Youcef Mammeri

Mathematical modelling unveils the essential role of cellular phosphatases in the inhibition of RAF-MEK-ERK signalling by sorafenib in hepatocellular carcinoma cells

The RAS-RAF-MEK-ERK cascade is a key oncogenic signal transduction pathway activated in many types of tumours in humans. Sorafenib, the medical treatment of reference against advanced stages of hepatocellular carcinoma (HCC), inhibits the RAF-MEK-ERK cascade in HCC cells. Based on previous studies suggesting that this cascade is an important target of sorafenib in HCC cells, we explored its regulation using mathematical modelling and ordinary differential equations. We analysed the dynamic regulation of the core components of the RAF-MEK-ERK cascade in three human HCC cell lines (Huh7, Hep3B and PLC/PRF5) with heterogeneous responses to sorafenib. In silico predictions derived from our mathematical model suggested that the disappearance of phosphorylated MEK and ERK proteins catalysed by cellular phosphatases is an essential mechanism underlying the anti-ERK efficacy of sorafenib in HCC cells. This prediction was experimentally validated using specific inhibitors of the phosphatases PP2A (Protein Phosphatase 2A) and DUSP1/6 (Dual-specificity phosphatases 1/6). These findings highlight an unexpected mode of action of sorafenib on the kinome of HCC cells, and open new perspectives regarding the therapeutic targeting of the RAF-MEK-ERK cascade in this context.

Asymptotic behavior of small solutions of the Benjamin–Ono equation with time-dependent coefficients

Abstract We study the behavior of small solutions depending on time of the generalized and regularized Benjamin–Ono equation in both continuous and periodic context. In particular, we prove that these solutions remain small for a time scale improving the natural time given by the local well-posedness. In the continuous case, the result becomes global-in-time.

Comparison of solutions of Boussinesq systems

Abstract. We compare the solution of the generalized Boussinesq systems, for various values of a,b,c,d

Numerical study of the regularizing effect of the 3D weakly transverse BBM equations for long times

{a,b,c,d}

Carleman estimates and unique continuation property for the Kadomtsev–Petviashvili equations

, η t +u x +ε((ηu) x +au xxx -bη xxt )=0

A microstructurally resolved model for Li-S batteries assessing the impact of the cathode design on the discharge performance

\eta _t +u_x +\varepsilon ((\eta u)_x +au_{xxx} -b\eta _{xxt}) = 0

A note on Carleman estimates and Unique continuation property for the Boussinesq system

, u t +η x +ε(uu x +cη xxx -du xxt )=0

Linking the Performances of Li–O2 Batteries to Discharge Rate and Electrode and Electrolyte Properties through the Nucleation Mechanism of Li2O2

u_t +\eta _x +\varepsilon (uu_x +c\eta _{xxx} -du_{xxt}) = 0

Perception-based foraging for competing resources: Assessing pest population dynamics at the landscape scale from heterogeneous resource distribution

. These systems describe the two-way propagation of small amplitude long waves in shallow water. We prove, using an energy method introduced by Bona, Pritchard and Scott [Fluid Dynamics in Astrophysics and Geophysics, American Mathematical Society, Providence (1983), 235–267], that respective solutions of Boussinesq systems, starting from the same initial datum, remain close on a time interval inversely proportional to the wave amplitude.

Long-time behavior of solutions of a BBM equation with generalized damping

From a spectral method combined with a predictor-corrector scheme, we numerically study the behavior in time of solutions of the three-dimensional generalized Kadomtsev-Petviashvili equations regularized using the BBM trick. The solution no longer blows up and the solitonic behavior is observed.