJ. Noise in eukaryotic gene expression. Nature. 2003;422(6932):633–637. doi: 10.1038/nature01546 12687005

36. Marr AG. Growth rate of Escherichia coli. Microbiological Reviews. 1991;55(2):316–333. 1886524

37. Neidhardt FC, Umbarger HE. Chemical composition of Escherichia coli. In: Escherichia coli and Salmonella: cellular and molecular biology. 2nd ed. ASM Press; 1996.

38. Klumpp S, Hwa T. Growth-rate-dependent partitioning of rna polymerases in bacteria. Proceedings of the National Academy of Sciences. 2008;105(51):20245–20250. doi: 10.1073/pnas.0804953105

39. Dessalles R, Fromion V, Robert P. A stochastic analysis of autoregulation of gene expression. Journal of Mathematical Biology. 2017;75(5):1253–1283. doi: 10.1007/s00285-017-1116-7 28289838

40. Siwiak M, Zielenkiewicz P. Transimulation—protein biosynthesis web service. PLOS ONE. 2013;8(9):e73943. doi: 10.1371/journal.pone.0073943 24040122

41. Collins JF, Richmond MH. Rate of growth of Bacillus cereus between divisions. Journal of General Microbiology. 1962;28(1):15–33. doi: 10.1099/00221287-28-1-15 13880594

42. Sharpe ME, Hauser PM, Sharpe RG, Errington J. Bacillus subtilis cell cycle as studied by fluorescence microscopy: constancy of cell length at initiation of dna replication and evidence for active nucleoid partitioning. Journal of Bacteriology. 1998;180(3):547–555. 9457856

Článek vyšel v časopise


2020 Číslo 1
Nejčtenější tento týden