1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Failure of one-dimensional Smoluchowski diffusion models to describe the duration of conformational rearrangements in floppy, diffusive molecular systems: A case study of polymer cyclization
Rent:
Rent this article for
USD
10.1063/1.3556750
/content/aip/journal/jcp/134/8/10.1063/1.3556750
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/8/10.1063/1.3556750
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

End-to-end distance trajectory of a polymer chain. Transition paths from A to B are the trajectory segments, where the end-to-end distance, R, enters the transition region at R A and reaches R B without first returning to R A . The transit time t AB is the time spent by a transition path within the transition region R B < R < R A . In contrast, trajectory segments that start at R A and later exit the transition region into A prior to reaching R B (duration t AA ) will contribute to the mean first passage time from A to B but not to the mean transit time.

Image of FIG. 2.
FIG. 2.

Transit times vs first passage times. The mean transit time from A to B (filled symbols) is independent of the chain length N, in contrast to the strongly chain-length-dependent mean first passage from A to B (empty symbols). Here both times are plotted as a function of the spatial extent of the transition region R A R B , with R B fixed at 2.5 equilibrium bond lengths.

Image of FIG. 3.
FIG. 3.

Polymer model vs Free diffusion model vs 1D Smoluchowski model for polymer cyclization transit times. The mean transit times for cyclization of a polymer chain (filled circles) are independent of the chain length. For small values of R A R B they agree with the free diffusion model (open circles), which ignores the polymer chain and assumes that the end monomers move freely. In contrast, the model of Eq. (2) (solid, dashed, and dotted lines) that assumes 1D diffusion in a one-dimensional potential of mean force is inconsistent with the polymer data and shows significant dependence on the chain length. As in Fig. 2, the distance R B is fixed here at 2.5 equilibrium bond lengths.

Image of FIG. 4.
FIG. 4.

Cyclization of a polymer chain can be achieved via straightening of a chain segment containing nN monomers.

Image of FIG. 5.
FIG. 5.

The effective number of monomers rearranging in a cyclization transition [estimated from Eqs. (5) and (6)]. The effective number of monomers n(R A , R B ) involved in the cyclization of a chain increases with the change in the end-to-end distance R A R B required to close the loop. For small values of R A R B loop closure is accomplished by moving only n(R A , R B ) = 2 end monomers. Here R B is fixed at 2.5 bond lengths. Dashed line shows Eq. (4), which predicts that n(R A , R B ) is proportional to the distance R A R B traveled during a transition.

Image of FIG. 6.
FIG. 6.

The distribution of transit times obtained from the free diffusion model, when rescaled according to Eq. (7) to account for the effective number of monomers involved, is nearly identical to the actual distribution obtained from simulations of polymer chains. (a): N = 160, R A = 10.39, and R B = 2.5. (b): N = 160, R A = 25.97, and R B = 2.5.

Loading

Article metrics loading...

/content/aip/journal/jcp/134/8/10.1063/1.3556750
2011-02-23
2014-04-24
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Failure of one-dimensional Smoluchowski diffusion models to describe the duration of conformational rearrangements in floppy, diffusive molecular systems: A case study of polymer cyclization
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/8/10.1063/1.3556750
10.1063/1.3556750
SEARCH_EXPAND_ITEM