-
1
-
-
0033083733
-
-
10.1016/S0168-9525(98)01659-X
-
H. H. McAdams and A. Arkin, Trends Genet. 15, 65 (1999). 10.1016/S0168-9525(98)01659-X
-
(1999)
Trends Genet.
, vol.15
, pp. 65
-
-
McAdams, H.H.1
Arkin, A.2
-
3
-
-
25444468618
-
-
10.1126/science.1105891
-
J. M. Raser and E. K. O'Shea, Science 309, 2010 (2005). 10.1126/science.1105891
-
(2005)
Science
, vol.309
, pp. 2010
-
-
Raser, J.M.1
O'Shea, E.K.2
-
4
-
-
19544379881
-
-
10.1038/nrg1615
-
M. Kærn, T. C. Elston, W. J. Blake, and J. J. Collins, Nat. Rev. Genet. 6, 451 (2005). 10.1038/nrg1615
-
(2005)
Nat. Rev. Genet.
, vol.6
, pp. 451
-
-
Kærn, M.1
Elston, T.C.2
Blake, W.J.3
Collins, J.J.4
-
5
-
-
33749506763
-
-
10.1038/nature05127
-
B. Di Ventura, C. Lemerle, K. Michalodimitrakis, and L. Serrano, Nature (London) 443, 527 (2006). 10.1038/nature05127
-
(2006)
Nature (London)
, vol.443
, pp. 527
-
-
Di Ventura, B.1
Lemerle, C.2
Michalodimitrakis, K.3
Serrano, L.4
-
10
-
-
0037119587
-
-
10.1126/science.1070919
-
M. B. Elowitz, A. J. Levine, E. D. Siggia, and P. S. Swain, Science 297, 1183 (2002). 10.1126/science.1070919
-
(2002)
Science
, vol.297
, pp. 1183
-
-
Elowitz, M.B.1
Levine, A.J.2
Siggia, E.D.3
Swain, P.S.4
-
11
-
-
0037119578
-
-
10.1126/science.1075988
-
N. Fedoroff and W. Fontana, Science 297, 1129 (2002). 10.1126/science.1075988
-
(2002)
Science
, vol.297
, pp. 1129
-
-
Fedoroff, N.1
Fontana, W.2
-
12
-
-
33845616177
-
-
10.1016/j.molcel.2006.11.003
-
W. J. Blake, G. Balázsi, M. A. Kohanski, F. J. Isaacs, K. F. Murphy, Y. Kuang, C. R. Cantor, D. R. Walt, and J. J. Collins, Mol. Cell 24, 853 (2006). 10.1016/j.molcel.2006.11.003
-
(2006)
Mol. Cell
, vol.24
, pp. 853
-
-
Blake, W.J.1
Balázsi, G.2
Kohanski, M.A.3
Isaacs, F.J.4
Murphy, K.F.5
Kuang, Y.6
Cantor, C.R.7
Walt, D.R.8
Collins, J.J.9
-
15
-
-
0037197850
-
-
10.1073/pnas.092133899
-
J. M. G. Vilar, H. Y. Kueh, N. Barkai, and S. Leibler, Proc. Natl. Acad. Sci. U.S.A. 99, 5988 (2002). 10.1073/pnas.092133899
-
(2002)
Proc. Natl. Acad. Sci. U.S.A.
, vol.99
, pp. 5988
-
-
Vilar, J.M.G.1
Kueh, H.Y.2
Barkai, N.3
Leibler, S.4
-
17
-
-
33750533388
-
-
10.1038/ncb1497
-
B. B. Aldridge, J. M. Burke, D. A. Lauffenburger, and P. K. Sorger, Nat. Cell Biol. 8, 1195 (2006). 10.1038/ncb1497
-
(2006)
Nat. Cell Biol.
, vol.8
, pp. 1195
-
-
Aldridge, B.B.1
Burke, J.M.2
Lauffenburger, D.A.3
Sorger, P.K.4
-
19
-
-
0017030517
-
-
10.1016/0021-9991(76)90041-3
-
D. T. Gillespie, J. Comput. Phys. 22, 403 (1976). 10.1016/0021-9991(76) 90041-3
-
(1976)
J. Comput. Phys.
, vol.22
, pp. 403
-
-
Gillespie, D.T.1
-
20
-
-
33645429016
-
-
10.1021/j100540a008
-
D. T. Gillespie, J. Phys. Chem. 81, 2340 (1977). 10.1021/j100540a008
-
(1977)
J. Phys. Chem.
, vol.81
, pp. 2340
-
-
Gillespie, D.T.1
-
21
-
-
34249950625
-
-
10.1146/annurev.physchem.58.032806.104637
-
D. T. Gillespie, Annu. Rev. Phys. Chem. 58, 35 (2007). 10.1146/annurev.physchem.58.032806.104637
-
(2007)
Annu. Rev. Phys. Chem.
, vol.58
, pp. 35
-
-
Gillespie, D.T.1
-
23
-
-
0035933994
-
-
10.1063/1.1378322
-
D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001). 10.1063/1.1378322
-
(2001)
J. Chem. Phys.
, vol.115
, pp. 1716
-
-
Gillespie, D.T.1
-
27
-
-
31344458755
-
-
10.1016/j.compbiolchem.2005.10.007
-
J. M. McCollum, G. D. Peterson, C. D. Cox, M. L. Simpson, and N. F. Samatova, Comput. Biol. Chem. 30, 39 (2006). 10.1016/j.compbiolchem.2005.10.007
-
(2006)
Comput. Biol. Chem.
, vol.30
, pp. 39
-
-
McCollum, J.M.1
Peterson, G.D.2
Cox, C.D.3
Simpson, M.L.4
Samatova, N.F.5
-
29
-
-
0942279178
-
-
10.1063/1.1627296
-
M. Rathinam, L. R. Petzold, Y. Cao, and D. T. Gillespie, J. Chem. Phys. 119, 12784 (2003). 10.1063/1.1627296
-
(2003)
J. Chem. Phys.
, vol.119
, pp. 12784
-
-
Rathinam, M.1
Petzold, L.R.2
Cao, Y.3
Gillespie, D.T.4
-
30
-
-
22944477377
-
-
10.1063/1.1823412
-
Y. Cao, L. R. Petzold, M. Rathinam, and D. T. Gillespie, J. Chem. Phys. 121, 12169 (2004). 10.1063/1.1823412
-
(2004)
J. Chem. Phys.
, vol.121
, pp. 12169
-
-
Cao, Y.1
Petzold, L.R.2
Rathinam, M.3
Gillespie, D.T.4
-
37
-
-
33847220720
-
-
10.1063/1.2436869
-
X. Cai and Z. Xu, J. Chem. Phys. 126, 074102 (2007). 10.1063/1.2436869
-
(2007)
J. Chem. Phys.
, vol.126
, pp. 074102
-
-
Cai, X.1
Xu, Z.2
-
42
-
-
42649105096
-
-
10.1063/1.2819665
-
D. F. Anderson, J. Chem. Phys. 128, 054103 (2008). 10.1063/1.2819665
-
(2008)
J. Chem. Phys.
, vol.128
, pp. 054103
-
-
Anderson, D.F.1
-
43
-
-
42449102270
-
-
10.1063/1.2894479
-
Z. Xu and X. Cai, J. Chem. Phys. 128, 154112 (2008). 10.1063/1.2894479
-
(2008)
J. Chem. Phys.
, vol.128
, pp. 154112
-
-
Xu, Z.1
Cai, X.2
-
48
-
-
1542400036
-
-
10.1093/bioinformatics/btg442
-
K. Takahashi, K. Kaizu, B. Hu, and M. Tomita, Bioinformatics 20, 538 (2004). 10.1093/bioinformatics/btg442
-
(2004)
Bioinformatics
, vol.20
, pp. 538
-
-
Takahashi, K.1
Kaizu, K.2
Hu, B.3
Tomita, M.4
-
51
-
-
1542345686
-
-
10.1016/S0006-3495(04)74207-1
-
J. Puchałka and A. M. Kierzek, Biophys. J. 86, 1357 (2004). 10.1016/S0006-3495(04)74207-1
-
(2004)
Biophys. J.
