Fusion-inducing liposomes for efficient intracellular delivery: Continuum models and experiments
DMS-1953535

Abstract

Bringing mathematical and computational scientists together with biomedical engineers, this project addresses an unmet and growing need for a simple, safe, and efficient system to deliver macromolecules to the cellular interior. Therapeutic macromolecules, e.g. peptides and proteins, have tremendous potential in medical fields but their clinical applications have remained limited as their delivery is much more challenging compared to small molecule therapeutics. A promising family of carriers, called fusognic liposomes, suffer from a key shotcoming: the high concentrations of fusogenic lipids needed to cross cellular membrane barriers lead to toxicity vivo. This limitation may be overcome by creating liposomes that contain relatively low concentrations of fusogenic lipids but can present them in dense patches on their surfaces. This may be achieved through membrane phase-separation, a mechanism that biological membranes often use to locally concentrate specific lipid species. This project will apply complementary mathematical, computational, and experimental tools to (i) design and develop a new class of liposomal carriers, called patchy fusogenic liposomes (PFLs), and (ii) investigate how the fusogenic patches affect the ability of PFLs to fuse with cellular membranes. Broader impacts include training opportunities for participating students. Undergraduate and graduate students will be trained to work at the interface of experimental bioengineering, applied mathematics, and scientific computing. Cross-disciplinary conversations will be fostered by close interactions and joint meetings.

The use of massive numerical experimentation to support and complement experimental practice in the design of liposomes requires highly efficient and computationally cheap numerical methods. Despite recent advances, molecular dynamics and coarse grain models still feature high computational costs. This project will focus on sophisticated novel continuum models and combine them with numerical algorithms and data analysis tools to produce a highly efficient computational platform. The multiphysics model under consideration accounts for lateral phase-separation, membrane fluidity, and electrostatic interaction and its predictive capability will be assessed against experimental data through a multi-stage validation process. High computational efficiency in implementing the model will be achieved through physics-based and directional splitting algorithms for a robust geometrically unfitted finite element method. Once validated, the software will be systematically deployed to investigate the role of critical PFL characteristics for membrane fusion. Ultimately, this project will deliver the design of PFLs that feature minimal amounts of fusogenic components while maximizing the chances of fusion with other membranes. The efficient computational methods for surface PDEs and coupled surface-bulk systems developed for this project could be used for a large variety of applications, from simulations of tumor growth to modeling of eukaryotic cell motility. In addition, the newly developed software will be open source.

Principal Investigators
Dr. S. Majd, University of Houston
Dr. M. Olshanskii, University of Houston
Dr. A. Quaini, University of Houston

Students Involved in the Project
Quang Hoang, Mathematics Undergraduate student (UH)
Yerbol Palzhanov, Mathematics Graduate student (UH)
Qi Sun, Mathematics Graduate student (UH)
Alexander Zhiliakov, Mathematics Graduate student (UH)
Yifei Wang, Biomedical Engineering Graduate student (UH)
Michele Girfoglio, Post-Doc (SISSA)
Martin Hess, Post-Doc (SISSA)

