Mathematical analysis and numerical simulations for the HSP70 synthesis model

MERAL G., Pelen N. N.

JOURNAL OF MATHEMATICAL CHEMISTRY, vol.56, no.10, pp.3089-3114, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 56 Issue: 10
  • Publication Date: 2018
  • Doi Number: 10.1007/s10910-018-0934-1
  • Journal Name: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3089-3114
  • Keywords: Existence and uniqueness, Permenance, HSP70 synthesis, Mathematical modelling, FDM, HEAT-SHOCK RESPONSE, PROTEIN, CELLS
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

The heat shock proteins (HSPs) protect the other proteins in the process of folding under stressful conditions such as oxygen deprivation, hypothermy or presence of alcohol. They have also an important role in tumour invasion. In this paper, the existence, uniqueness and permanence properties for the solution of the mathematical model which focuses on the synthesis of HSP70 is proved. Moreover the numerical simulations are performed by using FDM, namely a combination of backward and forward Euler methods, and the results confirm the expected behaviour of the solution.