, vol.86
, pp. 1357
-
-
Puchałka, J.1
Kierzek, A.M.2
-
53
-
-
33750970021
-
-
10.1093/bioinformatics/btl465
-
M. Griffith, T. Courtney, J. Peccoud, and W. H. Sanders, Bioinformatics 22, 2782 (2006). 10.1093/bioinformatics/btl465
-
(2006)
Bioinformatics
, vol.22
, pp. 2782
-
-
Griffith, M.1
Courtney, T.2
Peccoud, J.3
Sanders, W.H.4
-
54
-
-
33746516694
-
-
10.1021/jp056231f
-
D. C. Wylie, Y. Hori, A. R. Dinner, and A. K. Chakraborty, J. Phys. Chem. B 110, 12749 (2006). 10.1021/jp056231f
-
(2006)
J. Phys. Chem. B
, vol.110
, pp. 12749
-
-
Wylie, D.C.1
Hori, Y.2
Dinner, A.R.3
Chakraborty, A.K.4
-
55
-
-
0034225547
-
-
10.1063/1.481811
-
D. T. Gillespie, J. Chem. Phys. 113, 297 (2000). 10.1063/1.481811
-
(2000)
J. Chem. Phys.
, vol.113
, pp. 297
-
-
Gillespie, D.T.1
-
56
-
-
18744405416
-
-
10.1093/bioinformatics/bti308
-
A. Chatterjee, K. Mayawala, J. S. Edwards, and D. G. Vlachos, Bioinformatics 21, 2136 (2005). 10.1093/bioinformatics/bti308
-
(2005)
Bioinformatics
, vol.21
, pp. 2136
-
-
Chatterjee, A.1
Mayawala, K.2
Edwards, J.S.3
Vlachos, D.G.4
-
58
-
-
37849032458
-
-
10.1371/journal.pcbi.0030240
-
A. Handel, I. M. Longini, Jr., and R. Antia, PLOS Comput. Biol. 3, e240 (2007). 10.1371/journal.pcbi.0030240
-
(2007)
PLOS Comput. Biol.
, vol.3
, pp. 240
-
-
Handel, A.1
Longini, Jr.I.M.2
Antia, R.3
-
59
-
-
0033850017
-
-
10.1016/S0006-3495(00)76373-9
-
U. Kummer, L. F. Olsen, C. J. Dixon, A. K. Green, E. Bornberg-Bauer, and G. Baier, Biophys. J. 79, 1188 (2000). 10.1016/S0006-3495(00)76373-9
-
(2000)
Biophys. J.
, vol.79
, pp. 1188
-
-
Kummer, U.1
Olsen, L.F.2
Dixon, C.J.3
Green, A.K.4
Bornberg-Bauer, E.5
Baier, G.6
-
61
-
-
3142773575
-
-
10.1080/00018730410001703159
-
M. Falcke, Adv. Phys. 53, 255 (2004). 10.1080/00018730410001703159
-
(2004)
Adv. Phys.
, vol.53
, pp. 255
-
-
Falcke, M.1
-
63
-
-
24144463446
-
-
10.1529/biophysj.104.057216
-
U. Kummer, B. Drajnc, J. Pahle, A. K. Green, C. J. Dixon, and M. Marhl, Biophys. J. 89, 1603 (2005). 10.1529/biophysj.104.057216
-
(2005)
Biophys. J.
, vol.89
, pp. 1603
-
-
Kummer, U.1
Drajnc, B.2
Pahle, J.3
Green, A.K.4
Dixon, C.J.5
Marhl, M.6
-
64
-
-
0025195261
-
-
C. J. Dixon, N. M. Woods, K. S. R. Cuthbertson, and P. H. Cobbold, Biochem. J. 269, 499 (1990).
-
(1990)
Biochem. J.
