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

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Backbone Angles Determination

#### 2.2. Entropy Calculation

## 3. Results

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

HSA | human serum albumin |

HA | hyaluronic acid |

CS6 | chondroitin 6 sulfate |

GAG | glycosaminoglycan |

MD | molecular dynamics |

PDB | protein data bank |

## References

- Klein, J.; Raviv, U.; Perkin, S.; Kampf, N.; Chai, L.; Giasson, S. Fluidity of water and of hydrated ions confined between solid surfaces to molecularly thin films. J. Phys. Condens. Matter
**2004**, 16, S5437–S5448. [Google Scholar] [CrossRef] - Gadomski, A.; Pawlak, Z.; Oloyede, A. Directed ion transport as virtual cause of some facilitated friction–lubrication mechanism prevailing in articular cartilage: A hypothesis. Tribol. Lett.
**2008**, 30, 83–90. [Google Scholar] [CrossRef] - Gadomski, A.; Bełdowski, P.; Rubí, J.M.; Urbaniak, W.; Augé, W.K.; Santamaría-Holek, I.; Pawlak, Z. Some conceptual thoughts toward nanoscale oriented friction in a model of articular cartilage. Math. Biosci.
**2013**, 244, 188–200. [Google Scholar] [CrossRef] - Dėdinaitė, A.; Claesson, P.M. Synergies in lubrication. Phys. Chem. Chem. Phys.
**2017**, 19, 23677–23689. [Google Scholar] [CrossRef] [Green Version] - Raj, A.; Wang, M.; Zander, T.; Wieland, D.F.; Liu, X.; An, J.; Garamus, V.M.; Willumeit-Römer, R.; Fielden, M.; Claesson, P.M.; et al. Lubrication synergy: Mixture of hyaluronan and dipalmitoylphosphatidylcholine (DPPC) vesicles. J. Colloid Interface Sci.
**2017**, 488, 225–233. [Google Scholar] [CrossRef] [Green Version] - Klein, J. Molecular mechanisms of synovial joint lubrication. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
**2006**, 220, 691–710. [Google Scholar] [CrossRef] - Liu, C.; Wang, M.; An, J.; Thormann, E.; Dėdinaitė, A. Hyaluronan and phospholipids in boundary lubrication. Soft Matter
**2012**, 8, 10241–10244. [Google Scholar] [CrossRef] - Siódmiak, J.; Bełdowski, 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
**2017**, 22, 1436. [Google Scholar] [CrossRef] [PubMed] - Ghosh, S.; Choudhury, D.; Das, N.S.; Pingguan-Murphy, B. Tribological role of synovial fluid compositions on artificial joints—A systematic review of the last 10 years. Lubr. Sci.
**2014**, 26, 387–410. [Google Scholar] [CrossRef] - Boldt, J. Use of albumin: An update. BJA Br. J. Anaesth.
**2010**, 104, 276–284. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Moman, R.N.; Gupta, N.; Varacallo, M. Physiology Albumin; StatPearls Publishing: Treasure Island, FL, USA, 2021. [Google Scholar]
- Ghosh, S.; Choudhury, D.; Pingguan-Murphy, B. Lubricating ability of albumin and globulin on artificial joint implants: A tribological perspective. Int. J. Surf. Sci. Eng.
