Frédéric Paquin-Lefebvre

I am a NSERC Postdoctoral Fellow at École Normale Supérieure de Paris, working in the Applied Math and Computational Biology Lab of David Holcman. I completed my PhD at The University of British Columbia under the supervision of Michael J. Ward and Wayne Nagata. I also did a master's degree in Mathematics at the Université de Montréal under the supervision of Jacques Bélair.

Je suis chercheur postdoctoral CRSNG à l'École Normale Supérieure de Paris, membre du Laboratoire de Mathématiques Appliquées et Biologie Computationnelle de David Holcman. J'ai soutenu une thèse à l'Université de la Colombie-Britannique sous la direction de Michael J. Ward et Wayne Nagata. J'ai aussi travaillé avec le Professeur Jacques Bélair durant mes études de maîtrise à l'Université de Montréal.

CV: EN FR

Contact: paquin at bio dot ens dot psl dot eu

Research / Recherche

The overarching theme of my research is the analysis of ordinary and partial differential equation models that arise in biology, using combined analytical and numerical approaches. During my PhD I studied the stability of spatio-temporal patterns in certain coupled bulk-surface reaction-diffusion systems, a novel class of models motivated by the compartmentalization of intracellular proteins between membrane-bound and cytosolic species.

Keywords: Dynamical Systems Theory, Asymptotic and Perturbation Methods, Reaction-Diffusion Theory, Electrodiffusion Theory, Mathematical Biology, Scientific Computation and Numerical Continuation Methods.

Dans mes travaux de recherche, je combine théorie des systèmes dynamiques, analyse asymptotique et méthodes numériques pour étudier des modèles d'équations aux dérivées ordinaires et partielles qui proviennent de la biologie. J'ai rédigé une thèse sur l'analyse des structures de Turing spatio-temporelles dans les équations de réaction-diffusion.

Mots-clés : Systèmes Dynamiques, Méthodes de Perturbation et Analyse Asymptotique, Équations de Réaction-Diffusion, Électrodiffusion, Biologie Mathématique, Calcul Scientifique et Méthodes de Continuation.

Publications

  1. Paquin-Lefebvre F, Holcman D. Modeling Ionic Flow Between Small Targets: Insights from Diffusion and Electro-Diffusion Theory. arXiv
  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, vol 2772. Humana, New York, NY, (2024). DOI biorXiv

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

  3. Paquin-Lefebvre F, Basnayake K, Holcman D. Narrow Escape in Composite Domains Forming Heterogeneous Networks. Physica D: Nonlinear Phenomena, Vol 454, 133837, (2023). DOI arXiv

    4. COMSOL codes available here: 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, (2021). DOI arXiv

    6. Sample COMSOL and MATLAB codes available here: BioNewMetrics blog post

    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, (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, 23 pages, (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

Theses / Thèses

  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.

Past teaching at UBC / Cours enseignés à 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.