, vol.269
, pp. 499
-
-
Dixon, C.J.1
Woods, N.M.2
Cuthbertson, K.S.R.3
Cobbold, P.H.4
-
65
-
-
0035319006
-
-
10.1038/35066056
-
J. Hasty, D. McMillen, F. Isaacs, and J. J. Collins, Nat. Rev. Genet. 2, 268 (2001). 10.1038/35066056
-
(2001)
Nat. Rev. Genet.
, vol.2
, pp. 268
-
-
Hasty, J.1
McMillen, D.2
Isaacs, F.3
Collins, J.J.4
-
69
-
-
0037079015
-
-
10.1038/nature01259
-
A. Goldbeter, Nature (London) 420, 238 (2002). 10.1038/nature01259
-
(2002)
Nature (London)
, vol.420
, pp. 238
-
-
Goldbeter, A.1
-
70
-
-
33745725676
-
-
10.1063/1.2211767
-
D. Gonze and A. Goldbeter, Chaos 16, 026110 (2006). 10.1063/1.2211767
-
(2006)
Chaos
, vol.16
, pp. 026110
-
-
Gonze, D.1
Goldbeter, A.2
-
71
-
-
33846240672
-
-
Oxford University Press, Oxford, England
-
J. P. Sethna, Statistical Mechanics: Entropy, Order Parameters, and Complexity (Oxford University Press, Oxford, England, 2006).
-
(2006)
Statistical Mechanics: Entropy, Order Parameters, and Complexity
-
-
Sethna, J.P.1
-
72
-
-
66849120345
-
-
J. P. Sethna and C. R. Myers, http://www.physics.cornell.edu/sethna/ StatMech/ComputerExercises/Repressilator/Repressilator.html
-
-
-
Sethna, J.P.1
Myers, C.R.2
-
75
-
-
26844554514
-
-
10.1016/j.aml.2005.02.033
-
A. J. Kearsley, W. E. Wallace, J. Bernal, and C. M. Guttman, Appl. Math. Lett. 18, 1412 (2005). 10.1016/j.aml.2005.02.033
-
(2005)
Appl. Math. Lett.
, vol.18
, pp. 1412
-
-
Kearsley, A.J.1
Wallace, W.E.2
Bernal, J.3
Guttman, C.M.4
-
76
-
-
66849086143
-
-
Obviously, deterministic simulations should exhibit zero variance in their results. However, due to sampling and curve-fitting inaccuracies we do see slight variations. It is these variations that we use as the criteria for determining when a system attribute has converged to the deterministic limit. Clearly, if the PLA results show equal or less variation than the deterministic results then we can deem that the property has converged to determinism.
-
Obviously, deterministic simulations should exhibit zero variance in their results. However, due to sampling and curve-fitting inaccuracies we do see slight variations. It is these variations that we use as the criteria for determining when a system attribute has converged to the deterministic limit. Clearly, if the PLA results show equal or less variation than the deterministic results then we can deem that the property has converged to determinism.
-
-
-
-
78
-
-
29144488933
-
-
10.1016/j.jcp.2005.06.012
-
Y. Cao and L. Petzold, J. Comput. Phys. 212, 6 (2006). 10.1016/j.jcp.2005.06.012
-
(2006)
J. Comput. Phys.
, vol.212
, pp. 6
-
-
Cao, Y.1
Petzold, L.2
-
79
-
-
66849126990
-
-
The self-distance is a measure of the difference between a sample histogram (i.e., one based on a finite amount of data) and the "true" (unattainable) histogram. Since the measure is based on absolute differences two sample histograms can have equal self-distances but arising from opposite sources (e.g., one histogram might be slightly taller and thinner, while the other shorter and wider, than the true histogram). This means that two sample histograms can be as dissimilar as twice the self-distance and still be considered indistinguishable from the true histogram and hence each other. In the Appendix of Ref., it was incorrectly stated that two histograms can be considered distinct if they differ by only a single self-distance.
