Skip to main content
SpringerLink
Log in

Digital Seed Train Twins and Statistical Methods

  • Chapter
  • First Online:
Digital Twins

Part of the book series: Advances in Biochemical Engineering/Biotechnology ((ABE,volume 176))

Abstract

Model-based concepts and simulation techniques in combination with digital tools emerge as a key to explore the full potential of biopharmaceutical production processes, which contain several challenging development and process steps. One of these steps is the time- and cost-intensive cell proliferation process (also called seed train) to increase cell number from cell thawing up to production scale. Challenges like complex cell metabolism, batch-to-batch variation, variabilities in cell behavior, and influences of changes in cultivation conditions necessitate adequate digital solutions to provide information about the current and near future process state to derive correct process decisions.

For this purpose digital seed train twins have proved to be efficient, which digitally display the time-dependent behavior of important process variables based on mathematical models, strategies, and adaption procedures.

This chapter will outline the needs for digitalization of seed trains, the construction of a digital seed train twin, the role of parameter estimation, and different statistical methods within this context, which are applicable to several problems in the field of bioprocessing. The results of a case study are presented to illustrate a Bayesian approach for parameter estimation and prediction of an industrial cell culture seed train for seed train digitalization.

Graphical Abstract

This chapter outlines the needs for digitalization of cell proliferation processes (seed trains), the construction of a digital seed train twin as well as the role of parameter estimation and different statistical methods within this context, which are applicable to several problems in the field of bioprocessing. The results of a case study are presented to illustrate a Bayesian approach for parameter estimation and prediction of an industrial cell culture seed, as an example for seed train digitalization. It has been shown in which way prior knowledge and input uncertainty can be considered and be propagated to predictive uncertainty.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Abbreviations

CHO:

Chinese hamster ovary

cv:

Coefficient of variation

MAPE:

Mean absolute percentage error

MC:

Monte Carlo

MCMC:

Markov chain Monte Carlo

ML:

Maximum likelihood

NRMSE:

Normalized root mean square error

PAT:

Process analytical technology

QbD:

Quality by Design

WLS:

Weighted least squares

α:

Shape parameter of gamma distribution

λ:

Rate parameter of gamma distribution

μ:

Cell-specific growth rate

μd:

Cell-specific death rate

μd,min:

Minimum cell-specific death rate

μmax:

Maximum cell-specific growth rate

σ2:

Measurement variance

θ:

Parameter vector

\( \hat{\theta} \):

Estimated parameter vector

aLag:

Correction factor for lag phase

CI:

Confidence interval

cGlc:

Glucose concentration

cGln:

L-glutamine concentration

cLac:

Lactate concentration

cAmm:

Ammonia concentration

D:

Experimental data

kAmm:

Correction factor for ammonia uptake

kGlc:

Monod kinetic constant for glucose uptake

kGln:

Monod kinetic constant for glutamine uptake

KLys:

Cell lysis constant

KS,Glc:

Monod kinetic constant for glucose

KS,Gln:

Monod kinetic constant for glutamine

L:

Likelihood function

qAmm:

Cell-specific ammonia production rate

qAmm,uptake:

Cell-specific ammonia uptake rate

qGlc:

Cell-specific glucose uptake rate

qGlc,max:

Maximum cell-specific glucose uptake rate

qGln:

Cell-specific glutamine uptake rate

qGln,max:

Maximum cell-specific glutamine uptake rate

qLac:

Cell-specific lactate production rate

qLac,uptake:

Maximum cell-specific lactate uptake rate

t:

Time

tLag:

Duration of lag phase

V:

Culture volume

X:

Matrix containing simulated data (Xinit, initial data matrix; Xprop, proposed data matrix)

Xt:

Total cell concentration

Xv:

Viable cell concentration

y0:

Initial concentrations

Y:

Random variable

YAmm/Gln:

Kinetic production constant (stoichiometric ratio of ammonia production and glutamine uptake)

YLac/Glc:

Kinetic production constant (stoichiometric ratio of lactate production and glucose uptake)

ysim:

Simulated data

\( {z}_{1-\frac{\alpha }{2}} \):

(\( 1-\frac{\alpha }{2} \))-quantile of the standard normal distribution

References

  1. U.S. Department of Health and Human Services, Food and Drug Administration Guidance for Industry PAT - A Framework for Innovative Pharmaceutical Development, manufacturing, and Quality Assurance. U.S. Department of Health and Human Services, Food and Drug Administration: Guidance for industry:PAT – a framework for innovative pharmaceutical development, manufacturing and quality assurance. http://www.fda.gov/down

