Skip to main content
Log in

A Bayesian Computational Approach to Explore the Optimal Duration of a Cell Proliferation Assay

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

Cell proliferation assays are routinely used to explore how a low-density monolayer of cells grows with time. For a typical cell line with a doubling time of 12 h (or longer), a standard cell proliferation assay conducted over 24 h provides excellent information about the low-density exponential growth rate, but limited information about crowding effects that occur at higher densities. To explore how we can best detect and quantify crowding effects, we present a suite of in silico proliferation assays where cells proliferate according to a generalised logistic growth model. Using approximate Bayesian computation we show that data from a standard cell proliferation assay cannot reliably distinguish between classical logistic growth and more general non-logistic growth models. We then explore, and quantify, the trade-off between increasing the duration of the experiment and the associated decrease in uncertainty in the crowding mechanism.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Bosco DB, Kenworthy R, Zorio DAR, Sang Q-XA (2015) Human mesenchymal stem cells are resistant to paclitaxel by adopting a non-proliferative fibroblastic state. PLOS ONE 10:e0128511

    Article  Google Scholar 

  • Bourseguin J et al (2016) FANCD2 functions as a critical factor downstream of MiTF to maintain the proliferation and survival of melanoma cells. Sci Rep 6:36539

    Article  Google Scholar 

  • Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach. Springer, Berlin

    MATH  Google Scholar 

  • Cai AQ, Landman KA, Hughes BD (2007) Multi-scale modeling of a wound-healing cell migration assay. J Theor Biol 245:576–594

    Article  MathSciNet  Google Scholar 

  • Collis J, Connor AJ, Paczkowski M, Kannan P, Pitt-Francis J, Byrne HM, Hubbard ME (2017) Bayesian calibration, validation and uncertainty quantification for predictive modelling of tumour growth: a tutorial. B Math Biol 79:939–973

    Article  MathSciNet  Google Scholar 

  • Dale PD, Sherratt JA, Maini PK (1994) The speed of corneal epithelial wound healing. Appl Math Lett 9:11–14

    Article  MATH  Google Scholar 

  • Deroulers C, Aubert M, Badoual M, Grammaticos B (2009) Modeling tumor cell migration: from microscopic to macroscopic models. Phys Rev E 79:031917

    Article  MathSciNet  Google Scholar 

  • Doran MR, Mills RJ, Parker AJ, Landman KA, Cooper-White JJ (2009) A cell migration device that maintains a defined surface with no cellular damage during wound edge generation. Lab on a Chip 9:2364–2369

    Article  Google Scholar 

  • Edelstein-Keshet L (1988) Mathematical models in biology. Random House, New York

    MATH  Google Scholar 

  • Gelman A, Carlin JB, Stern HS, Rubin DB (2004) Bayesian data analysis. CRC Press, Florida

    MATH  Google Scholar 

  • Gerlee P (2013) The model muddle: in search of tumour growth laws. Cancer Res 73:2407–2411

    Article  Google Scholar 

  • Jin W, Shah ET, Penington CP, McCue SW, Chopin LK, Simpson MJ (2016a) Reproducibility of scratch assays is affected by the initial degree of confluence: experiments, modelling and model selection. J Theor Biol 390:136–145

    Article  MATH  Google Scholar 

  • Jin W, Penington CJ, McCue SW, Simpson MJ (2016b) Stochastic simulation tools and continuum models for describing two-dimensional collective cell spreading with universal growth functions. Phys Biol 13:056003

    Article  Google Scholar 

  • Jin W, Shah ET, Penington CJ, McCue SW, Maini PK, Simpson MJ (2017) Logistic proliferation of cells in scratch assays is delayed. B Math Biol 79:1028–1050

    Article  MathSciNet  MATH  Google Scholar 

  • Johnston ST, Shah ET, Chopin LK, McElwain DLS, Simpson MJ (2015) Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOM\(^{\rm TM}\) assay data using the Fisher–Kolmogorov model. BMC Syst Biol 9:38

    Article  Google Scholar 

  • Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22:79–86

    Article  MathSciNet  MATH  Google Scholar 

  • Laird AK (1964) Dynamics of tumour growth. Br J Cancer 18:490–502

    Article  Google Scholar 

  • Liang CC, Park AY, Guan J-L (2007) In vitro scratch assay: a convenient and inexpensive method for analysis of cell migration in vitro. Nat Protoc 2:329–333

    Article  Google Scholar 

  • Liepe J, Kirk P, Filippi S, Toni T, Barnes CP, Stumpf MPH (2014) A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation. Nat Protoc 9:439–456

    Article  Google Scholar 

  • Liggett TM (1999) Stochastic interacting systems: contact, voter and exclusion processes. Springer, Berlin

