Infrared spectral signatures of CDCP1-induced effects in colon carcinoma cells

Metastasis is the major cause of death by cancer. Indeed, metastatic colonies can reactivate and become life threatening, sometimes months or years after the initial diagnosis and surgery of the primary tumor. Therefore, there is a crucial need to develop methods for diagnosis of tumor cells that exhibit high metastatic potential. Here, we addressed the capability of vibrational spectroscopy for investigating the effects induced by CDCP1 expression in colon carcinoma cells. This transmembrane protein has been suggested to play a key role in metastasis by its pleiotropic function. We focused on a cellular model constituted by the cell lines SW480 and SW620 derived respectively from the primary tumor and a lymph node metastasis of the same patient. Induced CDCP1 expression in SW480 led to marked changes in cell morphology. Whereas SW480 form a cell layer, the SW480/CDCP1 cells exhibited reduced cell-to-cell contact. On collagen I, SW480 was more spread and filopodia were observed. In contrast, SW480/CDCP1 cells exhibited lower spreading with no formation of filopodia. Synchrotron Fourier transform infrared microspectroscopy experiments were performed on this cellular model. High quality spectroscopic information at sub-cellular resolution, provided by the use of the synchrotron source in infrared microspectroscopy, was recorded on numerous individual cells. Multivariate analysis of spectra recorded using principal component analysis indicated a highest intensity increase of the 970 and 1080 cm(-1) bands, and a modest intensity increase of the 1240 cm(-1) band in the SW480/CDCP1 cells. These bands were correlated with an increased content of phosphorylated proteins as confirmed by in situ labelling using a monoclonal antibody directed against phosphorylated tyrosines. Altogether, these results demonstrate that the vibrational technique used in this study exhibits the capability to characterize spectral signatures of CDCP1-induced effects in colon carcinoma cells. This study may open new avenues for rapid diagnosis of cells with a metastatic potential.     

The Damped Nonlinear Quasiperiodic Mathieu Equation Near 2:2:1 Resonance

We investigate the damped cubic nonlinear quasiperiodic Mathieu equation $$ \frac{d^2x}{dt^2}+(\delta+\varepsilon \cos t+\varepsilon \mu \cos\omega t)x+\varepsilon \mu c\frac{dx}{dt}+\varepsilon \mu \gamma x^3=0$$ in the vicinity of the principal 2:2:1 resonance. By using a double perturbation method which assumes that both ε and μ are small, we approximate analytical conditions for the existence and bifurcation of nonlinear quasiperiodic motions in the neighborhood of the middle of the principal instability region associated with 2:2:1 resonance. The effect of damping and nonlinearity on the resonant quasiperiodic motions of the quasiperiodic Mathieu equation is also provided. We show that the existence of quasiperiodic solutions does not depend upon the nonlinearity coefficient γ, whereas the amplitude of the associated quasiperiodic motion does depend on γ.     

Three-Period Quasi-Periodic Solutions in the Self-Excited Quasi-Periodic Mathieu Oscillator

In this work, we investigate three-period quasi-periodic (QP) oscillations in the vicinity of 2:2:1 resonance in a self-excited QP Mathieu equation using perturbation method. Two successive averaging are performed to reduce the original QP equation to an autonomous amplitude and phase system describing the modulation of the slow flow dynamic. Approximation of three-period QP solution is obtained via the study of limit cycle of the reduced autonomous system. The efficiency of the method is illustrated by comparison between analytical approximations and numerical integration. The double reduction procedure, applied in previous works to construct two-period QP solution, can be implemented to approximate excplicit analytical three-period QP solutions.     

Two models for the parametric forcing of a nonlinear oscillator

Instabilities associated with 2:1 and 4:1 resonances of two models for the parametric forcing of a strictly nonlinear oscillator are analyzed. The first model involves a nonlinear Mathieu equation and the second one is described by a 2 degree of freedom Hamiltonian system in which the forcing is introduced by the coupling. Using averaging with elliptic functions, the threshold of the overlapping phenomenon between the resonance bands 2:1 and 4:1 (Chirikov’s overlap criterion) is determined for both models, offering an approximation for the transition from local to global chaos. The analytical results are compared to numerical simulations obtained by examining the Poincaré section of the two systems.