**2016**, 10, 193–206. [Google Scholar] [CrossRef] - Nečas, D.; Sadecká, K.; Vrbka, M.; Galandáková, A.; Wimmer, M.; Gallo, J.; Hartl, M. The effect of albumin and γ-globulin on synovial fluid lubrication: Implication for knee joint replacements. J. Mech. Behav. Biomed. Mater.
**2021**, 113, 104117. [Google Scholar] [CrossRef] - Kubiak-Ossowska, K.; Jachimska, B.; Mulheran, P.A. How Negatively Charged Proteins Adsorb to Negatively Charged Surfaces: A Molecular Dynamics Study of BSA Adsorption on Silica. J. Phys. Chem. B
**2016**, 120, 10463–10468. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Bełdowski, P.; Przybyłek, M.; Raczyński, P.; Dedinaite, A.; Górny, K.; Wieland, F.; Dendzik, Z.; Sionkowska, A.; Claesson, P.M. Albumin–Hyaluronan Interactions: Influence of Ionic Composition Probed by Molecular Dynamics. Int. J. Mol. Sci.
**2021**, 22, 12360. [Google Scholar] [CrossRef] [PubMed] - Guizado, T.R.C. Analysis of the structure and dynamics of human serum albumin. J. Mol. Model.
**2014**, 20, 2450. [Google Scholar] [CrossRef] [PubMed] - Shi, D.; Sheng, A.; Chi, L. Glycosaminoglycan-Protein Interactions and Their Roles in Human Disease. Front. Mol. Biosci.
**2021**, 8, 639666. [Google Scholar] [CrossRef] - Qiu, H.; Jin, L.; Chen, J.; Shi, M.; Shi, F.; Wang, M.; Li, D.; Xu, X.S.; Su, X.; Yin, X.; et al. Comprehensive Glycomic Analysis Reveals That Human Serum Albumin Glycation Specifically Affects the Pharmacokinetics and Efficacy of Different Anticoagulant Drugs in Diabetes. Diabetes
**2020**, 69, 760–770. [Google Scholar] [CrossRef] - Krieger, E.; Vriend, G. YASARA View—Molecular graphics for all devices–From smartphones to workstations. Bioinformatics
**2014**, 30, 2981–2982. [Google Scholar] [CrossRef] [Green Version] - Gandhi, N.S.; Mancera, R.L. The Structure of Glycosaminoglycans and their Interactions with Proteins. Chem. Biol. Drug Des.
**2008**, 72, 455–482. [Google Scholar] [CrossRef] - Bełdowski, P.; Yuvan, S.; Dėdinaitė, A.; Claesson, P.M.; Pöschel, T. Interactions of a short hyaluronan chain with a phospholipid membrane. Colloids Surf. B Biointerfaces
**2019**, 184, 110539. [Google Scholar] [CrossRef] - Ben-Naim, A. Molecular Theory of Water and Aqueous Solutions; World Scientific Publishing Company: Singapore, 2011. [Google Scholar]
- Baruah, A.; Rani, P.; Biswas, P. Conformational entropy of intrinsically disordered proteins from amino acid triads. Sci. Rep.
**2015**, 5, 11740. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kruszewska, N.; Bełdowski, P.; Domino, K.; Lambert, K.D. Investigating conformation changes and network formation of mucin in joints functioning in human locomotion. In Multiscale (Loco)motion—Toward Its Active-Matter Addressing Physical Principles; Gadomski, A., Ed.; UTP Publishing Department: Bydgoszcz, Poland, 2019; pp. 121–138. [Google Scholar]
- Sapienza, P.J.; Lee, A.L. Using NMR to study fast dynamics in proteins: Methods and applications. Curr. Opin. Pharmacol.
