Molecular chains under tension: Thermal and mechanical activation of statistically interacting extension and contraction particles

Abstract

This work introduces a methodology for the statistical mechanical analysis of polymeric chains under tension controlled by optical or magnetic tweezers at thermal equilibrium with an embedding fluid medium. The response of single bonds between monomers or of entire groups of monomers to tension is governed by the activation of statistically interacting particles representing quanta of extension or contraction. This method of analysis is capable of describing thermal unbending of the freely-jointed or worm-like chain kind, linear or nonlinear contour elasticity, and structural transformations including effects of cooperativity. The versatility of this approach is demonstrated in an application to double-stranded DNA undergoing torsionally unconstrained stretching across three regimes of mechanical response including an overstretching transition. The three-regime forceextension characteristic, derived from a single free-energy expression, accurately matches empirical evidence. (c) J τ J J (b) (d) (a) FIG. 1: (Color online) Schematic representations for a chain of N = 7 monomers of (a) the reference state, (b) a state under tension with extension particles activated, (c) a state under tension and torque with twist-contraction particles activated, and (d) a state under tension with extension particles and contact particles activated.

Mechanical response to tension and torque of molecular chains via statistically interacting particles associated with extension, contraction, twist, and supercoiling

“…The approach has already proven its usefulness in numerous quantum and classical applications [42][43][44][45][46][47], notably for ds-DNA subjected to torsionally unconstrained stretching [32]. The results of this approach aligned with experimental data of the force-extension characteristic across regimes of entropic elasticity (thermal umbending), enthalpic elasticity (beyond contour length), and an overstretching transition.…”

“…These thermodynamic functions can also be inferred from particle population averages via Eqs. ( 6) [32,35,44]:…”

“…In Ref. [32] we explained the different categories of particles: compact particles, which exist side by side, and nested particles, which form hierarchical structures. Particles at level 1 modify individual bonds and particles at level 2 modify entire segments of the molecular chain.…”

“…Thermodynamic relations are readily inverted to produce relations amenable to direct comparisons with experimental data. This method of analysis was previously introduced in some detail for applications to molecular chains under tension without torsional constraints [32].…”

“…II with emphasis on those aspects that are in need of eloborations beyond the account given in Ref. [32]. One elementary application, which illustrates the coupling between the two pairs (J, L) and (τ, φ) of conjugate thermodynamic variables in the context of torsionally constrained twisting and stretching, is worked out in Sec.…”