Moving interfaces in rod-like macromolecules

Abstract

We present a model that describes mechanical unfolding behavior in rod-like macromolecules. We propose that the unfolding occurs via the motion of a folded/unfolded interface along the molecule. We predict the speed of this interface as a function of the pulling velocity such that the resulting force-extension curve replicates the overstretching transition typical of coiled coils and DNA. We model the molecules as one-dimensional continua capable of existing in two metastable states under an applied tension. The interface separates these two metastable states and represents a jump in stretch, which is related to the applied force by the worm-like chain relation. The Abeyaratne-Knowles theory of phase transitions in continua governs the mechanics of the interface.

Combined molecular/continuum modeling reveals the role of friction during fast unfolding of coiled-coil proteins

“…Note, however, that these equations do not include the movement of the interfaces S 1 and S 2 or the nodes next to them. To represent propagating phase boundaries we follow the approach by Raj and Purohit 61 , 75 and follow them with two additional nodes, of position S 1 and S 2 , that move along the reference configuration. Across these moving nodes, ε can be discontinuous.…”

Entropically driven motion of polymers in nonuniform nanochannels

“…7 without the entropic force term has been used to model macromolecules stretched in fluid flow [26]. Here we show that a non-uniform spatial constraint gives rise to an effective entropic force term that must be included in the macroscopic force balance equation.…”

“…Under strong confinement, a DNA molecule (or any semi-flexible polymer) can be modelled as a fluctuating 1D rod (Fig. 3) [26]. The rod is parametrized by its arc length s ∈ [0, L], with L being the contour length of the polymer.…”

“…To solve for the two unknowns z(s, t) and f int (s, t), we also need a constitutive equation [26]. In particular, following Marko and Siggia [32], we will apply the constitutive relation locally on the polymer.…”

(Adiabatic) phase boundaries in a bistable chain with twist and stretch

“…where ρ(x, t) is the mass per unit length and and T (x, t) is the tension in the rod [22,24,23]. If we localize this equation to a discontinuity s(t) (with x 1 ≤ s(t) ≤ x 2 ) then we get the linear momentum jump condition…”