Frédéric Paquin-Lefebvre
I am a NSERC Postdoctoral Fellow at École normale supérieure ‐ Université PSL, working in the Applied Math and Computational Biology Lab of David Holcman. I completed my PhD at The University of British Columbia (UBC) under the supervision of Michael J. Ward and Wayne Nagata and my MSc at Université de Montréal (UdeM), where I worked with Jacques Bélair.
Je suis chercheur boursier du CRSNG à l'École normale supérieure ‐ Université PSL, 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 Jacques Bélair durant mes études de maîtrise à l'Université de Montréal.
Google Scholar CV
Contact: paquin (at) bio (dot) ens (dot) psl (dot) eu
Research
My research focuses on the analysis of mathematical models arising in cellular biology using a variety of numerical (time-dependent simulations, path-following continuation methods, etc) and analytical (dynamical systems and bifurcation theory, asymptotic analysis, etc) tools. Most recently I studied the dynamics of ions in neuronal nano-compartments using electro-diffusion theory, where I show how the geometry of neuronal structures can modulate voltage dynamics. During my PhD I have studied the stability of spatio-temporal patterns in certain coupled bulk-surface reaction-diffusion systems, a class of models motivated by the compartmentalization of intracellular proteins between membrane-bound and cytosolic species.
Publications
Book chapters
- 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
Contributed chapter to the book Target Search Problems
- 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
Contributed chapter to the book The Plant Endoplasmic Reticulum: Methods and Protocols, part of the Springer series on Methods in Molecular Biology
Journal articles
- Paquin-Lefebvre F, Barea Moreno A, Holcman D. Voltage Laws in Nanodomains Revealed by Asymptotics and Simulations of Electro-Diffusion Equations. arXiv
- Paquin-Lefebvre F, Holcman D. Voltage Mapping in Subcellular Nanodomains Using Electro-Diffusion Modeling. J. Chem. Phys. 161(3), 034108 (2024). DOI arXiv
- Paquin-Lefebvre F, Basnayake K, Holcman D. Narrow Escape in Composite Domains Forming Heterogeneous Networks. Physica D: Nonlinear Phenomena. 454, 133837 (2023). DOI arXiv
COMSOL codes available on Zenodo
- 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
- 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
Sample COMSOL and MATLAB codes available on BioNewMetrics
Online presentation at the UBC Mathematical Biology Seminar, February 9th 2022
- 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
- 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
Special theme issue of the Philosophical Transactions of the Royal Society A on Turing's theory of morphogenesis.
- 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
- 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
- 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
- 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
- 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
- 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
- On the weakly nonlinear analysis of coupled bulk-surface reaction-diffusion systems: theory, numerics and applications. PhD Thesis, UBC, 2020.
- 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.