Dynalets: a new method for modelling and compressing biological signals. Applications to physiological and molecular signals.

The biological information coming from electrophysiologic sensors like ECG, pulse sensor or from molecular signal devices like NMR spectrometry has to be visualized and manipulated in a compressed way for an efficient medical use by clinicians, if stored in scientific data bases or in personalized patient records repositories. Here, we define a new transform called Dynalet based on Liénard ordinary differential equations susceptible to model the mechanism at the source of the studied signal, and we propose to apply this new technique first to the modelling and compression of real biological periodic signals like ECG and pulse rhythm. We consider that the cardiovascular activity results from the summation of cellular oscillators located in the cardiac sinus node and we show that, as a result, the van der Pol oscillator (a particular Liénard system) fits well the ECG signal and the pulse signal. The reconstruction of the original signal (pulse or ECG) using Dynalet transform is then compared with that of Fourier, counting the number of parameters to be set for obtaining an expected signal-to-noise ratio. Then, we apply the Dynalet transform to the modelling and compression of molecular spectra obtained by protein NMR spectroscopy. The reconstruction of the original signal (peak) using Dynalet transform is again compared with that of Fourier. After reconstructing visually the peak, we propose to periodize the signal and give it to hear, the whole process being called the protein "stethoscope".

Numerical modelling of the V-J combinations of the T cell receptor TRA/TRD locus.

T-Cell antigen Receptor (TR) repertoire is generated through rearrangements of V and J genes encoding alpha and beta chains. The quantification and frequency for every V-J combination during ontogeny and development of the immune system remain to be precisely established. We have addressed this issue by building a model able to account for Valpha-Jalpha gene rearrangements during thymus development of mice. So we developed a numerical model on the whole TRA/TRD locus, based on experimental data, to estimate how Valpha and Jalpha genes become accessible to rearrangements. The progressive opening of the locus to V-J gene recombinations is modeled through windows of accessibility of different sizes and with different speeds of progression. Furthermore, the possibility of successive secondary V-J rearrangements was included in the modelling. The model points out some unbalanced V-J associations resulting from a preferential access to gene rearrangements and from a non-uniform partition of the accessibility of the J genes, depending on their location in the locus. The model shows that 3 to 4 successive rearrangements are sufficient to explain the use of all the V and J genes of the locus. Finally, the model provides information on both the kinetics of rearrangements and frequencies of each V-J associations. The model accounts for the essential features of the observed rearrangements on the TRA/TRD locus and may provide a reference for the repertoire of the V-J combinatorial diversity.

An open issue: the inner mitochondrial membrane (IMM) as a free boundary problem.

The inner mitochondrial membrane (IMM) is structured in cristae, which contributes to the best functioning of ions and adenylates exchange between the matrix and the intermembrane space. The central hypothesis of this paper is that the cristae structure favours a minimal mean free path of adenylates between translocation sites (translocase/ANT sites) and metabolic sites (ATPase sites). We propose a mathematical model and then give simulations. Based on simple hypotheses about cristae growth, they show that we can account for the major features of the IMM organization and functioning by minimizing the mean interdistance between ADP/ATP translocation and transformation sites.