    Book  MATH  Google Scholar 

  • Maini PK, McElwain DLS, Leavesley DI (2004a) Traveling wave model to interpret a wound-healing cell migration assay for human peritoneal mesothelial cells. Tissue Eng 10:475–482

    Article  Google Scholar 

  • Maini PK, McElwain DLS, Leavesley D (2004b) Travelling waves in a wound healing assay. Appl Math Lett 17:575–580

    Article  MathSciNet  MATH  Google Scholar 

  • Mathworks (2017) Kernel smoothing function estimate for univariate and bivariate data. Mathworks. http://au.mathworks.com/help/stats/ksdensity.html. Accessed June 2007

  • Murray JD (2002) Mathematical biology. Springer, Berlin

    MATH  Google Scholar 

  • O’Dea RD, Byrne HM, Waters SL (2012) Continuum modelling of in vitro tissue engineering: a review. Springer, Berlin

    Google Scholar 

  • Pearl R (1927) The growth of populations. Q Rev Biol 2:532–548

    Article  Google Scholar 

  • Sarapata EA, de Pillis LG (2014) A comparison and catalog of intrinsic tumor growth models. B Math Biol 76:2010–2024

    Article  MathSciNet  MATH  Google Scholar 

  • Savla U, Olson LE, Waters CM (2004) Mathematical modeling of airway epithelial wound closure during cyclic mechanical strain. J Appl Physiol 96:566–574

    Article  Google Scholar 

  • Sengers BG, Please CP, Oreffo ROC (2007) Experimental characterization and computational modelling of two-dimensional cell spreading for skeletal regeneration. J R Soc Interface 4:1107

    Article  Google Scholar 

  • Shakeel M, Matthews PC, Graham RS, Waters SL (2013) A continuum model of cell proliferation and nutrient transport in a perfusion bioreactor. Math Med Biol 30:21–44

    Article  MathSciNet  MATH  Google Scholar 

  • Sheardown H, Cheng YL (1996) Mechanisms of corneal epithelial wound healing. Chem Eng Sci 51:4517–4529

    Article  Google Scholar 

  • Sherratt JA, Murray JD (1990) Models of epidermal wound healing. Proc R Soc Lond B 241:29–36

    Article  Google Scholar 

  • Simpson MJ, Treloar KK, Binder BJ, Haridas P, Manton KJ, Leavesley DI, McElwain DLS, Baker RE (2013) Quantifying the roles of cell motility and cell proliferation in a circular barrier assay. J R Soc Interface 10:20130007

    Article  Google Scholar 

  • Sunnaker M, Busetto AG, Numminen E, Corander J, Foll M, Dessimoz C (2013) Approximate Bayesian Computation. PLOS Comput Biol 9:e1002803

    Article  MathSciNet  Google Scholar 

  • Tanaka MM, Francis AR, Luciani F, Sisson SA (2006) Using approximate Bayesian computation to estimate tuberculosis transmission parameters from genotype data. Genetics 173:1511–1520

    Article  Google Scholar 

  • Treloar KK, Simpson MJ, Haridas P, Manton KJ, Leavesley DI, McElwain DLS, Baker RE (2013) Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies. BMC Syst Biol 7:137

    Article  Google Scholar 

  • Treloar KK, Simpson MJ, McElwain DLS, Baker RE (2014) Are in vitro estimates of cell diffusivity and cell proliferation rate sensitive to assay geometry? J Theor Biol 356:71–84

    Article  Google Scholar 

  • Tsoularis A, Wallace J (2002) Analysis of logistic growth models. Math Biosci 179:21–55

    Article  MathSciNet  MATH  Google Scholar 

  • Vo BN, Drovandi CC, Pettit AN, Simpson MJ (2015) Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation. Math Biosci 263:133–142

    Article  MathSciNet  MATH  Google Scholar 

  • West GB, Brown JH, Enquist BJ (2001) A general model for ontogenetic growth. Nature 413:628–631

    Article  Google Scholar 

  • Zwietering MH, Jongenburger I, Rombouts FM, van’t Riet K (1990) Modeling of the bacterial growth curve. Appl Environ Microbiol 56:1875–1881

    Google Scholar 

Download references

Acknowledgements

This work was supported by the Australian Research Council (DP140100249, DP170100474). Computational resources were provided by the High Performance Computing and Research Support Group. We thank the two anonymous referees for their helpful comments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Matthew J. Simpson.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 1899 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Browning, A.P., McCue, S.W. & Simpson, M.J. A Bayesian Computational Approach to Explore the Optimal Duration of a Cell Proliferation Assay. Bull Math Biol 79, 1888–1906 (2017). https://doi.org/10.1007/s11538-017-0311-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-017-0311-4

Keywords

Navigation