In the following table, rows represent species, and columns reactions.
(x) = currently running
(@) = Too big to run
Estimated times are from Frank's Vista Machine: About those estimations, they are obviously rather rough, one 1-2 hour estimate is running since 6 hours, with 3 more to go. The estimate will get more accurate, the further along the computation goes.
| | 1 Reaction | 2 Reactions | 3 Reactions | 4 Reactions | 5 Reactions | 6 Reactions | 7 Reactions |
| 2 Species | 8 | 64 | 280 | 924 | 2,184 | 4,032 | 5,720 |
| 3 Species | 5 | 312 | 7,418 | 119,522 | 1,488,296 | 15,142,831 | 129,802,440 (349 hrs) |
| 4 Species | 1 | 326 | 28,917 | 1,423,221 | 50,828,0581 (10 hours) | (@) (G5, 9%, 4 months, stopped) | (@) Lucian on edifice Est: 2 years (stopped) |
| 5 Species | 0 | 144 | 39,138 | 4,980,679 | 418,601,348 (5 days) | (@) 10 months (est on Lucian's machine) | |
| 6 Species | 0 | 29 | 25,539 | 7,625,248 | (@) (6%, 10 months, stopped) | (@) 47 Years | |
| 7 Species | 0 | 3 | 9,206 | 6,248,017 | (@) 4-6 months | (@) 900 Years | |
| 8 Species | 0 | 0 | 1,917 | 3,064,916 (108 hrs) | (@) 6-9 years | (@) 600 to 1000 years | |
| 9 Species | 0 | 0 | 225 | 955,610 (34 days) | (@) Insufficient Memory | | |
| 10 Species | 0 | 0 | 14 | (@) Insufficient Memory | (@) | | |
| Total | 14 | 878 | 112,654 | 23,462,527 | 52,318,538 | 15,146,863 | 5720 |
1 Time estimates: 1 hour @1%, 5 hours @50%, 10 hours final
Final Networks: 50,828,058
Run Time: 36,046.00
Possible Networks: 47,405,462,528
Fully Generated: 109,612,353
Bad Reactions: 12,024,919
Zero Degrees: 29,431,978
Redundancies: 7,055,688
Isomorphisms: 10,271,710
Isomorphism Tests: 5,439,643,848
Thanks to:
Michal Galdzicki
Sean Sleight
Frank Bergmann
Anastasia Deckard
Lucian Smith
for the use of their computers.
LS: Just to get some information out of the lower right quadrant of the chart, I did some analyses restricting the reactions to the single type of uni-uni reactions:
| | 1 Reaction | 2 Reactions | 3 Reactions | 4 Reactions | 5 Reactions | 6 Reactions | 7 Reactions |
| 2 Species | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 3 Species | 0 | 3 | 4 | 4 | 1 | 1 | 0 |
| 4 Species | 0 | 0 | 8 | 22 | 37 | 47 | 38 |
| 5 Species | 0 | 0 | 0 | 27 | 108 | 326 | 667 |
| 6 Species | 0 | 0 | 0 | 0 | 91 | 582 | 2437 |
| 7 Species | 0 | 0 | 0 | 0 | 0 | 350 | ? (6+days) |
Results from Feinberg's analysis of the first network in batch 2/4:
BASIC REPORT: FIRSTNETWORK
Reaction network:
S1 -> 2S0
S1 -> S0 + S1
S1 => S0
Remark: First network from enumeration.
Deficiency of FIRSTNETWORK = 1
For arbitrary kinetics (subject to very weak constraints), the corresponding differential equations cannot admit a steady state at which all species concentrations are positive, nor can they admit a cyclic composition trajectory that passes through a point at which all species concentrations are positive.
Feinberg, M., Chemical reaction network structure and the stability of complex isothermal reactors. I. The deficiency zero and deficiency one theorems, Chem. Eng. Science, 42, 2229-2268 (1987).
Taken with mass action kinetics, the network CANNOT admit multiple positive steady states or a degenerate steady state NO MATTER WHAT (POSITIVE) VALUES THE RATE CONSTANTS MIGHT HAVE.
In fact, this network cannot support ANY positive steady state, NO MATTER WHAT (POSITIVE) VALUES THE RATE CONSTANTS TAKE.
