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.
Computing stationary distributions in equilibrium and nonequilibrium systems with forward flux sampling
Rent:
Rent this article for
USD
10.1063/1.2767625
/content/aip/journal/jcp/127/11/10.1063/1.2767625
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/11/10.1063/1.2767625

Figures

Image of FIG. 1.
FIG. 1.

Sketch of all the possible trajectories that contribute to the stationary distribution [see Eq. (3)]: Trajectory 1 comes from and goes back to ; trajectory 2 comes from and goes to ; trajectory 3 comes from and goes back to ; trajectory 4 comes from and goes to . The FFS simulation from to harvests the trajectories corresponding to types 1 and 2, while the FFS simulation for the reverse transition generates trajectories of types 3 and 4. The interfaces used in the FFS simulation are also shown.

Image of FIG. 2.
FIG. 2.

Stationary distribution (solid line) obtained using the procedure described above, compared to the normalized Boltzmann distribution (circles) for a symmetric double well potential. The dotted and dashed lines show and , respectively.

Image of FIG. 3.
FIG. 3.

Asymmetric double well potential (a): (dotted line) and (dashed line). (b) Final result for obtained from Eq. (3) (solid line) compared to the expected Boltzmann distribution (circles).

Image of FIG. 4.
FIG. 4.

(a) Computed stationary distribution as a function of for (solid line), (dashed line), and (dot-dashed line), compared to the expected Boltzmann distribution (indicated by circles) for the Maier-Stein system with and . (b) as a function of for (solid line), (dashed line), and (dot-dashed line).

Image of FIG. 5.
FIG. 5.

for the Maier-Stein system with , , and . (a) as a function of for (solid line), (dashed line), and (dot-dashed line). (b) as a function of for (solid line), (dashed line), and (dot-dashed line). The results of long brute-force simulations are indicated by circles.

Image of FIG. 6.
FIG. 6.

Schematic view of the free energy landscape. is the metastable “down state,” is the “real” thermodynamically stable state, and is the “artificial” stable state, constructed by introducing a reflecting wall at .

Image of FIG. 7.
FIG. 7.

Free energy barrier for and calculated using FFS (dashed line; gray) and umbrella sampling (continuous line; black). Error bars are shown for both calculations.

Image of FIG. 8.
FIG. 8.

Schematic representation of our model switch, corresponding to Eq. (28). Two divergently transcribed genes are under the control of a shared regulatory binding site on the DNA (the operator). Each protein can bind, in homodimer form, to the operator and block the production of the other species.

Image of FIG. 9.
FIG. 9.

Probability distribution as a function of the order parameter . The results are obtained both via long, steady state simulations (continuous line) and forward flux sampling (circles). The region around can be accurately sampled only with FFS: the inset shows, on a logarithmic scale, a much smoother profile of the region close to the unstable steady state when FFS is used over brute force (BF). A scaling factor has been applied to the FFS results since they were originally normalized over while the BF results are normalized over .

Tables

Generic image for table
Table I.

Interfaces and the number of trials at each interface for the FFS sampling of the symmetric one dimensional double-well potential.

Generic image for table
Table II.

Interfaces and the number of trials at each interface for the FFS sampling of the asymmetric one dimensional double-well potential.

Generic image for table
Table III.

Interfaces and the number of trials per interface for the Maier-Stein system.

Generic image for table
Table IV.

Interfaces and the number of trials per interface for the FFS sampling for the two-dimensional Ising nucleation problem.

Generic image for table
Table V.

Interfaces and the number of trials per interface for the FFS simulations for the model genetic switch.

Loading

Article metrics loading...

/content/aip/journal/jcp/127/11/10.1063/1.2767625
2007-09-21
2014-04-18
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Computing stationary distributions in equilibrium and nonequilibrium systems with forward flux sampling
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/11/10.1063/1.2767625
10.1063/1.2767625
SEARCH_EXPAND_ITEM