AIMS Mathematics, 2020, 5(6): 7191-7213. doi: 10.3934/math.2020460

Research article

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

A mathematical study of effects of delays arising from the interaction of anti-drug antibody and therapeutic protein in the immune response system

Applied Mathematics Laboratory, Department of Mathematics, Hasanuddin University, Makassar, Indonesia

Immunogenicity is the ability of substances to evoke an immune response such as a therapeutic protein drug that is considered as a foreign object in the human body. The rise of the immune response results in the production of Anti-Drug Antibody (ADA) that requires a certain period to be activated since it is influenced by the number of injected doses of the drug. The entry of ADA from the depot into the plasma also requires a certain period since the ADA must pass through a series of compartments, hence rises a delay. Both processes are considered as a natural process where the system experiences delay with different delay periods. Immunogenicity on therapeutic protein pharmacokinetics is modelled as a nonlinear delay differential system. From the formulated model, one positive equilibrium solution is obtained under some conditions. Qualitative analysis gives a pair of critical delays in terms of a time delay of the accumulation of protein drug injection and a time required by the ADA to enter the plasma and binding the drug in the plasma. Numerical simulations show that the critical delays result in the appearance of oscillatory behavior in the system. For the system to remain stable, the entering process of ADA into the plasma is delayed in accordance with the obtained critical delay. It is intended such that the injected therapeutic protein drugs provide an optimal effect.
  Figure/Table
  Supplementary
  Article Metrics

References

1. J. A. Pedras-Vasconcelos, The Immunogenicity of Therapeutic Proteins-What you Don't Know Can Hurt YOU and the Patient. SBIA REdI Fall, Ed.; U.S. Food and Drug Administration: Silver Spring, MD, USA, 2014. Available from: https://www.fda.gov/files/drugs/published/The-immunogenicity-of-therapeutic-proteins--what-you-don%E2%80%99t-know-can-hurt-YOU-and-the-patient--Fall-2014.pdf.

2. J. M. Carton, W. R. Strohl, Chapter 4-Protein therapeutics (introduction to biopharmaceuticals), Intro. Biol. Small Mole. Drug Rese. Develop., (2013), 127-159.

3. N. Chirmule, V. Jawa, B. Meibohm, Immunogenicity to therapeutic proteins: Impact on PK/PD and Efficacy, AAPS J., 14 (2012), 296-302.    

4. K. D. Ratanji, J. P. Derrick, R. J. Dearman, et al. Immunogenicity of therapeutic proteins: Influence of aggregation, J. Immunotoxicol, 11 (2014), 99-109.    

5. A. Kuriakose, N. Chirmule, P. Nair, Immunogenicity of biotherapeutics: Causes and association with posttranslational modifications, J. Immunol. Res., 2016 (2016), 1-18.

6. S. Tourdot, T. P. Hickling, Nonclinical immunogenicity risk assessment of therapeutic proteins, Bioanalysis, 11 (2019), 1631-1643.    

7. G. Shankar, S. Arkin, L. Cocea, et al. Assessment and reporting of the clinical immunogenicity of therapeutic proteins and peptides-harmonized terminology and tactical recommendations, AAPS J., 16 (2014), 658-673.    

8. B. Chen, J. Q. Dong, W. J. Pan, et al. Pharmacokinetics/pharmacodynamics model supported early drug development, Curr Pharm Biotechnol., 13 (2012), 1360-1375.    

9. A. Smith, H. Manoli, S. Jaw, et al. Unraveling the effect of immunogenicity on the PK/PD, efficacy, and safety of therapeutic proteins, J. Immunol. Res., 2016 (2016), 1-9.

10. W. H. Boehncke, N. C. Brembilla, Immunogenicity of biologic therapies: Causes and consequences, Exp. Rev. Clin. Immunol., 14 (2018), 513-523.

11. B. W. Neun, Y. Barenholz, J. Szebeni, et al. Understanding the Role of Anti-PEG Antibodies in the Complement Activation by Doxil in Vitro, Molecule, 23 (2018), 1700.

12. S. Kathman, T. M. Thway, L. Zhou, et al. Utility of a bayesian mathematical model to predict the impact of immunogenicity on pharmacokinetics of therapeutic proteins, AAPS J., 18 (2016), 424.

13. E. M. J. van Brummelen, W. Ros, G. Wolbink, et al. Antidrug antibody formation in oncology: Clinical relevance and challenges, Oncologist, 21 (2016), 1260-1268.    

14. S. Gupta, S. R. Indelicato, V. Jethwa, et al. Recommendations for the design, optimization, and qualification of Cell-Based assays used for the detection of neutralizing antibody responses elicited to biologycal therapeutics, J. Immunol. Methods, 32 (2007), 1-18.

15. X. Chen, T. P. Hickling, P. Vicini, A mechanistic, multiscale mathematical model of immunogenicity for therapeutic proteins: Part 1-Theoretical model, CPT Pharmacometrics Syst. Pharmacol., 3 (2014), e133.

16. L. Hamuro, G. S. Tirucherai, S. M. Crawford, et al. Evaluating a multiscale mechanistic model of the immune system to predict human immunogenicity for a biotherapeutic in Phase 1, AAPS J., 21 (2019), 94.

17. G. I. Bell, Mathematical model of clonal selection and antibody production, J Theor Biol., 29 (1970), 191-232.    

18. H. Y. Lee, D. J. Topham, S. Y. Park, et al. Simulation and prediction of the adaptive immune response to influenza a virus infection, J. Virol., 83 (2009), 7151-7165.    

19. Z. H. Xu, H. Lee, T. Vu, et al. Populations pharmacokinetics of golimumab in patients with anklosing spondylitis: Impact of body weight and immunogenicity, Int J Clin Pharmacol Ther., 48 (2010), 596-607.    

20. P. L. Bonate, C. Sung, K. Welch, et al. Conditional modeling of antibody titers using A Zero-Inflated poisson random effect model: Application to fabrazyme, J Pharmacokinet Phar., 35 (2009), 449-459.

21. X. Chen, T. P. Hickling, E. Kraynov, et al. A mathematical model of the effect of immunogenicity on therapeutic protein pharmacokinetics, AAPS J., 15 (2013), 1141-1154.    

22. J. Foote, C. Milstein, Kinetic maturation of an immune response, Nature, 352 (1991), 530-532.    

23. B. S. Alexandra, N. Radhika, H. Paul, Novel Approaches and Strategies for Biologics, Vaccines and Cancer Therapies, Chapter 9-Biobetter Biologics, New York: Academic Press, (2015), 199-217.

24. Pacific Immunology, Learning Center: Antibody Affinity and Affinity Maturation, 2020., Available from: https://www.pacificimmunology.com/resources/antibody-introduction/antibody-affinity-and-affinity-maturation/.

25. S. Yi, P. W. Nelson, A. G. Ulsoy, Time-delay sistems: Analysis and control using the Lambert W function, World Scientific, Singapore, 2010.

26. Kasbawati, A. Y. Gunawan, R. Hertadi, et al. Effects of time delay on the dynamics of a kinetic model of a microbial fermentation process, ANZIAM J., 55 (2014), 336-356.

27. J. D. Murray, (1990) Mathematical biology, 2Eds., New York: Springer.

28. L. F. Shampine, S. Thompson, Solving DDEs in MATLAB, Appl. Numer. Math. 37 (2001), 441-458.    

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved