Force-induced Elastic Softening and Conformational Transitions in a Polyampholyte Chain

TL;DR

This work links charge sequence and electrostatic correlations to nonlinear elastic responses in polyampholyte chains and IDPs using MD simulations and GRPA theory. The authors identify four distinct mechanical regimes under extensional forcing, including a force-induced elastic softening near a transition governed by the dimensionless parameter Γ_e, and demonstrate hysteresis between stretching and relaxation. A GRPA-based free energy framework captures both continuous and first-order-like globule–coil transitions, aligning with simulations and revealing a universal scaling with f/Γ_e across regimes. The findings illuminate how microscopic charge arrangement tunes macroscopic mechanics, with implications for designing responsive soft materials and understanding IDP mechanics in biological contexts.

Abstract

The mechanical response of intrinsically disordered proteins (IDPs) and polyampholyte (PA) chains is vital for understanding their biological functions and designing functional materials. We investigate the force-extension behavior of a PA chain with distinct charge sequences using molecular dynamics simulations and a theoretical approach based on the generalized random-phase approximation (GRPA). A diblock PA chain under extensional force undergoes a continuous coil-to-stretch transition at weak electrostatic coupling, which sharpens into a globule-coil-like transition at stronger coupling. The GRPA theory quantitatively captures these behaviors, including the sharp conformational transition and its dependence on electrostatic strength. Simulations reveal pronounced hysteresis during the force-extension and relaxation processes. Additionally, the elastic modulus exhibits four regimes: an initial plateau, stress stiffening, an exponential stress-softening behavior, and a stress stiffening regime. Using the theoretical model and structural input of the PA chain, we have demonstrated that the elastic modulus in the elastic softening regime decreases exponentially, $E\sim \exp(-α_0 f/Γ_e)$, as a function of $f$, which aligns with the simulation results. The elastic response of the PA chain is further examined across different charge sequences, where both elastic softening and sharp transitions are absent at smaller block lengths. Finally, coarse-grained models of IDPs such as LAF-1 and DDX4 exhibit similar nonlinear elasticity, highlighting the universality of these mechanisms. Our results establish a fundamental link between electrostatic correlations, charge sequence, and nonlinear elasticity, bridging molecular interactions and macroscopic mechanics.

Figures (16)

• Figure 1: A schematic of a diblock PA chain consists of positive(blue) and negative(red) charged monomers, subjected to an external tensile force applied at its terminal monomers in opposite directions.
• Figure 2: Figure illustrates a force-induced, first-order-like discontinuous conformational transition of the diblock PA chain under a constant stretching force. The end-to-end distance is plotted for various electrostatic interaction strengths, $\Gamma_e$, for both the force-extension (solid lines) and force-relaxation (dashed lines). The inset displays the energy dissipation during the force-extension and relaxation cycles.
• Figure 3: Figure (a) illustrates four different elastic regimes of the diblock chain. It shows one linear and three distinct non-linear regimes observed in the force-extension curves, and (b) the corresponding variation in elastic modulus $\mathrm E$ as a function of the external force $f$ at a fixed $\Gamma_e = 5$ and $N=200$.
• Figure 4: Various conformations of the PA chain under external force. Snapshots demonstrate structural transitions of a diblock PA chain under stretching force for various $f=2,10,20,$ and $38$ at $\Gamma_e=5$ and $N=200$.
• Figure 5: The variation of the normalized elastic modulus $E/E_0$ as a function of scaled external force $f/\Gamma_e$ of the diblock PA chain at various electrostatic strengths $\Gamma_e$ from $0.01-5$ for the case of force-extension. The solid lines represent the power-law variations in region NLR3 with exponents $\alpha=3/2$.