Laboratoire de Physique Théorique
Toulouse - UMR 5152

The purpose of this talk is to discuss our recent works to describe the hybridization melting of DNA with simple models under two different approaches : a kinetic model applied on DNA microarrays (at the surface) and Monte Carlo simulations of polymers (in the bulk). The first part of the talk is about the dynamics of hybridization in DNA microarrays. Microarrays are devices which consist of tens of thousands single stranded DNA sequences tethered on the surface. They are an efficient tool allowing namely the analysis of gene expression experiments on a large scale. However, the knowledge of hybridization in microarrays is still not well understood. In the past, the Langmuir model, a two-state model, has been used to describe the kinetics of the hybridization process. However, recently it has been shown that under certain circumstances the equilibration time exceeds the actual experimental time resulting in a deviation from the Langmuir isotherm. We have observed such behavior and we have presented an extension of the two-state Langmuir model to a three-state kinetic model. In a second part we present a numerical study of a system closely related to the unwinding of the double-helical structure of DNA. Namely, the unwinding of a single polymer initially wound around a fixed bar. The advantage of this latter system is that it has a cleanly defined reaction coordinate : the winding angle of the free end. We restricted our study to identify the equilibrium properties of a single polymer wound around a bar, thereby providing a solid basis for further research on the dynamics of unwinding. The winding angle probability distribution of a planar self-avoiding walk has been known exactly since a long time. For the three-dimensional case of a walk winding around a bar, the same scaling is suggested, based on a first-order epsilon-expansion. We tested this three-dimensional case by means of Monte Carlo simulations and using exact enumeration data. Our findings are at odds with the existing first-order epsilon-expansion results.