*© Inria – Christian Tourniaire*

Directeur de Recherche INRIA

Contact : Frederique.Clement@inria.fr

### Research activity : multiscale mathematical modeling for biology

My research activity consists in addressing crucial questions arising from biological issues from a mathematical perspective.

The underlying motivation is to contribute to the understanding of biological processes in the context of developmental and/or reproductive biology from cell biology concepts.

The models are designed within either continuous, deterministic formalisms, or discrete, stochastic formalisms, mostly related to structured populations dynamics. In both cases, combined theoretical and numerical approaches are deployed and confronted to the available biological knowledge, with the ultimate goal of fostering the understanding of the biological processes and possibly suggesting new experimental studies.

### Main publications

- G. Ballif, F. Clément, R. Yvinec. Nonlinear compartmental modeling to monitor ovarian follicle population dynamics on the whole lifespan.
*Journal of Mathematical Biology*, 2024, 89: 9. - F. Clément, J. Olayé. A stochastic model for neural progenitor dynamics in the mouse cerebral cortex.
*Mathematical Biosciences*, 2024, 372: 109185. - G. Ballif, F. Clément, R. Yvinec. Averaging of a stochastic slow-fast model for population dynamics: Application to the development of ovarian follicles.
*SIAM Journal on Applied Mathematics*, 2022, 82(1): 359-380. - F. Clément, F. Robin, R. Yvinec. Stochastic nonlinear model for somatic cell population dynamics during ovarian follicle activation.
*Journal of Mathematical Biology*, 2021, 82:12. - F. Clément, D. Monniaux. Mathematical modeling of ovarian follicle development: A population dynamics viewpoint.
*Current Opinion in Endocrinology and Metabolism Research*, 2021, 18:54-61. - F. Clément, P. Crépieux, R. Yvinec, D. Monniaux. Mathematical modeling approaches of cellular endocrinology within the hypothalamo-pituitary-gonadal axis.
*Molecular and Cellular Endocrinology*, 2020, 518:110877. - M. Postel, A. Karam, G. Pézeron, S. Schneider-Maunoury, F. Clément. A multiscale mathematical model of cell dynamics during neurogenesis in the mouse cerebral cortex.
*BMC Bioinformatics*, 2019, 20(1):470. - F. Clément, B. Laroche, F. Robin. Analysis and numerical simulation of an inverse problem for a structured cell population dynamics model.
*Mathematical Biosciences and Engineering*, 2019, 16(4):3018-3046. - F. Clément, F. Robin, R. Yvinec. Analysis and calibration of a linear model for structured cell populations with unidirectional motion : Application to the morphogenesis of ovarian follicles.
*SIAM Journal on Applied Mathematics*, 2019, 79(1):207–229. - R. Yvinec, P. Crépieux, E. Reiter, A. Poupon, F. Clément. Advances in computational modeling approaches of pituitary gonadotropin signaling.
*Expert Opinion on Drug Discovery*, 2018, 13(9):799-813. - E. Köksal-Ersöz, A. Vidal, F. Clément. Coupled multiple timescale dynamics in populations of endocrine neurons: Pulsatile and surge patterns of GnRH secretion.
*SIAM Journal on Applied Dynamical Systems*, 2018, 17(1):1052-1090. - F. Clément, F. Coquel, M. Postel, L. Tran. Dimensional Reduction of a Multiscale Model Based on Long Time Asymptotics.
*Multiscale Modeling & Simulation*, 2017, 15(3):1198-1241. - B. Aymard, F. Clément, D. Monniaux, M. Postel. Cell-kinetics based calibration of a multiscale model of structured cell populations in ovarian follicles.
*SIAM Journal on Applied Mathematics*2016, 76(4):1471-1491. - S. Fernández-García, M. Krupa, F. Clément. Mixed-Mode Oscillations in a piece-wise linear system with multiple time scale coupling.
*Physica D*, 2016, 332: 9-22. - F. Clément. Multiscale mathematical modeling of the hypothalamo-pituitary-gonadal axis.
*Theriogenology*, 2016, 86(1): 11-21. - D. Monniaux, P. Michel, M. Postel, F. Clément. Multiscale modeling of ovarian follicular development: from follicular morphogenesis to selection for ovulation.
*Biology of the Cell.*2016, 108(6) : 149-160. - E. Köksal-Ersöz, M. Desroches, M. Krupa, F. Clément. Canard-Mediated (De)Synchronization in Coupled Phantom Bursters.
