Conformational transformations induced by the charge-curvature interaction: Mean-field approach

A simple phenomenological model for describing the conformational dynamics of biological macromolecules via the nonlinearity-induced instabilities is proposed. It is shown that the interaction between charges and bending degrees of freedom of closed molecular aggregates may act as drivers giving impetus to conformational dynamics of biopolymers. It is demonstrated that initially circular aggregates may undergo transformation to polygonal shapes and possible application to aggregates of bacteriochlorophyl $a$ molecules is considered.

Figure 1

The shape of the chain: in the ellipselike state $(n=2)$, in the polygon states $(n=3,4,5)$.

Figure 2

The normalized energy difference ${\Delta }_n$ from Eq. (49) for the ellipselike $n=2$ ( solid line ) and triagonlike chain $n=3$ (dashed line) with $2\chi =4$ $J=k$.

Figure 3

The top panel shows the initial shape of the chain; the bottom panel shows the initial charge (solid line) and curvature (dashed line) distribution along the chain.

Figure 4

The top panel shows the equilibrium shape of the chain and the bottom panel shows the charge distribution (solid line) and curvature variation (dashed line) along the chain in the case of hardening electron-curvature interaction with $\nu =0.22$, $\chi =-2$, $k=1$ $J=0.4$.

Figure 5

The top panel shows the equilibrium shape of the chain and the bottom panel shows the charge distribution (solid line) and curvature variation (dashed line) along the chain in the case of softening electron-curvature interaction with $\nu =0.22$, $\chi =2.15$, and $k=J=1$.

Figure 6

Same as Fig. 5 with $\nu =0.23$, $\chi =2.15$, $k=J=1$.

Figure 7

Arrangement of densely packed ringlike aggregates.

Figure 8

Arrangement of densely packed ellipselike aggregates.

Figure 9

Energy per aggregate [Eq. (65)] as a function of the trial anisotropy parameter $\gamma$ for the charge density below the threshold (dashed) and above the threshold (solid).