**2010**, 10, 723–730. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Thompson, J.B.; Hansma, H.G.; Hansma, P.K.; Plaxco, K.W. The backbone conformational entropy of protein folding: Experimental measures from Atomic Force Microscopy. J. Mol. Biol.
**2002**, 322, 645–652. [Google Scholar] [CrossRef] - Fitter, J. A Measure of Conformational Entropy Change during Thermal Protein Unfolding Using Neutron Spectroscopy. Biophys. J.
**2003**, 84, 3924–3930. [Google Scholar] [CrossRef] [Green Version] - Meirovitch, H.; Cheluvaraja, S.; White, R. Methods for calculating the entropy and free energy and their application to problems involving protein flexibility and ligand binding. Curr. Protein Pept. Sci.
**2009**, 10, 229–243. [Google Scholar] [CrossRef] [Green Version] - Bhattacharjee, N.; Biswas, P. Are ambivalent α-helices entropically driven? Protein Eng. Des. Sel. PEDS
**2012**, 25, 73–79. [Google Scholar] [CrossRef] - Baxa, M.C.; Haddadian, E.J.; Jumper, J.M.; Freed, K.F.; Sosnick, T.R. Loss of conformational entropy in protein folding calculated using realistic ensembles and its implications for NMR-based calculations. Proc. Natl. Acad. Sci. USA
**2014**, 111, 15396–15401. [Google Scholar] [CrossRef] [Green Version] - Haxaire, K.; Braccini, I.; Milas, M.; Rinaudo, M.; Pérez, S. Conformational behavior of hyaluronan in relation to its physical properties as probed by molecular modeling. Glycobiology
**2000**, 10, 587–594. [Google Scholar] [CrossRef] [Green Version] - Trott, O.; Olson, A.J. AutoDock Vina: Improving the speed and accuracy of docking with a new scoring function, efficient optimization, and multithreading. J. Comput. Chem.
**2010**, 31, 455–461. [Google Scholar] [CrossRef] [Green Version] - Duan, Y.; Wu, C.; Chowdhury, S.; Lee, M.C.; Xiong, G.; Zhang, W.; Yang, R.; Cieplak, P.; Luo, R.; Lee, T.; et al. A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations. J. Comput. Chem.
**2003**, 24, 1999–2012. [Google Scholar] [CrossRef] - Maier, J.A.; Martinez, C.; Kasavajhala, K.; Wickstrom, L.; Hauser, K.E.; Simmerling, C. ff14SB: Improving the Accuracy of Protein Side Chain and Backbone Parameters from ff99SB. J. Chem. Theory Comput.
**2015**, 11, 3696–3713. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kirschner, K.N.; Yongye, A.B.; Tschampel, S.M.; González-Outeiriño, J.; Daniels, C.R.; Foley, B.L.; Woods, R.J. GLYCAM06: A generalizable biomolecular force field. Carbohydrates. J. Comput. Chem.
**2008**, 29, 622–655. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Krieger, E.; Dunbrack, R.L.; Hooft, R.W.; Krieger, B. Assignment of protonation states in proteins and ligands: Combining PKA prediction with hydrogen bonding network optimization. Methods Mol. Biol.
**2012**, 819, 405–421. [Google Scholar] [CrossRef] [PubMed] - Krieger, E.; Vriend, G. New ways to boost molecular dynamics simulations. J. Comput. Chem.
**2015**, 36, 996–1007. [Google Scholar] [CrossRef] - Hornak, V.; Abel, R.; Okur, A.; Strockbine, B.; Roitberg, A.E.; Simmerling, C. Comparison of multiple Amber force fields and development of improved protein backbone parameters. Proteins Struct.
**2006**, 65, 712–725. [Google Scholar] [CrossRef] [Green Version] - Essmann, U.; Perera, L.E.; Berkowitz, M.L.; Darden, T.A.; Lee, H.C.; Pedersen, L.G. A smooth particle mesh Ewald method. J. Chem. Phys.
