Fractional Calculus Evaluation of Hyaluronic Acid Crosslinking in a Nanoscopic Part of Articular Cartilage Model System - Publication - Bridge of Knowledge

Your account

login

Search

Fractional Calculus Evaluation of Hyaluronic Acid Crosslinking in a Nanoscopic Part of Articular Cartilage Model System

Abstract

This work presents a study of the mechanism of physical crosslinking of hyaluronic acid in the presence of common phospholipids in synovial joint organ systems. Molecular dynamic simulations have been executed to understand the formation of hyaluronan networks at various phospholipid concentrations. The results of the simulations suggest that the mechanisms exhibit subdiffusion characteristics. Transportation quantities derive as a function of time during numerical calculations of mean square displacement, and observations of sublinear growth were noted. Coarse-grained models are deployed to obtain a mathematical description where a random walker and several subdiffusion schemes of its motion describe the models. The findings of this study may establish mechanisms of biopolymer network formations in normal and pathologic synovial fluid and help elucidate the mechanism of facilitated AC biolubrication.

Citations

  • 0

    CrossRef

  • 0

    Web of Science

  • 0

    Scopus

Authors (5)

Cite as

Full text

download paper
downloaded 27 times
Publication version
Accepted or Published Version
License
Creative Commons: CC-BY open in new tab

Keywords

Details

Category:
Monographic publication
Type:
rozdział, artykuł w książce - dziele zbiorowym /podręczniku w języku o zasięgu międzynarodowym
Title of issue:
W : Dynamical Systems in Theoretical Perspective strony 25 - 35
Language:
English
Publication year:
2018
Bibliographic description:
Bełdowski P., Weber P., De Leon T., Auge W., Gadomski A.: Fractional Calculus Evaluation of Hyaluronic Acid Crosslinking in a Nanoscopic Part of Articular Cartilage Model System// Dynamical Systems in Theoretical Perspective/ ed. Jan Awrejcewicz Cham: Springer, 2018, s.25-35
DOI:
Digital Object Identifier (open in new tab) 10.1007/978-3-319-96598-7
Bibliography: test
  1. Dédinaté, A.: Biomimetic lubrication. Soft Matter, 8, 273-284 (2012)
  2. M. Doi, S. F. Edwards, The theory of polymer dynamics, (Oxford University Press, Oxford, 1994)
  3. Gadomski, A.: Nucleation-and-growth problem in model lipid membranes undergoing subgel phase transitions is a problem of time scale. Eur. Phys. J. B, 9, 569-571 (1999) open in new tab
  4. Goudoulas, T.B., Kastrinakis, E.G., Nychas, S.G., Papazoglou, L.G., Kazakos, G.M., Kosmas, P.V.: Rheological study of synovial fluid obtained from dogs: healthy, pathological, and post- surgery, after spontaneous rupture of cranial cruciate ligament. Ann. Biomed. Eng., 38, 57-65 (2010) open in new tab
  5. G.G. Hari, C.A. Hales, Chemistry and Biology of Hyaluronan, Elsevier Science, Amsterdam, (2008)
  6. Haubol, H.J., Matha, A.M., Saxena, R.K.: Mittag-Leffler functions and their applications. Journal of Applied Mathematics, 2011, (2011) open in new tab
  7. Hills, B.A.: Boundary lubrication in vivo. Proc. Inst. Mech. Eng. H, 214, 83-94 (2000) open in new tab
  8. Jung, S., Petelska, A., Be ldowski, P., Augé, W., Casey, T., Walczak, D., Lemke, K., Gadomski, A.: Hyaluronic acid and phospholipid interactions useful for repaired articular cartilage surfaces -a mini review toward tribological surgical adjuvants. Colloid Polym. Sci., 295, 403-412 (2017) open in new tab
  9. Nitzan, D.W., Nitzan, U., Dan, P., Yedgar, S.: The role of hyaluronic acid in protecting surface?active phospholipids from lysis by exogenous phospholipase A2. Rheumatology, 40, 335-340 (2001) open in new tab
  10. Panja, D.: Anomalous Polymer Dynamics Is Non-Markovian: Memory Effects and The Gen- eralized Langevin Equation Formulation. J. Stat. Mech., 6, P06011 (2010) open in new tab
  11. Pasquali-Ronchetti, I., Quaglino, D., Mori, G., Bacchelli, B., Ghosh, P.: Hyaluronan- phospholipid interactions J. Struct. Biol., 120, 1-10 (1997) open in new tab
  12. Podlubny, I., Fractional differential equations, (Academic Press, San Diego, 1999) open in new tab
  13. Podlubny, I.: Matrix approach to discrete fractional calculus. Fractional Calculus and Applied Analysis, 3, 359-386 (2000) open in new tab
  14. Richmond, T.J.: Solvent accessible surface area and excluded volume in proteins. Analytical equations for overlapping spheres and implications for the hydrophobic effect. J. Mol. Biol., 178, 63-89 (1984) open in new tab
  15. Rouse, P. E.: A Theory of the Linear Viscoelastic Properties of Dilute Solutions of Coiling Polymers. J. Chem. Phys., 21, 1272-1280 (1953) open in new tab
  16. Samko, S. G., Kilbas, A. A., Marichev, O. I.: Fractional integrals and derivatives -theory and applications, (Gordon and Breach, Amsterdam, 1993) open in new tab
  17. Siódmiak, J., Be ldowski, P., Augé, W., Ledziński, D.,Śmigiel, S., Gadomski, A.: Molecular Dynamic Analysis of Hyaluronic Acid and Phospholipid Interaction in Tribological Surgical Adjuvant Design for Osteoarthritis. Molecules, 22, 1436-1456 (2017) open in new tab
  18. Sorkin, R., Kampf, N., Zhu, L., Klein, J.: Hydration lubrication and shear-induced self- healing of lipid bilayer boundary lubricants in phosphatidylcholine dispersions. Soft Matter, 12, 2773-2784 (2016) open in new tab
  19. Wang, M., Liu, C., Thormann, E., Dédinaité, A.: Hyaluronan and phospholipid association in biolubrication. Biomacromolecules, 14, 4198-4206 (2013) open in new tab
  20. Wieland, D.C.F., Degen, P., Zander, T., Gayer, S., Raj, A., An, J., Dédinaité, A., Claesson, P., Willumeit-RȂ ¶mer, R.: Structure of DPPC-hyaluronan interfacial layers?effects of molecu- lar weight and ion composition. Rheumatology, 412, 729-740 (2016) open in new tab
Verified by:
Gdańsk University of Technology

seen 93 times

Recommended for you

Anomalous Behavior of Hyaluronan Crosslinking Due to the Presence of Excess Phospholipids in the Articular Cartilage System of Osteoarthritis

  • P. Bełdowski,
  • P. Weber,
  • T. Andrysiak
  • + 4 authors
2017

Physical crosslinking of hyaluronic acid in the presence of phospholipids in an aqueous nano-environment

  • P. Bełdowski,
  • P. Weber,
  • A. Dedinaite
  • + 2 authors
2018

Effect of Ion and Binding Site on the Conformation of Chosen Glycosaminoglycans at the Albumin Surface

  • P. Sionkowski,
  • P. Bełdowski,
  • N. Kruszewska
  • + 3 authors
2022

Hyaluronan-Chondroitin Sulfate Anomalous Crosslinking Due to Temperature Changes

  • T. Andrysiak,
  • P. Bełdowski,
  • J. Siódmiak
  • + 2 authors
2018
Meta Tags