  2. Glassey J, Gernaey KV, Clemens C, Schulz TW, Oliveira R, Striedner G, Mandenius C-F (2011) Process analytical technology (PAT) for biopharmaceuticals. Biotechnol J 6(4):369–377. https://doi.org/10.1002/biot.201000356

    Article  CAS  PubMed  Google Scholar 

  3. Abt V, Barz T, Cruz Bournazou MN, Herwig C, Kroll P, Möller J, Pörtner R, Schenkendorf R (2018) Model-based tools for optimal experiments in bioprocess engineering. Curr Opin Chem Eng 22:244–252. https://doi.org/10.1016/j.coche.2018.11.007

  4. Le H, Kabbur S, Pollastrini L, Sun Z, Mills K, Johnson K, Karypis G, Hu W-S (2012) Multivariate analysis of cell culture bioprocess data--lactate consumption as process indicator. J Biotechnol 162(2–3):210–223. https://doi.org/10.1016/j.jbiotec.2012.08.021

    Article  CAS  PubMed  Google Scholar 

  5. Brunner M, Fricke J, Kroll P, Herwig C (2017) Investigation of the interactions of critical scale-up parameters (pH, pO2 and pCO2) on CHO batch performance and critical quality attributes. Bioprocess Biosyst Eng 40(2):251–263. https://doi.org/10.1007/s00449-016-1693-7

    Article  CAS  PubMed  Google Scholar 

  6. International Council for Harmonisation of technical requirements for registration of pharmaceuticals for human use (2009) ICH Q8(R2) pharmaceutical development Q8. https://vnras.com/wp-content/uploads/2017/05/Q8R2_PHARMACEUTICAL-DEVELOPMENT.pdf

  7. Herwig C, Garcia-Aponte OF, Golabgir A, Rathore AS (2015) Knowledge management in the QbD paradigm. Manufacturing of biotech therapeutics. Trends Biotechnol 33(7):381–387. https://doi.org/10.1016/j.tibtech.2015.04.004

    Article  CAS  PubMed  Google Scholar 

  8. Carrondo MJT, Alves PM, Carinhas N, Glassey J, Hesse F, Merten O-W, Micheletti M, Noll T, Oliveira R, Reichl U, Staby A, Teixeira AP, Weichert H, Mandenius C-F (2012) How can measurement, monitoring, modeling and control advance cell culture in industrial biotechnology? Biotechnol J 7(12):1522–1529. https://doi.org/10.1002/biot.201200226

    Article  CAS  PubMed  Google Scholar 

  9. Narayanan H, Luna MF, von Stosch M, Bournazou MNC, Polotti G, Morbidelli M, Butté A, Sokolov M (2019) Bioprocessing in the digital age - the role of process models. Biotechnol J 15:1900172. https://doi.org/10.1002/biot.201900172

    Article  CAS  Google Scholar 

  10. Möller J, Rosenberg M, Riecken K, Pörtner R, Zeng A-P, Jandt U (2020) Quantification of the dynamics of population heterogeneities in CHO cultures with stably integrated fluorescent markers. Anal Bioanal Chem 412(9):2065–2080. https://doi.org/10.1007/s00216-020-02401-5

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. Möller J, Korte K, Pörtner R, Zeng A-P, Jandt U (2018) Model-based identification of cell-cycle-dependent metabolism and putative autocrine effects in antibody producing CHO cell culture. Biotechnol Bioeng 115(12):2996–3008. https://doi.org/10.1002/bit.26828

    Article  CAS  PubMed  Google Scholar 

  12. Wurm F, Wurm M (2017) Cloning of CHO cells, productivity and genetic stability—a discussion. PRO 5(4):20. https://doi.org/10.3390/pr5020020

    Article  CAS  Google Scholar 

  13. Möller J, Bhat K, Riecken K, Pörtner R, Zeng A-P, Jandt U (2019) Process-induced cell cycle oscillations in CHO cultures: online monitoring and model-based investigation. Biotechnol Bioeng 116(11):2931–2943. https://doi.org/10.1002/bit.27124

    Article  CAS  PubMed  Google Scholar 

  14. Paul K, Rajamanickam V, Herwig C (2019) Model-based optimization of temperature and pH shift to increase volumetric productivity of a Chinese hamster ovary fed-batch process. J Biosci Bioeng 128(6):710–715. https://doi.org/10.1016/j.jbiosc.2019.06.004