**1995**, 103, 8577–8593. [Google Scholar] [CrossRef] [Green Version] - Berendsen, H.J.C.; Postma, J.P.M.; van Gunsteren, W.F.; Dinola, A.; Haak, J.R. Molecular dynamics with coupling to an external bath. J. Chem. Phys.
**1984**, 81, 3684–3690. [Google Scholar] [CrossRef] [Green Version] - Sionkowski, P.; Domino, K.; Kruszewska, N. Polymer_Entropy. 2022. Available online: https://github.com/iitis/polymer_entropy (accessed on 9 June 2022).
- Ramachandran, G.; Ramakrishnan, C.; Sasisekharan, V. Stereochemistry of polypeptide chain configurations. J. Mol. Biol.
**1963**, 7, 95–99. [Google Scholar] [CrossRef] - Shannon, C.E. A mathematical theory of communication. ACM SIGMOBILE Mob. Comput. Commun. Rev.
**2001**, 5, 3–55. [Google Scholar] [CrossRef] - Weber, P.; Bełdowski, P.; Domino, K.; Ledziński, D.; Gadomski, A. Changes of Conformation in Albumin with Temperature by Molecular Dynamics Simulations. Entropy
**2020**, 22, 405. [Google Scholar] [CrossRef] [Green Version] - Fasano, M.; Curry, S.; Terreno, E.; Galliano, M.; Fanali, G.; Narciso, P.; Notari, S.; Ascenzi, P. The extraordinary ligand binding properties of human serum albumin. IUBMB Life
**2005**, 57, 787–796. [Google Scholar] [CrossRef] [PubMed] - Nagarajan, B.; Sankaranarayanan, N.V.; Desai, U.R. In-depth molecular dynamics study of all possible chondroitin sulfate disaccharides reveals key insight into structural heterogeneity and dynamism. Biomolecules
**2022**, 12, 77. [Google Scholar] [CrossRef] [PubMed] - Burges, C.J. A tutorial on support vector machines for pattern recognition. Data Min. Knowl. Discov.
**1998**, 2, 121–167. [Google Scholar] [CrossRef] - Khemchandani, R.; Saigal, P. Color image classification and retrieval through ternary decision structure based multi-category TWSVM. Neurocomputing
**2015**, 165, 444–455. [Google Scholar] [CrossRef] - Grady, L. Random walks for image segmentation. IEEE Trans. Pattern Anal. Mach. Intell.
**2006**, 28, 1768–1783. [Google Scholar] [CrossRef] [Green Version] - Dong, X.; Shen, J.; Shao, L.; Van Gool, L. Sub-Markov random walk for image segmentation. IEEE Trans. Image Process.
**2015**, 25, 516–527. [Google Scholar] [CrossRef] [Green Version] - Blachowicz, T.; Ehrmann, A.; Domino, K. Statistical analysis of digital images of periodic fibrous structures using generalized Hurst exponent distributions. Phys. A Stat. Mech. Appl.
**2016**, 452, 167–177. [Google Scholar] [CrossRef] - Blachowicz, T.; Domino, K.; Koruszowic, M.; Grzybowski, J.; Böhm, T.; Ehrmann, A. Statistical analysis of nanofiber mat AFM images by Gray-scale-resolved Hurst exponent distributions. Appl. Sci.
**2021**, 11, 2436. [Google Scholar] [CrossRef] - Domino, K. Multivariate cumulants in outlier detection for financial data analysis. Phys. A Stat. Mech. Appl.
**2020**, 558, 124995. [Google Scholar] [CrossRef] - Snetkov, P.; Zakharova, K.; Morozkina, S.; Olekhnovich, R.; Uspenskaya, M. Hyaluronic Acid: The Influence of Molecular Weight on Structural, Physical, Physico-Chemical, and Degradable Properties of Biopolymer. Polymers
**2020**, 12, 1800. [Google Scholar] [CrossRef]

