Simulation of the response of a magnetic polymersome in an inhomogeneous magnetic field

Purpose. Identification of the behavior of a magnetic polymersome placed in an inhomogeneous field of a point dipole using coarse-grained molecular dynamics simulations.

Methods. The system under the study is represented as a set of interacting particles of two types: polymeric particles simulating a double layer of an amphiphilic membrane, and magnetic nanoparticles located in the membrane layer. Polymeric particles interact through elastic potentials designed to maintain an equilibrium spherical vesicular geometry. Magnetic nanoparticles interact with each other and external fields as point dipoles. The excluded volume and steric interaction of magnetic particles with polymeric walls are modeled in the form of soft repulsion. The entire system is under isothermal conditions, and the model parameters are chosen according to typical interaction energies relative to thermal fluctuations. A model polymersome with a diameter of about 100 nm in an aqueous solution at 25°C is considered. An inhomogeneous magnetic field is created by a dipole of constant direction located at a fixed distance. The dynamics of the system is monitored by numerical solution of the equations of particles motion with introduced interactions and imposed conditions.

Results. In numerical experiments, the response of the polymersome to a magnetic field was obtained for three values of the parameter describing the inhomogeneity of the field. The problem with a gradual increase in the strength (and its gradient) of the magnetic field near the polymersome is considered. Changes in the magnetization of the system are shown, and the redistribution of the concentration of nanoparticles is analyzed. A simulation of the situation when the center of the polymersome at the initial moment was placed at a point with a fixed value of the magnetic field for three cases of inhomogeneity of the field was carried out. A significant restructuring of the magnetic layer of the vesicle combined with movement of the entire capsule was detected. Estimates are made about the average velocity based on the displacement of the object.

Conclusion. The model allows to evaluate the features of the combined magnetic, structural and mechanical response of the polymersome to an inhomogeneous field in the context of potential applications for controlled delivery of contents into cells.

1. Discher B.M., Won Y.Y., Ege D.S., Lee J.C., Bates F. S., Discher D.E., et al. Polymersomes: tough vesicles made from diblock copolymers. Science. 1999;284(5417):1143–1146. https://doi.org/10.1126/science.284.5417.1143

2. Meng F.H., Zhong Z.Y., Feijen J. Stimuli-responsive polymersomes for programmed drug delivery. Biomacromolecules. 2009;10(2):197–209. https://doi.org/10.1021/bm801127d

3. Zhu Y., Yang B., Chen S., Du J. Polymer vesicles: Mechanism, preparation, application, and responsive behavior. Prog. Polym. Sci. 2017;64:1–22. https://doi.org/10.1016/j.progpolymsci.2015.05.001

4. Lecommandoux S., Sandre O., Checot F., Hernandez J. R., Perzynski R. Magnetic nanocomposite micelles and vesicles. Adv. Mater. 2005;17(6):712–718. https://doi.org/10.1002/adma.200400599

5. Sanson C., Diou O., Thévenot J., Ibarboure E., Soum A., Brûlet A. Doxorubicin loaded magnetic polymersomes: theranostic nanocarriers for mr imaging and magneto-chemotherapy. ACS Nano. 2011;5(2):1122–1140. https://doi.org/10.1021/nn102762f

6. Hickey R.J., Haynes A.S., Kikkawa J.M., Park S.-J. Controlling the self-assembly structure of magnetic nanoparticles and amphiphilic block-copolymers: from micelles to vesicles. J. Am. Chem. Soc. 2011;133(5):1517–1525. https://doi.org/10.1021/ja1090113

7. Hickey R.J., Koski J., Meng X., Riggleman R.A., Zhang P., Park S.-J. Size-controlled selfassembly of superparamagnetic polymersomes. ACS Nano. 2014;8(1):495–502. https://doi.org/10.1021/nn405012h

8. Oliveira H., Pérez-Andrés E., Thevenot J., Sandre O., Berra E., Lecommandoux S. Magnetic field triggered drug release from polymersomes for cancer therapeutics. J. Control. Release. 2013;169(3):165–170. https://doi.org/10.1016/j.jconrel.2013.01.013

9. Bleul R., Thiermann R., Marten G.U., House M.J., St. Pierre T.G., Häfeli U.O, et al. Continuously manufactured magnetic polymersomes – a versatile tool (not only) for targeted cancer therapy. Nanoscale. 2013;5(23):11385. https://doi.org/10.1039/C3NR02190D

