The "sticky chain":: A kinetic model for the deformation of biological macromolecules

The deformation behavior of certain biologic macromolecules is modeled by the "sticky chain," a freely jointed chain with weak bonds between subsequent joints. Straining the chain leads to thermally assisted breaking of the weak bonds, yielding a characteristic shape of the force-elongation curve, usually with a pronounced plateau, but sometimes displaying a pseudo-Hookean behavior over a wide range of deformations. The number of individual links is assumed to be large, so the stochastic time evolution of the individual events can be approximated by a differential equation. The cases of individual and collective bond breaking are treated and formulae given for various measurable quantities. A threshold strain rate is found, below which the deformation force no longer depends on the deformation velocity. The method is applied to experimental results for the deformation of single molecules like titin or DNA and the results agree with the parameters deduced from the same experiments by the original authors using Monte Carlo (MC) calculations. Despite its intrinsic continuous character, the model, therefore, is applicable even for the deformation of macromolecules with only a few discrete unfolding elements, yielding physical quantities from experimental results using simple formulae instead of a host of MC computations.