Biological processes span several scales in space, from the single molecules to organisms and ecosystems. Multiscale modelling approaches in biology are useful to take into account the complex interactions between different organisation levels in those systems. We are interested in approaches based on master equations for stochastic processes, individual-based models, hybrid continuous-discrete models and structured PDE models.

Selected publicationProkopiou, SA; Barbarroux L; Bernard S; Mafille J; Leverrier Y; Arpin C; Marvel J; Gandrillon O; Crauste F,
**Multiscale Modeling of the Early CD8 T-Cell Immune Response in Lymph Nodes: An Integrative Study**
(2014) Computation 2:159-181

Human tissues continually replace dying cells with newborn cells. However, the rate of renewal varies by orders of magnitudes between blood cells, which are renewed every day and neurons, for which renewal is non-existent or limited to specific regions of the brain. Between those extreme are many tissues that turn over on a time scale of years, although no direct measurements have been done. We have developed a mathematical method to estimate cell turnover in slowly renewing biological systems. Age distribution of DNA can be estimated from the integration of radiocarbon derived from nuclear bomb testing during 1955-1963. For slowly renewing tissues, this method provides a better estimate of the average age of the tissue than direct estimate from the bomb curve. Moreover, death, birth and turnover rates can be estimated.

Selected publication
S Bernard, J FrisÃ©n, KL Spalding. **A mathematical model for the interpretation of nuclear bomb test derived 14C incorporation in biological systems** (2010) Nucl. Instr. and Meth. B 268:1295-1298 doi:10.1016/j.nimb.2009.10.156

Chronotherapy of cancers aims at exploiting daily physiological rhythms to improve anti-cancer efficacy and tolerance to drugs by administering treatments at a specific time each day. Recent clinical trials have shown that chronotherapy can be beneficial in improving quality of life and median life span in patients, but that it can also have negative effects if the timing is wrong. A theoretical basis for the rational development of individualized therapy schedules is still lacking. We use a simple cell population model to study how biological rhythms and the cell cycle interact to modulate the response to cancer therapy. A better understanding of the dyamical feature of clock regulation is important for designing individualized chronotherapy treatments.

Selected publication
R El Cheikh, S Bernard, N El Khatib,
**Modeling circadian clock-cell cycle interaction effects on cell population growth rates**
(2014) J Theor Biol, 363:318-331

Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote oscillation around steady states, and their stability depends on the particular shape of the delay distribution. Since in applications the mean delay is often the only reliable information available about the distribution, it is desirable to find conditions for stability that are independent from the shape of the distribution.