    Article  CAS  PubMed  Google Scholar 

  15. Frahm B (2014) Seed train optimization for cell culture. In: Pörtner R (ed) Animal cell biotechnology. Methods Mol Biol 1104:355–367. https://doi.org/10.1007/978-1-62703-733-4_22

  16. Heidemann R, Mered M, Wang DQ, Gardner B, Zhang C, Michaels J, Henzler H-J, Abbas N, Konstantinow K (2002) A new seed-train expansion method for recombinant mammalian cell lines. Cytotechnology 38:99–108. https://doi.org/10.1023/A:1021114300958

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Yang J, Sui L (2012) Development and application of perfusion culture producing seed cells in WAVE bioreactor. Sheng Wu Gong Cheng Xue Bao 28(3):358–367

    CAS  PubMed  Google Scholar 

  18. Stepper L, Filser FA, Fischer S, Schaub J, Gorr I, Voges R (2020) Pre-stage perfusion and ultra-high seeding cell density in CHO fed-batch culture: a case study for process intensification guided by systems biotechnology. Bioprocess Biosyst Eng 43:1431. https://doi.org/10.1007/s00449-020-02337-1

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Hernández Rodríguez T, Frahm B (2020) Design, optimization, and adaptive control of cell culture seed trains. In: Pörtner R (ed) Animal cell biotechnology. Methods Mol Biol 2095:251–267. https://doi.org/10.1007/978-1-0716-0191-4_14

  20. Hernández Rodríguez T, Posch C, Schmutzhard J, Stettner J, Weihs C, Pörtner R, Frahm B (2019) Predicting industrial-scale cell culture seed trains-A Bayesian framework for model fitting and parameter estimation, dealing with uncertainty in measurements and model parameters, applied to a nonlinear kinetic cell culture model, using an MCMC method. Biotechnol Bioeng 116(11):2944–2959. https://doi.org/10.1002/bit.27125

    Article  CAS  PubMed  Google Scholar 

  21. Sadino-Riquelme MC, Rivas J, Jeison D, Hayes RE, Donoso-Bravo A (2020) Making sense of parameter estimation and model simulation in bioprocesses. Biotechnol Bioeng 117(5):1357–1366. https://doi.org/10.1002/bit.27294

    Article  CAS  PubMed  Google Scholar 

  22. Liu Y, Gunawan R (2017) Bioprocess optimization under uncertainty using ensemble modeling. J Biotechnol 244:34–44. https://doi.org/10.1016/j.jbiotec.2017.01.013

    Article  CAS  PubMed  Google Scholar 

  23. Anane E, López C, Barz T, Sin G, Gernaey KV, Neubauer P, Cruz Bournazou MN (2019) Output uncertainty of dynamic growth models. Effect of uncertain parameter estimates on model reliability. Biochem Eng J:107247. https://doi.org/10.1016/j.bej.2019.107247

  24. del Rio-Chanona EA, Zhang D, Vassiliadis VS (2016) Model-based real-time optimisation of a fed-batch cyanobacterial hydrogen production process using economic model predictive control strategy. Chem Eng Sci 142:289–298. https://doi.org/10.1016/j.ces.2015.11.043

    Article  CAS  Google Scholar 

  25. Hedengren JD, Shishavan RA, Powell KM, Edgar TF (2014) Nonlinear modeling, estimation and predictive control in APMonitor. Comput Chem Eng 70:133–148. https://doi.org/10.1016/j.compchemeng.2014.04.013

    Article  CAS  Google Scholar 

  26. Jewaratnam J, Zhang J, Hussain A, Morris J (2012) Batch-to-batch iterative learning control using updated models based on a moving window of historical data. Proc Eng 42:206–213. https://doi.org/10.1016/j.proeng.2012.07.411

    Article  Google Scholar 

  27. de Andrade RR, Rivera EC, Atala DIP, Filho RM, Filho FM, Costa AC (2009) Study of kinetic parameters in a mechanistic model for bioethanol production through a screening technique and optimization. Bioprocess Biosyst Eng 32(5):673–680. https://doi.org/10.1007/s00449-008-0291-8

    Article  CAS  PubMed  Google Scholar 

  28. Bradford E, Schweidtmann AM, Zhang D, Jing K, del Rio-Chanona EA (2018) Dynamic modeling and optimization of sustainable algal production with uncertainty using multivariate Gaussian processes. Comput Chem Eng 118:143–158. https://doi.org/10.1016/j.compchemeng.2018.07.015