*SIAM Journal on Applied Dynamical Systems.*2016, 15(1): 580-608. - S. Fernández-García, M. Desroches, M. Krupa, F. Clément. A multiple time scale coupling of piecewise linear oscillators. Application to a neuroendocrine system.
*SIAM Journal on Applied Dynamical Systems*2015, 14 (2): 643-673. - B. Aymard, F. Clément, M. Postel. Adaptive mesh refinement strategy for a non conservative transport problem.
*ESAIM: Mathematical Modelling and Numerical Analysis*, 2014, 48(5): 1381-1412. - P.A. Fletcher, F. Clément, A. Vidal, J. Tabak, R. Bertram. Interpreting frequency responses to dose-conserved pulsatile input signals in simple cell signaling motifs.
*PloS One*, 2014, 9(4): e95613. - B. Aymard, F. Clément, F. Coquel, M. Postel. A Numerical Method for Transport Equations with Discontinuous Flux Functions: Application to Mathematical Modeling of Cell Dynamics.
*SIAM Journal on Scientific Computing*, 2013, 35(6): A2442-A2468. - F. Clément, D. Monniaux, P. Michel, T. Stiehl. Coupled somatic cell kinetics and germ cell growth: multiscale model-based insight on ovarian follicular development.
*Multiscale Modeling & Simulation*, 2013, 11(3): 719-746. - M. Krupa, A. Vidal, F. Clément. A network model of the periodic synchronization process in the dynamics of calcium concentration in GnRH neurons.
*The Journal of Mathematical Neuroscience*, 2013, 3: 4. - F. Clément, D. Monniaux. Multiscale modelling of ovarian follicle selection.
*Progress in Biophysics and Molecular Biology*, 2013, 113(3): 398-408. - F. Clément, J.-M. Coron, P. Shang. Optimal control of cell mass and maturity in a model of follicular ovulation.
*SIAM Journal on Control and Optimization*, 2013, 51(2): 824-847. - M. Krupa, A. Vidal, M. Derosches, F. Clément. Mixed-mode oscillations in a multiple time scale phantom bursting system.
*SIAM Journal on Applied Dynamical Systems*, 2012, 11(4): 1458-1498. - A. Vidal, Q. Zhang, C. Médigue, S. Fabre, F. Clément. DynPeak : An algorithm for pulse detection and frequency analysis in hormonal time series.
*PloS One*, 2012, 7: e39001. - D. Heitzler, G. Durand, N. Gallay, A. Rizk, S. Ahn, J. Kim, J.D. Violin, L. Dupuy, C. Gauthier, V. Piketty, P. Crépieux, A. Poupon, F. Clément, F. Fages, R.J. Lefkowitz, E. Reiter. Competing G protein-coupled receptor kinases balance G protein and -β arrestin signaling.
*Molecular Systems Biology*, 2012, 8:590. - A. Vidal, F. Clément. A dynamical model for the control of the GnRH neurosecretory system.
*Journal of Neuroendocrinology*, 2010, 22(12): 1251-1266. - F. Clément, A. Vidal. Foliation-based parameter tuning in a model of the GnRH pulse and surge generator.
*SIAM Journal on Applied Dynamical Systems*, 2009, 8(4): 1591-1631. - A. Vidal, C. Médigue, B. Malpaux, F. Clément. Endogenous circannual rhythm in LH secretion: insight from signal analysis coupled with mathematical modeling.
*Philosophical Transactions of the Royal Society A*, 2009, 367, 4759-4777. - N. Echenim, F. Clément, M. Sorine. Multiscale modeling of follicular ovulation as a reachability problem.
*Multiscale Modeling & Simulation*, 2007, 6(3): 895-912. - F. Clément, J.-P. Françoise. Mathematical modeling of the GnRH-pulse and surge generator.
*SIAM Journal on Applied Dynamical Systems*, 2007, 6(2): 441-456. - N. Echenim, D. Monniaux, M. Sorine, F. Clément. Multi-scale modeling of the follicle selection process in the ovary.
*Mathematical Biosciences*, 2005, 198: 57-79. - F. Clément, D. Monniaux, J. Stark, K. Hardy, J.C. Thalabard, S. Franks, D.Claude. A mathematical model of FSH-induced cAMP production in ovarian follicles.
*American Journal of Physiology (Endocrinology & Metabolism)*, 281: E35-E53, 2001. - F. Clément. Optimal control of the cell dynamics in the granulosa of ovulatory follicles.
*Mathematical Biosciences*, 152: 123-142, 1998. - F. Clément, M.A. Gruet, P. Monget, M. Terqui, E. Jolivet,D. Monniaux. Growth kinetics of the granulosa cell population in ovarian

follicles : an approach by mathematical modelling.*Cell Proliferation*,

30: 255-270, 1997.