Polymers provide physical realizations of stochastic processes such as Brownian motion or self-avoiding random walks. Other types of stochastic processes control the functioning of molecular motors and the folding of proteins. Some universal aspects of membranes (flexible films, biological membranes) are closely related to the random geometries studied in string theories and quantum gravity. When objects are charged (polyelectrolytes, charged membranes) or possess internal degrees of freedom, their physical and geometrical properties may be deeply modified: new phases may appear. Random polymer physics governs the complex interactions between chemically different monomers in biopolymers. One can study the denaturation of DNA or protein folding and RNA within this framework. For the latter, the classification of folded forms can be done using tools of topology (genus, Euler characteristic), leading to the development of powerful algorithms for structure prediction. In addition, most biopolymers carry charges, and the Coulomb interaction determines their universal properties of aggregation and solvation in the cell.
Non-equilibrium transition paths between different states of a complex system can be modeled by a constrained Langevin equation. An exact mathematical formulation of this dynamics was found and applied to sampling the paths between folded and unfolded states of a protein. It was also applied to transitions amongst different knotted states in DNA, in presence of a topoisomerase
DNA molecules are knotted and so are roughly 3% of proteins; we have performed a statistical study of known RNA structures in data bases and have concluded that RNA strands are not knotted, a fact that has far reaching biological and evolutionary implications
Amyloid fibrils are misfolded aggregates of proteins that are responsible of major diseases including diabetes, Alzheimer and Parkinson. Using CreateFibril, a computational framework we developed, we explore the stability of fibrils and demonstrate that nucleation of stable aggregates becomes energetically favorable beyond a certain size limit. Using field-theoretical techniques, we have revisited the Onsager-Samaras theory of electrolytes surface tension for ions located at the interface of two media with different dielectric constants (such as water and air) and have calculated precisely the shape of the ionic density profile at the vicinity of the interface.
|Guillaume Le Treut
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