    Article  CAS  Google Scholar 

  29. Narayanan H, Sokolov M, Morbidelli M, Butté A (2019) A new generation of predictive models. The added value of hybrid models for manufacturing processes of therapeutic proteins. Biotechnol Bioeng 116(10):2540–2549. https://doi.org/10.1002/bit.27097

    Article  CAS  PubMed  Google Scholar 

  30. Heumann C, Schomaker M, Shalabh (2016) Introduction to statistics and data analysis. With exercises, solutions and applications in R. Springer, Cham

    Google Scholar 

  31. Ruppert D, Matteson DS (2015) Statistics and data analysis for financial engineering. With R examples, 2. Aufl. Springer texts in statistics. Springer, New York

    Google Scholar 

  32. Daume S, Kofler S, Kager J, Kroll P, Herwig C (2020) Generic workflow for the setup of mechanistic process models. In: Pörtner R (ed) Animal cell biotechnology. Methods and protocols. Humana Press, New York. https://doi.org/10.1007/978-1-0716-0191-4_11

  33. Sin G, Gernaey KV, Lantz AE (2009) Good modeling practice for PAT applications. Propagation of input uncertainty and sensitivity analysis. Biotechnol Prog 25(4):1043–1053. https://doi.org/10.1002/btpr.166

    Article  CAS  PubMed  Google Scholar 

  34. Saltelli A et al (2008) Global sensitivity analysis. The primer. Wiley, Chichester. ISBN 978-0-470-05997-5

    Google Scholar 

  35. Arora N, Biegler LT (2001) Redescending estimators for data reconciliation and parameter estimation. Comput Chem Eng 25(11–12):1585–1599. https://doi.org/10.1016/S0098-1354(01)00721-9

    Article  CAS  Google Scholar 

  36. Spiess A-N, Neumeyer N (2010) An evaluation of R2 as an inadequate measure for nonlinear models in pharmacological and biochemical research: a Monte Carlo approach. BMC Pharmacol 10:6. https://doi.org/10.1186/1471-2210-10-6

    Article  PubMed  PubMed Central  Google Scholar 

  37. Carlin BP, Louis TA (2009) Bayesian methods for data analysis. 3. Aufl. A Chapman & Hall book, vol 78. CRC Press, Boca Raton

    Google Scholar 

  38. Levy R, Choi J (2013) Bayesian structural equation modeling. In: Hancock GR, Mueller RO (eds) Structural equation modeling. A second course. Information Age Publishing, Charlotte, pp S563–S624

    Google Scholar 

  39. Press WH (1996) Numerical recipes in C. The art of scientific computing, Chapter 10.4.2nd edn. University Press, Cambridge, pp 408–412

    Google Scholar 

  40. Zeugmann T, Poupart P, Kennedy J, Jin X, Han J, Saitta L, Sebag M, Peters J, Bagnell JA, Daelemans W, Webb GI, Ting KM, Shirabad JS, Fürnkranz J, Hüllermeier E, Matwin S, Sakakibara Y, Flener P, Schmid U, Procopiuc CM, Lachiche N (2011) Particle swarm optimization. In: Sammut C, Webb GI (eds) Encyclopedia of machine learning. With 78 tables. Springer, New York, pp S760–S766

    Chapter  Google Scholar 

  41. Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7(4):308–313. https://doi.org/10.1093/comjnl/7.4.308

    Article  Google Scholar 

  42. Deppe S, Frahm B, Hass VC, Hernández Rodríguez T, Kuchemüller KB, Möller J, Pörtner R Estimation of process model parameters animal cell culture. In: Pörtner R (ed) Animal cell biotechnology. Methods Mol Biol 2095:S213–S234. https://doi.org/10.1007/978-1-0716-0191-4_12

  43. Kroll P, Hofer A, Stelzer IV, Herwig C (2017) Workflow to set up substantial target-oriented mechanistic process models in bioprocess engineering. Process Biochem 62:24–36. https://doi.org/10.1016/j.procbio.2017.07.017

    Article  CAS  Google Scholar 

  44. López CDC, Barz T, Körkel S, Wozny G (2015) Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental design. Comput Chem Eng 77:24–42. https://doi.org/10.1016/j.compchemeng.2015.03.002

    Article  CAS  Google Scholar 

  45. Raue A, Kreutz C, Maiwald T, Bachmann J, Schilling M, Klingmüller U, Timmer J (2009) Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics 25(15):1923–1929. https://doi.org/10.1093/bioinformatics/btp358

