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.
Reduction of chemical reaction networks through delay distributions
Rent:
Rent this article for
USD
10.1063/1.4793982
/content/aip/journal/jcp/138/10/10.1063/1.4793982
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/10/10.1063/1.4793982

Figures

Image of FIG. 1.
FIG. 1.

Linear sequence of unimolecular reactions (example 1). (Left) Histogram for the number of S 9 molecules at time T = 80 obtained from 104 SSA (blue) and DSSA (red) simulations where delays were drawn from the 8-exponential iCDF with parameters (the eigenvalues of the system's rate matrix A for species S 1S 8). (Right) Average time evolution of species S 9 in steps of Δt = 2 until T = 80 for SSA and DSSA.

Image of FIG. 2.
FIG. 2.

Linear sequence of reactions with time-scale separation (example 2). (Left) Histogram for the number of S 9 molecules at time T = 1000 for 106 SSA simulations (blue) and 104 DSSA simulations where delays were drawn from the corresponding 8-exponential iCDF (red) or 1-exponential iCDF for the smallest absolute eigenvalue (green). (Right) Average time evolution of species S 9 in steps of Δt = 10 for SSA (blue) and DSSA (red/green). The blue and red trajectories are undistinguishable while the green trajectory is above the other two.

Image of FIG. 3.
FIG. 3.

Sequence of unimolecular reactions with backward bypass reactions (example 3). (Left) Histogram for the number of S 9 molecules at time T = 120 obtained from SSA simulations (blue) and DSSA (red) where delays were drawn from the corresponding 8-exponential iCDF. (Right) Average time evolution of species S 9 in steps of Δt = 10 using SSA and DSSA.

Image of FIG. 4.
FIG. 4.

Sequence of unimolecular reactions with forward bypass reactions (example 4). (Left) Histogram for the number of S 9 molecules at time T = 30 for 106 SSA simulations (blue) and 104 DSSA simulations (red, green) where delays were obtained from first-passage time distributions based on 102 (red) and 103 (green) sample times. (Right) Average time evolution of species S 9 in steps of Δt = 10 for SSA and DSSA.

Image of FIG. 5.
FIG. 5.

Sequence of unimolecular reactions with backward and forward bypass reactions (example 5). (Left) Histogram for the number of S 9 molecules at time T = 50 for 106 SSA simulations (blue) and 104 DSSA simulations where delays were either drawn from first-passage time distributions based on 102 (black x) or 103 (green x) samples or obtained (via inverse sampling) from the numerical solution of the CDF evaluated at 6401 time points in the interval [0, 640] (black dot). (Right) Average time evolution of species S 9 in steps of Δt = 10 for SSA and DSSA.

Image of FIG. 6.
FIG. 6.

Sequence of unimolecular reactions with additional degradation reactions (example 6). (Left) Histogram for the number of S 9 molecules at time T = 80 for 104 SSA (blue) and DSSA (black dots) simulations where delays were drawn from the inverse of the numerical solution of the CDF (using matrix exponentials). (Right) Average time evolution of species S 9 in steps of Δt = 10 for SSA and DSSA. For this scenario, we computed w = 0.194.

Image of FIG. 7.
FIG. 7.

Histogram (normalized) of species S 9 at time T = 80 from 10 000 simulations of the full (SSA, blue) and the abridged system (DSSA, red).

Image of FIG. 8.
FIG. 8.

Histograms of species S and P at time T = 10 from 10 000 simulations of the full (SSA, blue) and the abridged system (DSSA, red) for the parameter set c 1 = 1, c 2 = 10, c 3 = 10 and initial conditions S 0 = 105, E 0 = 102, ES 0 = 0, P = 0. Here, we use k = 1015.

Image of FIG. 9.
FIG. 9.

(a) and (c) Complete model and kinetic parameters used in modelling MFA2pG-mRNA degradation as stated in Ref. 12 . 3 fragments (L + I1 + I2) and 5 fragments (G + M) are highlighted in grey, all other species are considered full length mRNA. (b) Abridged model. The dotted line in (a) refers to the process that is represented by a delay distribution in our abridged model. Moreover, reactions C → E and D → F are lumped into a single degradation reaction. The probability for such a degradation is 1 − w (cf. Sec. III G ).

Image of FIG. 10.
FIG. 10.

(Left) Histogram for the number of I2 molecules at time T = 10 000 for SSA simulations (blue) and DSSA (black) where delays were drawn from the inverse of the numerical solution of the CDF (using matrix exponentials). (Right) Average time evolution of species I2 for SSA (blue line) and DSSA (black dots). For this scenario, we computed w = 0.7745, i.e., a 77.45% probability that the former full length mRNA is degraded via this pathway.

Tables

Generic image for table
Table I.

Computational savings in terms of average numbers of SSA reactions per single DSSA reaction and speed-up (runtime of SSA over runtime of DSSA runs). Simulations ran until T = 100. Mean values are calculated over 100 simulations.

Loading

Article metrics loading...

/content/aip/journal/jcp/138/10/10.1063/1.4793982
2013-03-13
2014-04-23
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Reduction of chemical reaction networks through delay distributions
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/10/10.1063/1.4793982
10.1063/1.4793982
SEARCH_EXPAND_ITEM