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

Labder Besabe, Mathematics Graduate student (UH)
Nicola Clinco, Mathematics Graduate student (SISSA)
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. P. Siena, M. Girfoglio, A. Quaini, G. Rozza: Stabilized POD Reduced Order Models for convection-dominated incompressible flows. Submitted.
    arXiv:2404.19600
  2. N. Clinco, M. Girfoglio, A. Quaini, G. Rozza: Computational study of numerical flux schemes for mesoscale atmospheric flows in a Finite Volume framework. Submitted.
    arXiv2402.19559
  3. L. Besabe, M. Girfoglio, A. Quaini, G. Rozza: Linear and nonlinear filtering for a two-layer quasi-geostrophic ocean model. Submitted.
    arXiv:2404.11718
  4. M. Girfoglio, A. Quaini, G. Rozza: A comparative computational study of different formulations of the compressible Euler equations for mesoscale atmospheric flows in a finite volume framework. Submitted.
    arXiv:2402.18136
  5. Y. Wang, Y. Palzhanov, D.~T.~Dang, A. Quaini, M. Olshanskii, S. Majd: Fusogenicity of cationic liposomes with phase-separating multicomponent lipid compositions. Abstract in Biophysical Journal, 123(3):304a, 2024.
  6. 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, Biomolecules, 13(10):1473, 2023.
    arXiv:2308.08425 | link
  7. A. Hajisharifi, M. Girfoglio, A. Quaini, G. Rozza: A Comparison of data-driven Reduced Order Models for the simulation of mesoscale atmospheric flow, Finite Elements in Analysis & Design, 228:104050, 2024.
    arXiv:2307.08790 | link
  8. M. Olshanskii, Y. Palzhanov, A. Quaini: A scalar auxiliary variable unfitted FEM for the surface Cahn-Hilliard equation, J. Sci. Comput., 97:57, 2023.
    arXiv:2306.00318 | link
  9. N. Clinco, M. Girfoglio, A. Quaini, G. Rozza: Filter stabilization for the mildly compressible Euler equations with application to atmosphere dynamics simulations, Computers & Fluids, 266:106057, 2023.
    arXiv:2305.12978 | link
  10. M. Girfoglio, A. Quaini, G. Rozza: GEA: a new finite volume-based open source code for the numerical simulation of atmospheric and ocean flows, In: Finite Volumes for Complex Applications X -- Volume 2, Hyperbolic and Related Problems, 151-159, Springer, 2023.
    arXiv:2303.10499
  11. 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
  12. 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
  13. 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
  14. 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
  15. M. Hess, A. Quaini, G. Rozza: Data-Driven Enhanced Model Reduction for Bifurcating Models in Computational Fluid Dynamics. Submitted.
    arXiv:2202.09250
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. Y. Wang, A. Zhiliakov, A. Quaini, M. Olshanskii, S. Majd: Lipid domain formation and dynamics in multicomponent membranes: Experimental validation of a phase-field model, Abstract in Biophysical Journal, 120(3): 225a, 2021.
  29. 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
  30. M. Hess, A. Quaini, G. Rozza: A spectral element reduced basis method for Navier-Stokes equations with geometric variations, In: Sherwin S., Moxey D., Peiro' J., Vincent P., Schwab C. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018. Lecture Notes in Computational Science and Engineering, vol 134, Springer Cham, 2020.
    link | arXiv:1812.11051
  31. 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
  32. 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.