    Article  CAS  PubMed  Google Scholar 

  46. Möller J, Hernández Rodríguez T, Müller J, Arndt L, Kuchemüller KB, Frahm B, Eibl R, Eibl D, Pörtner R (2019) Model uncertainty-based evaluation of process strategies during scale-up of biopharmaceutical processes. Comput Chem Eng:106693. https://doi.org/10.1016/j.compchemeng.2019.106693

  47. Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB (2013) Bayesian data analysis, 3rd edition. In: Chapman & Hall/CRC texts in statistical science. CRC Press, Hoboken. ISBN-13: 978-1439840955

    Google Scholar 

  48. Gilks WR, Richardson S, Spiegelhalter DJ (eds) (1998) Markov chain Monte Carlo in practice. Interdisciplinary statistics. Chapman & Hall, Boca Raton. ISBN-13: 978-0412055515

    Google Scholar 

  49. Galagali N, Marzouk YM (2015) Bayesian inference of chemical kinetic models from proposed reactions. Chem Eng Sci 123:170–190. https://doi.org/10.1016/j.ces.2014.10.030

    Article  CAS  Google Scholar 

  50. Vrugt JA (2016) Markov chain Monte Carlo simulation using the DREAM software package. Theory, concepts, and MATLAB implementation. Environ Model Softw 75:273–316. https://doi.org/10.1016/j.envsoft.2015.08.013

    Article  Google Scholar 

  51. Xing Z, Bishop N, Leister K, Li ZJ (2010) Modeling kinetics of a large-scale fed-batch CHO cell culture by Markov chain Monte Carlo method. Biotechnol Prog 26(1):208–219. https://doi.org/10.1002/btpr.284

    Article  CAS  PubMed  Google Scholar 

  52. Schenkendorf R, Gerogiorgis D, Mansouri S, Gernaey K (2020) Model-based tools for pharmaceutical manufacturing processes. Processes 8(1):49. https://doi.org/10.3390/pr8010049

    Article  Google Scholar 

  53. Xie X, Schenkendorf R (2019) Robust process Design in Pharmaceutical Manufacturing under batch-to-batch variation. PRO 7(8):509. https://doi.org/10.3390/pr7080509

    Article  Google Scholar 

  54. Luce B, Anthony OH, Dennis F (2003) A primer on Bayesian statistics in health economics and outcomes research. MEDTAP International, Bethesda

    Google Scholar 

  55. O’Hagan A (2008) The Bayesian approach to statistics. In: Rudas T (ed) Handbook of probability. Theory and applications. Sage, Los Angeles, pp S85–S100

    Chapter  Google Scholar 

  56. Kern S, Platas-Barradas O, Pörtner R, Frahm B (2016) Model-based strategy for cell culture seed train layout verified at lab scale. Cytotechnology 68(4):1019–1032. https://doi.org/10.1007/s10616-015-9858-9

    Article  PubMed  Google Scholar 

  57. Zhang D, Del Rio-Chanona EA, Petsagkourakis P, Wagner J (2019) Hybrid physics-based and data-driven modeling for bioprocess online simulation and optimization. Biotechnol Bioeng 157(3):293. https://doi.org/10.1002/bit.27120

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Biotechnology and Bioprocess Engineering, Ostwestfalen-Lippe University of Applied Sciences and Arts, Lemgo, Germany

    Tanja Hernández Rodríguez & Björn Frahm

Authors
  1. Tanja Hernández Rodríguez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Björn Frahm
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Björn Frahm .

Editor information

Editors and Affiliations

  1. Institute of Chemical, Environmental and Bioscience Engineering, Vienna University of Technology, Wien, Austria

    Christoph Herwig

  2. Institute of Bioprocess and Biosystems Engineering, Hamburg University of Technology, Hamburg, Germany

    Ralf Pörtner

  3. Institute of Bioprocess and Biosystems Engineering, Hamburg University of Technology, Hamburg, Germany

    Johannes Möller

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Hernández Rodríguez, T., Frahm, B. (2020). Digital Seed Train Twins and Statistical Methods. In: Herwig, C., Pörtner, R., Möller, J. (eds) Digital Twins. Advances in Biochemical Engineering/Biotechnology, vol 176. Springer, Cham. https://doi.org/10.1007/10_2020_137

Download citation

Publish with us

Policies and ethics

Search

Navigation