10. Hannecart A., Stanicki D., Vander Elst L., Muller R. N., Brûlet A., Sandre O., et al. Embedding of superparamagnetic Iron oxide nanoparticles into membranes of well-defined poly(ethylene oxide)- block -poly(ε-caprolactone) nanoscale magnetovesicles as ultrasensitive MRI probes of membrane bio-degradation. J. Mater. Chem. B. 2019;7(30):4692–4705. https://doi.org/10.1039/C9TB00909D

11. Geilich B.M., Gelfat I., Sridhar S., van de Ven A.,Webster T. J. Superparamagnetic iron oxideencapsulating polymersome nanocarriers for biofilm eradication. Biomaterials. 2017;119:78–85. https://doi.org/10.1016/j.biomaterials.2016.12.011

12. Yang K., Liu Y., Liu Y., Zhang Q., Kong C., Yi C., et al. Cooperative assembly of magnetonanovesicles with tunable wall thickness and permeability for mri-guided drug delivery. J. Am. Chem. Soc. 2018;140(13):4666–4677. https://doi.org/10.1021/jacs.8b00884

13. Nuñez-Magos L., Lira-Escobedo J., Rodríguez-López R., Muñoz-Navia M., Castillo- Rivera F., Viveros-Méndez P.X., et al. Effects of DC magnetic fields on magnetoliposomes. Front. Mol. Biosci. 2021;8:1–11. https://doi.org/10.3389/fmolb.2021.703417

14. Novikau I.S., Sánchez P.A., Kantorovich S.S. The influence of an applied magnetic field on the self-assembly of magnetic nanogels. Journal of Molecular Liquids. 2020;307:112902. https://doi.org/10.1016/j.molliq.2020.112902

15. Melenev P.V., Ryzhkov A.V., Balasoiu M. Simulation of magneto-mechanical response of ferrogel samples with various polymer structure. Soft Materials. 2022;20(1):S50–S58. https://doi.org/10.1080/1539445X.2021.1998119

16. Khardina A.S., Melenev P.V. The model of the small ferrogel sample with representation of polymer matrix as lennard-jones fluid with elastic cross-links. Izvestiya Yugo-Zapadnogo gosudarstvennogo universiteta. Seriya: Tekhnika i tekhnologii = Proceedings of the Southwest State University. Series: Engineering and Technology. 2022;12(4):124-139. (In Russ.) https://doi.org/10.21869/2223-15282022-12-4-124-139

17. Ryzhkov A.V., Raikher Y.L. Simulation of shape and structure response of nonspherical magnetosensitive vesicles subjected to magnetic fields. IEEE Magnetics Letters. 2022;13:1–5. https://doi.org/10.1109/LMAG.2021.3130850

18. Lorenz C., Doltsinis N.L. Molecular dynamics simulation: from “Ab Initio” to “Coarse Grained”. In: Leszczynski J. (ed.) Handbook of Computational Chemistry. Springer Netherlands; 2012. Р. 195–238. https://doi.org/10.1007/978-94-007-0711-5_7

19. Berendsen H.J.C., Postma J.P.M., van Gunsteren W.F., Di Nola A., Haak J.R. Molecular dynamics with coupling to an external bath. The Journal of Chemical Physics. 1984;81(8):3684–3690. https://doi.org/10.1063/1.448118

20. Weeks J.D., Chandler D., Andersen H.C. Role of repulsive forces in determining the equilibrium structure of simple liquids. The Journal of Chemical Physics. 1971;54(12):5237–5247. https://doi.org/10.1063/1.1674820

21. Rapaport D.C. The Art of Molecular Dynamics Simulation. 2nd Edition. Cambridge University Press; 2004. 548 р. https://doi.org/10.1017/CBO9780511816581

22. Weik F., Weeber R., Szuttor K., Breitsprecher K., de Graaf J., Kuronet M., et al. ESPResSo 4.0 – an extensible software package for simulating soft matter systems. The European Physical Journal Special Topics. 2019;227(14):1789–1816. https://doi.org/10.1140/epjst/e2019-800186-9

23. Krack M., Hohenberg H., Kornowski A., Lindner P., Weller H., Förster S. Nanoparticleloaded magnetophoretic vesicles. Journal of the American Chemical Society. 2008;130(23):7315–7320. https://doi.org/10.1021/ja077398k

24. Sokolov E.A., Kalyuzhnaya D.A., Reks A.G., Kalenchuk V.I., Zhukov G.A., Politov R.E., et al. Dynamics of active bubbles in a magnetic fluid in an inhomogeneous magnetic field. Izvestiya Yugo-Zapadnogo gosudarstvennogo universiteta. Seriya: Tekhnika i tekhnologii = Procee-dings of the Southwest State University. Series: Engineering and Technology. 2023;13(1):102–119. (In Russ.) https://doi.org/10.21869/2223-1528-2023-13-1-102-119