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.
Steady-state simulation of metastable stochastic chemical systems
Rent:
Rent this article for
USD
10.1063/1.4804191
/content/aip/journal/jcp/138/18/10.1063/1.4804191
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/18/10.1063/1.4804191

Figures

Image of FIG. 1.
FIG. 1.

A simulated trajectory for set 1, demonstrating the metastable behavior of the system. Blue line corresponds to protein X, and green to protein Y. Notice that when X is high, Y is low and vice versa, and that the system spends very little time in the region where the proteins have relatively the same abundance.

Image of FIG. 2.
FIG. 2.

Logarithm of the invariant distribution for the first parameter set computed from a large finite truncation.

Image of FIG. 3.
FIG. 3.

Approximation error for the invariant distribution for the first parameter set, obtained by SSA and complement-based simulation, plotted against the simulation of length time units for the censored chain. The results are based on 50 simulation runs. Empty circles and horizontal bands inside boxes denote means and medians, respectively, upper and lower ends of boxes correspond to 75th and 25th percentiles, and whiskers extend to extreme data points.

Image of FIG. 4.
FIG. 4.

Logarithm of the invariant distribution for set 2 computed from a large finite truncation.

Image of FIG. 5.
FIG. 5.

Approximation error for the invariant distribution of the second parameter set, obtained by complement-based simulation plotted against the simulation length of t.u. for the censored chain. The results are based on 20 simulation runs. Empty circles and horizontal bands inside boxes denote means and medians, respectively, upper and lower ends of boxes correspond to 75th and 25th percentiles, and box whiskers extend to approximately 95% percentiles. Outliers are denoted by dots.

Image of FIG. 6.
FIG. 6.

Deviation from equality for the stationary probabilities of the two metastable regions, plotted against the simulation length for the censored chain. The results are based on 50 simulation runs. Empty circles and horizontal bands inside boxes denote means and medians, respectively, upper and lower ends of boxes correspond to 75th and 25th percentiles, and box whiskers extend to approximately 95% percentiles. Outliers are denoted by dots.

Image of FIG. 7.
FIG. 7.

Logarithm of the steady-state marginal probability distribution of the total numbers of and molecules in the system, approximated from a simulation run of 5 × 10 t.u. for the censored chain. To produce the simulated trajectory that yielded this approximation, a total computation time of about 15 min (including matrix calculations) was needed.

Tables

Generic image for table
Table I.

The two largest eigenvalues of and , along with the average time spent in each metastable region prior to the first exit.

Generic image for table
Table II.

Chemical reactions for the toggle switch model. denotes the common regulatory region of both genes, which can either be bound to ( ) or ( ). The reaction rates are taken from Ref. and are equal for the corresponding reactions of the two proteins, leading to a symmetric bimodal stationary distribution.

Loading

Article metrics loading...

/content/aip/journal/jcp/138/18/10.1063/1.4804191
2013-05-13
2014-04-19
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Steady-state simulation of metastable stochastic chemical systems
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/18/10.1063/1.4804191
10.1063/1.4804191
SEARCH_EXPAND_ITEM