**Figure 1.**Structure of (

**a**) HSA-HA, (

**b**) HSA-CS6 complexes for highest affinity result in CaCl${}_{2}$ solution (solution is transparent on the picture). HSA is depicted as ribbon (bottom parts of picture), and its domains are colored as follows: IA-pink, IB-violet, IIA-light green, IIB-green, IIIA-light blue, and IIIB-blue. HA and CS6 are depicted as ball-stick (top parts of picture). Light blue atoms represent carbon, dark blue nitrogen, red oxygen, green sulfur and white hydrogen. Snapshots was taken using YASARA software after 100 ns MD simulations [19].

**Figure 2.**Structures of (

**a**) HA and (

**b**) CS6 with dihedral angles: ${\mathrm{\Phi}}_{1-4}$—red circles, ${\mathrm{\Psi}}_{1-4}$—blue circles (N-G linkage), ${\mathrm{\Phi}}_{1-3}$—green circles, ${\mathrm{\Psi}}_{1-3}$—violet circles (G-N linkage).

**Figure 3.**Normalized histograms of values of angles (${\mathrm{\Phi}}_{1-4}$, ${\mathrm{\Psi}}_{1-4}$) (top) and (${\mathrm{\Phi}}_{1-3}$,${\mathrm{\Psi}}_{1-3}$) (bottom) for main chain CS6 with (

**a**) Na${}^{+}$, (

**b**) Ca${}^{2+}$, and (

**c**) Mg${}^{2+}$. Angles were taken from the whole time series of the YASARA simulation. The symbol n is a number of angles’ pairs and is equal to number of angles type (24 for angles $1,4$ and 23 for angles $1,3$, cf. Section 2.1) multiplied by number of time points ($1,000$).

**Figure 4.**Normalized histograms of values of angles (${\mathrm{\Phi}}_{1-4}$, ${\mathrm{\Psi}}_{1-4}$) (top) and (${\mathrm{\Phi}}_{1-3}$,${\mathrm{\Psi}}_{1-3}$) (bottom) for main chain HA with (

**a**) Na${}^{+}$, (

**b**) Ca${}^{2+}$, and (

**c**) Mg${}^{2+}$. Angles were taken from the whole time series of the YASARA simulation. The symbol n is a number of angles’ pairs and is equal to number of angles type (24 for angles $1,4$ and 23 for angles $1,3$, cf. Section 2.1) multiplied by number of time points ($1,000$).

**Figure 5.**Median, maximal and minimal entropy (over $N=10$ realizations) for chosen ions and angles pairs for CS6

**(left panel)**and HA (

**right panel**). As we have $N=10$ realizations, the minimal entropy can by considered as the estimate of the 10’th percentile (first quantile), and the maximal one as the estimate of the 90’th percentile (9’th quantile).

**Figure 6.**Conformational entropy for CS6 with (

**a**) Na${}^{+}$, (

**b**) Ca${}^{2+}$, and (

**c**) Mg${}^{2+}$, and HA with (

**d**) Na${}^{+}$, (

**e**) Ca${}^{2+}$ and (

**f**) Mg${}^{2+}$.

**Table 1.**Binding ranks of HSA-CS6 complexes. The first column contains: rank after docking (averaged rank after MD simulations). The strongest connected domains are marked in bold letters.

HSA-CS6 Complex Rank | HSA Binding Sites |
---|---|

1(5) | IA-IIA-IIIA-IIIB |

2(1) | IA-IB-IIA-IIIA-IIIB |

3(8) | IA-IIA |

4(6) | IA-IIA-IIIA-IIIB |

5(7) | IA-IIA-IIIA-IIIB |

6(2) | IB-IIIA-IIIB |

7(3) | IA-IIA-IIB-IIIA |

8(10) | IA-IB |

9(4) | IB-IIIA-IIIB |

10(9) | IIA-IIB |

**Table 2.**Binding ranks of HSA-HA complexes. The first column contains: rank after docking (averaged rank after MD simulations). The strongest connections are marked in bold letters.

HSA-HA Complex Rank | HSA Binding Sites |
---|---|

1(4) | IA-IB-IIIA-IIIB |

2(1) | IA-IB-IIIA-IIIB |

3(6) | IA-IB-IIIA-IIIB |

4(10) | IIIA-IIIB |

5(5) | IIB-IIIA-IIIB |

6(8) | IA-IIIA-IIIB |

7(2) | IA-IB-IIIA-IIIB |

8(9) | IIIA-IIIB |

9(7) | IA-IB-IIIA-IIIB |

10(3) | IIA-IIB-IIIA |

**Table 3.**Most frequent (${\mathrm{\Phi}}_{1-4}$, ${\mathrm{\Psi}}_{1-4}$) and (${\mathrm{\Phi}}_{1-3}$, ${\mathrm{\Psi}}_{1-3}$) angles for the best bound complexes of HSA-GAG.

