Frédéric Paquin-Lefebvre

NSERC Postdoctoral Fellow at École normale supérieure ‐ Université PSL, member of the Group of Applied Mathematics and Computational Biology of David Holcman.

Google Scholar CV

Contact: paquin (at) bio (dot) ens (dot) psl (dot) eu

Research area

Development and analysis of mathematical models in biology:

  1. Pattern formation in reaction-diffusion systems
  2. Analysis of spatio-temporal patterns in coupled bulk-membrane models
  3. PDE models of subcellular electrical activity
  4. Poisson-Nernst-Planck equations and electro-diffusion theory
  5. Narrow escape theory and first-passage times modeling
  6. Mixed Neumann-Dirichlet boundary value problems
  7. Application of extreme statistics in biology
  8. Age-structured modeling of blood cell populations

Publications

Book chapters

  1. Paquin-Lefebvre F, Holcman D. Modeling Ionic Flow Between Small Targets: Insights from Diffusion and Electro-Diffusion Theory. In: Grebenkov, D., Metzler, R. and Oshanin, G. (eds.), Target Search Problems, Springer Cham, pp 433-461 (2024). DOI arXiv

    2. Contributed chapter to the book Target Search Problems

  2. Dora M, Paquin-Lefebvre F, Holcman D. Analyzing Photoactivation with Diffusion Models to Study Transport in the Endoplasmic Reticulum Network. In: Kriechbaumer, V. (eds) The Plant Endoplasmic Reticulum. Methods in Molecular Biology. 2772, Springer US, pp 407-432 (2024). DOI bioRxiv

    3. Contributed chapter to the book The Plant Endoplasmic Reticulum: Methods and Protocols, part of the Springer series on Methods in Molecular Biology

Journal articles

  1. Paquin-Lefebvre F, Barea Moreno A, Holcman D. Voltage Laws in Nanodomains Revealed by Asymptotics and Numerical Simulations of Electro-Diffusion Equations, Multiscale Modeling and Simulations, in press, 2025. arXiv
  2. Paquin-Lefebvre F, Holcman D. Voltage Mapping in Subcellular Nanodomains Using Electro-Diffusion Modeling. J. Chem. Phys. 161(3), 034108 (2024). DOI arXiv
  3. Paquin-Lefebvre F, Basnayake K, Holcman D. Narrow Escape in Composite Domains Forming Heterogeneous Networks. Physica D: Nonlinear Phenomena. 454, 133837 (2023). DOI arXiv

    4. COMSOL codes available on Zenodo

  4. Paquin-Lefebvre F, Toste S, Holcman D. How Large the Number of Redundant Copies Should Be to Make a Rare Event Probable. Phys. Rev. E. 106, 064402 (2022). DOI arXiv
  5. Paquin-Lefebvre F, Holcman D. Modeling and Asymptotic Analysis of the Concentration Difference in a Nanoregion Between an Influx and Outflux Diffusion Across Narrow Windows. Proc. R. Soc. A. 477, 20210501 (2021). DOI arXiv

    6. Sample COMSOL and MATLAB codes available on BioNewMetrics

    Online presentation at the UBC Mathematical Biology Seminar, February 9th 2022

  6. Paquin-Lefebvre F, Iyaniwura S, Ward MJ. Asymptotics of the Principal Eigenvalue of the Laplacian in 2-D Periodic Domains with Small Traps. Europ. J. Appl. Math. 1-28 (2021). DOI Preprint
  7. Gomez D, Iyaniwura S, Paquin-Lefebvre F, Ward MJ. Pattern Forming Systems Coupling Linear Bulk Diffusion to Dynamically Active Membranes or Cells. Phil. Trans. R. Soc. A. 379, 20200276 (2021). DOI Preprint

    8. Special theme issue of the Philosophical Transactions of the Royal Society A on Turing's theory of morphogenesis.

  8. Kolokolnikov T, Paquin-Lefebvre F, Ward MJ. Competition Instabilities of Pulse Patterns for the 1-D Gierer-Meinhardt and Schnakenberg Models are Subcritical. Nonlinearity. 34(1), 273-312 (2021). DOI Preprint
  9. Kolokolnikov T, Paquin-Lefebvre F, Ward MJ. Stable Asymmetric Spike Equilibria for the Gierer-Meinhardt Model with a Precursor Field. IMA J. Appl. Math. 85(4), 605-634 (2020). DOI arXiv
  10. Paquin-Lefebvre F, Nagata W, Ward MJ. Weakly Nonlinear Theory for Oscillatory Dynamics in a 1-D PDE-ODE Model of Membrane Dynamics Coupled by a Bulk Diffusion Field. SIAM J. Appl. Math. 80(3), 1520-1545 (2020). DOI arXiv
  11. Paquin-Lefebvre F, Xu B, DiPietro KL, Lindsay AE, Jilkine A. Pattern Formation in a Coupled Membrane-Bulk Reaction-Diffusion Model for Intracellular Polarization and Oscillations. J. Theor. Biol. 497, 110242 (2020). DOI arXiv
  12. Paquin-Lefebvre F, Bélair J. On the Effect of Age-Dependent Mortality on the Stability of a System of Delay-Differential Equations Modeling Erythropoiesis. Acta Biotheor. 68, 5-19 (2020). DOI PDF
  13. Paquin-Lefebvre F, Nagata W, Ward MJ. Pattern Formation and Oscillatory Dynamics in a Two-Dimensional Coupled Bulk-Surface Reaction-Diffusion System. SIAM J. Appl. Dyn. Syst. 18(3), 1334-1390 (2019). DOI arXiv PDF

Master and PhD theses

  1. On the weakly nonlinear analysis of coupled bulk-surface reaction-diffusion systems: theory, numerics and applications. PhD Thesis, UBC, 2020.
  2. Sur un modèle d'érythropoïèse comportant un taux de mortalité dynamique. Mémoire de Maîtrise, UdeM, 2015.

Teaching at UBC

2020 WT1: Teaching assistant for MATH406 Variational and Approximate Methods in Applied Mathematics.

2019 WT2: Instructor for MATH101 Integral Calculus with Applications to Physical Sciences and Engineering.