-
The self-distance is a measure of the difference between a sample histogram (i.e., one based on a finite amount of data) and the "true" (unattainable) histogram. Since the measure is based on absolute differences two sample histograms can have equal self-distances but arising from opposite sources (e.g., one histogram might be slightly taller and thinner, while the other shorter and wider, than the true histogram). This means that two sample histograms can be as dissimilar as twice the self-distance and still be considered indistinguishable from the true histogram and hence each other. In the Appendix of Ref., it was incorrectly stated that two histograms can be considered distinct if they differ by only a single self-distance.
-
-
-
-
80
-
-
66849126991
-
-
note
-
We found that significant speed ups can be achieved in the PLA simulations of the reduced repressilator model (Table 3) if we remove the ES classification (see Fig. 9). The problem lies in the iterative τ -selection procedure designed to account for the randomness of the ES reactions. In this particular case, we experienced an unexpected "classification cascade," whereby reactions classified as ES led to a reduced τ, which then led to more ES reactions (via reclassification), which further reduced τ, and so on and so forth. Removing the ES classification eliminated this problem with no major effect on the accuracy. However, this cannot be done in all cases. Removing the ES classification when simulating the full model led to numerous instances of negative populations, specifically for the species gx, { gx □ pr }, and { gx □ pr □ pr }, which can only have populations of zero or unity. These required costly reversals that significantly increased the run time. Further investigation of this issue is warranted and will be undertaken in the near future. Also note that all results reported in Figs. 7 8 were performed with the ES classification included.
-
-
-
-
81
-
-
0142116225
-
-
10.1063/1.1603738
-
T. Shibata, J. Chem. Phys. 119, 6629 (2003). 10.1063/1.1603738
-
(2003)
J. Chem. Phys.
, vol.119
, pp. 6629
-
-
Shibata, T.1
-
84
-
-
18844402156
-
-
10.1063/1.1889434
-
J. Goutsias, J. Chem. Phys. 122, 184102 (2005). 10.1063/1.1889434
-
(2005)
J. Chem. Phys.
, vol.122
, pp. 184102
-
-
Goutsias, J.1
-
88
-
-
38849117209
-
-
10.1063/1.2821957
-
M. J. Morelli, R. J. Allen, S. Tçnase-Nicola, and P. R. ten Wolde, J. Chem. Phys. 128, 045105 (2008). 10.1063/1.2821957
-
(2008)
J. Chem. Phys.
, vol.128
, pp. 045105
-
-
Morelli, M.J.1
Allen, R.J.2
Tçnase-Nicola, S.3
Ten Wolde, P.R.4
-
89
-
-
33747366698
-
-
10.1126/stke.3442006re6
-
W. S. Hlavacek, J. R. Faeder, M. L. Blinov, R. G. Posner, M. Hucka, and W. Fontana, Sci. STKE 2006, re6 (2006). 10.1126/stke.3442006re6
-
(2006)
Sci. STKE
, vol.2006
, pp. 6
-
-
Hlavacek, W.S.1
Faeder, J.R.2
Blinov, M.L.3
Posner, R.G.4
Hucka, M.5
Fontana, W.6
-
91
-
-
42749109054
-
-
10.1103/PhysRevE.68.021904
-
K. S. Brown and J. P. Sethna, Phys. Rev. E 68, 021904 (2003). 10.1103/PhysRevE.68.021904
-
(2003)
Phys. Rev. e
, vol.68
, pp. 021904
-
-
Brown, K.S.1
Sethna, J.P.2
-
92
-
-
22144498043
-
-
10.1529/biophysj.104.053405
-
R. Gunawan, Y. Cao, L. Petzold, and F. J. Doyle III, Biophys. J. 88, 2530 (2005). 10.1529/biophysj.104.053405
-
(2005)
Biophys. J.
, vol.88
, pp. 2530
-
-
Gunawan, R.1
Cao, Y.2
Petzold, L.3
Doyle Iii, F.J.4
-
93
-
-
0033764285
-
-
10.1038/81125
-
B. Palsson, Nat. Biotechnol. 18, 1147 (2000). 10.1038/81125
-
(2000)
Nat. Biotechnol.
, vol.18
, pp. 1147
-
-
Palsson, B.1
|