CS6 | ||||||
---|---|---|---|---|---|---|

n.o. Realization | Na${}^{+}$ | Ca${}^{2+}$ | Mg${}^{2+}$ | |||

2 | ${\mathrm{\Phi}}_{1-4}$ | ${\mathrm{\Psi}}_{1-4}$ | ${\mathrm{\Phi}}_{1-4}$ | ${\mathrm{\Psi}}_{1-4}$ | ${\mathrm{\Phi}}_{1-4}$ | ${\mathrm{\Psi}}_{1-4}$ |

−72${}^{\circ}$ | −76${}^{\circ}$ | −104${}^{\circ}$ | −76${}^{\circ}$ | −68${}^{\circ}$ | −76${}^{\circ}$ | |

${\mathrm{\Phi}}_{1-3}$ | ${\mathrm{\Psi}}_{1-3}$ | ${\mathrm{\Phi}}_{1-3}$ | ${\mathrm{\Psi}}_{1-3}$ | ${\mathrm{\Phi}}_{1-3}$ | ${\mathrm{\Psi}}_{1-3}$ | |

−76${}^{\circ}$ | 169${}^{\circ}$ | −86${}^{\circ}$ | −76${}^{\circ}$ | −79${}^{\circ}$ | 173${}^{\circ}$ | |

HA | ||||||

n.o. Realization | Na${}^{+}$ | Ca${}^{2+}$ | Mg${}^{2+}$ | |||

2 | ${\mathrm{\Phi}}_{1-4}$ | ${\mathrm{\Psi}}_{1-4}$ | ${\mathrm{\Phi}}_{1-4}$ | ${\mathrm{\Psi}}_{1-4}$ | ${\mathrm{\Phi}}_{1-4}$ | ${\mathrm{\Psi}}_{1-4}$ |

−72${}^{\circ}$ | −126${}^{\circ}$ | −68${}^{\circ}$ | −126${}^{\circ}$ | −97${}^{\circ}$ | −155${}^{\circ}$ | |

${\mathrm{\Phi}}_{1-3}$ | ${\mathrm{\Psi}}_{1-3}$ | ${\mathrm{\Phi}}_{1-3}$ | ${\mathrm{\Psi}}_{1-3}$ | ${\mathrm{\Phi}}_{1-3}$ | ${\mathrm{\Psi}}_{1-3}$ | |

−115${}^{\circ}$ | −61${}^{\circ}$ | −47${}^{\circ}$ | −47${}^{\circ}$ | −54${}^{\circ}$ | 151${}^{\circ}$ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sionkowski, P.; Bełdowski, P.; Kruszewska, N.; Weber, P.; Marciniak, B.; Domino, K.
Effect of Ion and Binding Site on the Conformation of Chosen Glycosaminoglycans at the Albumin Surface. *Entropy* **2022**, *24*, 811.
https://doi.org/10.3390/e24060811

**AMA Style**

Sionkowski P, Bełdowski P, Kruszewska N, Weber P, Marciniak B, Domino K.
Effect of Ion and Binding Site on the Conformation of Chosen Glycosaminoglycans at the Albumin Surface. *Entropy*. 2022; 24(6):811.
https://doi.org/10.3390/e24060811

**Chicago/Turabian Style**

Sionkowski, Piotr, Piotr Bełdowski, Natalia Kruszewska, Piotr Weber, Beata Marciniak, and Krzysztof Domino.
2022. "Effect of Ion and Binding Site on the Conformation of Chosen Glycosaminoglycans at the Albumin Surface" *Entropy* 24, no. 6: 811.
https://doi.org/10.3390/e24060811