Contact Kinetics in Fractal Macromolecules

Abstract

We consider the kinetics of first contact between two monomers of the same macromolecule. Relying on a fractal description of the macromolecule, we develop an analytical method to compute the Mean First Contact Time (MFCT) for various molecular sizes. In our theoretical description, the non-Markovian feature of monomer motion, arising from the interactions with the other monomers, is captured by accounting for the non-equilibrium conformations of the macromolecule at the very instant of first contact. This analysis reveals a simple scaling relation for the MFCT between two monomers, which involves only their equilibrium distance and the spectral dimension of the macromolecule, independently of its microscopic details. Our theoretical predictions are in excellent agreement with numerical stochastic simulations.

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• Dynamics of "comb-of-comb" networks
• Marginally compact hyperbranched polymer trees
• Non-Markovian closure kinetics of flexible polymers with hydrodynamic interactions
• Evidence and quantification of memory effects in competitive first passage events
• Exactly solvable tight-binding models on two scale-free networks with identical degree distribution