Publications

1. Y. Wang, Y. Palzhanov, D. T. Dang, A. Quaini, M. Olshanskii, S. Majd: On fusogenicity of positively charged phased-separated lipid vesicles: experiments and computational simulations. Submitted.
   arXiv:2308.08425
2. A. Hajisharifi, M. Girfoglio, A. Quaini, G. Rozza: A Comparison of data-driven Reduced Order Models for the simulation of mesoscale atmospheric flow. Submitted.
   arXiv:2307.08790
3. M. Olshanskii, Y. Palzhanov, A. Quaini: A scalar auxiliary variable unfitted FEM for the surface Cahn-Hilliard equation. Submitted.
   arXiv:2306.00318
4. N. Clinco, M. Girfoglio, A. Quaini, G. Rozza: Filter stabilization for the mildly compressible Euler equations with application to atmosphere dynamics simulations. Submitted.
   arXiv:2305.12978
5. M. Girfoglio, A. Quaini, G. Rozza: GEA: a new finite volume-based open source code for the numerical simulation of atmospheric and ocean flows. Submitted.
   arXiv:2303.10499
6. M. Girfoglio, A. Quaini, G. Rozza: Validation of an OpenFOAM-based solver for the Euler equations with benchmarks for mesoscale atmospheric modeling. AIP Advances, 13(5):055024, 2023.
   arXiv:2302.04836 | link
7. Y. Tissaoui, S. Marras, A. Quaini, F. A.V. De Braganca Alves, F.X. Giraldo: A non-column based, fully unstructured implementation of Kessler's microphysics with warm rain using continuous and discontinuous spectral elements. J. Adv. Model. Earth Syst., 15(3):e2022MS003283, 2023.
   arXiv:2207.02190 | link
8. M. Girfoglio, A. Quaini, G. Rozza: A Hybrid Reduced Order Model for nonlinear LES filtering, J. Comput. Phys., 486:112127, 2023.
   arXiv:2107.12933 | link
9. M. Girfoglio, A. Quaini, G. Rozza: A linear filter regularization for POD-based Reduced Order Models of the quasi-geostrophic equations. Comptes-Rendus Mecaniques, 351(S1):1-21, 2023.
   arXiv:2211.16851 | link
10. M. Hess, A. Quaini, G. Rozza: Data-Driven Enhanced Model Reduction for Bifurcating Models in Computational Fluid Dynamics. Submitted.
    arXiv:2202.09250
11. M. Hess, A. Quaini, G. Rozza: A data-driven surrogate modeling approach for time-dependent incompressible Navier-Stokes equations with Dynamic Mode Decomposition and manifold interpolation. Adv. Comput. Math., Adv. Comput. Math., 49, 22, 2023.
    arXiv:2201.10872 | link
12. M. Girfoglio, A. Quaini, G. Rozza: A novel Large Eddy Simulation model for the Quasi-Geostrophic Equations in a Finite Volume setting, J. Comput. Appl. Math., 418:114656, 2023.
    arXiv:2202.00295 | link
13. C. Balzotti, P. Siena, M. Girfoglio, A. Quaini, G. Rozza: A data-driven Reduced Order Method for parametric optimal blood flow control: application to coronary bypass graft. Commun. Optim. Theory, 2022:1-19, Article ID 26, 2022.
    arXiv:2206.15384
14. M. Olshanskii, Y. Palzhanov, A. Quaini: A comparison of Cahn-Hilliard and Navier-Stokes-Cahn-Hilliard models on manifolds. Vietnam Journal of Mathematics, 50:929–945, 2022.
    arXiv:2110.15873 | link
15. M. Girfoglio, A. Quaini, G. Rozza: A POD-Galerkin reduced order model for the Navier-Stokes equations in stream function-vorticity formulation, Computers & Fluids, 244:105536, 2022.
    arXiv:2201.00756 | link
16. Y. Wang, Y. Palzhanov, A. Quaini, M. Olshanskii, S. Majd: Lipid domain coarsening and fluidity in multicomponent lipid vesicles: A continuum based model and its experimental validation. BBA - Biomembranes, 1864(7):183898, 2022.
    arXiv:2111.03022 | link
17. Olshanskii, A. Quaini, Q. Sun: A finite element method for two-phase flow with material viscous interface, Comput. Methods Appl. Math. Published online.
    arXiv:2106.02922 | link
18. M. Girfoglio, A. Quaini, G. Rozza: Pressure stabilization strategies for a LES filtering Reduced Order Model, Fluids, 6(9): 302, 2021.
    arXiv:2106.15887 | link
19. M. Hess, A. Quaini, G. Rozza: A comparison of reduced-order modeling approaches for PDEs with bifurcating solutions, Electron. Trans. Numer. Anal. (ETNA), 56, 52-65, 2022.
    arXiv:2010.07370 | link
20. Y. Palzhanov, A. Zhiliakov, A. Quaini, and M. Olshanskii: A decoupled, stable, and linear FEM for a phase-field model of variable density two-phase incompressible surface flow, Comput. Methods Appl. Mech. Engrg., 387:114167, 2021.
    arXiv:2104.08996 | link
21. M. Girfoglio, A. Quaini, G. Rozza: Fluid-structure interaction simulations with a LES filtering approach in solids4Foam, Commun. Appl. Ind. Math.,12 (1): 13-28, 2021.
    arXiv:2102.08011 | link
22. Olshanskii, A. Quaini, Q. Sun: An unfitted finite element method for two-phase Stokes problems with slip between phases, J. Sci. Comput., 89(2), 41, 2021.
    arXiv:2101.09627 | link
23. M. Girfoglio, A. Quaini, G. Rozza: A POD-Galerkin reduced order model for a LES filtering approach, J. Comput. Phys., 436:110260, 2021.
    ariXiv:2009.13593 | link
24. A. Zhiliakov, Y. Wang, A. Quaini, M. Olshanskii, S. Majd: Experimental validation of a phase-field model to predict coarsening dynamics of lipid domains in multicomponent membranes, BBA - Biomembranes, 1863(1):183446, 2021.
    arXiv:2006.14125 | link
25. V. Yushutin, A. Quaini, M. Olshanskii: Numerical modelling of phase separation on dynamic surfaces, J. Comput. Phys., 407:109126, 2020.
    link | arXiv:1907.11314

Reports
Year 1 (Math) - Year 2 (Math) - Year 3 (Math)

Software

The software used for the simulations in the above papers is:

• GEA, freely available under the GPL 3 License.

• ITHACA-FV, freely available under the GPL 3 License.

• DROPS, distributed under the GNU Lesser General Public License.

• NGSolve, distributed under the GNU Lesser General Public License.

• ngsxfem, add-on to NGSolve for unfitted finite element discretizations.