Structural transitions of a Semi-Flexible Polyampholyte

Polyampholytes (PA) are charged polymers composed of positively and negatively charged monomers along their backbone. The sequence of the charged monomers and the bending of the chain significantly influence the conformation and dynamical behavior of the PA. Using coarse-grained molecular dynamics simulations, we comprehensively study the structural and dynamical properties of flexible and semi-flexible polyampholytes'. The simulation results demonstrate a flexible polyampholyte (PA) chain, displaying a transition from a coil to a globule in the parameter space of the charge sequence. Additionally, the behavior of the mean-square displacement (MSD), denoted as $<(\Delta r(t))^2>$, reveals distinct dynamics, specifically for the alternating and charge-segregated sequences. The MSD follows a power-law behavior, where $<(\Delta r(t))^2> \sim t^\beta$, with $\beta \approx 3/5$ and $\beta \approx 1/2$ for the alternating sequence and charge-segregated sequence in the absence of hydrodynamic interactions, respectively. However, when hydrodynamic interactions are incorporated, the exponent $\beta$ shifts to approximately 3/5 for the charge-segregated sequence and 2/3 for the well-mixed alternating sequence. For a semi-flexible PA chain, varying the bending rigidity and electrostatic interaction strength ($\Gamma_e$) leads to distinct, fascinating conformational states, including globule, bundle, and torus-like conformations. We show that PA acquires circular and hairpin-like conformations in the intermediate bending regime. The transition between various conformations is identified in terms of the shape factor estimated from the ratios of eigenvalues of the gyration tensor.