Conformational transformations induced by the charge-curvature interaction at finite temperature

The role of thermal fluctuations in the conformational dynamics of a single closed filament is studied. It is shown that, due to the interaction between charges and bending degrees of freedom, initially circular aggregates may undergo transformation to a polygonal shape. The transition occurs in the cases of hardening and softening charge-bending interaction. In the former case the charge and curvature are smoothly distributed along the chain, while in the latter spontaneous kink formation is initiated. The transition to a noncircular conformation is analogous to a phase transition of the second kind.

Figure 1

Probability distribution phase diagram. In the shaded area the probability distribution is bimodal and in the unshaded area it is unimodal.

Figure 2

Probability density distribution of $c$ variable for $J=k_e=1$, $\nu =0.25$, $\chi =2$, $\sigma ={10}^5$, and three different values of the temperature: $T=0.05$ (dashed curve), 0.1 (thin curve), and 0.3 (thick curve)

Figure 3

Top panel: Equilibrium shape of the chain (solid line) against the initial circular shape (dashed line). Bottom panel Charge distribution ${\mid \psi \mid }^2$ (solid line) and curvature $\kappa$ (dashed line) for different noise intensity $D=0.01$ (a), 0.2 (b), and 0.4 (c) in the case of hardening, $\nu =0.5$, $\chi =-4$, $\sigma ={10}^5$, and $J=0.25$ at time $t=4000$. The gray shadow represents the local charge density in the chain.

Figure 4

Aspherity versus time for different noise intensity, $D=0$ (thin line), 0.05 (thick line), and 0.25 (dotted line). The parameters used are $\nu =0.5$, $\chi =-4$, $\sigma ={10}^5$, and $J=0.25$. (a) Full time simulation $0⩽t⩽4000$; (b) detailed behavior after transient time $2000⩽t⩽4000$

Figure 5

Intermediate shape of the filament at time $t=500$ (left panel) and the corresponding charge distribution ${\mid \psi \mid }^2$ (solid line) and curvature $\kappa$ (dashed line) along the chain (right panel) for $D=0.01$. The parameters used are the same as in Fig. 3.

Figure 6

Normalized mean value of the aspherity $⟨A⟩∕⟨A_0⟩$ (thick solid line) and its relative standard deviation $\sqrt{⟨{\left(\Delta A\right)}^2⟩}∕⟨A⟩$ (thick dashed line) versus noise from the simulations and as stationary solution of the Fokker-Planck equation (thin solid and dotted line, respectively) in the case of hardening, $\nu =0.5$, $\chi =-4$, $\sigma ={10}^5$, and $J=0.25$.

Figure 7

Same as Fig. 4 for the case of softening, $\nu =0.29$, $\chi =2$, $\sigma ={10}^5$, and $J=0.22$. (a) Full time simulation $0⩽t⩽4000$; (b) detailed behavior after transient time $3000⩽t⩽4000$

Figure 8

Normalized mean value of the aspherity $⟨A⟩∕⟨A_0⟩$ (solid line) and the relative standard deviation $\sqrt{⟨{\left(\Delta A\right)}^2⟩}∕⟨A⟩$ (dashed line) versus noise for the case of softening with $\nu =0.29$, $\chi =2$, $\sigma ={10}^5$, and $J=0.22$.

Figure 9

Equilibrium configurations of the chain in the case of softening, $\nu =0.29$, $\chi =2$, $\sigma ={10}^5$, and $J=0.22$, for noise intensities $D=\left(\mathrm{a}\right)$ 0.05, (b) 0.10, (c) 0.20, and (d) 0.30 (solid line) against the initial circular conformation (dashed line). The gray shading represents the charge density.

Figure 10

Equilibrium charge distribution ${\mid \psi \mid }^2$ (solid line) and curvature $\kappa$ (dashed line) along the chain for the same parameters as in Fig. 9.